url
stringlengths 6
1.61k
| fetch_time
int64 1,368,856,904B
1,726,893,854B
| content_mime_type
stringclasses 3
values | warc_filename
stringlengths 108
138
| warc_record_offset
int32 9.6k
1.74B
| warc_record_length
int32 664
793k
| text
stringlengths 45
1.04M
| token_count
int32 22
711k
| char_count
int32 45
1.04M
| metadata
stringlengths 439
443
| score
float64 2.52
5.09
| int_score
int64 3
5
| crawl
stringclasses 93
values | snapshot_type
stringclasses 2
values | language
stringclasses 1
value | language_score
float64 0.06
1
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
http://au.metamath.org/mpegif/mremre.html
| 1,529,403,656,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-26/segments/1529267862248.4/warc/CC-MAIN-20180619095641-20180619115641-00559.warc.gz
| 26,675,650
| 9,455
|
Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > mremre Structured version Unicode version
Theorem mremre 13821
Description: The Moore collections of subsets of a space, viewed as a kind of subset of the power set, form a Moore collection in their own right on the power set. (Contributed by Stefan O'Rear, 30-Jan-2015.)
Assertion
Ref Expression
mremre Moore Moore
Proof of Theorem mremre
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 mresspw 13809 . . . . 5 Moore
2 vex 2951 . . . . . 6
32elpw 3797 . . . . 5
41, 3sylibr 204 . . . 4 Moore
54ssriv 3344 . . 3 Moore
65a1i 11 . 2 Moore
7 ssid 3359 . . . 4
87a1i 11 . . 3
9 pwidg 3803 . . 3
10 intssuni2 4067 . . . . . 6
11103adant1 975 . . . . 5
12 unipw 4406 . . . . 5
1311, 12syl6sseq 3386 . . . 4
14 elpw2g 4355 . . . . 5
15143ad2ant1 978 . . . 4
1613, 15mpbird 224 . . 3
178, 9, 16ismred 13819 . 2 Moore
18 n0 3629 . . . . 5
19 intss1 4057 . . . . . . . . 9
2019adantl 453 . . . . . . . 8 Moore
21 simpr 448 . . . . . . . . . 10 Moore Moore
2221sselda 3340 . . . . . . . . 9 Moore Moore
23 mresspw 13809 . . . . . . . . 9 Moore
2422, 23syl 16 . . . . . . . 8 Moore
2520, 24sstrd 3350 . . . . . . 7 Moore
2625ex 424 . . . . . 6 Moore
2726exlimdv 1646 . . . . 5 Moore
2818, 27syl5bi 209 . . . 4 Moore
29283impia 1150 . . 3 Moore
30 simp2 958 . . . . . . 7 Moore Moore
3130sselda 3340 . . . . . 6 Moore Moore
32 mre1cl 13811 . . . . . 6 Moore
3331, 32syl 16 . . . . 5 Moore
3433ralrimiva 2781 . . . 4 Moore
35 elintg 4050 . . . . 5
36353ad2ant1 978 . . . 4 Moore
3734, 36mpbird 224 . . 3 Moore
38 simp12 988 . . . . . . 7 Moore Moore
3938sselda 3340 . . . . . 6 Moore Moore
40 simpl2 961 . . . . . . 7 Moore
41 intss1 4057 . . . . . . . 8
4241adantl 453 . . . . . . 7 Moore
4340, 42sstrd 3350 . . . . . 6 Moore
44 simpl3 962 . . . . . 6 Moore
45 mreintcl 13812 . . . . . 6 Moore
4639, 43, 44, 45syl3anc 1184 . . . . 5 Moore
4746ralrimiva 2781 . . . 4 Moore
48 intex 4348 . . . . . 6
49 elintg 4050 . . . . . 6
5048, 49sylbi 188 . . . . 5
51503ad2ant3 980 . . . 4 Moore
5247, 51mpbird 224 . . 3 Moore
5329, 37, 52ismred 13819 . 2 Moore Moore
546, 17, 53ismred 13819 1 Moore Moore
Colors of variables: wff set class Syntax hints: wi 4 wb 177 wa 359 w3a 936 wex 1550 wcel 1725 wne 2598 wral 2697 cvv 2948 wss 3312 c0 3620 cpw 3791 cuni 4007 cint 4042 cfv 5446 Moorecmre 13799 This theorem is referenced by: mreacs 13875 mreclatdemo 17152 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1555 ax-5 1566 ax-17 1626 ax-9 1666 ax-8 1687 ax-13 1727 ax-14 1729 ax-6 1744 ax-7 1749 ax-11 1761 ax-12 1950 ax-ext 2416 ax-sep 4322 ax-nul 4330 ax-pow 4369 ax-pr 4395 This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1328 df-ex 1551 df-nf 1554 df-sb 1659 df-eu 2284 df-mo 2285 df-clab 2422 df-cleq 2428 df-clel 2431 df-nfc 2560 df-ne 2600 df-ral 2702 df-rex 2703 df-rab 2706 df-v 2950 df-sbc 3154 df-dif 3315 df-un 3317 df-in 3319 df-ss 3326 df-nul 3621 df-if 3732 df-pw 3793 df-sn 3812 df-pr 3813 df-op 3815 df-uni 4008 df-int 4043 df-br 4205 df-opab 4259 df-mpt 4260 df-id 4490 df-xp 4876 df-rel 4877 df-cnv 4878 df-co 4879 df-dm 4880 df-iota 5410 df-fun 5448 df-fv 5454 df-mre 13803
Copyright terms: Public domain W3C validator
| 1,672
| 3,436
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.765625
| 3
|
CC-MAIN-2018-26
|
latest
|
en
| 0.122741
|
https://ilnumerics.net/apidoc/html/M_ILNumerics_ExtensionMethods_sum_16.htm
| 1,659,955,055,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882570793.14/warc/CC-MAIN-20220808092125-20220808122125-00654.warc.gz
| 313,382,930
| 4,332
|
ExtensionMethods.sum Method (ConcreteArray(Single, Array(Single), InArray(Single), OutArray(Single), RetArray(Single), Storage(Single)), Boolean)
ILNumerics Ultimate VS Documentation
ILNumerics - Technical Application Development
[numpy API] Create a scalar array with the sum of all elements of A.
[ILNumerics numpy Module]
Namespace: ILNumerics
Assembly: ILNumerics.numpy (in ILNumerics.numpy.dll) Version: 5.5.0.0 (5.5.7503.3146)
Syntax
```public static RetArray<float> sum(
this ConcreteArray<float, Array<float>, InArray<float>, OutArray<float>, RetArray<float>, Storage<float>> A,
bool keepdims = false
)```
#### Parameters
A
Type: ILNumerics.Core.ArraysConcreteArraySingle, ArraySingle, InArraySingle, OutArraySingle, RetArraySingle, StorageSingle
The source array. This will not be altered.
keepdims (Optional)
Type: SystemBoolean
[Optional] accumulated dimensions remain in the resulting array. Default: (false) accumulated singleton dimensions are removed.
#### Return Value
Type: RetArraySingle
A scalar array with the sum of all elements of A.
#### Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ConcreteArraySingle, ArraySingle, InArraySingle, OutArraySingle, RetArraySingle, StorageSingle. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).
Remarks
Depending on the value of keepdims the array returned will have the same number of dimensions as A (keepdims = true) or with a number of dimensions according to MinNumberOfArrayDimensions.
Empty arrays A produce a scalar array with the default element value for the element data type.
[ILNumerics numpy Module]
| 414
| 1,782
|
{"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-2022-33
|
latest
|
en
| 0.562609
|
https://mail.scipy.org/pipermail/numpy-discussion/2008-March/031909.html
| 1,508,798,210,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-43/segments/1508187826840.85/warc/CC-MAIN-20171023221059-20171024001059-00501.warc.gz
| 751,847,856
| 2,364
|
# [Numpy-discussion] What should be the return type of average?
Charles R Harris charlesr.harris@gmail....
Sun Mar 16 06:59:12 CDT 2008
```On Sun, Mar 16, 2008 at 4:11 AM, Sebastian Haase <haase@msg.ucsf.edu> wrote:
> On Sun, Mar 16, 2008 at 1:08 AM, Charles R Harris
> <charlesr.harris@gmail.com> wrote:
> > Hi,
> >
> > I want to fix up the average function. I note that the return dtype is
> not
> > specified, nor is the precision of the accumulator. Both of these can be
> > specified for the mean method and I wonder what should be the case for
> > average. Or should we just use double precision? That would seem
> appropriate
> > to me most of the time, but wouldn't match what happens with mean and
> would
> > lose precision in the case of extended precision doubles. There is also
> no
> > out keyword, do we want one?
> >
>
> Hi,
> I'm starting to forget... but faintly I'm remembering that there might
> We work with large multi-dimensional image data, so if, for example, I
> have n (small) 50x512x512 3D-images that I want to average into one
> 50x512x512 image, the most memory I can afford is single precession
> float32. (Also the original dynamic range is 16bit at best anyway)
>
> I was just checking my archives:
> http://projects.scipy.org/scipy/numpy/ticket/465#comment:2 (by
> oliphant) actually already says this.
What I ended up with is double for integer input types and preservation of
float types. Thus float32 will be preserved but int8 will return double.
These are the same rules one gets with A + 0.0, which is how I did it. That
isn't really the most space efficient, however, as in your case a copy of
the data cube will be made.
As to accumulator type and an out variable, there are already so many
parameters in the function that I have become loath to add more at this
point, but it would be easy to specify an accumulator type and specifying an
out variable shouldn't be much worse.
Chuck
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://projects.scipy.org/pipermail/numpy-discussion/attachments/20080316/2a352445/attachment.html
```
| 567
| 2,115
|
{"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-2017-43
|
latest
|
en
| 0.914545
|
http://www.dailypaul.com/325525/the-real-us-rate-of-inflation?page=1
| 1,419,469,269,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-52/segments/1419447543571.19/warc/CC-MAIN-20141224185903-00039-ip-10-231-17-201.ec2.internal.warc.gz
| 193,156,057
| 39,985
|
# The real rate of US inflation
I've just gathered some data from the US bureau of labor statistics.
They track prices for different commodities. I've just done a quick comparison on 14 of the most widely tracked items. Things like a gallon of milk, gallon of gas, loaf of bread, 1 lb of ground beef, 1 lb of chicken, 1 lb of coffee, ETC....
When charted out, those 14 common household goods have shown an average inflation rate of 50% over the last 10 yrs.
This is a far more accurate measurement of actual inflation than the crap their trying to sell us via the CPI, or any of their other under estimated figures as of late.
1 gal Fuel oil 148.95%
1 Gal of gas 128.2%
1 lb of ground beef 51.53%
1 lb of chicken 40.77%
1 doz eggs 24%
1 gal of milk 26.6%
1 lb apples 36.5%
1 lb oranges 75.28%
1 lb bananas 18.36%
1 lb of tomatoes 10.94%
12 oz orange juice 30.15%
1 lb of coffee 76.31%
1 KW electricity 57.14%
Piped gas per therm 6.22%
check it out for yourselves.
http://data.bls.gov/cgi-bin/surveymost
Trending on the Web
## Comment viewing options
### You do realize that
what you are stating is the result of, but not inflation. Inflation is an increases in the medium of change (both printing and credit creation).
The Fed actually states that:
inflation in the U.S. should have been about 31 percent per year between 2008 and 2013, when the money supply grew at an average pace of 33 percent per year and output grew at an average pace just below 2 percent.
### The money supply doesn't
The money supply doesn't determine inflation.
### Right on.
Right on.
Plan for eliminating the national debt in 10-20 years:
Specific cuts; defense spending: http://rolexian.wordpress.com/2011/01/03/more-detailed-look-a
### Try and convince the people of zimbabwe
LOL!
Surviving the killing fields of Minnesota
Todays brainwashing: GMO's are safe
### Inflation is the general increase in money supply
Goldspan is right, I just learned this last week actually. Govt redefined inflation, they want us to think of it as increase in prices, then they can blame other factors, such as greedy businesses.
This link explains it real well:
http://wiki.mises.org/wiki/Inflation
### :) I loved the downvotes on
:) I loved the downvotes on my post. A lot of people here that truly don't understand the cause of inflation. Inflation is NOT just the increase in money supply. Sure, increasing the money supply is not a good idea, but it is not what actually causes inflation.
Monetarist Milton Friedman would obviously disagree with this, as he was a huge proponent of the Quantity Theory. Except, Ludwig von Mises obliterated the Quantity Theory decades earlier in his book Theory of Money and Credit. In it he explains how the money supply could double, yet you won't see double the inflation and you could even see no inflation! It's a great book, and I won't give away any spoilers. Although be warned, it's long and it took me a couple months to get through.
### thanks doin
But remember inflation by definition is an increase in the money supply. The result is the loss of purchasing power of the medium of exchange. It's no more complicated than good old supply and demand.
### You're not worng .....if you trust the Fed
They can't tell the truth.....they can't say "inflation is an increase in the medium of exchange".....if they did they would be admitting that.....1)they are doing it and.....2) an increases in one decreases the other. They can't say we are providing more money to the system....but don't worry you won't be able to purchase as much.
They would rather try and sell you this " inflation is a general increase in the overall price level of the goods and services in the economy".
To believe that you would have to believe that the Fed is so powerful over the entire economy that they can raise the prices of goods and services by an specific amount whenever they want. Just the experience right now would tell you they can't. They want a 2% inflation rate. The only power they have is to dilute the purchasing power of the dollars in existence ......by increasing the number of dollars...by "inflating" the number of dollars....anything after that is the "result" of that action.
You may think I am splitting hairs....but this is a very important distinction.....because when the SHTF the Fed will be looking for scapegoats... but they won't look in the mirror. One of the cornerstones of Libertarian/Austrian thought is "Sound Money".
So the hair I am splitting is actually the difference between Austrian and Keynesian Economics.
This is a HUGE DEAL!
### I was joking :)
Thanks Goldspan for being passionate about the subject. I am too. My sarcasm wasn't captured in my previous message. I totally meant it as a joke, given the source.
### Thanks for clarify that for me Max,
humor and sarcasm gets lost on an old fart like me in this modern forum where there is no expression.
### Man I really wanted an answer from this guy
and y'all stepped all over my question.....so allow me to ask it again.
What exactly do you think they are inflating?
### My comment was short,
My comment was short, intentionally left with no context, as I was only going to explain if I got replies and downvotes...which I did, so here's the comment fleshed out.
Mises laid out almost 100 years ago in Theory of Money and Credit how money supply can increase but the purchasing power may not decrease. There is no direct correlation between increase of money supply and decrease of purchasing power. There's another more important factor, and it's the individual. This is why the Fed has been able to quadruple the monetary base since 2008, yet we don't have quadruple the prices. It goes much deeper than that. Mises laid out some great examples on why the Quantity Theory is a fallacy, and I would really recommend checking the book out if you're interested.
### Thanks for bringing up Mises
.....it's been oh so long since I have read him, I've forgotten how eloquent he can be.
I wasn't necessarily talking about the Quantity Theory of Money as much as The Quantity of Money vs the Demand for Money which Mises addresses on page 137.
When Mises is addressing The Quantity Theory of Money he is talking about the "subjective value of money" and not the objective exchange value when a increases in the money stock occurs.
"The demand for money and its relations to the stock of money forms the starting-point for an explanation of fluctuations in the objective exchange-value of money. Not to understand the nature of the demand for money is to fail at the very outset of any attempt to grapple With the problem of variations in the value of money."
"In the history of money a particularly important part has been played by those variations in its objective exchange-value that have arisen in consequence of an increase in the stock of money while the demand for it has remained unchanged or has at least not increased to the same extent. These variations, in fact, were what first attracted the attention of economists; it was in order to explain them that the Quantity Theory of Money was first propounded."
"In whatever way we care to picture to ourselves the increase in the stock of money, whether as arising from increased production or importation of the substance of which commodity money is made, or through a new issue of fiat or credit money, the new money always increases the stock of money at the disposal of certain individual economic agents. An increase in the stock of money in a community always means an increase in the money incomes of a number of
individuals; but it need not necessarily mean at the same time an increase in the quantity of goods that are at the disposal of the community, that is to say, it need not mean an increase in the national dividend. An increase in the amount of fiat or credit money is only to be regarded as an increase in the stock of goods at the disposal of society if it permits the satisfaction of a demand for money which would otherwise have been satisfied by commodity money instead, since the material for the commodity money would then have had to be procured by the surrender of other goods in exchange or produced at the cost of renouncing some other sort of production. If, on the other hand, the non-existence of the new issue of fiat or credit money would not have involved an increase in the quantity of commodity money, then the increase of money cannot be regarded as an increase of the income or wealth of society."
"An increase in a community's stock of money always means an increase in the amount of money held by a number of economic agents, whether these are the issuers of fiat or credit money or the producers of the substance of which commodity money is made. For these persons, the ratio between the demand for money and the stock of it is altered; they have a relative superfluity of money and a relative shortage of other economic goods. The immediate consequence of both
circumstances is that the marginal utility to them of the monetary unit diminishes. This necessarily influences their behavior in the market. They are in a stronger position as buyers. They will now express in the market their demand for the objects they desire more intensively than before; they are able to offer more money for the commodities that they wish to acquire. It will be the obvious result of this that the prices of the goods concerned will rise, and that the objective exchange-value of money will fall in comparison. But this rise of prices will by no means be restricted to the market for those goods that are desired by those who originally have the new money at their disposal. In addition, those who have brought these goods to market will have their incomes and their proportionate stocks of money increased and, in their tum, will be in a position to demand more intensively the goods they want, so that these goods
will also rise in price. Thus the increase of prices continues, having a diminishing effect, until all commodities, some to a greater and some to a lesser extent, are reached by it."
"The increase in the quantity of money does not mean an increase of income for all individuals. On the contrary, those sections of the community that are the last to be reached by the additional quantity of money have their incomes reduced, as a consequence of the decrease in the value of money called forth by the increase in its quantity; this will be referred to later. The reduction in the income of these classes now starts a counter-tendency, which opposes the tendency to a diminution of the value of money due to the increase of income of the other classes~ without being able to rob it completely of its effect."
It's like read poetry isn't it......So the question remain....what do you think they are inflating? The answer should have been the money supply.....and the resulting price increases are the result. That's the only thing I was after......can we now agree?
### Mises was definitely a pleasure to read
If were just asking what are they trying to inflate with the increase of money supply? Then yes, you're absolutely correct, they're trying to inflate prices.
I was just pointing out that there's not a science in that increasing the money supply by x will also increase prices by x. If I misunderstood you, sorry about that.
### Here is another thread on here
where the topic was velocity in the Quantity of Theory equation you might like. I pulled from Henry Hazlitt.
http://www.dailypaul.com/325479/fed-us-consumers-have-decide...
If you decide to read the thread.....check out the St Louis Fed white paper referenced to write the CNBC article......it's really not very well done, shallow and a lot of assumptions, it's hard to believe they publish this and don't have it called out as the crap it is. But hey it was good enough for CNBC.
### I'll check out your
I'll check out your referenced material later tonight.
### It's technically true, since
It's technically true, since a trillion dollars lost at sea doesn't affect prices. Upvote for da TROOF.
Author of Shades of Thomas Paine, a common sense blog with a Libertarian slant.
Also author of Stick it to the Man!
http://www.amazon.com/Stick-Man-Richard-Moyer/dp/1484036417
### Um, yes, that's the definition of inflation
whether the consequence is rising prices depends on a multitude of economic factors that take place in a world of supply and demand. If there is more money produced, that money is going somewhere, and thus there is rising prices where it is used. There is certainly higher prices in the area which that extra money was used. If they money is parked at banks that are buying bonds to take advantage of the spread and real estate, then there are two areas where price inflation is happening and actual price discovery doesn't occur.
Tu ne cede malis.
Candidates for Liberty Webpage:
http://candidates4liberty.com/home.html
### Two types of inflation
There are two types of inflation: Monetary inflation and price inflation. Monetary inflation generally precedes price inflation. It takes some amount of time before the increase in the money supply starts to drive-up the prices of goods and services, but once it gets going, price inflation will catch-up-with, and often surpass the monetary inflation. What matters in the long term is monetary inflation, but in the short term, human perception governs price inflation.
### Then tell us
What exactly are they inflating?
### Bananas only 18%
Banana Republic, coincidence?
To my Liberal Trolls:
"Really Don't mind if you sit this one out. Your words but a whisper, your deafness a shout. I may make you feel, but I can't make you think."
Ian Anderson 1972
### BLS says their database
is unavailable now. They're on to ya!!
| 2,990
| 13,818
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2014-52
|
latest
|
en
| 0.927655
|
https://au.mathworks.com/matlabcentral/answers/1764500-histogram-bin-location-to-place-text-for-categorical-data
| 1,679,984,210,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00067.warc.gz
| 148,433,042
| 28,089
|
# Histogram bin location to place text for categorical data
37 views (last 30 days)
Alessandro Maria Laspina on 20 Jul 2022
Answered: Adam Danz on 20 Jul 2022
Hello,
I'm trying to find the bin location for categorical data for histogram. Using text I can place the number of the counts for each bin like the following example:
C = categorical(X,1:1:length(categorical_edges_x),categorical_edges_x);
h1=histogram(C);
xloc = h1.BinEdges ;
yloc = h1.Values ;
text(xloc(1:end-1),yloc,num2str(yloc'),'vert','bottom','horiz','center');
The issue is that it doesn't like it when it is categorical, and it returns the following error:
Unrecognized method, property, or field 'BinEdges' for class 'matlab.graphics.chart.primitive.categorical.Histogram'.
Any suggestions?
##### 1 CommentShowHide None
Jonas on 20 Jul 2022
try
double(xticks())
to see the xvalues
Voss on 20 Jul 2022
You can use h1.Categories instead of h1.BinEdges
% a guess at what your X and categorical_edges_x look like
categorical_edges_x = {'A' 'B' 'C' 'D' 'E'};
X = randi(numel(categorical_edges_x),10);
% make the categorical array
C = categorical(X,1:numel(categorical_edges_x),categorical_edges_x);
% make the histogram
h1=histogram(C);
% make the texts
xloc = 1:numel(h1.Categories);
yloc = h1.Values;
text(xloc,yloc,sprintfc('%d',yloc),'vert','bottom','horiz','center')
### More Answers (1)
Adam Danz on 20 Jul 2022
Since you x-data are categorical, you're working with a categorical ruler. This makes it difficult to position text at numeric x-values.
Option 1: don't use categorical data
Produce the histogram using your numeric data and then apply x-tick labels with your category names. You can do this with bar too if you want to keep the gap between cateogries. This will create a numeric xruler and you can position text anywhere along the x-axis.
Option 2: Place your labels along the cateogory values
@Voss provided a nice example of this in the other answer on this page. You could also place the text at the bottom of the bars in white font color, to suggest another style.
Option 3: Add a second row of tick labels in a categorical ruler
If you'd rather use cateogrical values and you want the labels to be at the bottom of the axes but not overlapping the categorical names
A = [1 3 3; 2 1 3; 1 1 2];
values = [1,2,3];
categoryNames = {'red' 'green' 'blue'};
C = categorical(A,values,categoryNames);
h1 = histogram(C);
ax = ancestor(h1,'axes');
tickValues = vertcat(ax.XTickLabel', num2cell(values));
newTickLabels = sprintf('%s\\newline%.0f\n',tickValues{:});
ax.XTickLabel = newTickLabels;
| 702
| 2,576
|
{"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}
| 2.515625
| 3
|
CC-MAIN-2023-14
|
longest
|
en
| 0.695192
|
https://www.mathsisfun.com/definitions/thousandth.html
| 1,585,555,209,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-16/segments/1585370496669.0/warc/CC-MAIN-20200330054217-20200330084217-00317.warc.gz
| 1,052,057,059
| 2,330
|
Definition of
# Thousandth
One part in a thousand equal parts: 1/1000th
Example: 1 meter is a thousandth of 1 kilometer
Each of the small squares is one-thousandth of the whole lot.
| 53
| 185
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.046875
| 3
|
CC-MAIN-2020-16
|
longest
|
en
| 0.84553
|
https://wikidiff.com/achronal/spacetime
| 1,571,654,478,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570987769323.92/warc/CC-MAIN-20191021093533-20191021121033-00305.warc.gz
| 787,572,646
| 6,384
|
# Spacetime vs Achronal - What's the difference?
spacetime | achronal |
## In physics|lang=en terms the difference between spacetime and achronal
is that spacetime is (physics) an n''-dimensional continuum consisting of dimensions of both space & time normally spacetime is considered as having 4 dimensions (''x'', ''y'', ''z'', ''t ), but higher-dimensional spacetimes are often encountered in theoretical physics, eg the 5-dimensional spacetime of kaluza-klein theory or the 11 dimensions of spacetime in m-theory while achronal is (physics) describing a set of points in a spacetime, no two of which have timelike separation.
## As a noun spacetime
is (uncountable|physics) the four-dimensional continuum of the three spatial dimensions plus time.
## As an adjective achronal is
(physics) describing a set of points in a spacetime, no two of which have timelike separation.
# spacetime
## English
(wikipedia spacetime)
### Noun
• (uncountable, physics) The four-dimensional continuum of the three spatial dimensions plus time.
• An event is a point in spacetime , specified by the coordinates x,y,z and t.
• (physics) An n''-dimensional continuum consisting of dimensions of both space & time. Normally spacetime is considered as having 4 dimensions (''x'', ''y'', ''z'', ''t ), but higher-dimensional spacetimes are often encountered in theoretical physics, e.g. the 5-dimensional spacetime of Kaluza-Klein theory or the 11 dimensions of spacetime in M-theory.
• (relativity) A specific region of the universe with mathematically different properties than the surrounding spacetime. Synonymous with "metric" within the context of general relativity.
• "a Schwarzschild spacetime," "a Reissner-Nordström spacetime," etc. as opposed to sense (2) describing the universe's spacetime as a whole: "a Minkowski spacetime," "a 5-dimensional spacetime," etc.
*
| 449
| 1,871
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.125
| 3
|
CC-MAIN-2019-43
|
latest
|
en
| 0.913095
|
https://en.wikipedia.org/wiki/Specificity_and_sensitivity
| 1,503,384,643,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-34/segments/1502886110471.85/warc/CC-MAIN-20170822050407-20170822070407-00508.warc.gz
| 763,767,443
| 30,625
|
# Sensitivity and specificity
(Redirected from Specificity and sensitivity)
Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function:
• Sensitivity (also called the true positive rate, the recall, or probability of detection[1] in some fields) measures the proportion of positives that are correctly identified as such (i.e. the percentage of sick people who are correctly identified as having the condition).
• Specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified as such (i.e., the percentage of healthy people who are correctly identified as not having the condition).
Another way to understand in the context of medical tests is that sensitivity is the extent to which true positives are not missed/overlooked (so false negatives are few) and specificity is the extent to which positives really represent the condition of interest and not some other condition being mistaken for it (so false positives are few). Thus a highly sensitive test rarely overlooks a positive (for example, showing "nothing bad" despite something bad existing); a highly specific test rarely registers a positive for anything that is not the target of testing (for example, finding one bacterial species when another closely related one is the true target); and a test that is highly sensitive and highly specific does both, so it "rarely overlooks a thing that it is looking for" and it "rarely mistakes anything else for that thing." Because most medical tests do not have sensitivity and specificity values above 99%, "rarely" does not equate to certainty. But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.
Sensitivity therefore quantifies the avoiding of false negatives, and specificity does the same for false positives. For any test, there is usually a trade-off between the measures – for instance, in airport security since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity), in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity). This trade-off can be represented graphically using a receiver operating characteristic curve. A perfect predictor would be described as 100% sensitive, meaning all sick individuals are correctly identified as sick, and 100% specific, meaning no healthy individuals are incorrectly identified as sick. In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.
## Definitions
(number of) positive samples (P) (number of) negative samples (N) (number of) true positive (TP) eqv. with hit (number of) true negative (TN) eqv. with correct rejection (number of) false positive (FP) eqv. with false alarm, Type I error (number of) false negative (FN) eqv. with miss, Type II error sensitivity or true positive rate (TPR) eqv. with hit rate, recall ${\displaystyle {\mathit {TPR}}={\mathit {TP}}/P={\mathit {TP}}/({\mathit {TP}}+{\mathit {FN}})}$ specificity (SPC) or true negative rate ${\displaystyle {\mathit {SPC}}={\mathit {TN}}/N={\mathit {TN}}/({\mathit {TN}}+{\mathit {FP}})}$ precision or positive predictive value (PPV) ${\displaystyle {\mathit {PPV}}={\mathit {TP}}/({\mathit {TP}}+{\mathit {FP}})}$ negative predictive value (NPV) ${\displaystyle {\mathit {NPV}}={\mathit {TN}}/({\mathit {TN}}+{\mathit {FN}})}$ fall-out or false positive rate (FPR) ${\displaystyle {\mathit {FPR}}={\mathit {FP}}/N={\mathit {FP}}/({\mathit {FP}}+{\mathit {TN}})=1-{\mathit {SPC}}}$ false negative rate (FNR) ${\displaystyle {\mathit {FNR}}={\mathit {FN}}/({\mathit {TP}}+{\mathit {FN}})=1-{\mathit {TPR}}}$ false discovery rate (FDR) ${\displaystyle {\mathit {FDR}}={\mathit {FP}}/({\mathit {TP}}+{\mathit {FP}})=1-{\mathit {PPV}}}$ accuracy (ACC) ${\displaystyle {\mathit {ACC}}=({\mathit {TP}}+{\mathit {TN}})/({\mathit {TP}}+{\mathit {FP}}+{\mathit {FN}}+{\mathit {TN}})}$ F1 score is the harmonic mean of precision and sensitivity ${\displaystyle {\mathit {F1}}=2{\mathit {TP}}/(2{\mathit {TP}}+{\mathit {FP}}+{\mathit {FN}})}$ Matthews correlation coefficient (MCC) ${\displaystyle {\frac {{\mathit {TP}}\times {\mathit {TN}}-{\mathit {FP}}\times {\mathit {FN}}}{\sqrt {({\mathit {TP}}+{\mathit {FP}})({\mathit {TP}}+{\mathit {FN}})({\mathit {TN}}+{\mathit {FP}})({\mathit {TN}}+{\mathit {FN}})}}}}$ Informedness ${\displaystyle {\mathit {TPR}}+{\mathit {SPC}}-1}$ Markedness ${\displaystyle {\mathit {PPV}}+{\mathit {NPV}}-1}$ Sources: Fawcett (2006) and Powers (2011).[2][3]
### Application to screening study
Imagine a study evaluating a new test that screens people for a disease. Each person taking the test either has or does not have the disease. The test outcome can be positive (classifying the person as having the disease) or negative (classifying the person as not having the disease). The test results for each subject may or may not match the subject's actual status. In that setting:
• True positive: Sick people correctly identified as sick
• False positive: Healthy people incorrectly identified as sick
• True negative: Healthy people correctly identified as healthy
• False negative: Sick people incorrectly identified as healthy
In general, Positive = identified and negative = rejected. Therefore:
• True positive = correctly identified
• False positive = incorrectly identified
• True negative = correctly rejected
• False negative = incorrectly rejected
### Confusion matrix
Let us consider a group with P positive instances and N negative instances of some condition. The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows:
True condition Accuracy (ACC) = Σ True positive + Σ True negative/Σ Total population Total population Condition positive Condition negative Prevalence = Σ Condition positive/Σ Total population Predicted condition Predicted condition positive True positive False positive (Type I error) Positive predictive value (PPV), Precision = Σ True positive/Σ Predicted condition positive False discovery rate (FDR) = Σ False positive/Σ Predicted condition positive Predicted condition negative False negative (Type II error) True negative False omission rate (FOR) = Σ False negative/Σ Predicted condition negative Negative predictive value (NPV) = Σ True negative/Σ Predicted condition negative True positive rate (TPR), Recall, Sensitivity, probability of detection = Σ True positive/Σ Condition positive False positive rate (FPR), Fall-out, probability of false alarm = Σ False positive/Σ Condition negative Positive likelihood ratio (LR+) = TPR/FPR Diagnostic odds ratio (DOR) = LR+/LR− F1 score = 2/1/recall+1/precision False negative rate (FNR), Miss rate = Σ False negative/Σ Condition positive True negative rate (TNR), Specificity (SPC) = Σ True negative/Σ Condition negative Negative likelihood ratio (LR−) = FNR/TNR
## Sensitivity
Sensitivity refers to the test's ability to correctly detect patients who do have the condition.[4] In the example of a medical test used to identify a disease, the sensitivity of the test is the proportion of people who test positive for the disease among those who have the disease. Mathematically, this can be expressed as:
{\displaystyle {\begin{aligned}{\text{sensitivity}}&={\frac {\text{number of true positives}}{{\text{number of true positives}}+{\text{number of false negatives}}}}\\\\&={\frac {\text{number of true positives}}{\text{total number of sick individuals in population}}}\\\\&={\text{probability of a positive test given that the patient has the disease}}\end{aligned}}}
A negative result in a test with high sensitivity is useful for ruling out disease.[4] A high sensitivity test is reliable when its result is negative, since it rarely misdiagnoses those who have the disease. A test with 100% sensitivity will recognize all patients with the disease by testing positive. A negative test result would definitively rule out presence of the disease in a patient.
A positive result in a test with high sensitivity is not useful for ruling in disease. Suppose a 'bogus' test kit is designed to show only one reading, positive. When used on diseased patients, all patients test positive, giving the test 100% sensitivity. However, sensitivity by definition does not take into account false positives. The bogus test also returns positive on all healthy patients, giving it a false positive rate of 100%, rendering it useless for detecting or "ruling in" the disease.
Sensitivity is not the same as the precision or positive predictive value (ratio of true positives to combined true and false positives), which is as much a statement about the proportion of actual positives in the population being tested as it is about the test.
The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, indeterminate samples either should be excluded from the analysis (the number of exclusions should be stated when quoting sensitivity) or can be treated as false negatives (which gives the worst-case value for sensitivity and may therefore underestimate it).
## Specificity
Specificity relates to the test's ability to correctly detect patients without a condition. Consider the example of a medical test for diagnosing a disease. Specificity of a test is the proportion of healthy patients known not to have the disease, who will test negative for it. Mathematically, this can also be written as:
{\displaystyle {\begin{aligned}{\text{specificity}}&={\frac {\text{number of true negatives}}{{\text{number of true negatives}}+{\text{number of false positives}}}}\\\\&={\frac {\text{number of true negatives}}{\text{total number of well individuals in population}}}\\\\&={\text{probability of a negative test given that the patient is well}}\end{aligned}}}
A positive result in a test with high specificity is useful for ruling in disease. The test rarely gives positive results in healthy patients. A test with 100% specificity will read negative, and accurately exclude disease from all healthy patients. A positive result signifies a high probability of the presence of disease.[5]
A test with a higher specificity has a lower type I error rate.
## Medical examples
In medical diagnosis, test sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), whereas test specificity is the ability of the test to correctly identify those without the disease (true negative rate). If 100 patients known to have a disease were tested, and 43 test positive, then the test has 43% sensitivity. If 100 with no disease are tested and 96 return a negative result, then the test has 96% specificity. Sensitivity and specificity are prevalence-independent test characteristics, as their values are intrinsic to the test and do not depend on the disease prevalence in the population of interest.[6] Positive and negative predictive values, but not sensitivity or specificity, are values influenced by the prevalence of disease in the population that is being tested. These concepts are illustrated graphically in this applet Bayesian clinical diagnostic model which show the positive and negative predictive values as a function of the prevalence, the sensitivity and specificity.
### Misconceptions
It is often claimed that a highly specific test is effective at ruling in a disease when positive, while a highly sensitive test is deemed effective at ruling out a disease when negative.[7][8] This has led to the widely used mnemonics SPIN and SNOUT, according to which a highly SPecific test, when Positive, rules IN disease (SP-P-IN), and a highly 'SeNsitive' test, when Negative rules OUT disease (SN-N-OUT). Both rules of thumb are, however, inferentially misleading, as the diagnostic power of any test is determined by both its sensitivity and its specificity.[9][10][11]
The tradeoff between Specificity and Sensitivity is explored in ROC analysis as a trade off between TPR and FPR (that is Recall and Fallout).[2] Giving them equal weight optimizes Informedness = Specificity+Sensitivity-1 = TPR-FPR, the magnitude of which gives the probability of an informed decision between the two classes (>0 represents appropriate use of information, 0 represents chance-level performance, <0 represents perverse use of information).[3]
### Sensitivity index
The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory. It provides the separation between the means of the signal and the noise distributions, compared against the standard deviation of the noise distribution. For normally distributed signal and noise with mean and standard deviations ${\displaystyle \mu _{S}}$ and ${\displaystyle \sigma _{S}}$, and ${\displaystyle \mu _{N}}$ and ${\displaystyle \sigma _{N}}$, respectively, d' is defined as:
${\displaystyle d'={\frac {\mu _{S}-\mu _{N}}{\sqrt {{\frac {1}{2}}(\sigma _{S}^{2}+\sigma _{N}^{2})}}}}$ [12]
An estimate of d' can be also found from measurements of the hit rate and false-alarm rate. It is calculated as:
d' = Z(hit rate) – Z(false alarm rate),[13]
where function Z(p), p ∈ [0,1], is the inverse of the cumulative Gaussian distribution.
d' is a dimensionless statistic. A higher d' indicates that the signal can be more readily detected.
## Worked example
A worked example
A diagnostic test with sensitivity 67% and specificity 91% is applied to 2030 people to look for a disorder with a population prevalence of 1.48%
Patients with bowel cancer (as confirmed on endoscopy) Condition positive Condition negative Fecal occult blood screen test outcome Test outcome positive True positive (TP) = 20 False positive (FP) = 180 Positive predictive value = TP / (TP + FP) = 20 / (20 + 180) = 10% Test outcome negative False negative (FN) = 10 True negative (TN) = 1820 Negative predictive value = TN / (FN + TN) = 1820 / (10 + 1820) ≈ 99.5% Sensitivity = TP / (TP + FN) = 20 / (20 + 10) ≈ 67% Specificity = TN / (FP + TN) = 1820 / (180 + 1820) = 91%
Related calculations
• False positive rate (α) = type I error = 1 − specificity = FP / (FP + TN) = 180 / (180 + 1820) = 9%
• False negative rate (β) = type II error = 1 − sensitivity = FN / (TP + FN) = 10 / (20 + 10) = 33%
• Power = sensitivity = 1 − β
• Likelihood ratio positive = sensitivity / (1 − specificity) = 0.67 / (1 − 0.91) = 7.4
• Likelihood ratio negative = (1 − sensitivity) / specificity = (1 − 0.67) / 0.91 = 0.37
Hence with large numbers of false positives and few false negatives, a positive screen test is in itself poor at confirming the disorder (PPV = 10%) and further investigations must be undertaken; it did, however, correctly identify 66.7% of all cases (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have the disorder (NPV = 99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).
## Estimation of errors in quoted sensitivity or specificity
Sensitivity and specificity values alone may be highly misleading. The 'worst-case' sensitivity or specificity must be calculated in order to avoid reliance on experiments with few results. For example, a particular test may easily show 100% sensitivity if tested against the gold standard four times, but a single additional test against the gold standard that gave a poor result would imply a sensitivity of only 80%. A common way to do this is to state the binomial proportion confidence interval, often calculated using a Wilson score interval.
Confidence intervals for sensitivity and specificity can be calculated, giving the range of values within which the correct value lies at a given confidence level (e.g., 95%).[14]
## Terminology in information retrieval
In information retrieval, the positive predictive value is called precision, and sensitivity is called recall. Unlike the Specificity vs Sensitivity tradeoff, these measures are both independent of the number of true negatives, which is generally unknown and much larger than the actual numbers of relevant and retrieved documents. This assumption of very large numbers of true negatives versus positives is rare in other applications.[3]
The F-score can be used as a single measure of performance of the test for the positive class. The F-score is the harmonic mean of precision and recall:
${\displaystyle F=2\times {\frac {{\text{precision}}\times {\text{recall}}}{{\text{precision}}+{\text{recall}}}}}$
In the traditional language of statistical hypothesis testing, the sensitivity of a test is called the statistical power of the test, although the word power in that context has a more general usage that is not applicable in the present context. A sensitive test will have fewer Type II errors.
## References
1. ^ "Detector Performance Analysis Using ROC Curves – MATLAB & Simulink Example". www.mathworks.com. Retrieved 11 August 2016.
2. ^ a b Fawcett, Tom (2006). "An Introduction to ROC Analysis". Pattern Recognition Letters. 27 (8): 861–874. doi:10.1016/j.patrec.2005.10.010.
3. ^ a b c Powers, David M W (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation" (PDF). Journal of Machine Learning Technologies. 2 (1): 37–63.
4. ^ a b Altman, D. G.; Bland, J. M. (11 June 1994). "Statistics Notes: Diagnostic tests 1: sensitivity and specificity". BMJ. 308 (6943): 1552. PMC . PMID 8019315. doi:10.1136/bmj.308.6943.1552 – via www.bmj.com.
5. ^ "SpPins and SnNouts". Centre for Evidence Based Medicine (CEBM). Retrieved 26 December 2013.
6. ^ Mangrulkar, Rajesh. "Diagnostic Reasoning I and II". Retrieved 24 January 2012.
7. ^ "Evidence-Based Diagnosis". Michigan State University.
8. ^ "Sensitivity and Specificity". Emory University Medical School Evidence Based Medicine course.
9. ^ Baron, JA (Apr–Jun 1994). "Too bad it isn't true.....". Medical decision making : an international journal of the Society for Medical Decision Making. 14 (2): 107. PMID 8028462. doi:10.1177/0272989X9401400202.
10. ^ Boyko, EJ (Apr–Jun 1994). "Ruling out or ruling in disease with the most sensitive or specific diagnostic test: short cut or wrong turn?". Medical decision making : an international journal of the Society for Medical Decision Making. 14 (2): 175–179. PMID 8028470. doi:10.1177/0272989X9401400210.
11. ^ Pewsner, D; Battaglia, M; Minder, C; Marx, A; Bucher, HC; Egger, M (Jul 24, 2004). "Ruling a diagnosis in or out with "SpPIn" and "SnNOut": a note of caution". BMJ (Clinical research ed.). 329 (7459): 209–13. PMC . PMID 15271832. doi:10.1136/bmj.329.7459.209.
12. ^ Gale, SD; Perkel, DJ (Jan 20, 2010). "A basal ganglia pathway drives selective auditory responses in songbird dopaminergic neurons via disinhibition". The Journal of neuroscience : the official journal of the Society for Neuroscience. 30 (3): 1027–1037. PMC . PMID 20089911. doi:10.1523/JNEUROSCI.3585-09.2010.
13. ^ Macmillan, Neil A.; Creelman, C. Douglas (15 September 2004). Detection Theory: A User's Guide. Psychology Press. p. 7. ISBN 978-1-4106-1114-7.
14. ^
| 4,737
| 19,408
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 20, "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-2017-34
|
latest
|
en
| 0.944943
|
https://brilliant.org/discussions/thread/nmtc-problem/
| 1,627,134,941,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-31/segments/1627046150266.65/warc/CC-MAIN-20210724125655-20210724155655-00288.warc.gz
| 168,033,604
| 16,340
|
NMTC Problem
$\dfrac{x^3}{z^3+x^2y}+\dfrac{y^3}{x^3+y^2z}+\dfrac{z^3}{y^3+z^2x}\geq \dfrac{3}{2}$
Given that $x,y$ and $z$ are positive reals, prove the inequality above.
Note by Abdur Rehman Zahid
5 years, 4 months ago
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$
Sort by:
Here is a short solution I found:
$\sum_{cyc} \dfrac{x^4}{xz^3+x^3z} \geq \dfrac{(x^2+y^2+z^2)^2}{2(xz^3+x^3y+y^3z)}\geq \dfrac{3}{2}$
Hence it suffices to prove that
$(x^2+y^2+z^2)^2\geq 3(xz^3+x^3y+y^3z)$
Which is the famous Vasc's inequality
- 5 years, 4 months ago
Well, proving the Vasc Inequality might be slightly more difficult.
- 5 years, 4 months ago
To be exact Tremendously difficult
It does not yeild to most classical inequalities!
- 5 years, 4 months ago
Yes, I know. I doubt it can be quoted in contests either.
- 5 years, 4 months ago
I found this amazingly elegant proof on AoPS:
$\left(a^2 + b^2 + c^2\right)^2 - 3\left(a^3b + b^3c + c^3a\right) \\ = \frac {1}{2}\left( \left( a^{2} - 2ab + bc - c^{2} + ca\right) ^2 + \left(b^{2} - 2bc + ca - a^{2} + ab\right)^2 + \left( c^{2} - 2ca + ab - b^{2} + bc\right)^2 \right) \geq 0$
- 5 years, 4 months ago
Awesome!!! (speechless)
- 5 years, 4 months ago
This is basically the only relatively clean proof!
- 5 years, 4 months ago
Yep! Titu and Vasc killed this... =D
- 5 years, 4 months ago
- 5 years, 4 months ago
You really want my long, expanded solution?
- 5 years, 4 months ago
Yes :P
- 5 years, 4 months ago
- 5 years, 4 months ago
I still haven't seen your long and expanded solution Sharky :P
- 5 years, 2 months ago
It isnt very difficult that way. Try yourself expanding the whole inequality,without any denominators. Then work with AM-GM and Shur. (And post the expanded stuff)
- 5 years, 2 months ago
| 1,129
| 3,387
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 14, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.53125
| 4
|
CC-MAIN-2021-31
|
latest
|
en
| 0.810706
|
https://www.coursehero.com/file/29772722/p04pdf/
| 1,544,806,600,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00097.warc.gz
| 868,380,337
| 111,984
|
# p04.pdf - htotal hcone R 10 3 2 33.7 m m m...
• 1
This preview shows page 1. Sign up to view the full content.
h total : 10 m h cone : 3 m R: 2 m : 33.7 ° =DEGREES(ATAN(C5/C4)) Cone Volume: 12.6 m 3 =(1/3)*PI()*C5^2*C4 Cylinder Volume: 88.0 m 3 =PI()*C5^2*(C3-C4) Total Volume: 100.5 m 3 =C8+C9 4.9 Finding the Volume of a Storage Bin II h total : 10 m h cone : 3 m R: 2 m : 33.7 ° =DEGREES(ATAN(C5/C4)) Height Radius Volume (m) (m) (m 3 ) 0.0 0.0 0.0 0.5 0.3 0.1 =B12*TAN(RADIANS(\$C\$6)) 1.0 0.7
This is the end of the preview. Sign up to access the rest of the document.
• Spring '17
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern
| 471
| 1,552
|
{"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-2018-51
|
latest
|
en
| 0.864003
|
https://www.jiskha.com/display.cgi?id=1351811470
| 1,511,548,179,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934808742.58/warc/CC-MAIN-20171124180349-20171124200349-00266.warc.gz
| 830,753,182
| 4,012
|
# math
posted by .
Jacob opens a savings account on January 1 with a deposit of \$350. He has "direct deposit," in which \$25 is deposited every other week. The bank also charges a \$3 monthly processing fee. How much money will he have at the end of the year?
## Similar Questions
1. ### Math
Can you help me with this problem? At the beginning of January, Lisa had some money in her savings account. Each month she was able to deposit enough from her allowance to double the amount currently in the account. However, she had
2. ### math
Jacob opens a savings account on January 1 with a deposit of \$350. He has "direct deposit," in which \$25 is deposited every other week. The bank also charges a \$3 monthly processing fee. How much money will he have at the end of the …
3. ### Math
(a) Themba wants to deposit a sum of money into a savings account so that he will have R30 000 in 3 years time for an overseas holiday how much money must he deposit into the account if the interest paid on the savings is 8,5% p.a …
4. ### Math
From January 1, 2000 to December 31, 2004, First Bank paid 5% interest, compounded monthly. On January 1, 2005, they lowered their rate to 3% interest, compounded monthly. I deposited \$100 at the end of each month beginning in January, …
5. ### Finance
. On the day that you were born, your grandfather opened a savings account in your name. At that time, he deposited a certain amount of money into the account, and has deposited the same amount on each of your first 20 birthdays. Today …
6. ### Math
Jacob opens a savings account on Jan 1 with a deposit of \$250. Every other week \$25 is deposited. The bank charges \$3 for a processing fee monthly. How much will he have at the end of the year?
7. ### math
Ed will deposit \$10 every week to his bank account for the next 4 weeks. How much money will ed have in his bank account after 4 weeks?
8. ### Math
Jean has \$280 in her savings account starting next week she will deposit \$30 in her account every week is the amount of money in her account proportional to the number of weeks. Thank you for helping
9. ### Finite math
A bank account pays interest at 12% compounded monthly, and has a monthly fee of \$10, deducted at the end of each month. If \$13,000 is deposited on January 1, 2013, how much is in the account on January 1, 2016?
10. ### math
Suppose you deposit \$275.00 in your savings account on December 31. Your bank pays 3 percent annual interest on savings accounts. If you do not deposit any more money into the account, what would be the balance on December 31 of the …
More Similar Questions
| 632
| 2,617
|
{"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}
| 3.171875
| 3
|
CC-MAIN-2017-47
|
latest
|
en
| 0.977294
|
https://books.google.co.ve/books?qtid=d7e7847&dq=editions:UOM39076001949697&id=5lN1sy51SwYC&output=html_text&lr=&sa=N&start=60
| 1,713,497,976,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296817253.5/warc/CC-MAIN-20240419013002-20240419043002-00819.warc.gz
| 119,611,981
| 5,991
|
Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Libros Libros
If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
The Elements of Euclid - Página 78
por Euclid - 1838 - 416 páginas
Vista completa - Acerca de este libro
## Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...
Peter Nicholson - 1856 - 518 páginas
...alternate angles, GFE, FGH, are also equal ; therefore the two triangles GEF, HFG, have two angles of the one equal to two angles of the other, each to each ; and the side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ; and FH is...
Vista completa - Acerca de este libro
## Elements of Geometry and Conic Sections
Elias Loomis - 1857 - 242 páginas
...alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.) ; and the...
Vista completa - Acerca de este libro
## Elements of Geometry and Conic Sections
Elias Loomis - 1858 - 256 páginas
...alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.) ; and the...
Vista completa - Acerca de este libro
## Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...
Euclides - 1858 - 248 páginas
...following propositions. PROP. 26.— THEOR. — (Important.) If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz., either the sides adjacent to the equal angles in each, or the sides...
Vista completa - Acerca de este libro
## Examination papers used at the examinations for admission to the Royal ...
Sandhurst roy. military coll - 1859 - 672 páginas
...right angles, or are together equal to two right angles. 2. If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, namely, either the sides adjacent to the equal angles, or the sides which...
Vista completa - Acerca de este libro
## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...
Euclides - 1860 - 288 páginas
...is equal to KCF, and the right angle FHC equal to the right angle FKC ; in the triangles FHC and FKC there are two angles of one equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both ; therefore...
Vista completa - Acerca de este libro
## Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...
Horatio Nelson Robinson - 1860 - 470 páginas
...we have the remaining [_'s, AFC and AEB, equal. Hence, the A's, AFC and AEB, have two angles of the one equal to two angles of the other, each to each, and the included sides equal; the remaining sides and angles are therefore equal, (Cor., Prop. 9). Therefore,...
Vista completa - Acerca de este libro
## The Elements of Euclid with Many Additional Propositions and Explanatory Notes
Eucleides - 1860 - 396 páginas
...the angle AEG is equal to the angle BEH (a) ; therefore the triangles AEG, BEH have two angles of the one, equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another ; wherefore they have their other...
Vista completa - Acerca de este libro
## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...
Robert Potts - 1860 - 380 páginas
...Wherefore, if two triangles, &c. QED PROPOSITION XXVI. THEOREM. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz, either the sides adjacent to the equal angles in each, or the sides...
Vista completa - Acerca de este libro
## The examination papers as set for the preliminary literary examination of ...
Royal college of surgeons of England - 1860 - 332 páginas
...other, then the sides AB, BC shall lie in one straight line. 3. If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz., the sides adjacent to the equal angles in each triangle ; then shall...
Vista completa - Acerca de este libro
| 1,154
| 4,556
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.96875
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.749866
|
http://www.sparknotes.com/biography/newton/section3.rhtml
| 1,369,467,413,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-20/segments/1368705749262/warc/CC-MAIN-20130516120229-00073-ip-10-60-113-184.ec2.internal.warc.gz
| 704,081,475
| 21,261
|
# Isaac Newton
Get this SparkNote to go!
### "The Miraculous Year"
As we saw in the previous section, the year 1666 marked the peak of Newton's achievements. Here we will explore the details and significance of these astonishing accomplishments, which included the invention of calculus, groundbreaking work in optics, and the invention of the notion of gravity as a universal force.
The branch of mathematics known as calculus is difficult to define. Very roughly, it can be defined as the calculation of variable quantities, such as weight, distance, or time, using forms of algebraic notation. For example, as water is poured at a uniform rate into an inverted cone, its level rises less and less rapidly; calculus can be used to determine how much the level will rise in any given interval. In more complicated forms, calculus can be used to find the slope of curves, and to determine the area under, and within, curves. It has proved an indispensable tool for engineers and architects, and yet it effectively did not exist before the 17th century. Isaac Newton cannot claim to be its sole inventor--credit must go to any number of mathematicians, particularly the German Gottfried von Leibniz--however, Newton unquestionably made significant contributions to the field. In 1666 he formulated the binomial theorem, which enabled one to calculate any power of a binomial (an algebraic expression involving two variables being added or subtracted, such as [x + y] or [4y - 7z]) without multiplying the entire expression out. Also in 1666, he discovered how find the slope of a curve at any point on a curve, by a process he called "fluxions." However, while he mentioned the "fluxions" in a letter to Isaac Barrow in 1669, he did not publish the system until 1704, and so must share credit for the innovation with Leibniz, who developed his own method in the 1670s.
Newton's work in optics, the study of light, was equally pioneering. For decades scholars had debated the nature of light, its composition and its properties, without reaching conclusions. One puzzling characteristic of light was its ability to break down into various shards of color when shining through a prism. Now Newton, using a prism that he had purchased at a local fair, made a groundbreaking discovery: in his own words, Newton "procured me a Triangular glass-Prisme, to try therewith the celebrated Phaenomena of colours. And in order thereto having darkened my chamber, and made a small hole in my window shuts, to let in a convenient quantity of the Sun light, I placed my Prisme at its entrance, that it might be thereby refracted to the opposite wall." What appeared was a row of bands, a spectrum of color, with red at one end and violet at the other, each refracted at a slightly greater angle. He hypothesized that white light was composed of "a Heterogeneous mixture of differently refrangible rays," each a different color, and each refracted at a different angle by the prism. Using a lens, he was able to prove his hypothesis by bending the colored rays back together, into a single beam of white light.
This idea--that white light is a combination of differently colored rays--was a completely new notion in the 17th century: most people assumed that red light, green light, and so on, were all just slight modifications of white light, not components of it. Yet while Newton's insight caused changes in the way people of his lifetime thought about light, its vast consequences for science would not be realized until the 20th century. Newton's discoveries in optics have allowed modern scientists to make much progress in astronomy, for example: because different substances radiate different colors in the spectrum when they burn, astronomers have been able to determine the chemical composition of distant stars by observing which colors they produce. Close examination of the spectrum of colors produced by stars has also enabled scientists to calculate these stars' rate of motion toward or away from Earth; these calculations have in turn enabled us to estimate its distance from us, and, more generally, the size of galaxies and the universe itself.
The innovations of calculus and optics alone would have made the year 1666 famous in the annals of science. But it was also in this year that the twenty- four-year old first began to conceive his greatest idea: the concept of gravity. Years later, Voltaire would recount the legend that arose around the discovery: "One day, in the year 1666, Newton, then retired to the country, seeing some fruit fall from the tree... fell into a profound meditation upon the cause which draws all bodies in a line which, if prolonged, would pass very nearly through the center of the earth." This story of how Newton came to his revelation by watching a falling apple amounts, alas, to no more than popular fiction; however, the event of the revelation itself is quite true. Gravitation, the invisible force exerted between objects, was by no means original to the English scientist--minds as eminent as Johannes Kepler, the German astronomer, had speculated on the attraction of interstellar bodies, and contemporaries like Robert Hooke and Edmund Halley discussed the idea in the 1660s and '70s. But Descartes's idea of particles and planet-propelling vortices now seemed to make a gravitational force unnecessary. Newton, however, was suspicious of Descartes's theory, and continued to calculate the interaction of the heavenly bodies: in 1666 he calculated the force of attraction that held planets in their orbits, and the Moon in its orbit around Earth, as varying inversely with the square of their distance from the sun. This was the fundamental law of gravity, and Newton knew it as he sat alone in his mother's house in Woolsthorpe.
But Newton did not publish the idea immediately. Indeed, Newton did not publish any of his great discoveries directly after making them--as we have seen, his "fluxions" would not come into print for nearly four decades; his work in optics waited six years to be published. But in the case of his work on gravitational attraction, publication was stalled for a particularly ironic reason: he delayed because he could not get the sizes of the Earth and the Moon to agree with his inverse square equation. In fact, the existing data on these two sizes was faulty, but he would not realize that until the 1670s, when new research proved that he had been right all along.
## Newton having been inFatioated
### by martinuddin, September 09, 2012
Please note that G.W. von Leibniz died in 1716, not 1714 as stated in the time line.
In the test, the question where Isaac studied mentions the year 1616, err for 1661.
I took the test and came to 94 % but I contend that he never had any lovers at no point. He was inFatioated as far as I know so the right answer is not in the list!
3 out of 4 people found this helpful
0
## More Help
### Buy the ebook of this SparkNote on BN.com
EVEN MORE HELP! ↓
## Take a Study Break
### What's your Pretty Little Liars name?
Take this quiz to find out!
### Which young actress just got married?
Click to find out!
### Cat bearding WINS THE INTERNET
Have you seen this yet?
### Scary movies with funny posters
These. Are. Hilarious.
### Geeky Actors: Then and Now
Travel back in time!
### Villains We Want These Actresses to Play
From super cute to super bad!
### 10 Movies Better Than Their Books
What do you think?
| 1,612
| 7,452
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.21875
| 3
|
CC-MAIN-2013-20
|
longest
|
en
| 0.95903
|
http://gmatclub.com/forum/preparation-time-61589.html?kudos=1
| 1,485,291,052,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-04/segments/1484560285244.23/warc/CC-MAIN-20170116095125-00169-ip-10-171-10-70.ec2.internal.warc.gz
| 117,499,387
| 54,048
|
preparation time .. : Share GMAT Experience
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack
It is currently 24 Jan 2017, 12:50
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# preparation time ..
Author Message
TAGS:
### Hide Tags
Manager
Joined: 21 Mar 2006
Posts: 132
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
21 Mar 2008, 05:47
Hi:
I passed my eengineering degree 10 years ago .. Now I want to do MBA. What would an avg preparation time needed for gmat preparation ?
thnks.
Manager
Joined: 02 Mar 2008
Posts: 210
Concentration: Finance, Strategy
Followers: 1
Kudos [?]: 46 [1] , given: 1
### Show Tags
12 Apr 2008, 04:07
1
KUDOS
the official GMATPrep, closest to the real
Manager
Joined: 23 Feb 2008
Posts: 51
Followers: 0
Kudos [?]: 4 [0], given: 0
### Show Tags
21 Mar 2008, 07:17
I would plan on 2-3 months, but don't schedule your GMAT until you've gotten far enough into your prep to see if that is the right amount of time.
Some people start by taking a practice test cold to see how they do, but without any prep, you're just wasting a test and not getting a decent baseline anyway, if you know nothing about the GMAT. Get a good prep book (I used Cracking the GMAT and would recommend it; great overview of the test), and read through it, do some practice questions. Also get the Official Guide, 11th edition -- it has a ton of practice questions and it's a must.
After you've done several practice questions for each question type, take a practice test. Either the Cracking tests (get the version with the DVD) or the official GMATPrep tests will give you the best idea of your progress. Then you can see where your weaknesses are and come back to ask for suggestions on how to set up your studies. Or just explore the forums...I've found a lot of good info here just browsing around.
Senior Manager
Joined: 18 Oct 2007
Posts: 449
Location: USA
Schools: Tepper '11
Followers: 5
Kudos [?]: 57 [0], given: 2
### Show Tags
21 Mar 2008, 11:28
Depends on the person. I have also been out of school for 9 years. I scheduled 4 months before test date, started studying 3 months before date.
Manager
Joined: 02 Jan 2008
Posts: 194
Location: Toronto
Followers: 1
Kudos [?]: 35 [0], given: 0
### Show Tags
21 Mar 2008, 12:27
Take a self assessment test.
If you want 700(min)....and
If you score around 550-600 in your diagonastic test, then plan for 3 months atleast.
If your score is around 600-650 in your diag., then plan for 2 months atleast.
if you scored 700, then don't plan, just take it next weekend like kruton and come back with a killing post.
if you scored less then 500, plan for 3-5 months.
This is not THE RULE, but just my 2 cents.
I hope that helps.
Intern
Joined: 10 Mar 2008
Posts: 30
Followers: 0
Kudos [?]: 7 [0], given: 0
### Show Tags
27 Mar 2008, 01:47
Just assess yourself and then decide.
Manager
Joined: 21 Mar 2006
Posts: 132
Followers: 3
Kudos [?]: 16 [0], given: 0
### Show Tags
12 Apr 2008, 03:46
Hi;
I went through lot experiences posted in forum.... which test shouold i piick up for diagnostic test ?
thanks,
abhay singh
Senior Manager
Joined: 02 Dec 2007
Posts: 457
Followers: 2
Kudos [?]: 197 [0], given: 6
### Show Tags
12 Apr 2008, 04:06
GMAT prep is the best one and i believe its a good indicator.
Re: preparation time .. [#permalink] 12 Apr 2008, 04:06
Similar topics Replies Last post
Similar
Topics:
Preparation and Resources 3 11 Sep 2009, 09:37
Preparation strategy 3 10 Nov 2008, 18:09
Not completely prepared 4 25 Jul 2008, 09:05
Sugestions On Preparation 2 18 Jun 2008, 17:35
Preparing for the 5th Time 15 08 Jan 2008, 07:08
Display posts from previous: Sort by
| 1,242
| 4,237
|
{"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-2017-04
|
latest
|
en
| 0.894455
|
http://www.lconvert.com/volume/cubic_meter/barrel_uk/
| 1,555,663,117,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-18/segments/1555578527518.38/warc/CC-MAIN-20190419081303-20190419103303-00083.warc.gz
| 250,416,490
| 6,182
|
hjghjghj
# Cubic Meter to Barrel (UK) Converter
1 Cubic Meter = 6.110602 Barrel (UK)
## How to convert from Cubic Meter to Barrel (UK)?
Every 1 Cubic Meter equals 6.110602 Barrel (UK). For example, 100 Cubic Meters equal 100 * 6.110602 = 611.0602 Barrel (UK)s and so on..
## Cubic Meter to Barrel (UK) Convesions Table
1 Cubic Meter = 6.110602 Barrel (UK)
2 Cubic Meter = 12.221204 Barrel (UK)
4 Cubic Meter = 24.442408 Barrel (UK)
5 Cubic Meter = 30.55301 Barrel (UK)
10 Cubic Meter = 61.10602 Barrel (UK)
20 Cubic Meter = 122.21204 Barrel (UK)
25 Cubic Meter = 152.76505 Barrel (UK)
50 Cubic Meter = 305.5301 Barrel (UK)
100 Cubic Meter = 611.0602 Barrel (UK)
200 Cubic Meter = 1222.1204 Barrel (UK)
250 Cubic Meter = 1527.6505 Barrel (UK)
500 Cubic Meter = 3055.301 Barrel (UK)
1000 Cubic Meter = 6110.602 Barrel (UK)
2000 Cubic Meter = 12221.204 Barrel (UK)
2500 Cubic Meter = 15276.505 Barrel (UK)
5000 Cubic Meter = 30553.01 Barrel (UK)
10000 Cubic Meter = 61106.02 Barrel (UK)
20000 Cubic Meter = 122212.04 Barrel (UK)
25000 Cubic Meter = 152765.05 Barrel (UK)
50000 Cubic Meter = 305530.1 Barrel (UK)
100000 Cubic Meter = 611060.2 Barrel (UK)
200000 Cubic Meter = 1222120.4 Barrel (UK)
500000 Cubic Meter = 3055301 Barrel (UK)
1000000 Cubic Meter = 6110602 Barrel (UK)
1 Barrel (UK) = 0.16364999716886 Cubic Meter
2 Barrel (UK) = 0.32729999433771 Cubic Meter
4 Barrel (UK) = 0.65459998867542 Cubic Meter
5 Barrel (UK) = 0.81824998584428 Cubic Meter
10 Barrel (UK) = 1.6364999716886 Cubic Meter
20 Barrel (UK) = 3.2729999433771 Cubic Meter
25 Barrel (UK) = 4.0912499292214 Cubic Meter
50 Barrel (UK) = 8.1824998584428 Cubic Meter
100 Barrel (UK) = 16.364999716886 Cubic Meter
200 Barrel (UK) = 32.729999433771 Cubic Meter
250 Barrel (UK) = 40.912499292214 Cubic Meter
500 Barrel (UK) = 81.824998584428 Cubic Meter
1000 Barrel (UK) = 163.64999716886 Cubic Meter
2000 Barrel (UK) = 327.29999433771 Cubic Meter
2500 Barrel (UK) = 409.12499292214 Cubic Meter
5000 Barrel (UK) = 818.24998584428 Cubic Meter
10000 Barrel (UK) = 1636.4999716886 Cubic Meter
20000 Barrel (UK) = 3272.9999433771 Cubic Meter
25000 Barrel (UK) = 4091.2499292214 Cubic Meter
50000 Barrel (UK) = 8182.4998584428 Cubic Meter
100000 Barrel (UK) = 16364.999716886 Cubic Meter
200000 Barrel (UK) = 32729.999433771 Cubic Meter
500000 Barrel (UK) = 81824.998584428 Cubic Meter
1000000 Barrel (UK) = 163649.99716886 Cubic Meter
| 890
| 2,403
|
{"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-2019-18
|
latest
|
en
| 0.48051
|
https://www.ohiomortgageproducts.com/2019/10/11/whats-a-interest-rate/
| 1,571,162,655,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570986660067.26/warc/CC-MAIN-20191015155056-20191015182556-00200.warc.gz
| 988,731,021
| 8,095
|
# Whats A Interest Rate
APR, or Average Percentage Rate, is a more specific term that describes how much interest a balance will accrue over the course of a year. But interest is assessed daily, so a credit card’s interest rate is its APR divided by 365 (days in a year). If your APR is 15%, for example, you would be charged interest at a rate of 15%/365 per day. That is, if you have a balance you don’t pay in full by the due date.
U.S. advertising revenue, specifically, accelerated to a rate of 29% — up from 26% growth in the prior quarter. Without.
Police stations filled with 600 obstructing demonstrators arrested in a deliberate drive to clog the system. Adam Smith.
A more personal Health app. For a more informed you. Now it’s easier than ever to organize and access your important health information. The new health app consolidates data from your iPhone, Apple Watch, and third-party apps you already use, so you can view all your progress in one convenient place.
Become debt free sooner than you’d think! The idea of this site is to build a number of free, easy to use, on-line calculators to help you calculate the cost of various.
Fha Loans Interest Rates Fha Loans Interest Rates – If you are looking for a loan to buy new home or for refinance option to reduce monthly payment of present loan then visit refinance mortgage services from our review.
{{configCtrl2.info.metaDescription}} The following represent additions to UpToDate from the past six months that were considered by the editors and authors to be of particular interest.
What is APR? Understand what is an annual percentage rate, how it’s calculated and the different types of APR to help you make more informed credit card decisions with this article from Better Money Habits.
The interest rate is the percent of principal charged by the lender for the use of its money. They impact the economy by controlling the money supply. The Balance
What Mortgage Rate Can I Get Find Unit Rate Calculator Apply Unit Rates and Ratios in the Real World | Common Core Math. Word Problem – Unit Rate and Proportion to Solve for Equivalent Ratios – duration: 6:43. maria Morrisson Copolillo.Instead of choosing a lender solely based on current mortgage rates, Russ Anderson, senior vice president and a centralized sales executive with Bank of America in Los Angeles, says you need to find a lender you can trust. "People get too wrapped up in the rate rather than finding someone who will communicate with them," he says.
“The mindset has long been that our products that have been successful in the US and Europe can be taken to Asia. But in.
Chase Savings SM Interest Rates. Interest is compounded and credited monthly, based on the daily collected balance. Interest rates are variable and determined daily at Chase’s discretion. Rates are effective for 10/08/2019 only, and are subject to change without notice. Web site rates are.
Privacy | Terms and Conditions
| 620
| 2,949
|
{"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-2019-43
|
latest
|
en
| 0.945103
|
https://www.ludu.co/course/c-programming/creating-your-first-project
| 1,590,405,180,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347388427.15/warc/CC-MAIN-20200525095005-20200525125005-00152.warc.gz
| 775,262,535
| 36,006
|
Lesson 3
2
Now that we have learnt about variables and printing out text to the console, we are ready to create our first project in Dev-C++!
Follow these steps and then we will write the code together!
Once you are done saving the project you should see your code in the editor!
Now let's edit this code a little bit and do something.
Notice that we have specified int argc, char *argv[] as arguments of the main function. Don't worry about that for now, it will work anyways and we will talk about what this is later in this course!
Our code now has three int variables called sum, num1 and num2, all of which are initialised with the value $0$.
On the lines below we are giving num1 the value of 12 and num2 the value of 13. sum has the value of num1 + num2 (and as we know, $12 + 13 = 25$). We will discuss the arithmetic symbols later in this course!
Then we simply use a printf function call to output our result. We use %d three times and then enter the arguments in the correct order.
You can also see that I have written a comment in the code. A comment is something you write to help yourself and others remember and explain what you have done to make it easier understanding the code. This text will not be seen by the compiler and will not affect your code in any way. You can write comments using double slash (//) or by using slash + star (/*). For example:
When your program is done, go ahead and click the square on the top of the IDE ("Compile and run"). Save your project first and then it will run!
You can see that the result of this in the console window in the picture.
At the bottom of our IDE we have a compiler log. This tells us if we get any errors when trying to compile the program, or if we have any warnings. If you forget a semicolon for one instruction, this is where the error will be shown. It is a common mistake to forget semicolons or other syntax related things when you are a beginner, but it does not matter, it happens all the time!
In the next chapter, we will discuss arithmetic operators!
| 464
| 2,047
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.96875
| 3
|
CC-MAIN-2020-24
|
longest
|
en
| 0.909483
|
https://www.unitsconverters.com/en/Btu(Th)Persecondperfoot2-To-Kilocalorie(It)Perhourpermeter2/Unittounit-4392-4366
| 1,656,540,316,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-27/segments/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00068.warc.gz
| 1,120,377,631
| 38,319
|
Formula Used
1 Watt per Meter² = 8.81140418274228E-05 Btu (th) per second per foot²
1 Watt per Meter² = 0.859845227858985 Kilocalorie (IT) per Hour per Meter²
1 Btu (th) per second per foot² = 9758.32239681186 Kilocalorie (IT) per Hour per Meter²
## Btu (th) per second per foot²s to Kilocalorie (IT) per Hour per Meter²s Conversion
BTU/s*ft² stands for btu (th) per second per foot²s and kcal(IT)/h*m² stands for kilocalorie (it) per hour per meter²s. The formula used in btu (th) per second per foot²s to kilocalorie (it) per hour per meter²s conversion is 1 Btu (th) per second per foot² = 9758.32239681186 Kilocalorie (IT) per Hour per Meter². In other words, 1 btu (th) per second per foot² is 9759 times bigger than a kilocalorie (it) per hour per meter². To convert all types of measurement units, you can used this tool which is able to provide you conversions on a scale.
## Convert Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter²
How to convert btu (th) per second per foot² to kilocalorie (it) per hour per meter²? In the heat flux density measurement, first choose btu (th) per second per foot² from the left dropdown and kilocalorie (it) per hour per meter² from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from kilocalorie (it) per hour per meter² to btu (th) per second per foot²? You can check our kilocalorie (it) per hour per meter² to btu (th) per second per foot² converter.
How to convert Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter²?
The formula to convert Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter² is 1 Btu (th) per second per foot² = 9758.32239681186 Kilocalorie (IT) per Hour per Meter². Btu (th) per second per foot² is 9758.3224 times Bigger than Kilocalorie (IT) per Hour per Meter². Enter the value of Btu (th) per second per foot² and hit Convert to get value in Kilocalorie (IT) per Hour per Meter². Check our Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter² converter. Need a reverse calculation from Kilocalorie (IT) per Hour per Meter² to Btu (th) per second per foot²? You can check our Kilocalorie (IT) per Hour per Meter² to Btu (th) per second per foot² Converter.
How many Watt per Meter² is 1 Btu (th) per second per foot²?
1 Btu (th) per second per foot² is equal to 9758.3224 Watt per Meter². 1 Btu (th) per second per foot² is 9758.3224 times Bigger than 1 Watt per Meter².
How many Kilowatt per Meter² is 1 Btu (th) per second per foot²?
1 Btu (th) per second per foot² is equal to 9758.3224 Kilowatt per Meter². 1 Btu (th) per second per foot² is 9758.3224 times Bigger than 1 Kilowatt per Meter².
How many Watt per Centimeter² is 1 Btu (th) per second per foot²?
1 Btu (th) per second per foot² is equal to 9758.3224 Watt per Centimeter². 1 Btu (th) per second per foot² is 9758.3224 times Bigger than 1 Watt per Centimeter².
How many Watt per Inch² is 1 Btu (th) per second per foot²?
1 Btu (th) per second per foot² is equal to 9758.3224 Watt per Inch². 1 Btu (th) per second per foot² is 9758.3224 times Bigger than 1 Watt per Inch².
## Btu (th) per second per foot²s to Kilocalorie (IT) per Hour per Meter²s Converter
Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Measurement like heat flux density finds its use in a number of places right from education to industrial usage. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. unitsconverters.com helps in the conversion of different units of measurement like BTU/s*ft² to kcal(IT)/h*m² through multiplicative conversion factors. When you are converting heat flux density, you need a Btu (th) per second per foot²s to Kilocalorie (IT) per Hour per Meter²s converter that is elaborate and still easy to use. Converting Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter² is easy, for you only have to select the units first and the value you want to convert. If you encounter any issues to convert, this tool is the answer that gives you the exact conversion of units. You can also get the formula used in Btu (th) per second per foot² to Kilocalorie (IT) per Hour per Meter² conversion along with a table representing the entire conversion.
Let Others Know
| 1,266
| 4,410
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.96875
| 3
|
CC-MAIN-2022-27
|
latest
|
en
| 0.433287
|
https://www.daniweb.com/programming/software-development/threads/314098/classes-without-constructors
| 1,540,251,997,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-43/segments/1539583515555.58/warc/CC-MAIN-20181022222133-20181023003633-00200.warc.gz
| 934,794,688
| 13,564
|
## jtylerboy222
Creating a program with a circle class that has 3 private variables and 3 public functions and then have accessor & mutator functions.
I know this isn't right, but I've gone through the book and my notes and I feel like I've mixed up a few ways of doing it and combined it together...just need a little guidance from where I'm at now.
This is what I have so far.
``````#include <iostream>
using namespace std;
const float PI = 3.14;
class Circle
{
public:
double CalculateArea();
double CalculateCircumference();
void DisplayOutPut();
private:
double circumference;
double area;
};
int main()
{
Circle myCircle;
myCircle.CalculateArea;
myCircle.CalculateCircumference;
myCircle.DisplayOutPut;
}
{
}
double Circle::CalculateArea()
{
}
double Circle::CalculateCircumference()
{
}
void Circle::DisplayOutPut();
{
cout << "Circumference: " << circumference << endl;
cout << "Area: " << area << endl;
}``````
## firstPerson 761
Your function delcared with a return type of double should return a double.
Here is what you should do :
``````double Circle::getArea(){ return _area; }
double Circle::getCircumference(){ return _circumference; }``````
``````Circle::Circle(float radius){
}``````
## jtylerboy222
I don't understand...
does this go in my class?
``````double Circle::getArea(){ return _area; }
double Circle::getCircumference(){ return _circumference; }``````
and I am not using constructors...
``````Circle::Circle(float radius){
}``````
## firstPerson 761
The point is to use the constructors. Its there exactly for this job, to initialize
things. Not using it is just a bad and redundant idea.
## griswolf 304
@firstPerson: Disagree that you need to greedy calculate the various things about the circle: If the program never uses that information, it was a waste of space and CPU. Minimize... Of course, once the program uses it, it might be cached to avoid re-calculate (or not: A simple multiply is very inexpensive)... of course you are correct if the class really does have those three data members: I'm suggesting that it should not.
When you design a Circle, you think: "What does a Circle need to know about itself?" and the minimum answer is very often the right one: It needs a radius (and probably a center point).
@jtylerboy222: You are using constructors: The default that the language gives you (which approximately zero-initializes class members). And yes, you need to both declare class member functions and provide the implementations of them (define them). Definitions can be inline in the header file, or out of line in a file that will be compiled to object file and later linked, when used.
## firstPerson 761
@griswolf:
You really shouldn't have to worry about pre-optimizations. This is will not affect
the program. And for the record, if Area() is called a lot, then the function calculateArea() will be more expensive than if it were already pre calculated.
## jtylerboy222
It may be better to use constructors, but the assignment says NOT to use them.
## kes166 37
You don't need one, it auto initializes everything.
``````double getRadius();
double CalculateArea();
double CalculateCircumference();``````
You need a return statement in each one of those. Also, you need to assign what is returned to a variable. I think if it errors or gives a warning is dependant on what compiler you use. In your main, you don't assign the returned value to anything. change CaluclateArea and CalculateCircumference to voids.
I also think you need
``myCircle = new Circle;``
Do you get any errors when you compile or run?
Edit:
## jtylerboy222
Got it.
``````#include <iostream>
using namespace std;
const double PI = 3.14;
class Circle
{
public:
double CalculateArea();
double CalculateCircumference();
void DisplayOutPut();
private:
double circumference;
double area;
};
int main()
{
Circle myCircle;
myCircle.CalculateArea();
myCircle.CalculateCircumference();
myCircle.DisplayOutPut();
}
{
}
{
}
double Circle::CalculateArea()
{
| 964
| 4,008
|
{"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-2018-43
|
latest
|
en
| 0.846226
|
https://studylib.net/doc/13178118/biostatistics-in-biomedical-and-clinical-research
| 1,618,286,430,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038072082.26/warc/CC-MAIN-20210413031741-20210413061741-00357.warc.gz
| 643,476,823
| 14,047
|
# Biostatistics in Biomedical and Clinical Research
### Biostatistics in Biomedical and Clinical Research
Sandra Taylor, Ph.D.
Clinical and Translational Science Center
University of California, Davis
30 April 2013
### Do I really need a statistician?
“My study is really simple.”
“I don’t have funding to support a statistician.”
“I don’t know any statisticians.”
“A statistician will make my study more complicated or turn it into a statistics research project.”
### Goals and objectives
Understand the role of statisticians in biomedical research and clinical trials
What we can do for you
When we should be involved
Why it’s important
Provide pointers for working with statisticians
Understand what resources are available and how to access those resources
Where are statisticians involved in research projects/clinical trials?
Where are statisticians involved in research projects/clinical trials?
Why and when to work with a statistician?
Planning the study
Study design, randomization, sample size
Proposal preparation
Conducting the study
Interim analyses, DSMB
Evaluating the results
Conducting statistical analyses
Reporting the results
Interpreting the results
Manuscript preparation
### The Research Process
“Gee, I wonder if…”
### Planning Stage Involvement
Statistics can’t fix a poorly designed study!
Planning Stage Activities
Not just sample size calculations
Develop specific aims
Identify endpoints and formulate testable hypotheses
Identify confounding factors, biases
Develop study design, randomization scheme, matching protocol
Conduct sample size calculations and prepare statistical analysis plan
### Formulating specific aims
Identify parameters of interest
Specify testable hypotheses
Determines statistical methods
Specific aims determine
Study design
Sample size calculations
Identify fatal flaws
Specific Aim 1: Determine if new treatment is better than standard care.
What constitutes better?
What measureable parameter reflects
better?
Survival, number of events, mean value?
What testable hypothesis addresses the specific aim?
H
0
: Mean cholesterol under new treatment does not differ from standard care
H a
: Mean cholesterol under new treatment differs from standard care
Study type and design considerations
Prospective Study
Randomization
Stratification
Matching
Interim analyses, adaptive or sequential designs
Retrospective Study
Confounding variables
Site effects and biases in data often overlooked
### How many subjects do I need?
Too few – insufficient power to detect differences
Too many – unnecessary costs
Statisticians need input from researchers to determine sample size requirements.
Sample size determination comes at the end of a series of steps.
Specific Aim
Testable
Hypothesis
Study
Design
Statistical
Methods
Sample Size
Calculations
How is sample size determined?
Depends on:
Specific aim – primary hypothesis of the study
Study design
These two influence the statistical test.
Effect size to be detected
Variability of the response variable
Researchers need to provide this information
Example: New medication study
Test: H o
: µ new
= µ old
vs. H a
: µ new
≠ µ
Design: Randomized into each arm old
Statistical method: t-test
σ
2
= variance; Δ = effect size to detect
Researchers need to provide this information .
Published results
Pilot data
Clinically meaningful change
Sample size calculations may not be straight-forward
More complex designs require more complex calculations
Examples:
Longitudinal studies
Cross-over studies
Correlation of outcomes
Sometimes simulations are required
Sample size calculations may not be straight-forward
More complex designs require more complex calculations
Examples:
Longitudinal studies
Cross-over studies
Correlation of outcomes
Sometimes simulations are required
# NUMBER.
### Proposal Content
Proposal sections involving statistics
Sample size justification
Statistical analysis plan
Statistical methods for each aim
For clinical trials,
Interim analyses/Early stopping rules
Engage a statistician to write or at least review these sections.
Common statistical problems in proposals
Sample size justification absent or insufficiently justified
Lack of statistical analysis plan for all aims, including secondary aims
Inappropriate statistical analysis methods
Common statistical problems in proposals
Sample size justification absent or insufficiently justified
Lack of statistical analysis plan for all aims, including secondary aims
Inappropriate statistical analysis methods
These issues can doom a proposal.
Data Collection and Compilation
Data Collection and Compilation
Valid results require
Collection of accurate data
Clear and accurate data compilation
Create workable and documented data sets
QA/QC procedures
Validation during data entry
Periodically audit the data
Conduct internal validation of final data
RedCAP is user-friendly alternative.
Leverage informatics and biostatistics expertise
Medical informatics group can
Create forms for data collection
Extract information from EMR
Use inter-disciplinary team to determine what information to collect and how
Investigator, practitioners, biostatistician, informatics specialist
Ensures information is collected and compiled in a manner that facilitates analysis
### Data Do’s and Don’ts
Use RedCAP where possible
Assign unique ID to each subject and use consistently
Remove all PHI prior submitting to statistician
Unambiguously and consistently specify missing values
Avoid using “0” or blanks for missing values
Avoid free text fields
### Go forth and collect data!
Statistician activities during the study
Sometimes limited involvement by statistician
Involvement can include
Conducting interim analyses
Serving on DSMB
Some study designs entail periodic reassessments and statistician will necessarily be involved during the study
### Analyzing the data
Conduct statistical analyses
Data validation
Run statistical tests
Interpret the results
Prepare tables and figures to illustrate findings
Working with a Statistician to
Range of support provided
One-time
Select methods
Conduct all analyses
If statistician analyzes the data…
Remove PHI
Provide “clean”, documented data set
Allow sufficient time for analysis
Rule of Thumb is 4 to 6 weeks
Provide references from similar studies if available
Iterative and interactive process
Report/Publication Preparation
Craft statistical analysis section
Contribute to results section
Generate tables and figures
Biostatistics Resources at UC Davis
Clinical and Translational Science
Center
Biostatistics Workshop: 12-1 on Tuesdays [email protected]
Biostatistics Core
Assist with study design, grant writing, data analysis and interpretation
Application for Resource Use (AFRU) http://www.ucdmc.ucdavis.edu/ctsc/
Division of Biostatistics
### Other CTSC Resources
Biomedical Informatics
Clinical Research Center
Clinical Trials Resource Group
Community Engagement
Clinical Research Ethics
Translational Technologies
Pilot Studies Funding www.ucdmc.ucdavis.edu/ctsc/
| 1,410
| 7,190
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2021-17
|
latest
|
en
| 0.847802
|
https://aprove.informatik.rwth-aachen.de/eval/JAR06/JAR_TERM/TRS/SK90/4.59.trs.Thm12:POLO_FILTER:NO.html.lzma
| 1,719,176,445,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198864850.31/warc/CC-MAIN-20240623194302-20240623224302-00463.warc.gz
| 89,699,708
| 2,488
|
Term Rewriting System R:
[x, y, z]
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Termination of R to be shown.
` R`
` ↳Dependency Pair Analysis`
R contains the following Dependency Pairs:
QSORT(.(x, y)) -> QSORT(lowers(x, y))
QSORT(.(x, y)) -> LOWERS(x, y)
QSORT(.(x, y)) -> QSORT(greaters(x, y))
QSORT(.(x, y)) -> GREATERS(x, y)
LOWERS(x, .(y, z)) -> LOWERS(x, z)
GREATERS(x, .(y, z)) -> GREATERS(x, z)
Furthermore, R contains three SCCs.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Argument Filtering and Ordering`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳AFS`
Dependency Pair:
LOWERS(x, .(y, z)) -> LOWERS(x, z)
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
The following dependency pair can be strictly oriented:
LOWERS(x, .(y, z)) -> LOWERS(x, z)
The following rules can be oriented:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(qsort(x1)) = x1 POL(LOWERS(x1, x2)) = 1 + x1 + x2 POL(greaters) = 0 POL(++(x1, x2)) = x1 + x2 POL(nil) = 0 POL(.(x1, x2)) = 1 + x1 + x2 POL(<=) = 0
resulting in one new DP problem.
Used Argument Filtering System:
LOWERS(x1, x2) -> LOWERS(x1, x2)
.(x1, x2) -> .(x1, x2)
qsort(x1) -> qsort(x1)
++(x1, x2) -> ++(x1, x2)
lowers(x1, x2) -> x2
greaters(x1, x2) -> greaters
if(x1, x2, x3) -> x1
<=(x1, x2) -> <=
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 4`
` ↳Dependency Graph`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳AFS`
Dependency Pair:
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Using the Dependency Graph resulted in no new DP problems.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳Argument Filtering and Ordering`
` →DP Problem 3`
` ↳AFS`
Dependency Pair:
GREATERS(x, .(y, z)) -> GREATERS(x, z)
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
The following dependency pair can be strictly oriented:
GREATERS(x, .(y, z)) -> GREATERS(x, z)
The following rules can be oriented:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(qsort(x1)) = x1 POL(greaters) = 0 POL(++(x1, x2)) = x1 + x2 POL(GREATERS(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(.(x1, x2)) = 1 + x1 + x2 POL(<=) = 0
resulting in one new DP problem.
Used Argument Filtering System:
GREATERS(x1, x2) -> GREATERS(x1, x2)
.(x1, x2) -> .(x1, x2)
qsort(x1) -> qsort(x1)
++(x1, x2) -> ++(x1, x2)
lowers(x1, x2) -> x2
greaters(x1, x2) -> greaters
if(x1, x2, x3) -> x1
<=(x1, x2) -> <=
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 5`
` ↳Dependency Graph`
` →DP Problem 3`
` ↳AFS`
Dependency Pair:
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Using the Dependency Graph resulted in no new DP problems.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳Argument Filtering and Ordering`
Dependency Pairs:
QSORT(.(x, y)) -> QSORT(greaters(x, y))
QSORT(.(x, y)) -> QSORT(lowers(x, y))
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
The following dependency pairs can be strictly oriented:
QSORT(.(x, y)) -> QSORT(greaters(x, y))
QSORT(.(x, y)) -> QSORT(lowers(x, y))
The following rules can be oriented:
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(qsort(x1)) = x1 POL(greaters(x1, x2)) = x1 + x2 POL(nil) = 0 POL(.(x1, x2)) = 1 + x1 + x2 POL(lowers(x1, x2)) = x1 + x2 POL(QSORT(x1)) = 1 + x1 POL(<=(x1, x2)) = x1 + x2
resulting in one new DP problem.
Used Argument Filtering System:
QSORT(x1) -> QSORT(x1)
.(x1, x2) -> .(x1, x2)
greaters(x1, x2) -> greaters(x1, x2)
lowers(x1, x2) -> lowers(x1, x2)
if(x1, x2, x3) -> x1
<=(x1, x2) -> <=(x1, x2)
qsort(x1) -> qsort(x1)
++(x1, x2) -> x1
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳AFS`
` →DP Problem 6`
` ↳Dependency Graph`
Dependency Pair:
Rules:
qsort(nil) -> nil
qsort(.(x, y)) -> ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y))))
lowers(x, nil) -> nil
lowers(x, .(y, z)) -> if(<=(y, x), .(y, lowers(x, z)), lowers(x, z))
greaters(x, nil) -> nil
greaters(x, .(y, z)) -> if(<=(y, x), greaters(x, z), .(y, greaters(x, z)))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes
| 2,716
| 6,779
|
{"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
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.552072
|
https://www.convertunits.com/from/pony/to/quart
| 1,653,172,347,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00196.warc.gz
| 809,790,154
| 17,171
|
››Convert pony to quart [US, liquid]
pony quart
Did you mean to convert pony to quart [US, liquid] quart [US, dry] quart [ancient hebrew] quart [Germany] quart [UK]
How many pony in 1 quart? The answer is 32.
We assume you are converting between pony and quart [US, liquid].
You can view more details on each measurement unit:
pony or quart
The SI derived unit for volume is the cubic meter.
1 cubic meter is equal to 33814.022558919 pony, or 1056.6882049662 quart.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between pony and quarts.
Type in your own numbers in the form to convert the units!
››Quick conversion chart of pony to quart
1 pony to quart = 0.03125 quart
10 pony to quart = 0.3125 quart
20 pony to quart = 0.625 quart
30 pony to quart = 0.9375 quart
40 pony to quart = 1.25 quart
50 pony to quart = 1.5625 quart
100 pony to quart = 3.125 quart
200 pony to quart = 6.25 quart
››Want other units?
You can do the reverse unit conversion from quart to pony, or enter any two units below:
Enter two units to convert
From: To:
››Definition: Quart
The quart is a US customary unit of volume equal to a quarter of a gallon.
››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!
| 443
| 1,691
|
{"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-2022-21
|
latest
|
en
| 0.851839
|
https://www.teacherspayteachers.com/Product/4th-Grade-Multi-Step-Word-Problem-of-the-Day-Story-Problems-BTS-Freebie-4128685?utm_source=TFOTC%20Math%20Problem%20Solving&utm_campaign=4th%20BTS%20Word%20Problems
| 1,660,808,060,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882573172.64/warc/CC-MAIN-20220818063910-20220818093910-00067.warc.gz
| 856,518,492
| 41,513
|
EASEL BY TPT
# 4th Grade Multi-Step Word Problem of the Day Story Problems- BTS Freebie
Tessa Maguire
14.3k Followers
3rd - 4th
Subjects
Standards
Resource Type
Formats Included
• PDF
Pages
10 pages
Tessa Maguire
14.3k Followers
### Description
Students are not truly able to master the math standards until they're able to apply them in real world contexts. Build your students' success with word problems and the fourth grade math standards with a Problem of the Day.
These 4th grade multi-step story problems contain rigorous, real-world applications of the math standards and are guided and independent practice activities with varying levels of difficulty. With daily, on-going practice with the standards spiraled throughout the year, students build their understanding of they types of word problems on state assessments and build their strategies, comfort, and mastery of the standards.
These free 10 pages are the perfect jumpstart to your Problem of the Day with review of the 3rd grade standards.
The other 4th Grade Word Problems of the Day:
Sept | Oct | Nov | Dec | Jan | Feb
CLICK HERE to follow me and be notified of future products as soon as they are posted.
_______________________________________________________________
You may not redistribute, edit, sell, or otherwise post this product on the internet. You may, however, post a link for others to purchase themselves.
Total Pages
10 pages
Not Included
Teaching Duration
N/A
Report this Resource to TpT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TpT’s content guidelines.
### Standards
to see state-specific standards (only available in the US).
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
| 1,104
| 5,947
|
{"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-2022-33
|
latest
|
en
| 0.914727
|
http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0001b&L=sas-l&D=0&F=P&P=5983
| 1,386,314,403,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-48/segments/1386163049967/warc/CC-MAIN-20131204131729-00022-ip-10-33-133-15.ec2.internal.warc.gz
| 423,414,269
| 4,020
|
Date: Mon, 10 Jan 2000 09:16:38 -0500 Y.Huang@ORGANONINC.COM "SAS(r) Discussion" Ya Huang Re: Weird duplicates To: johnmegargee@NETSCAPE.NET text/plain; charset="iso-8859-1"
John,
It looks like that the first thing to solve your problem is to find a way to calculate the frequency key, the following code provides a very simple algorithm, thought I don't know if it is efficient enough, but at least it is in one run. Once you get the freq key, you can find many way to "dedup" the dataset, the simplest one in syntax might be proc sort nondupkey;
-------
data xx; input a; cards; 1090823644557 1705950484263 4001475563289 ;
data xx; set xx; length b c \$ 13; b=put(a,13.); c=put(13-length(compress(b,'0')),1.)|| put(13-length(compress(b,'1')),1.)|| put(13-length(compress(b,'2')),1.)|| put(13-length(compress(b,'3')),1.)|| put(13-length(compress(b,'4')),1.)|| put(13-length(compress(b,'5')),1.)|| put(13-length(compress(b,'6')),1.)|| put(13-length(compress(b,'7')),1.)|| put(13-length(compress(b,'8')),1.)|| put(13-length(compress(b,'9')),1.);
proc print; run;
------------- The SAS System 08:44 Monday, January 10, 2000 1
OBS A B C
1 1.0908E12 1090823644557 2111221111 2 1.706E12 1705950484263 2111221111 3 4.0015E12 4001475563289 2111221111
HTH
Ya Huang Organon Inc.
> -----Original Message----- > From: John Megargee [mailto:johnmegargee@NETSCAPE.NET] > Sent: Sunday, January 09, 2000 8:14 PM > To: SAS-L@LISTSERV.UGA.EDU > Subject: Weird duplicates > > > Hi: > > I'm asking for an advise regarding an unusual problem. MVS > Sas dataset 'test' > contains 240 million obs. Each obs has a single numeric > variable 'key' between > 0 and 9999999999999 (13 digit integer key). I'm trying to > identify the keys > whose digits have the same frequency. For example I may have > some observations > anywhere in the file like > > 1090823644557 > ..... > 1705950484263 > ..... > 4001475563289 > ..... > Note that these keys are different but their digits have the same > frequencies: > > digit: 0 1 2 3 4 5 6 7 8 9 > freq: 2 1 1 1 2 2 1 1 1 1 > > I only need to output the first key, i.e. 1090823644557. In > other words, if > the frequency of digits is the same for some group of keys > they are considered > 'duplicate' and I want to 'dedup' the file in this sense, > i.e. output only the > first key with each particular frequency of digits. I > principally know how to > do it in several passes through the file by reshaping, > sorting, reshaping, > etc. but with this many obs the run-times I get are > prohibitive. Any ideas of > doing this most efficiently are greatly appreciated. > > Thanks in advance, John > > > > > > ____________________________________________________________________ > Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.
Back to: Top of message | Previous page | Main SAS-L page
| 862
| 2,856
|
{"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-2013-48
|
latest
|
en
| 0.686397
|
https://proofwiki.org/wiki/Power_Series_Expansion_for_Logarithm_of_1_%2B_x
| 1,679,510,378,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00396.warc.gz
| 545,806,870
| 12,447
|
# Power Series Expansion for Logarithm of 1 + x
## Theorem
The Newton-Mercator series defines the natural logarithm function as a power series expansion:
$\ds \map \ln {1 + x}$ $=$ $\ds \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} \frac {x^n} n$ $\ds$ $=$ $\ds x - \frac {x^2} 2 + \frac {x^3} 3 - \frac {x^4} 4 + \cdots$
valid for all $x \in \R$ such that $-1 < x \le 1$.
### Corollary
$\ds \map \ln {1 - x}$ $=$ $\ds -\sum_{n \mathop = 1}^\infty \frac {x^n} n$ $\ds$ $=$ $\ds -x - \frac {x^2} 2 - \frac {x^3} 3 - \frac {x^4} 4 - \cdots$
valid for $-1 < x < 1$.
## Proof
From Sum of Infinite Geometric Sequence, putting $-x$ for $x$:
$(1): \quad \ds \sum_{n \mathop = 0}^\infty \paren {-x}^n = \frac 1 {1 + x}$
for $-1 < x < 1$.
From Power Series Converges Uniformly within Radius of Convergence, $(1)$ is uniformly convergent on every closed interval within the interval $\openint {-1} 1$.
From Power Series is Termwise Integrable within Radius of Convergence, $(1)$ can be integrated term by term:
$\ds \int_0^x \frac 1 {1 + t} \rd t$ $=$ $\ds \sum_{n \mathop = 0}^\infty \int_0^x \paren {-t}^n \rd t$ $\ds \leadsto \ \$ $\ds \map \ln {1 + x}$ $=$ $\ds \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{n + 1} } {n + 1}$ Primitive of Reciprocal and Integral of Power $\ds \leadsto \ \$ $\ds \map \ln {1 + x}$ $=$ $\ds \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} \frac {x^n} n$ letting $n \to n - 1$
$\blacksquare$
| 578
| 1,442
|
{"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": 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-2023-14
|
latest
|
en
| 0.410312
|
https://byjus.com/maths/498-in-words/
| 1,701,508,172,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100381.14/warc/CC-MAIN-20231202073445-20231202103445-00017.warc.gz
| 182,744,806
| 109,918
|
# 498 in Words
498 in words is written as Four hundred ninety-eight. In both the International System of Numerals and the Indian System of Numerals, 498 is written as Four hundred ninety-eight. The number 498 is a Cardinal Number as it represents some quantity. For example, “the area of this land is 498 square feet”.
498 in Words Four hundred ninety-eight Four hundred ninety-eight in Number 498
## 498 in English Words
We write 498 in Words using the letters of the English alphabet. Therefore, we read 498 in English as “Four hundred ninety-eight.”
## How to Write 498 in Words?
To write 498 in words, we shall use the place value chart. In the place value chart, write 4 in the hundreds, 9 in the tens, and 8 in the ones, respectively. Now let us make a place value chart to write the number 498 in words.
Hundreds Tens Ones 4 9 8
Thus, we can write the expanded form as
4 × Hundred + 9 × Ten + 8 × One
= 4 × 100 + 9 × 10 + 8 × 1
= 400 + 90 + 8
= 498
= Four hundred ninety-eight.
498 is a natural number, the successor of 497 and the predecessor of 499.
498 in words – Four hundred ninety-eight
• Is 498 an odd number? – No
• Is 498 an even number? – Yes
• Is 498 a perfect square number? – No
• Is 498 a perfect cube number? – No
• Is 498 a prime number? – No
• Is 498 a composite number? – Yes
## Frequently Asked Questions on 498 in Words
Q1
### How to write 498 in words?
498 in words is written as Four hundred ninety-eight.
Q2
### How to write 498 in the International and Indian System of Numerals?
In both, the system of numerals, 498 in words, is written as Four hundred ninety-eight.
Q3
### What is the preceding number of 498?
The number that precedes 498 is 497.
| 462
| 1,705
|
{"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-2023-50
|
latest
|
en
| 0.918972
|
https://justaaa.com/math/825987-what-is-the-difference-between-a-polynomial-or
| 1,708,790,507,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474541.96/warc/CC-MAIN-20240224144416-20240224174416-00665.warc.gz
| 345,609,037
| 9,596
|
Question
# What is the difference between a polynomial or rational equation and polynomial or rationl inequality?
What is the difference between a polynomial or rational equation and polynomial or rationl inequality?
An polynomial equation has an equality sign and, in the case of only 1 variable, it translates geometrically into a line.
f(x) =a0 + a1 x + a2 x^2 + ... an x^n
we could write y = a0 + a1 x + a2 x^2 + ... an x^n
An polynomial inequality has a greater than or less than sign and, in the case of only 1 variable, it translates geometrically into a surface.
y > a0 + a1 x + a2 x^2 + ... an x^n
y <= a0 + a1 x + a2 x^2 + ... an x^n
y >= a0 + a1 x + a2 x^2 + ... an x^n
In this case, we usually don't ewrite f(x) < , > etc, because it would have problems with the definition of function.
#### Earn Coins
Coins can be redeemed for fabulous gifts.
| 240
| 864
|
{"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}
| 3.671875
| 4
|
CC-MAIN-2024-10
|
latest
|
en
| 0.894546
|
https://scholar.uprm.edu/handle/20.500.11801/1983?show=full
| 1,679,821,552,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00772.warc.gz
| 579,303,608
| 10,979
|
dc.contributor.advisor Urintsev, Alexander dc.contributor.author Ruiz-Valle, Gloria B. dc.date.accessioned 2019-04-15T15:50:42Z dc.date.available 2019-04-15T15:50:42Z dc.date.issued 2007 dc.identifier.uri https://hdl.handle.net/20.500.11801/1983 dc.description.abstract The scope of this thesis investigation is to obtain an approximate numerical solution to the nonlinear one-dimensional Kuramoto-Sivashinsky partial differential equation. The Gaussian wave has been successfully applied to convert this equation by means of a wavelet transform into a nonlinear integro-differential equation for the transformant. A Cauchy problem was formulated. The wavelet coefficients were expanded by means of basis functions based on the classical Laguerre and Hermite orthogonal polynomials, and then the Galerkin method was used to get a system of ordinary differential equations that was solved numerically with the Mathematica system. en_US dc.description.abstract Esta tesis describe cómo obtener una solución numérica para la ecuación diferencial parcial no lineal de Kuramoto–Sivashinsky en una dimensión. La ondita (wavelet) “Gaussian wave” ha sido aplicada con éxito para convertir esta ecuación en una ecuación no lineal integro-diferencial para el transformante a través de una transformación de ondita. Se formuló un problema de Cauchy. Los coeficientes de ondita fueron expandidos a través de funciones bases fundamentadas en los polinomios ortogonales clásicos de Hermite y de Laguerre y entonces el método de Galerkin se usó para obtener un sistema de ecuaciones diferenciales ordinarias que fue resuelto numéricamente utilizando el sistema Mathematica. en_US dc.language.iso English en_US dc.subject Kuramoto-Sivashinsky equation en_US dc.title A wavelet-based solution of the Kuramoto-Sivashinsky equation en_US dc.type Thesis en_US dc.rights.license All rights reserved en_US dc.rights.holder (c) 2007 Gloria B. Ruiz-Valle en_US dc.contributor.committee Rózga, Krzysztof dc.contributor.committee Walker, Uroyoán dc.contributor.representative Cardona-Martínez, Nelson thesis.degree.level M.S. en_US thesis.degree.discipline Applied Mathematics en_US dc.contributor.college College of Arts and Sciences - Sciences en_US dc.contributor.department Department of Mathematics en_US dc.description.graduationYear 2007 en_US
This item appears in the following Collection(s)
• Theses & Dissertations
Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPR-Mayagüez.
| 601
| 2,565
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2023-14
|
latest
|
en
| 0.338611
|
https://mathoverflow.net/questions/152403/checking-complete-positivity-of-maps-between-c-algebras
| 1,702,148,083,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100942.92/warc/CC-MAIN-20231209170619-20231209200619-00454.warc.gz
| 445,997,120
| 25,900
|
# Checking complete positivity of maps between C* algebras
Let $\phi$ : $A \rightarrow A$ be a positive map, where $A$ is a (unital) C* algebra. Suppose we are given that $\phi$ is n positive whenever n= $2^k$ for some $k \in \mathbb{N}$. Can we conclude that $\phi$ is completely postive?
Yes, an $n$ positive map is also $n-1$ positive. Hence you map is $n$-positive for all $n$, i.e. completely positive.
For a proof, you include $M_{n-1}(A)$ as upper left block into $M_n(A)$.
| 151
| 482
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.703125
| 3
|
CC-MAIN-2023-50
|
latest
|
en
| 0.903099
|
https://www.expertsminds.com/content/how-to-complete-the-gpa-requirements-while-studying-in-the-usa-37663.html
| 1,716,952,229,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971059167.30/warc/CC-MAIN-20240529010927-20240529040927-00802.warc.gz
| 661,042,372
| 10,468
|
### What is the mean by Grade Point Average GPA? How to complete the GPA requirements while studying in the USA?
Home Study in USA
Previous << || >> Next
### What is the mean by Grade Point Average?
As you know grades are given considering the overall academic performance of the students similarly grade point average considering the academic performance of the students for the semester and the whole year and evaluating it is given in the form of a score. Grade points are given on the basis of average marks and are calculated from 0-4. A score of 0 is given for the student whose performance is the lowest and 4 for the student whose performance is the best. This off grade point average is calculated keeping in mind the semester or the whole year.
### How to calculate Grade Point Average - GPA
If you want to take admission in any of USA universities, then it is important that you know about the grade point average system there. Let us know how to calculate grade point average. Grade Point Average is mainly calculated in 2 ways out of which one is Weighted Average and one is Simple Average. In simple average, add up the scores of all the courses in a semester and divide that total by the number of courses. Let us understand this in the form of a table.
SUBJECTS GRADE GARDE SCORE Algebra A 4 French History B 3 Literature c 2 Chemistry B 3
To calculate the Simple Grade Point Average, you need to get the grade scores of all the subjects like (4+3+2+3= 12) will have to be added and then divided by the total number of subjects and thus the simple grade point average will be 3.
To calculate weighted grade point average you need to understand another US grading system Credits and Credit Hours. There are a pre-determined number of hours for each course. Let us understand about it in detail.
The weighted grade point average is calculated by multiplying your credit horse by the grade point and then the total number of credit is divided.
SUBJECTS GRADE CREDITS GRAGE POINTS Algebra B 4 3 French History A 3 4 Literature A 3 4 Chemistry B 4 3
Multiples the credits and grade points for all subjects to calculate the weighted grade point average (4*3 + 3*4 + 3*4 + 4*3 = 48) Whatever score is there, divide it by the total number of credit.
### What is the mean of good Grade Point Average (GPA)?
By now you must have come to know that how to calculate GAP, so let us now know what a good GPA should be for students.
A score of 3.0 - 3.5 is considered a good GPA in many universities in the United States of America, on which you can get admission on the back. But many universities do not consider GPA less than 3.5, due to which students are not considered eligible for scholarship.
| 607
| 2,721
|
{"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}
| 3.34375
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.941013
|
http://autodocbox.com/Electric_Vehicle/93467593-Letter-to-parents-science-news-dear-parents.html
| 1,591,097,382,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347424174.72/warc/CC-MAIN-20200602100039-20200602130039-00470.warc.gz
| 13,123,450
| 28,038
|
# LETTER TO PARENTS SCIENCE NEWS. Dear Parents,
Size: px
Start display at page:
## Transcription
2 PROJECT IDEAS Can you design a new investigation using the balance and magnets (like you did in Investigation 1)? For example, use washers in place of spacers, more magnets, or different magnets. Can you find a set of insulators and conductors at home? How would you prove that they are conductors or insulators? Can you make a conductor/insulator tester using a lightbulb as an indicator instead of the motor? Does a D-cell last longer in a series circuit or in a parallel circuit? Can you use iron filings to show the magnetic field around a wire carrying current? Can you think of more variables to test to change the strength of an electromagnet? What happens if you wind the wire half one way and half the opposite way to make an electromagnet? Look in the FOSS Science Stories or books in the library for ideas about projects you might like to present to the class. Can you make one of the toys you read about in the Magnificent Magnetic Models? Can you make a water compass? Can you design some magnetic art using magnets and iron filings? Can you design a magnetic message board? Can you write an instruction booklet to show someone how to set up five different circuits? Can you make a quiz board that lights up when someone has chosen the right answer? Can you build a model motor? Can you hook up more than two telegraphs to send and receive messages? Can you build a cardboard telegraph? Can you build a lunchbox alarm? Another kind of alarm? Can you create a new kind of electric message sender? Can you create a new code? Investigation 5: Click It No. 23 Student Sheet
3 PROJECT PROPOSAL 1. What is the question or the project that you are proposing? 2. What materials or references will you need to complete the project? 3. What steps will you follow to complete the project? Investigation 5: Click It No. 24 Student Sheet
5 BUYING MAGNETS Name MATH EXTENSION PROBLEM OF THE WEEK INVESTIGATION 1: THE FORCE A teacher wants to set up a Magnet Exploration Center where students can find out more about magnets during their free time. She has \$50.00 to spend. She looked in the magnet section of a science catalog and found these prices. ITEM QUANTITY PRICE Large bar magnets Set of 2 \$10.95 Small bar magnets Each \$2.75 Large horseshoe magnets Each \$7.95 Small horseshoe magnets Each \$4.50 Disk magnets Set of 4 \$4.50 Lodestones Set of 10 \$ What materials would you recommend she buy for the Magnet Exploration Center? (Remember, she has only \$50.00 to spend.) 2. Write a paragraph about why you chose the items you did. Problem of the Week No. 29 Student Sheet
6 MATH EXTENSION PROBLEM OF THE WEEK INVESTIGATION 2: MAKING CONNECTIONS TESTING C-CELLS The students in Mrs. Ray s fourth-grade class had a question: Do all brands of batteries last the same length of time, or do some kinds keep on going after the others have run out of energy? The students decided to do an experiment. They agreed they should use brand new C-cells for their test. Here is a list of the C-cells they got. 3 Charger industrial-strength C-cells 3 E-Z Volt alkaline C-cells 3 Amp-Champ alkaline C-cells The students connected each cell to a motor and let it run every day while they were in class. They disconnected the motors every night just before they went home. They kept track of the number of hours each motor ran. Here are the results they recorded. KIND OF C-CELL #1 #2 #3 Charger 30 hours 25 hours 20 hours E-Z Volt 30 hours 40 hours 35 hours Amp-Champ 25 hours 40 hours 40 hours 1. Based on these data, which brand of cell would you buy? (Show your math here.) 2. Explain why you chose that brand. Problem of the Week No. 30 Student Sheet
7 MATH EXTENSION PROBLEM OF THE WEEK INVESTIGATION 3: ADVANCED CONNECTIONS PREDICTING WIRES A student wants to know how many wires she will need to set up some circuits with different numbers of lightbulbs. She knows she will need two wires to connect one lightbulb to a battery. So she thinks maybe she will need two additional wires for each additional lightbulb she adds to her circuit. But she isn t sure. Can you help her figure out a way to predict how many wires she will need? 1. What if she were building series circuits with only one battery and some lightbulbs? 2. What if she were building a series circuit with one battery, a switch, and some lightbulbs? 3. What if she were building a series circuit and adding one battery for every lightbulb she added? 4. What if she were building a parallel circuit with one battery and some light bulbs? Problem of the Week No. 31 Student Sheet
8 MATH EXTENSION PROBLEM OF THE WEEK INVESTIGATION 4: CURRENT ATTRACTIONS COMPARING ELECTROMAGNETS A fourth-grade class in Texas had just finished building electromagnets. The students wanted to know if electromagnets worked the same in Florida, so they contacted their FOSS website penpals in Florida with a plan. Each class lifted little washers with 20-wind electromagnets and 40-wind electromagnets. After counting the number of washers, they each sent their results to the other class. When the numbers were organized, this is what they saw. TEXAS GROUP 20 WINDS 40 WINDS 1 14 washers 30 washers 2 15 washers 35 washers 3 14 washers 28 washers 4 13 washers 38 washers 5 16 washers 41 washers 6 17 washers 33 washers 7 19 washers 29 washers 8 20 washers 30 washers FLORIDA GROUP 20 WINDS 40 WINDS 1 18 washers 23 washers 2 13 washers 30 washers 3 16 washers 31 washers 4 17 washers 27 washers 5 20 washers 42 washers 6 18 washers 33 washers Do you think electromagnets work the same in Texas as in Florida? Why or why not? Problem of the Week No. 32 Student Sheet
9 MATH EXTENSION PROBLEM OF THE WEEK INVESTIGATION 5: CLICK IT PRESENTATION TIME A class was preparing to give project presentations. One student objected when the teacher told the class they would have only 3 minutes to present their project to the class. I really need 8 minutes, the student told the teacher. The teacher decided to leave it up to the students, but first they would have to calculate how much time that would be. They had to decide if they were willing to listen as long as it would take for everyone to give an 8- minute presentation. 1. If there were 15 students in this class, and everyone presented a project for 8 minutes, how many minutes would they have to be a good audience? How many hours is that? 2. If the class had 30 students, how long would the presentations take? 3. How long would 8-minute presentations take in your class? 4. How many minutes do you think each presentation should be? How long will that be for your class to listen? Why do you think this is a good plan? Problem of the Week No. 33 Student Sheet
10 HOME/SCHOOL CONNECTION INVESTIGATION 1: THE FORCE MAGNETS AT HOME How are permanent magnets used around your home? Places to check for magnets: Compasses Note holders on the refrigerator Cabinet and refrigerator door closers Toolboxes Can you think of another way to use magnets around the house? Can you invent a magnet game? Talk over some ideas with your family and try some games out if you can. Draw a picture of your invention to share with the class, and write a paragraph explaining what it does. STEEL PIE PAN Swinging Magnet Game Home/School Connection No. 34 Student Sheet
11 HOME/SCHOOL CONNECTION INVESTIGATION 2: MAKING CONNECTIONS WHERE S THE ELECTRICITY? Where s the electricity in your home? Take a tour and count the number of: Lights. Appliances that use electricity. Wall outlets where you can plug things in. Wall switches for turning on lights. Be sure to talk with your family about safety when using electric appliances. Write your family safety rules below. Home/School Connection No. 35 Student Sheet
12 HOME/SCHOOL CONNECTION INVESTIGATION 3: ADVANCED CONNECTIONS WHAT S INSIDE AN ELECTRONIC APPLIANCE? If you have an old, broken radio, portable tape player, calculator, cassette player, remote control, walkie-talkie, or just about anything else that works on electricity, take a look inside. Look for advanced circuits to see where your knowledge of electricity can lead you. Rules of engagement: Get approval from a parent before taking a device apart. Make sure the device is unplugged and batteries are removed. Get help opening the case. Remember, safety first. NO televisions, please. They can be dangerous to explore. Things to look for and do: 1. You may be surprised to find very few wires. What kind of conductors are used in modern circuits instead of wires? Can you draw an example? 2. Can you find any familiar components like motors and lights? What function do they serve in the device? 3. Make drawings of one or two of the most common components you find. NOTE: If you don t have an old device to take apart, draw a schematic of one circuit with two lightbulbs in parallel in series with a third lightbulb. Think about it...it can be done. Home/School Connection No. 36 Student Sheet
### LETTER TO FAMILY. Science News. Cut here and glue letter onto school letterhead before making copies.
LETTER TO FAMILY Cut here and glue letter onto school letterhead before making copies. Science News Dear Family, Our class is beginning a new science unit using the. We will investigate energy, build electric
### reflect energy: the ability to do work
reflect Have you ever thought about how much we depend on electricity? Electricity is a form of energy that runs computers, appliances, and radios. Electricity lights our homes, schools, and office buildings.
### Lesson Plan: Electricity and Magnetism (~100 minutes)
Lesson Plan: Electricity and Magnetism (~100 minutes) Concepts 1. Electricity and magnetism are fundamentally related. 2. Just as electric charge produced an electric field, electric current produces a
### Engaging Inquiry-Based Activities Grades 3-6
ELECTRICITY AND CIRCUITS Engaging Inquiry-Based Activities Grades 3-6 Janette Smith 2016 Janette Smith 2016 1 What s Inside Activity 1: Light it Up!: Students investigate different ways to light a light
### Electricity. Grade: 1 st grade Category: Physical Science NGSS: ETS1.A: Defining and Delimiting Engineering Problems
Electricity Grade: 1 st grade Category: Physical Science NGSS: ETS1.A: Defining and Delimiting Engineering Problems Description: In this lesson, the students will learn that some objects need electricity
### Fourth Grade. Multiplication Review. Slide 1 / 146 Slide 2 / 146. Slide 3 / 146. Slide 4 / 146. Slide 5 / 146. Slide 6 / 146
Slide 1 / 146 Slide 2 / 146 Fourth Grade Multiplication and Division Relationship 2015-11-23 www.njctl.org Multiplication Review Slide 3 / 146 Table of Contents Properties of Multiplication Factors Prime
### Fourth Grade. Slide 1 / 146. Slide 2 / 146. Slide 3 / 146. Multiplication and Division Relationship. Table of Contents. Multiplication Review
Slide 1 / 146 Slide 2 / 146 Fourth Grade Multiplication and Division Relationship 2015-11-23 www.njctl.org Table of Contents Slide 3 / 146 Click on a topic to go to that section. Multiplication Review
### Understanding Electricity and Electrical Safety Teacher s Guide
Understanding Electricity and Electrical Safety Teacher s Guide Note to Instructor: The activities and experiments in this booklet build on each other to develop a student s understanding of electricity
### What is electricity?
Electrical Safety Part 1 What is electricity? Note to Teachers: Behind the Lesson: Why is it important to understand the basics of electricity before learning about electrical safety? The world around
Using your Digital Multimeter The multimeter is a precision instrument and must be used correctly. The rotary switch should not be turned unnecessarily. To measure Volts, Milliamps or resistance, the black
### Stay Safe Around Electricity Teacher s Guide
Stay Safe Around Electricity Teacher s Guide INTRODUCTION The Stay Safe Around Electricity activity booklet can be used as a follow-up to an electric utility presentation or as a stand-alone piece to teach
### It s a Wired World Teacher s Guide
It s a Wired World Teacher s Guide Introduction It s a Wired World uses experiments and activities to explain electricity-related science concepts to students in grades 4-8. Through a focus on circuits,
### Electricity and Magnetism
Electricity and Magnetism Electric Current and Electric Circuits What do you think? Read the statement below and decide whether you agree or disagree with it. Place an A in the Before column if you agree
### 12 Electricity and Circuits
12 Electricity and Circuits We use electricity for many purposes to make our tasks easier. For example, we use electricity to operate pumps that lift water from wells or from ground level to the roof top
### Mandatory Experiment: Electric conduction
Name: Class: Mandatory Experiment: Electric conduction In this experiment, you will investigate how different materials affect the brightness of a bulb in a simple electric circuit. 1. Take a battery holder,
### 7.9.8 Elctromagnetism
7.9.8 Elctromagnetism 71 minutes 86 marks Page 1 of 25 Q1. The diagram shows an electromagnet used in a door lock. (a) The push switch is closed and the door unlocks. Explain in detail how this happens.
### Objects with opposite charges attract each other, on the contrary, objects with the same charges repel each other.
1. ELECTRICITY We uses enery everyday, we transfer energy in lots of ways every day. When a room is dark, we switch on the light. The light bulb transfers energy to the room. Electricity is a type of energy
### Q1. Figure 1 shows a straight wire passing through a piece of card.
THE MOTOR EFFECT Q1. Figure 1 shows a straight wire passing through a piece of card. A current (I) is passing down through the wire. Figure 1 (a) Describe how you could show that a magnetic field has been
### Orientation and Conferencing Plan Stage 1
Orientation and Conferencing Plan Stage 1 Orientation Ensure that you have read about using the plan in the Program Guide. Book summary Read the following summary to the student. Everyone plays with the
### ECOKIDS BATTERY BUSTERS AUDIT
DID YOU KNOW Most families have over 2 battery-powered devices at home. That adds up to a whole lot of batteries! Find out how many batteries your family uses by doing a battery audit. TIP 1: DON T MISS
### Physics Work with your neighbor. Ask me for help if you re stuck. Don t hesistate to compare notes with nearby groups.
Physics 9 2016-04-13 Work with your neighbor. Ask me for help if you re stuck. Don t hesistate to compare notes with nearby groups. Today we ll build on what we did Monday with batteries and light bulbs.
### Based on results from TIMSS Key. bulb. bulb. switch. wir. battery. wir. switch. Lesson plan on investigative science. wire.
bulb Based on results from TIMSS 2015 Key battery Key ba bu tte switch sw h itc bulb e wir battery switch wire bat sw Lesson plan on investigative science Electricity wir Electricity Pupils performed less
### Exploration 2: How Do Rotorcraft Fly?
Exploration 2: How Do Rotorcraft Fly? Students choose a model and use it to explore rotorcraft flight. They use a fair test and conclude that a spinning rotor is required for a rotorcraft to fly. Main
### Which Battery Is Better? Advertisers are always touting more powerful and longer lasting batteries, but which
Hess 1 Amber Hess Mrs. Garmon 6 th Grade Science March 1, 1999 Which Battery Is Better? Abstract Advertisers are always touting more powerful and longer lasting batteries, but which batteries really do
### Construction Set: Smart Grid System
Construction Set: Smart Grid System Curriculum for Grades 3-5 Student Edition Center for Mathematics, Science, and Technology Illinois State University 2017 www.smartgridforschools.org Look around your
### I N V E N T O R S M A N U A L
INVENTOR S MANUAL INTRODUCTION ELECTRIC CITY KIT Welcome to the hi-tech world of Logiblocs! These instructions will tell you all you need to know to make a Door Alarm, Security Mat, Water Bleeper, Light
### Is it Magnetic? 1. Fill in each table. List things ATTRACTED by a magnet on the LEFT and things NOT ATTRACTED on the RIGHT.
Is it Magnetic? 1. Fill in each table. List things ATTRACTED by a magnet on the LEFT and things NOT ATTRACTED on the RIGHT. MAGNETIC NON-MAGNETIC # Object Made from check # Object Made from check --- ------------
### 4 Electric Circuits. TAKE A LOOK 2. Identify Below each switch, label the circuit as a closed circuit or an open circuit.
CHAPTER 17 4 Electric Circuits SECTION Introduction to Electricity BEFORE YOU READ After you read this section, you should be able to answer these questions: What are the three main parts of a circuit?
### ACTIVITY 1: Electric Circuit Interactions
CYCLE 5 Developing Ideas ACTIVITY 1: Electric Circuit Interactions Purpose Many practical devices work because of electricity. In this first activity of the Cycle you will first focus your attention on
### ELECTRIC CURRENT. Name(s)
Name(s) ELECTRIC CURRT The primary purpose of this activity is to decide upon a model for electric current. As is the case for all scientific models, your electricity model should be able to explain observed
Your web browser (Safari 7) is out of date. For more security, comfort and Activitydevelop the best experience on this site: Update your browser Ignore Circuits with Friends What is a circuit, and what
### SPS10. Students will investigate the properties of electricity and magnetism.
ELECTRICITY SPS10. Students will investigate the properties of electricity and magnetism. a. Investigate static electricity in terms of Friction Induction Conduction b. Explain the flow of electrons in
### POWER and ELECTRIC CIRCUITS
POWER and ELECTRIC CIRCUITS Name For many of us, our most familiar experience with the word POWER (units of measure: WATTS) is when we think about electricity. Most of us know that when we change a light
### Introduction to Electricity & Electrical Current
Introduction to Electricity & Electrical Current Physical Science Georgia Performance Standards: SPS10a. Investigate static electricity in terms of friction, induction, and conduction. SPS10b. Explain
### 4 Electric Circuits. TAKE A LOOK 2. Identify Below each switch, label the circuit as a closed circuit or an open circuit.
CHAPTER 1 4 Electric Circuits SECTION Introduction to Electricity BEFORE YOU READ After you read this section, you should be able to answer these questions: What are the three main parts of a circuit?
Name: Date: Student Exploration: Advanced Circuits [Note to teachers and students: This Gizmo was designed as a follow-up to the Circuits Gizmo. We recommend doing that activity before trying this one.]
### 11.1 CURRENT ELECTRICITY. Electrochemical Cells (the energy source) pg Wet Cell. Dry Cell. Positive. Terminal. Negative.
Date: SNC1D: Electricity 11.1 CURRENT ELECTRICITY Define: CIRCUIT: path that electrons follow. CURRENT ELECTRICITY: continuous flow of electrons in a circuit LOAD: device that converts electrical energy
### a) Understand the conditions for lighting a light bulb by connecting it to batteries with wires to make it illuminate.
This area deals with simple electric circuits and electromagnets. In this area, students learn about electricity for the first time and build an electromagnet and a simple circuit to compare the brightness
### Physical Science Lesson on Cars Julie Smith
Physical Science Lesson on Cars Julie Smith Julie Smith Physical Science Lesson on Cars Title: Cars and Parts Grade level: Kindergarten Subject Area: Science and Technology and Engineering Education Standard
### Electromagnets ENERGY USE AND DELIVERY LESSON PLAN 3.3. Public School System Teaching Standards Covered
ENERGY USE AND DELIVERY LESSON PLAN 3.3 Electromagnets This lesson is designed for 3rd 5th grade students in a variety of school settings (public, private, STEM schools, and home schools) in the seven
### The Starter motor. Student booklet
The Starter motor Student booklet The Starter motor - INDEX - 2006-04-07-13:20 The Starter motor The starter motor is an electrical motor and the electric motor is all about magnets and magnetism: A motor
### Level 5-8 Little Lord Fauntleroy
Level 5-8 Little Lord Fauntleroy Workbook Teacher s Guide and Answer Key A. Summary 1. Book Summary Teacher s Guide Cedric was a kind seven-year-old boy. He was born in America, but his father was from
### Cub Scout Den Meeting Outline
Cub Scout Den Meeting Outline Month: August Week: 2 Point of the Scout Law: Clean Before the Meeting Gathering Opening Activity Games Business items/take home Closing After the meeting Tiger Wolf Bear
### Physics 144 Chowdary How Things Work. Lab #5: Circuits
Physics 144 Chowdary How Things Work Spring 2006 Name: Partners Name(s): Lab #5: Circuits Introduction In today s lab, we ll learn about simple electric circuits. All electrical and electronic appliances
### Science Olympiad Shock Value ~ Basic Circuits and Schematics
Science Olympiad Shock Value ~ Basic Circuits and Schematics Use a single D battery, a single bare wire and a light bulb. Find four different ways to light the light bulb using only a battery, one wire
### Electricity. Grade Level: 4 6
Electricity Grade Level: 4 6 Teacher Guidelines pages 1 2 Instructional Pages pages 3 5 Practice Page page 6 Activity Page page 7 Homework Page page 8 Answer Key page 9 Classroom Procedure: 1. Once students
### ELECTRIC CURRENT AND ITS EFFECT
14 ELECTRIC CURRENT AND ITS EFFECT TEXTBOOK EXERCISES AND THEIR ANSWERS Q.1. Draw in your notebook the symbols to represent the following components of electrical circuits, connecting wires, switch in
### Electricity. Teacher/Parent Notes.
Electricity. Teacher/Parent Notes. Caution. The yellow fan. If this is used with 6 Volts, the fan will fly into the air with some force so it is advisable to keep faces well away from it! Batteries. Please
### Unit 6: Electricity and Magnetism
Objectives Unit 6: Electricity and Magnetism Identify the factors influencing the electric force between objects. Explain the interaction between charged and uncharged objects. Design, construct, and explain
### The Shocking Truth About Electrical Safety Teacher s Guide
The Shocking Truth About Electrical Safety Teacher s Guide FOUR SIMPLE CONCEPTS ABOUT ELECTRICAL SAFETY 1. Electricity travels in a closed loop called a circuit. 2. Electricity flows easily through conductors,
### CHAPTER 6.3: CURRENT ELECTRICITY
CHAPTER 6.3: CURRENT ELECTRICITY These components are used in electric circuits. TASK: Draw how you could make this lamp light. Electricity will only flow through a complete circuit. The battery, wires
### Lighting the Way. This bulb also used a filament, but it burned up fast. So it could not replace gas street lamps and other lamps that ran on gas.
Unit 5 Assessment Read the passage about electric light. Then answer the questions. Lighting the Way 1 Electric light didn t happen overnight, and it didn t start with Thomas Edison. We call Edison the
### Exploring the Energy Grid Grades 6-8. Name:
Exploring the Energy Grid Grades 6-8 Name: Exploration 1 Rapidly turn the handles clockwise on all three generators at the end of the table, watching the System Voltage panel: 1. Draw the needle when the
### Imagine not being able to use anything that plugs into an electrical socket.
Physics 1003 Electromagnetism (Read objectives on screen.) (boy thinking on screen) Imagine your everyday life without talking on the telephone or watching TV. or listening to a radio or playing a CD.
### Lab 6: Magnetic Fields
Names: 1.) 2.) 3.) Lab 6: Magnetic Fields Learning objectives: Observe shape of a magnetic field around a bar magnet (Iron Filing and magnet) Observe how static charged objects interact with magnetic fields
### Given the following items: wire, light bulb, & battery, think about how you can light the bulb.
Light the Bulb! What You'll Do: Given the following items: wire, light bulb, & battery, think about how you can light the bulb. >>>>>>>>>Draw all the possible combinations that you can make with the bulb,
### Magnets. Unit 6. How do magnets work? In this Unit, you will learn:
Previously From Page 220 Forces appear whenever two objects interact. From Page 225 Unbalanced forces cause the motion of a body to change. Unit 6 Magnets How do magnets work? Magnets are interesting things
### Series circuits. The ammeter
Series circuits D o you remember how the parts of the torch on pages 272 3 were connected together? The circuit contained several components, connected one after the other. Conductors, like the metal strip
### HOW TO MAKE YOUR OWN BATTERIES
HOW TO MAKE YOUR OWN BATTERIES 1 Page TABLE OF CONTENTS Introduction....3 Usage....4 Aluminum Can Batteries/Cells....8 A Long Lasting, Yet Powerful Battery....10 PVC Pipe Batteries...13 Lab Notes....17
### Can You Light the Bulb?
3-5 Physical Science Southern Nevada Regional Professional Development Program Can You Light the Bulb? INTRODUCTION Electrical energy is easily transferred through loops that we call circuits. This activity
### Fourth Grade Physical Science. Magnetism and Electricity. Written By: Hortencia Garcia Christina Mavaro Kathleen Tomscha
Fourth Grade Physical Science Magnetism and Electricity Written By: Hortencia Garcia Christina Mavaro Kathleen Tomscha Developed in Conjunction with K-12 Alliance/WestED Table of Contents 1 Conceptual
### All Lit Up: Circuitry, Engineering, and the Last Great Race on Earth
All Lit Up: Circuitry, Engineering, and the Last Great Race on Earth Developed by: Laura Wright 2016 Iditarod Teacher on the Trail Discipline / Subject: Science Topic: Energy, STEM, STEAM Grade Level:
### A device that measures the current in a circuit. It is always connected in SERIES to the device through which it is measuring current.
Goals of this second circuit lab packet: 1 to learn to use voltmeters an ammeters, the basic devices for analyzing a circuit. 2 to learn to use two devices which make circuit building far more simple:
### Speakers and Motors. Three feet of magnet wire to make a coil (you can reuse any of the coils you made in the last lesson if you wish)
Speakers and Motors We ve come a long way with this magnetism thing and hopefully you re feeling pretty good about how magnetism works and what it does. This lesson, we re going to use what we ve learned
### U-Score U-Score AAC Rank AAC Rank Vocabulary Vocabulary
go 1 927 you 2 7600 i 3 4443 more 4 2160 help 5 659 it 6 9386 want 7 586 in 8 19004 that 9 10184 like 10 1810 what 11 2560 make 12 1264 is 13 10257 on 14 6674 out 15 2350 do 16 2102 here 17 655 eat 18
FOURTH GRADE TECHNOLOGY 3 WEEKS LESSON PLANS AND ACTIVITIES APPLIED SCIENCE OVERVIEW OF FOURTH GRADE SCIENCE AND MATH WEEK 1. PRE: Exploring conceptual science. LAB: Predicting volume. POST: Measuring
### Amtek Basic Electronics 1
Page 1 Page 2 Contents Worksheet 1 - Conductors and insulators 3 Worksheet 2 - Circuits 5 Worksheet 3 - Electric current 7 Worksheet 4 - Electromagnetism 9 Worksheet 5 - Electrolysis 11 Worksheet 6 - Switches
### All Worn Out! Measure the voltage of batteries as they discharge. Predict how different size batteries will behave when being discharged.
All Worn Out! Computer 43 Have you ever wondered why some flashlights use small batteries and some use big ones? What difference does it make? Do larger batteries make the light brighter? Will the size
### LET S FIND... ENERGY WORLD: Electricity around us ELECTRICAL APPLIANCES IN THE SCHOOL. What appliance? Who found it?? Who uses it?
1 LET S FIND... ELECTRICAL APPLIANCES IN THE SCHOOL Who found it?? What appliance? What is it for? Where does it get electricity from? Who uses it? Alex clock know time batteries everybody What electrical
### Magnetism and Electricity
Magnetism and Electricity Way back in the first lesson of this magnetism block, we talked about the fact that magnetic fields are caused by electrons moving in the same direction. Up to this point, we
### Activity 8: Solar-Electric System Puzzle
Section 3 Activities Activity 8: Solar-Electric System Puzzle ACTIVITY TYPE: Worksheet Overview: Introduces the basic components of the Solar 4R Schools (S4RS) solar-electric system and identifies the
### ECSE-2100 Fields and Waves I Spring Project 1 Beakman s Motor
Names _ and _ Project 1 Beakman s Motor For this project, students should work in groups of two. It is permitted for groups to collaborate, but each group of two must submit a report and build the motor
### Teacher s Guide: Safest Generation Ad Activity
Teacher s Guide: Safest Generation Ad Activity Introduction Today s 11- and 12-year-old preteens are very smart about vehicle safety. They have grown up using car seats and booster seats more consistently
### Hazard Hamlet Activity Book An Electrical Safety Activity Book
Hazard Hamlet Activity Book An Electrical Safety Activity Book Hydro One 1 Power probe Where is the electricity? Colour what uses electricity in orange. Colour what doesn t use electricity in other colours.
### IT'S MAGNETIC (1 Hour)
IT'S MAGNETIC (1 Hour) Addresses NGSS Level of Difficulty: 4 Grade Range: 3-5 OVERVIEW In this activity, students will create a simple electromagnet using a nail, a battery, and copper wire. They will
### What is Electricity? Lesson one
What is Electricity? Lesson one Static Electricity Static Electricity: an electrical charge that builds up on an object Most of the time, matter is electrically neutral. The same number of positive and
### Every Friday, Bart and Lisa meet their friends at an after-school club. They spend the afternoon playing Power Up, a game about batteries.
Battery Lab NAME Every Friday, Bart and Lisa meet their friends at an after-school club. They spend the afternoon playing Power Up, a game about batteries. The object of the game is to arrange battery
### Electricity Unit Review
Science 9 Electricity Unit Review Name: General Definitions: Neutral Object Charge Separation Electrical Discharge Electric Current Amperes (amps) Voltage (volts) Voltmeter Ammeters Galvanometer Multimeter
### Getting a Car J. Folta
Getting a Car Getting a Car J. Folta As the head of a family, I have many decisions to make about how my husband and I spend our money. We need to figure out the way to get the most out of what we make
### Busy Ant Maths and the Scottish Curriculum for Excellence Foundation Level - Primary 1
Busy Ant Maths and the Scottish Curriculum for Excellence Foundation Level - Primary 1 Number, money and measure Estimation and rounding Number and number processes Fractions, decimal fractions and percentages
### Scholastic s Early Childhood Program Correlated to the Minnesota Pre-K Standards
Scholastic s Early Childhood Program 5/2/07 Page 1 DOMAIN I: EMOTIONAL AND SOCIAL DEVELOPMENT EMOTIONAL DEVELOPMENT 2. 3. 4. 5. Demonstrate increasing competency in recognizing and describing own emotions
### Science Test Revision
John Buchan Middle School Science Test Revision 4F Circuits and Conductors 39 min 38 marks Name John Buchan Middle School 1 Level 3 1. Conducting electricity (a) Year 6 are testing objects to see if they
### DRIVING Question: Is it important to know how to drive? Are you a good driver? Complete the paragraph on the right with the words on the left.
Question: Is it important to know how to drive? Are you a good driver? Complete the paragraph on the right with the words on the left. The year is 2020, and it s 7:45 on a rainy, Monday morning. You are
### Electrical Safety World Video Teacher s Guide
Electrical Safety World Video Teacher s Guide The Electrical Safety World video explains electric science concepts and how to use electricity safely in daily life. The content addresses many state and
### Parts of an atom. Protons (P + ) Electrons (e - ) Neutrons. Have a positive electric charge. Have a negative electric charge
Electricity Parts of an atom Protons (P + ) Have a positive electric charge Electrons (e - ) Have a negative electric charge Neutrons Are neutral Have no charge Electric Charge In most atoms, the charges
### 2. There are 2 types of batteries: wet cells and dry cells.
How Batteries Work 1. Imagine a world where all electric devices had to be plugged in. we would need cords for our cell phones. Wires would run from our calculators and TV remotes. We would trip over cords
### Science 10-Electricity & Magnetism Activity 3 Activity 3D Voltage of Electrical Cells in Series and in Parallel
Science 10-Electricity & Magnetism Activity 3 Activity 3D oltage of Electrical Cells in Series and in Parallel Name Due Date Show Me Hand In Purpose: To see how connecting cells in series and in parallel
### MONTANA TEEN DRIVER CURRICULUM GUIDE Lesson Plan & Teacher Commentary. Module 2.1 Preparing to Drive
MONTANA TEEN DRIVER CURRICULUM GUIDE Lesson Plan & Teacher Commentary Module 2.1 Preparing to Drive Lesson Objective (from Essential Knowledge and Skills Topics): Identifying Vehicle Gauges, Alert and
### INSTRUCTIONS TO CANDIDATES
Kenya Certificate of Secondary Education NAME:.... SCHOOL: DATE:... ELECTROMAGNETISM 1 INSTRUCTIONS TO CANDIDATES Answer ALL questions in this paper in the spaces provided. 1 1. Fran has a balancing game.
### Porsche unveils 4-door sports car
www.breaking News English.com Ready-to-use ESL / EFL Lessons Porsche unveils 4-door sports car URL: http://www.breakingnewsenglish.com/0507/050728-porsche-e.html Today s contents The Article 2 Warm-ups
### Lesson Plan 11 Electric Experiments
Lesson Plan 11 Electric Experiments Brief description Students experiment with aluminium foil, batteries and cheap, readily availably low voltage light bulbs* to construct a simple conductivity tester.
### Magnetism can produce current.
Page of 5 KY CONCPT Magnetism can produce current. BFOR, you learned Magnetism is a force exerted by magnets lectric current can produce a magnetic field lectromagnets can make objects move NOW, you will
### 4. ELECTRICITY AND MAGNETS
4. ELECTRICITY AND MAGNETS 4.1 INTRODUCING ELECTRICITY AND MAGNETS Today almost everyone uses electricity. Electricity gives us light when we switch on a torch (flashlight), and sound when we switch on
### Electricity. An atom with more protons than electrons has a positive charge.
Electricity Lesson 1 How Are Electricity and Magnetism Related? Electricity Have you used electricity in the past hour? Did you turn on a lamp? Did you watch TV? Did you get something cold to drink from
### Tips on Reading This Book with Children:
Level: L Word Count: 337 100th Word: of (page 10) Teaching Focus: Phonics: Word Study Look at the words electricity and energy. How are the words alike? How are they different? Tips on Reading This Book
### Topic: Friction. Planes, Trains, and Automobiles. A Poppins Book Nook Science Experiment. My Name Is:
Planes, Trains, and Automobiles A Poppins Book Nook Science Experiment Topic: Friction My Name Is: ---------------------------------------------------------------------------------------------------------
| 8,022
| 35,145
|
{"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-2020-24
|
latest
|
en
| 0.89216
|
https://justaaa.com/statistics-and-probability/339484-assume-that-the-heights-of-women-are-normally
| 1,713,606,694,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296817576.41/warc/CC-MAIN-20240420091126-20240420121126-00177.warc.gz
| 296,950,543
| 9,387
|
Question
# Assume that the heights of women are normally distributed with a mean of 63.6 inches and...
Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. a) Find the probability that if an individual woman is randomly selected, her height will be greater than 64 inches. b) Find the probability that 16 randomly selected women will have a mean height greater than 64 inches.
solution:
mean = inch.
standard deviation = inch
a) we have to find the prbabiity of randoml selected women's height more than 64 inches = P(X > 64)
now calculating the z score
P(X > 64) 1 - value of z to the left of 0.16 = 1 - 0.5636 = 0.4364
b)
if we selected 16 women randomly , probability that their mean height is greater than 64 = P(M > 64)
finding z score
P(M > 64) = 1 - value of z to the left of 0.64 = 1 - 0.7389 = 0.2611
#### Earn Coins
Coins can be redeemed for fabulous gifts.
| 263
| 953
|
{"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}
| 3.90625
| 4
|
CC-MAIN-2024-18
|
latest
|
en
| 0.877201
|
https://www.sololearn.com/fr/Discuss/2374667/i-cannot-understand-quotient-and-remainder-stuff
| 1,716,276,051,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971058385.38/warc/CC-MAIN-20240521060250-20240521090250-00327.warc.gz
| 888,071,388
| 189,139
|
I cannot understand quotient and remainder stuff | Sololearn: Learn to code for FREE!
Nouvelle formation ! Tous les codeurs devraient apprendre l'IA générative !
+ 1
# I cannot understand quotient and remainder stuff
I can't explain it but you can say that i understood nothing in this quotient remainder thing
5th Jul 2020, 7:55 AM
Aditya Tyagi
5 Réponses
+ 4
Adding on above answer, "//" floor division. This is used for getting the quotient. As you can see the above example. print(10//4) # prints 2 i.e quotient print (10%4) # prints 2 i.e remainder. print(10/4) # prints 2.5 i.e in decimal form-accurate form
5th Jul 2020, 8:12 AM
Arctic Fox
+ 4
See Let's initialise a value of 10 to a variable a initialise another value of 4 to a variable b. So if ye use % (modulus) to find the remainder and / for quotient 😕 4|10|2 - quotient - 8 --------- 2. remainder --------- so here the remainder is 2 and the quotient is also 2. Have a look https://www.math-only-math.com/dividend-divisor-quotient-and-remainder.html
5th Jul 2020, 7:59 AM
Nilesh
+ 2
Please tell your programming language. So, that we can help you
5th Jul 2020, 7:56 AM
Arctic Fox
0
It's python
5th Jul 2020, 8:00 AM
Aditya Tyagi
0
Know what is remainder and quotient ghe thing is I just started python and i can't understand it in python terms
5th Jul 2020, 8:05 AM
Aditya Tyagi
Aujourd'hui en vedette
c++ help
1 Votes
My future
0 Votes
| 437
| 1,404
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.831871
|
https://cheapcustompapers.org/if-the-probability-of-being-born-on-a-specific-day-of-the-week-is-the-same-for-all-days-of-the-week/
| 1,632,270,198,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780057274.97/warc/CC-MAIN-20210921221605-20210922011605-00572.warc.gz
| 210,782,572
| 15,061
|
# If the probability of being born on a specific day of the week is the same for all days of the week,
If the probability of being born on a specific day of the week is the same for all days of the week, about how many of 100 babies will probably have a Friday birthday?
| 62
| 271
|
{"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-2021-39
|
latest
|
en
| 0.982363
|
http://bizindex.us/xuro/what-is-a-math-term-70.php
| 1,532,034,420,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-30/segments/1531676591296.46/warc/CC-MAIN-20180719203515-20180719223515-00039.warc.gz
| 48,609,533
| 4,866
|
# What is a math term
Mass is the quantity of matter in an object.Complete information about the mass, definition of an mass, examples of an mass,.What links here Related changes Upload file Special pages Permanent link Page information Wikidata item Cite this page.
First of all, we will look for a few extra hints for this entry: Math problem term.Each of the 89 math terms has been created in black and white for super easy printing.Terms included: Balance, Binomial, Bisect.The most commonly studied operations are binary operations of arity 2, such as addition and multiplication, and unary operations of arity 1, such as additive inverse and multiplicative inverse.The above describes what is usually called a finitary operation, referring to the finite number of arguments (the value k ).
### github.com
Our Math Glossary provides more than simple definitions: A link to a related lesson is provided for each term in our database.A math Glossary anyone can help edit. Here is a list of other great Math Glossary online. Home.There are obvious extensions where the arity is taken to be an infinite ordinal or cardinal, or even an arbitrary set indexing the arguments.
### Terms, factors, & coefficients (video) | Khan Academy
We have collected some basic definitions on this page. Illustrated Mathematics Dictionary: A: B: C: D: E: F: G: H: I: J: K: L: M: N: O: P.Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation.Math term is a crossword puzzle clue that we have spotted over 20 times.Includes a wide variety of math skills, including addition, subtraction, multiplication, division,.To a large extent, students and many of their teachers tend to define mathematics in terms of what they learn in math courses,.
The mixed product is an example of an operation of arity 3, or ternary operation.
### Nelson Education - Elementary Mathematics - Mathematics 6
Unary operations involve only one value, such as negation and trigonometric functions.
### Math "B" Terms - themathlab.com
A vector can be multiplied by a scalar to form another vector.
### math/What is a interval in math terms? - page 7 - jiskha.com
Operations on functions include composition and convolution.
To termin ate, or cause to end, is to take to a boundary or limit.Words from the Latin terminus have something to do with boundaries or limits.
### Elementary school math term -- Crossword clue | Crossword
By using this site, you agree to the Terms of Use and Privacy Policy.The values for which an operation is defined form a set called its domain.An operation may or may not have certain properties, for example it may be associative, commutative, anticommutative, idempotent, and so on.
### Math problem term - Crossword clues & answers - Global Clue
Term (mathematics) A term is a mathematical expression which may form a separable part of an equation, a series, or another expression. Definition.This second method works best when you have a large number of numbers.In this context, the usual operations, of finite arity are also called finitary operations.This article provides you with a glossary of math terms and definitions in order to simplify your. we use the term argument. Argument. the definitions of math.
### Math Term E - edobyte.brasilia.me
In mathematics, an operation is a calculation from zero or more input values (called operands ) to an output value.Main page Contents Featured content Current events Random article Donate to Wikipedia Wikipedia store.Browse and Read Math Term E Math Term E Title Type physical science question paper for term 1 grade 11 term one 2014 macmillan PDF.Generally, the arity is supposed to be finite, but infinitary operations are sometimes considered.An interactive math dictionary with enough math words, math terms, math formulas, pictures, diagrams,.Mathematics definition, (used with a singular verb) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities.
Glossary of Math Terms Compiled by Heather S. Benson. 2 Inverse operations.And the inner product operation on two vectors produces a scalar.Please help improve this article by adding citations to reliable sources.We are provide free online math dictionary for kids and also providing free solved math problems with step.
### What is a period in math terms? | Reference.com
He is currently serving his third term in the U.S. Senate. He was sentenced to a ten-year term in the state penitentiary.Untitled.
| 950
| 4,560
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.828125
| 4
|
CC-MAIN-2018-30
|
latest
|
en
| 0.909237
|
https://www.geeksforgeeks.org/rearrange-two-given-arrays-to-maximize-sum-of-same-indexed-elements/?ref=lbp
| 1,675,711,508,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-06/segments/1674764500357.3/warc/CC-MAIN-20230206181343-20230206211343-00120.warc.gz
| 774,242,507
| 28,204
|
# Rearrange two given arrays to maximize sum of same indexed elements
• Last Updated : 18 May, 2021
Given two arrays A[] and B[] of size N, the task is to find the maximum possible sum of abs(A[i] – B[i]) by rearranging the array elements.
Examples:
Input: A[] = {1, 2, 3, 4, 5}, B[] = {1, 2, 3, 4, 5}
Output: 12
Explanation:
One of the possible rearrangements of A[] is {5, 4, 3, 2, 1}.
One of the possible rearrangements of B[] is {1, 2, 3, 4, 4}.
Therefore, the sum of all possible values of abs(A[i] – B[i]) = { abs(5 – 1) + abs(4 – 2) + abs(3 – 3) + abs(2 – 4) + abs(1 – 5) } = 12
Input: A[] = {1, 2, 2, 4, 5}, B[] = {5, 5, 5, 6, 6}
Output: 13
Explanation:
One of the possible rearrangements of A[] is {5, 4, 2, 2, 1}.
One of the possible rearrangements of B[] is {5, 5, 5, 6, 6}.
Therefore, the sum of all possible values of abs(A[i] – B[i]) = { abs(5 – 5) + abs(4 – 5) + abs(2 – 5) + abs(2 – 6) + abs(1 – 6) } = 13
Approach: Follow the steps below to solve the problem:
Below is the implementation of the above approach:
## C++
`// C++ program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to find the maximum possible sum``// by rearranging the given array elements``int` `MaxRearrngeSum(``int` `A[], ``int` `B[], ``int` `N)``{`` ` ` ``// Sort the array A[]`` ``// in ascending order`` ``sort(A, A + N);`` ` ` ` ` ``// Sort the array B[]`` ``// in descending order`` ``sort(B, B + N,`` ``greater<``int``>());`` ` ` ` ` ``// Stores maximum possible sum`` ``// by rearranging array elements `` ``int` `maxSum = 0;`` ` ` ` ` ``// Traverse both the arrays`` ``for` `(``int` `i = 0; i < N; i++) {`` ` ` ` ` ``// Update maxSum`` ``maxSum += ``abs``(A[i] - B[i]);`` ``}`` ` ` ``return` `maxSum;` `}` `// Driver Code``int` `main()` `{` ` ``int` `A[] = { 1, 2, 2, 4, 5 };`` ``int` `B[] = { 5, 5, 5, 6, 6 };` ` ``int` `N = ``sizeof``(A) / ``sizeof``(A[0]);` ` ``cout<< MaxRearrngeSum(A, B, N);` ` ``return` `0;``}`
## Java
`// Java program to implement``// the above approach``import` `java.lang.Math;``import` `java.util.Arrays;``import` `java.util.Collections;` `class` `GFG{`` ` `// Function to find the maximum possible sum``// by rearranging the given array elements``static` `int` `MaxRearrngeSum(Integer A[],`` ``Integer B[],`` ``int` `N)``{`` ` ` ``// Sort the array A[]`` ``// in ascending order`` ``Arrays.sort(A);`` ` ` ``// Sort the array B[]`` ``// in descending order`` ``Arrays.sort(B, Collections.reverseOrder());`` ` ` ``// Stores maximum possible sum`` ``// by rearranging array elements `` ``int` `maxSum = ``0``;`` ` ` ``// Traverse both the arrays`` ``for``(``int` `i = ``0``; i < N; i++)`` ``{`` ``// Update maxSum`` ``maxSum += Math.abs(A[i] - B[i]);`` ``}`` ``return` `maxSum;``}`` ` `// Driver code``public` `static` `void` `main (String[] args)``{`` ``Integer A[] = { ``1``, ``2``, ``2``, ``4``, ``5` `};`` ``Integer B[] = { ``5``, ``5``, ``5``, ``6``, ``6` `};` ` ``int` `N = A.length;`` ` ` ``System.out.println(MaxRearrngeSum(A, B, N));``}``}` `// This code is contributed by ujjwalgoel1103`
## Python3
`# Python3 program to implement``# the above approach` `# Function to find the maximum possible sum``# by rearranging the given array elements``def` `MaxRearrngeSum(A, B, N):`` ` ` ``# Sort the array A[]`` ``# in ascending order`` ``A.sort()` ` ``# Sort the array B[]`` ``# in descending order`` ``B.sort(reverse ``=` `True``)` ` ``# Stores maximum possible sum`` ``# by rearranging array elements`` ``maxSum ``=` `0` ` ``# Traverse both the arrays`` ``for` `i ``in` `range``(N):` ` ``# Update maxSum`` ``maxSum ``+``=` `abs``(A[i] ``-` `B[i])` ` ``return` `maxSum` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` ` ``A ``=` `[ ``1``, ``2``, ``2``, ``4``, ``5` `]`` ``B ``=` `[ ``5``, ``5``, ``5``, ``6``, ``6` `]` ` ``N ``=` `len``(A)` ` ``print``(MaxRearrngeSum(A, B, N))` `# This code is contributed by chitranayal`
## C#
`// Java program to implement``// the above approach``using` `System;` `class` `GFG{`` ` `// Function to find the maximum possible sum``// by rearranging the given array elements``static` `int` `MaxRearrngeSum(``int` `[]A, ``int` `[]B, ``int` `N)``{`` ` ` ``// Sort the array A[]`` ``// in ascending order`` ``Array.Sort(A);`` ` ` ``// Sort the array B[]`` ``// in descending order`` ``Array.Sort(B);`` ``Array.Reverse(B);`` ` ` ``// Stores maximum possible sum`` ``// by rearranging array elements `` ``int` `maxSum = 0;`` ` ` ``// Traverse both the arrays`` ``for``(``int` `i = 0; i < N; i++)`` ``{`` ` ` ``// Update maxSum`` ``maxSum += Math.Abs(A[i] - B[i]);`` ``}`` ``return` `maxSum;``}`` ` `// Driver code``public` `static` `void` `Main()``{`` ``int` `[]A = { 1, 2, 2, 4, 5 };`` ``int` `[]B = { 5, 5, 5, 6, 6 };` ` ``int` `N = A.Length;`` ` ` ``Console.WriteLine(MaxRearrngeSum(A, B, N));``}``}` `// This code is contributed by ipg2016107`
## Javascript
``
Output:
`13`
Time Complexity: O(N * Log N)
Auxiliary Space: O(1)
My Personal Notes arrow_drop_up
| 2,078
| 5,449
|
{"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}
| 3.75
| 4
|
CC-MAIN-2023-06
|
latest
|
en
| 0.503598
|
http://www.ask.com/question/how-does-a-compass-work
| 1,406,229,776,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-23/segments/1405997890211.21/warc/CC-MAIN-20140722025810-00233-ip-10-33-131-23.ec2.internal.warc.gz
| 129,185,968
| 16,915
|
# How Does a Compass Work?
A compass consists of magnetized pointers which are unattached enabling them to move and align with the Earth's magnetic field. If the electrical charges of the Earth move south, a compass' pointer will also 'point' in that direction. Modern compasses are designed with markings to help the user tell dictions efficiently.
Q&A Related to "How Does a Compass Work"
1. Acknowledging that you may be experiencing some degree of compassion fatigue is the first step in measuring its extent. Oftentimes it is easy to discount feelings of hopelessness http://www.ehow.com/how_7863282_measure-compassion...
1. Stroke the needle with a piece of silk from the hole to the tip. Pinch the needle at the hole between two fingers and, with the other hand, rub the needle from the eye to the tip http://www.ehow.com/how_8686223_make-escape-compas...
1. The cardinal directions on a compass. Look at a compass. It has four cardinal directions: North(N) South(S) East(E) and West(W) There are also the additional directions northeast http://www.ehow.com/how_8294499_use-compass-kids.h...
1. Point the lubber line in the direction of your destination. The lubber line is either the red line running down the center of the compass face or the direction-of-travel arrow http://www.ehow.com/how_8423290_set-compass-bearin...
Ask.com Answer for: how does a compass work
How Does a Compass Work?
A majority of Westerners are introduced to the use of a compass as a Boy Scout or Girl Scout. This introduction happens on a trek through a forest or around a field. The purpose is to show that this ancient piece of technology is an effective means of... More »
Difficulty: Easy
Source: www.ehow.com
A compass has a pointer which works as a magnet. This magnetic pointer detects the Earth's magnetic fields, and generally is set to point in the Northern direction. You can find more information here: http://en.wikipedia.org/wiki/Compass
Top Related Searches
Explore this Topic
A compass works because they have magnetic pointers that are able to move and align with the earth's magnetic field. Compasses help millions of people everyday. ...
People use compasses to find direction if they are lost, and this has been used for centuries. The compass is basically a magnet which when it alligns itself with ...
A magnetic compass operates by suspending a magnetic element and observing the movement as it aligns itself with the poles or magnetic north. You can find more ...
About - Privacy - Careers - Ask Blog - Mobile - Help - Feedback - Sitemap © 2014 Ask.com
| 589
| 2,577
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.859375
| 3
|
CC-MAIN-2014-23
|
latest
|
en
| 0.916138
|
https://www.shaalaa.com/question-bank-solutions/find-speed-electron-ground-state-hydrogen-atom-description-ground-state-given-previous-problem-coulomb-s-law_68739
| 1,618,452,728,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00192.warc.gz
| 1,108,049,411
| 9,984
|
# Find the Speed of the Electron in the Ground State of a Hydrogen Atom. the Description of Ground State is Given in the Previous Problem. - Physics
Short Note
Find the speed of the electron in the ground state of a hydrogen atom. The description of ground state is given in the previous problem.
#### Solution
Given:
Separation between the two charges, r = 0.53 Å = 0.53 × 10−10 m
By Coulomb's Law, force,
$F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}$
Here,
$q_1 = q_2 = e$
$\Rightarrow F = \frac{9 \times {10}^9 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{\left( 0 . 53 \times {10}^{- 10} \right)^2}$
$= 8 . 2 \times {10}^{- 8} N$
Now, mass of an electron, Me = 9.12 × 1031 kg
The necessary centripetal force is provided by the Coulombian force.
$\Rightarrow F_e = \frac{M_e v^2}{r}$
$\Rightarrow v^2 = 0 . 4775 \times {10}^{13}$
$= 4 . 775 \times {10}^{12}$
$\Rightarrow v = 2 . 18 \times {10}^6$ m/s
Is there an error in this question or solution?
#### APPEARS IN
HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 7 Electric Field and Potential
Q 19 | Page 121
| 390
| 1,106
|
{"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}
| 3.734375
| 4
|
CC-MAIN-2021-17
|
latest
|
en
| 0.610015
|
http://www.docstoc.com/docs/15510412/%E7%84%A1%E6%8A%95%E5%BD%B1%E7%89%87%E6%A8%99%E9%A1%8C---IT-in-Education
| 1,405,259,413,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-23/segments/1404776438278.73/warc/CC-MAIN-20140707234038-00020-ip-10-180-212-248.ec2.internal.warc.gz
| 246,318,312
| 13,700
|
# 無投影片標題 - IT in Education
Document Sample
``` Locating Places on Maps -Grid Reference (格網座標)
Look at the relief map of H.K. Can you tell the location of Tai Mo Shan
X
Look at the seating plan of your classroom Can you tell the location of Carol’s seat in the classroom?
What is grid reference?
26 25 24 23 22 21 10
11
12
13
14
15
16
•A grid is a set of numbered vertical and horizontal lines which cross each other.
•Grid reference is a number which represents the location of a place on a grid.
Naming grid lines on maps
26 25 24 23 22 21 10
11
12
13
14
15
16
Map 1
•The vertical lines are numbered from west to east. The vertical lines are called eastings (東行線). •The horizontal lines are numbered from south to north. The horizontal lines are called northings (北行線).
How to read a grid reference?
•Grid reference is formed by the intersection of an easting and a northing. •To tell the position of a place, we put the easting first and then northing.
Example: The 4 - figure grid reference (grid square) of pig farm 3 is 1324
26
25
24
23 22 21 10 11 12 13 14 15 16 Map 1
Exercise 1: Complete the table.
Location Easting Northing Grid reference (4-figure)
Pig Farm 1 and 2 Ah jing’s home
Factory A Factory B
12
24
1224
14 25
1425
12
23
1223
15
23
1523
Exercise 2: Draw the following things on the map 1
26 25 24 23 22 21 10 Map 1
11
12
13
14
15
16
Sometimes, a 4 - figure grid reference does not give the exact location of a place. For example, on Map 1, both pig farm 1 and 2 are on the grid square 1224. It does not tell us the exact location of the pig farm 1and 2. To be more exact, we use a 6 - grid reference.
To do this, we divide each grid square into ten smaller squares numbered from 1 to 9.
26 25 24 23 22 21 10 11 12 13 14 15 16
Example: The 6 - figure grid reference of pig farm 1 is 125245 pig farm 2 is 129 244
Exercise 3:
Give a 6 - figure grid reference for each of these on Map 2.
129240 Railway station _______________
fire station ___________ 131243 hospital _____________ 137241
127245 police station_____________ 127237 church ________________ 131219 cultivated land __________
Why do we use grid references?
•Grid reference make it quick and easy to locate places on maps. •They also make it easier to tell someone else where something is.
The End
EDD 5161b Group 9
Prepared by : Lee Mei Ling 96010140 Chung Mei Yin 96010550 Leven Wong 97029110
```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views: 19 posted: 11/9/2009 language: English pages: 22
| 751
| 2,544
|
{"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}
| 4.5
| 4
|
CC-MAIN-2014-23
|
longest
|
en
| 0.853604
|
https://39bet.club/2024/01/26/how-much-can-you-bet-on-roulette/
| 1,709,196,858,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474795.48/warc/CC-MAIN-20240229071243-20240229101243-00677.warc.gz
| 74,701,413
| 18,272
|
• Home |
• How much can you bet on roulette
# How much can you bet on roulette
Title: Let's Gamble with Roulette! How Much Can You Bet on Roulette? Hey there, fellow thrill-seekers! Today, we're diving into the exciting world of roulette, where fortunes can be made in the blink of an eye. Now, before we roll the dice (or rather, spin the wheel), let's answer the burning question on everyone's minds: "How much can you bet on roulette?" Well, my friends, the good news is that roulette offers a wide range of betting options to accommodate all types of players. Whether you're a cautious gambler or a high roller, there's a spot at the table just for you. In the United States, where we're chilling with Lady Luck, the betting limits on roulette can vary between casinos and even between different tables within the same casino. So, it's always wise to check the specific rules of the house you're playing in. However, fret not, as we'll give you a general idea of what you can expect. Most casinos in the US have two main types of betting limits: inside bets and outside bets. Inside bets are placed on specific numbers or combinations, while outside bets cover larger groups of numbers with slightly higher odds of winning. For inside bets, the minimum and maximum bet
## How much should you bet in roulette?
If you are new to the game, it's a good idea to start with chips that have the minimum cost to play, say \$1 or \$5, to ease into it. Another way to enjoy the game without risking too much is to play the 50-50 bets. There are squares for landing on red or black numbers, odd or even, or 1-18 and 19-36.
## What happens if you put \$5 on a number in roulette?
In the game of roulette, a player can place a \$5 bet on the number 25 and have a 1/38 probability of winning. If the metal ball lands on 25, the player gets to keep the \$5 paid to play the game and the player is awarded in additional \$175. Otherwise, the player is awarded nothing and the casino takes the player \$5.
## What is the best bet to make on roulette?
The bets with the best odds in roulette are outside bets on either even or odd, red or black or numbers 1-18 or 19-36. Each of these bets has a 1:1 payout.
## How much does \$1 pay in roulette?
A bet on a single number pays 35 to 1, including the 0 and 00. Bets on red or black, odd or even pay 1 for 1, or even money.
## How much does \$5 win in roulette?
\$175 If you place a \$5 bet on a single number in roulette and that number hits, you will typically win \$175. This is because the payout for a successful single-number bet (also known as a "straight bet") in American roulette is usually 35 to 1.
## How much can you make from roulette?
Roulette Payouts Both European and American variants will pay 35:1 for a straight bet and 1:1 for an outside bet that covers 18 numbers.
#### What is the highest payout on roulette?
The maximum amount that you can win playing roulette at a casino depends on the type of roulette game being played. In American roulette, the maximum amount that can be won is 35:1, meaning that if you bet \$1, you will receive a payout of \$35.
#### What is the highest bet on roulette?
Buried Life: Roulette The boys put \$125,000 on even money roulette bets and tried to roll it over 3 times, and ended up making the largest roulette bet in Vegas history of \$250,000.
#### How many things can you bet on in roulette?
A player may bet on single numbers, rows of numbers, or on adjacent numbers. A player also may play colors, odd or even numbers, among others. A bet on a single number pays 35 to 1, including the 0 and 00. Bets on red or black, odd or even pay 1 for 1, or even money.
#### How much does a single number payout in roulette?
35 to 1 Each spin of the wheel provides a multitude of options for the player. A player may bet on single numbers, rows of numbers, or on adjacent numbers. A player also may play colors, odd or even numbers, among others. A bet on a single number pays 35 to 1, including the 0 and 00.
## FAQ
What are the odds for a single number in roulette?
What are the odds in roulette? The roulette odds of winning a round depend on the number of outcomes covered in the bet. If you bet on only one number, you are facing 1-in-37 odds in European roulette and 1-in-38 odds for the American version. In both cases however, the roulette payout for straight bets is 35:1.
What is the \$5 roulette strategy?
Bet \$5 on two dozens or columns, stack up to \$20 when one hits, take \$15 and go to \$45, pocket \$100 when \$45 hits twice, then spread remaining \$35 across 5 numbers to win \$1200 jackpot with just \$5 using roulette strategy.
What is the most successful roulette strategy?
The Martingale betting system What is the most successful roulette strategy? While there is no strategy that can guarantee a profit in the long run when playing roulette, the Martingale betting system is often regarded as the most successful strategy. It is easy to use and can provide good returns.
What is the maximum bet on a roulette table?
\$5,000 is often seen as a maximum bet at tables. There may also be limits for straight/outside bets (I.e. Red or black) versus limits for the inside numbers. However, a high roller or whale can get the casino to increase the limits to whatever it can stomach, including seven figure bets.
## How much can you bet on roulette
Can I bet on all 36 numbers in roulette? The short answer is yes, but it makes no sense whatsoever to do so and that's because of the house edge. The highest paying roulette bet is on a single number, as it can trigger wins equal to 36 times the stakes. What are the highest paying odds on a roulette table? 35:1 What is the best bet in roulette? According to the roulette payouts chart, the highest paying bet in the game is on a single number, offering a 35:1 payout. The odds of winning however are pretty slim. The more numbers you add to the bet, the lower the payout will be compared to the size of the wager. What is the most you can bet in Vegas? There really is no “Maximum”. Most casinos will indulge you if the odds are right. People have bet a cool million and beyond on anything from a roll of the dice to a football game. It depends what casino you are in, and if they'll take the bet. Do all roulette tables have a max bet? The roulette table usually imposes minimum and maximum bets, and these rules usually apply separately for all of a player's inside and outside bets for each spin. For inside bets at roulette tables, some casinos may use separate roulette table chips of various colors to distinguish players at the table.
• What is the maximum bet at a casino?
• Table maximums can be as low as \$50 at the small locals casino Poker Palace, but major strip casinos usually offer some tables with a \$10,000 maximum. Exceptions are the Golden Nugget in downtown which permits \$15,000 bets, and three tables at Caesars Palace which permit bets between \$5,000 and \$50,000.
• Will a casino kick you out for winning at roulette?
• Yes, it is possible to be asked to leave a casino for winning a large amount of money while playing roulette. Casinos have the right to refuse service to anyone, and they may consider a player's success at the roulette table to be undesirable for their business.
• What is the 3 2 rule in roulette?
• The 3/2 plan is a bet on both bets at once. Three chips are placed on Red, Black, Odd or Even, and two chips are placed on one of the three columns. The theory is that enough numbers are covered in one spin to give the player a chance to make a profit.
February 8, 2024
February 8, 2024
February 8, 2024
| 1,790
| 7,634
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2024-10
|
latest
|
en
| 0.95314
|
https://documen.tv/question/a-ball-is-thrown-straight-out-at-80-feet-per-second-from-an-upstairs-window-that-s-15-feet-off-t-24186359-15/
| 1,638,385,993,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964360881.12/warc/CC-MAIN-20211201173718-20211201203718-00015.warc.gz
| 277,303,612
| 16,794
|
## A ball is thrown straight out at 80 feet per second from an upstairs window that’s 15 feet off the ground. Find the ball’s horizontal distan
Question
A ball is thrown straight out at 80 feet per second from an upstairs window that’s 15 feet off the ground. Find the ball’s horizontal distance from the window at the moment it strikes the ground.
a. 0.96825
b. Can’t be found
c. 77.46
d. 6.33
e. 212.23
in progress 0
3 months 2021-07-31T17:44:00+00:00 1 Answers 18 views 0
Step-by-step explanation:
In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here’s what we know in the y-dimension:
a = -32 ft/s/s
v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)
Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)
t = ?? sec.
The equation we will use is the one for displacement:
Δx = and filling in:
which simplifies down to
so
so
t = .968 sec (That is not the correct number of sig fig’s but if I use the correct number, the answer doesn’t come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)
Now we use that time in the x-dimension. Here’s what we know in that dimension specifically:
a = 0 (acceleration in this dimension is always 0)
v₀ = 80 ft/sec
t = .968 sec
Δx = ?? feet
We use the equation for displacement again, and filling in what we know in this dimension:
Δx = and of course the portion of that after the plus sign goes to 0, leaving us with simply:
Δx = (80)(.968)
Δx = 77.46 feet
| 488
| 1,814
|
{"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}
| 4.5625
| 5
|
CC-MAIN-2021-49
|
latest
|
en
| 0.898683
|
https://community.fabric.microsoft.com/t5/Desktop/Variation-in-revenue-in-the-same-period-last-year/m-p/3441834
| 1,719,343,762,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198866218.13/warc/CC-MAIN-20240625171218-20240625201218-00664.warc.gz
| 152,650,749
| 112,919
|
cancel
Showing results for
Did you mean:
Find everything you need to get certified on Fabric—skills challenges, live sessions, exam prep, role guidance, and more. Get started
New Member
## Variation in revenue in the same period last year
Hey guys
I have a problem using SAMEPERIODLASTYEAR to calculate the billing variation per month. The current month is not complete but the formula is considering the current month of last year as complete and the variation is wrong
The page has a relative date filter like this year
When I put a filter between dates, for example 01/01/2023 to 09/19/2023, the billing variation is correct
My dCalendar table looks like this -> dCalendar = CALENDAR(DATE(2011,01,01),TODAY())
Measures:
Billing = SUM(SALES[VALUE])
Billing LY = CALCULATE(SALES[VALUE], SAMEPERIODLASTYEAR(dCalendar.[Date]))
Has anyone experienced this?
1 ACCEPTED SOLUTION
New Member
Hey guys
I broke my brain and found a solution lol
Created a new date table with the full period | calendario= date(2011,01,01),date(2100,12,31)) and connected the sales base after this, connected the old date table (dCalendar) with the new date table (calendario) and I'm using it as an automatic filter For dates
New Member
Hey guys
I broke my brain and found a solution lol
Created a new date table with the full period | calendario= date(2011,01,01),date(2100,12,31)) and connected the sales base after this, connected the old date table (dCalendar) with the new date table (calendario) and I'm using it as an automatic filter For dates
Announcements
#### Europe’s largest Microsoft Fabric Community Conference
Join the community in Stockholm for expert Microsoft Fabric learning including a very exciting keynote from Arun Ulag, Corporate Vice President, Azure Data.
#### Power BI Monthly Update - June 2024
Check out the June 2024 Power BI update to learn about new features.
#### Fabric Community Update - June 2024
Get the latest Fabric updates from Build 2024, key Skills Challenge voucher deadlines, top blogs, forum posts, and product ideas.
Top Solution Authors
Top Kudoed Authors
| 498
| 2,104
|
{"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-2024-26
|
latest
|
en
| 0.858396
|
https://www.teachoo.com/14637/2536/Ex-9.1---4-iii/category/Ex-9.1/
| 1,725,905,885,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651133.92/warc/CC-MAIN-20240909170505-20240909200505-00307.warc.gz
| 963,056,124
| 21,402
|
Ex 8.1
Chapter 8 Class 7 Rational Numbers
Serial order wise
### Transcript
Ex 8.1, 4 Draw the number line and represent the following rational numbers on it: (iii) (−7)/4 (−7)/4 Since (−7)/4 = –1 3/4 So, (−7)/4 < –1 Let’s draw number line from 0 to –2 Since in (−7)/4 , denominator is 4 We divide line between –1 & 0 into 4 equal parts.
| 118
| 339
|
{"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-2024-38
|
latest
|
en
| 0.871768
|
https://www.abovetopsecret.com/forum/thread1200793/pg32
| 1,721,394,237,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514902.63/warc/CC-MAIN-20240719105029-20240719135029-00006.warc.gz
| 550,490,735
| 12,860
|
It looks like you're using an Ad Blocker.
Thank you.
Some features of ATS will be disabled while you continue to use an ad-blocker.
# Debunking Flat Earth and the Hollow Earth
page: 32
9
share:
posted on May, 18 2018 @ 02:55 PM
American, JetBlue, and some others have started a program where you go from zero to flying for them. Part of the program is to get you your CFI rating and you work as an instructor at the school while you work towards your ATP. It's a two to three year program to get to your First Officer position.
posted on May, 18 2018 @ 03:06 PM
That's actually really cool. I know that something very similar is done in the helicopter world by a few companies, Especially in oil field country. The little brother of the guy who runs the demolition ranch YouTube channel talked about it pretty extensively while playing a match of squad or Arma once lol.
Too bad earth doesn't work like flerfers think though, because otherwise I'd totally start an intercontinental helicopter charter service!
Hell, you could train monkeys to ascend to a few thousand feet and let the earth spin under you!
Plus going through the continental divide and the Sierras or cascades would be like the ultimate game of frogger!
edit on 18-5-2018 by roguetechie because: (no reason given)
posted on May, 18 2018 @ 07:48 PM
originally posted by: dragonridr
Your wrong look up how a plane determines altitude. A plane uses air pressure to determine how high the aircraft is flying. Meaning that in order to show zero in climb or decent it has to fly along a path with the same air density.
According to this source, and others....
In aviation, altitude refers to how high an aircraft is above mean sea level; that is, how high the aircraft is above the average level of the Earth's oceans. ... It works to measure height above sea level because the air's pressure decreases at a more or less regular rate as you ascend
www.angelflightne.org...
But the point is about level flight, and how curvature is unaccounted for on flights.
originally posted by: dragonridr
So again explain how this instrument proves anything according to your theory. If the only determination of altitude is based off air density how would this differ following a curve or maintaining a straight course? One other thing could you explain why air gets thinner the higher we go? With gravity this makes sense but without it I'm curious what you think is happening
Because there are TWO instruments involved, not only one.
The VSI measures ascent, descent, and level flight, and the altimeter measures altitude at the same time.
Air pressure/density is used for both measurements, NOT the surface/ground below. As I've repeatedly said, over and over.
To ascend or descend in air has NOTHING to do with the ground. We have level flight when neither in ascent, nor in descent.
A plane cannot fly over curvature, at altitude, without a constant descent. It cannot be done. It is physically impossible.
That's what the VSI is measuring. No descent is measured in flight, and it is proof of a flat Earth.
posted on May, 18 2018 @ 08:03 PM
If you fly a plane in a constant descent, that means you are losing altitude constantly. If you're losing altitude constantly, eventually you end up at 0 feet. If your VSI shows a 500 foot per minute descent, and you're at 500 feet, then in one minute, you will have flown into the ground.
posted on May, 18 2018 @ 10:15 PM
originally posted by: Soylent Green Is People
originally posted by: OneBigMonkeyToo
A VSI tells you about changes in air pressure as you rise and fall. That air pressure is based on the point you are in now, not some distant point along the Earth's curve.
www.boldmethod.com...
Yes, and if you read the comments, you can see that some people talk about pilots sometimes "chasing" a particular VSI model that features an accelerometer because they are not accustomed to its sensitivity...
...Which brings me to a point I made a while earlier that pilots and autopilots are constantly making small adjustments to the controls (in all directions of flight, up, down, and other) in order to keep at level and true flight. If all of those instantaneous control adjustments (up, down, and other) are added up over a long period/long distance, it could be seen that to follow the VSI to keep a constant altitude, the plane will follow the curvature of the air pressure above the curved Earth.
So while a pilot does not need to "mindfully" dip the nose in order to follow the curvature of the Earth, that curvature would show itself in the sum of the component adjustments a plane makes in the normal course of flying level over a long distance.
After saying it over and over again, countless times, you STILL don't have a clue!
The surface below a plane is not used to determine 'level flight', or ascent, or descent, in a flight, EVER.
Air is NOT millions of tiny, distinct pressure layers identifying all planes being 'level' or not!!
It is complete nonsense, same as before.
We know that pressure changes occur within atmosphere.... but it's certainly not layered in millions of tiny, distinctly unique pressure values!!
There should be a point where you see excuses hit bottom. Like now.
The VSI measures pressure AROUND a plane, to determine level flight, or not level flight. It compares pressure above, to below, the plane. Three stages of flight - ascent, descent, level - are measured by the VSI.
posted on May, 18 2018 @ 10:44 PM
originally posted by: Zaphod58
If you fly a plane in a constant descent, that means you are losing altitude constantly. If you're losing altitude constantly, eventually you end up at 0 feet. If your VSI shows a 500 foot per minute descent, and you're at 500 feet, then in one minute, you will have flown into the ground.
That's correct.
Over a sphere, it would have to descend constantly in order to maintain it's altitude. No plane descends constantly, of course, and proves the flatness of Earth's surface is true.
It's a shock at first, to accept the reality. ..
posted on May, 19 2018 @ 12:39 AM
Wrong. There's a difference between pointing the nose and descending. You can point the nose without climbing or descending. Over a sphere or a flat earth, if you fly at a constant descent, you're going to crash.
posted on May, 19 2018 @ 12:57 AM
originally posted by: Zaphod58
Wrong. There's a difference between pointing the nose and descending. You can point the nose without climbing or descending. Over a sphere or a flat earth, if you fly at a constant descent, you're going to crash.
Not so.
If you fly over a sphere, a constant descent is required to maintain the same altitude.
On a flat Earth, a constant descent WOULD end in a crash to the surface.
They are different surfaces, and require very different flights.
posted on May, 19 2018 @ 01:04 AM
A descent is a descent, regardless of if the earth is flat or not. If you're flying over a sphere, you descend to land. If you're flying over a flat earth, you descend to land. If you descend in either case, you are going to impact the ground. You can point the nose up or down, and not climb or descend.
posted on May, 19 2018 @ 01:19 AM
You realize a plane can ascend or descend without pointing the nose...
posted on May, 19 2018 @ 01:32 AM
originally posted by: Zaphod58
A descent is a descent, regardless of if the earth is flat or not. If you're flying over a sphere, you descend to land. If you're flying over a flat earth, you descend to land. If you descend in either case, you are going to impact the ground. You can point the nose up or down, and not climb or descend.
A sphere is a curved surface. A plane has to fly a curved path to follow above the surface, to maintain the same altitude.
Why would such a descent 'impact the ground' when it holds the same altitude above the sphere, throughout the flight?
posted on May, 19 2018 @ 01:36 AM
And where did anyone say it that there are lots of different pressure layers?
VSI measures pressure in the instrument, nowhere else.
Your complete lack of knowledge is getting badly exposed now. Give it up.
posted on May, 19 2018 @ 01:45 AM
originally posted by: OneBigMonkeyToo
And where did anyone say it that there are lots of different pressure layers?
VSI measures pressure in the instrument, nowhere else.
Your complete lack of knowledge is getting badly exposed now. Give it up.
What 'pressure layers' hold planes around a curvature, and suggest this is being in 'level' flight?
The VSI measures ascent, descent, and level flight. How do planes fly around a sphere without any descent? Because it's not a sphere at all.
Where is all that 'missing curvature' over a 6 hour flight?
posted on May, 19 2018 @ 01:59 AM
The VSI measures ascent, descent, and level flight. How do planes fly around a sphere without any descent? Because it's not a sphere at all.
NO
a VSI measures change in barometric pressure - it REPORTS asscent // descent by inference
this has been explained to you so many different ways - it hurts
but still you persist in your delusions
hypothetical annecdote :
an aircraft is flying over a spherical planet [ equitorial diameter 12000km ] @ ASL 10000m . its velocity [ over ground = 700kph . the VSI reports no asccent // descent .
it flies for 90minuites from its " last waypoint ^ ] - what is its altitude at waypoint # 2 ?
posted on May, 19 2018 @ 02:24 AM
originally posted by: turbonium1
originally posted by: Zaphod58
A descent is a descent, regardless of if the earth is flat or not. If you're flying over a sphere, you descend to land. If you're flying over a flat earth, you descend to land. If you descend in either case, you are going to impact the ground. You can point the nose up or down, and not climb or descend.
A sphere is a curved surface. A plane has to fly a curved path to follow above the surface, to maintain the same altitude.
Why would such a descent 'impact the ground' when it holds the same altitude above the sphere, throughout the flight?
Correct on both counts.
Compared to space yes the plane is descending all the time, but the VSI and Altimeter essentially are reading the height of the air column above it and in level flight over a curved surface, this is not changing, so the VSI AND ALTIMETER WILL STAY PUT EVEN IF THE PLANE IS DESCENDING COMPARED TO SPACE.
posted on May, 19 2018 @ 02:28 AM
originally posted by: ignorant_ape
The VSI measures ascent, descent, and level flight. How do planes fly around a sphere without any descent? Because it's not a sphere at all.
NO
a VSI measures change in barometric pressure - it REPORTS asscent // descent by inference
this has been explained to you so many different ways - it hurts
but still you persist in your delusions
hypothetical annecdote :
an aircraft is flying over a spherical planet [ equitorial diameter 12000km ] @ ASL 10000m . its velocity [ over ground = 700kph . the VSI reports no asccent // descent .
it flies for 90minuites from its " last waypoint ^ ] - what is its altitude at waypoint # 2 ?
Ascent or descent is measured by pressure differential, within the VSI's diaphragm.
It is measured within air, uses air pressure to measure ascent, descent, and level flight of a plane.
Once again, this has NOTHING to do with the surface, far below the plane. Your endlessly claiming it.... is total nonsense.
I'm referring to YOUR argument of Earth's 'curvature', so that's what you need to address...
A plane flying 6 hours at cruising speed will require about 1800 feet of descent to maintain it's original altitude, say 38,000 feet.
Assume the VSI measures 0 feet per minute over the entire 6 hours, and the altitude remains at 38,000 feet, throughout the same 6 hours.
It is only possible for this to work flying over a flat Earth. It is impossible to explain over a round Earth.
posted on May, 19 2018 @ 02:28 AM
Double post
edit on 19-5-2018 by turbonium1 because: (no reason given)
posted on May, 19 2018 @ 02:46 AM
posted on May, 19 2018 @ 02:57 AM
originally posted by: Hyperboles
originally posted by: turbonium1
originally posted by: Zaphod58
A descent is a descent, regardless of if the earth is flat or not. If you're flying over a sphere, you descend to land. If you're flying over a flat earth, you descend to land. If you descend in either case, you are going to impact the ground. You can point the nose up or down, and not climb or descend.
A sphere is a curved surface. A plane has to fly a curved path to follow above the surface, to maintain the same altitude.
Why would such a descent 'impact the ground' when it holds the same altitude above the sphere, throughout the flight?
Correct on both counts.
Compared to space yes the plane is descending all the time, but the VSI and Altimeter essentially are reading the height of the air column above it and in level flight over a curved surface, this is not changing, so the VSI AND ALTIMETER WILL STAY PUT EVEN IF THE PLANE IS DESCENDING COMPARED TO SPACE.
The surface is not relevant, whether it is curved, or not curved, mountainous, or the Grand Canyon, an ocean, or a desert.....
What the VSI measures is atmospheric pressure, ON THE PLANE ITSELF, when in flight, at the specific moment.
Show me how the VSI would measure atmospheric pressure based on a 8 inch per mile squared curvature, 38,000 feet below it, which 'calibrates' it to read 'level' flight as being 'level' over curvature.....
Any sources you have, would be great....
I'll wait...
posted on May, 19 2018 @ 03:25 AM
originally posted by: turbonium1
originally posted by: OneBigMonkeyToo
And where did anyone say it that there are lots of different pressure layers?
VSI measures pressure in the instrument, nowhere else.
Your complete lack of knowledge is getting badly exposed now. Give it up.
What 'pressure layers' hold planes around a curvature, and suggest this is being in 'level' flight?
The ones around the wings.
The VSI measures ascent, descent, and level flight. How do planes fly around a sphere without any descent? Because it's not a sphere at all.
Where is all that 'missing curvature' over a 6 hour flight?
new topics
top topics
9
| 3,359
| 14,210
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2024-30
|
latest
|
en
| 0.94863
|
https://hackaday.io/project/10889-spdt16-16-bits-arithmetic-unit-with-relays/log/37371-multiplication-and-division
| 1,529,334,956,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-26/segments/1529267860570.57/warc/CC-MAIN-20180618144750-20180618164750-00613.warc.gz
| 616,981,391
| 6,945
|
# Multiplication and Division
A project log for SPDT16: 16-bits arithmetic unit with relays
Let's imagine I could get about 200 SPDT relays. Of course I would know what to do with them :-D But will 200 be enough ?
Yann Guidon / YGDES 05/02/2016 at 22:450 Comments
The circuits that perform addition and subtraction can be reused in the circuits shown in this page : http://fourier.eng.hmc.edu/e85_old/lectures/arithmetic_html/node8.html
Multiplication and division require a shift register that is large enough to store the product or dividend. In the case of multiplication, I tried to redesign it in my head but I stumbled on the problem of the carry... The below drawing (taken from the link above) solves it finally :-)
For a 16-bits multiplicand, the shift register needs 32 bits. The carry counts as a 33rd but it does not remain set at the end, at least for the unsigned multiplication. The maximal value is 0xFFFF×0xFFFF=0xFFFE0001
The multiplier should be loaded from the input so a row of relays is required to select the source of the input data. The accumulator (and carry) is cleared initially but another line of 16 relays must multiplex the accumulator's value to perform the shift, because in the add/sub mode, the accumulator is not shifted.
Division looks almost the same, but there's a catch.
The shift direction is reversed ! So that's 32 more MUXing relays ! (and 2A of consumption)
I have not yet decided if I'll implement restoring or non-restoring division. Both are possible because I can either add 0 or add/subtract at will, it's just a different control signal to toggle.
Overall, that's 64 relays for MUXing and 64 relays for the 32-bits shift register. 128 relays are added to perform the 4 operations. The ALU is 4×16=64 relays already, 192 relays are needed and I don't even count the control logic or the amplifiers !
It seems the budget of 200 relays is barely enough.
| 470
| 1,914
|
{"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}
| 2.921875
| 3
|
CC-MAIN-2018-26
|
latest
|
en
| 0.919539
|
http://math.stackexchange.com/questions/199797/estimating-the-derivative-of-a-c-0-infty-function/199827
| 1,469,535,261,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-30/segments/1469257824853.47/warc/CC-MAIN-20160723071024-00011-ip-10-185-27-174.ec2.internal.warc.gz
| 164,151,046
| 17,375
|
# Estimating the derivative of a $C_0^\infty$ function.
Let $w \in C_0^\infty(\mathbb{R},\mathbb{R}^+)$ be a function with $\int_\mathbb{R} w(x) = 1$.
What can we say about the first derivative, or what can we say about $\int_\mathbb{R} |\partial_xw|$ ?
I am especially interested in the case where $w$ can be written as $w(x) = \frac{1}{\epsilon^2} v(\frac{x}{\epsilon})$ with $v \in C_0^\infty(\mathbb{R},\mathbb{R}^+), v(x)=v(-x)$ and $\int_\mathbb{R} v(x) = 1$. Is there an estimation like $|w|_{1,1}\leq c\epsilon$ ?
Thanks!
-
Are you sure about the $\epsilon^2$ ? I doubt you get a normalized $w$. – vanna Sep 20 '12 at 16:27
You're right, it is just $\epsilon$. – AlexisZorbas Sep 21 '12 at 9:22
I'm assuming that as @vanna suggests, the $\epsilon^2$ is not valid: it looks like it should be $w(x)=\frac{1}{\epsilon}v(\frac{x}{\epsilon})$. In this case (let $x=\epsilon y$ in the $v$ integral and then change the name of $y$ to $x$), $$\int_\mathbb{R}w(x)dx=\int_\mathbb{R}v(x)dx=1.$$ With $w(x)=\frac{1}{\epsilon^2}v(\frac{x}{\epsilon})$, we'd have $$\int_\mathbb{R}w(x)dx=\frac{1}{\epsilon}\int_\mathbb{R}v(x)dx.$$
Writing $v'=r$, we then have $w'(x)=\frac{1}{\epsilon^2}r(\frac{x}{\epsilon})$, leading to $$\int_\mathbb{R}|w'(x)|dx=\frac{1}{\epsilon}\int_\mathbb{R}|r(x)|dx.$$ Since this $L^1$ norm of $r$ is independent of $\epsilon$, $|w|_{1,1}$ looks like it can be arbitrarily large.
So the estimation is simply $|w|_{1,1} \leq \frac{c}{\epsilon}$ ? – AlexisZorbas Sep 21 '12 at 9:27
Yes - it might be more accurate to say that $|w|_{1,1}\leq\frac{c}{\epsilon}$ is a valid estimate for $w\in C^\infty_0$ that can be written as $w=\frac{1}{\epsilon}v(\frac{x}{\epsilon})$ for $v\in C^\infty_0$. – user12477 Sep 21 '12 at 13:08
| 678
| 1,745
|
{"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}
| 3.8125
| 4
|
CC-MAIN-2016-30
|
latest
|
en
| 0.724474
|
https://isabelle.in.tum.de/repos/isabelle/file/tip/src/ZF/ZF.thy
| 1,660,138,364,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882571190.0/warc/CC-MAIN-20220810131127-20220810161127-00212.warc.gz
| 311,864,324
| 3,282
|
src/ZF/ZF.thy
author wenzelm Mon, 08 Aug 2022 20:27:54 +0200 changeset 75798 8b0dbfbde032 parent 69593 3dda49e08b9d permissions -rw-r--r--
```
section\<open>Main ZF Theory: Everything Except AC\<close>
theory ZF imports List IntDiv CardinalArith begin
(*The theory of "iterates" logically belongs to Nat, but can't go there because
primrec isn't available into after Datatype.*)
subsection\<open>Iteration of the function \<^term>\<open>F\<close>\<close>
consts iterates :: "[i=>i,i,i] => i" (\<open>(_^_ '(_'))\<close> [60,1000,1000] 60)
primrec
"F^0 (x) = x"
"F^(succ(n)) (x) = F(F^n (x))"
definition
iterates_omega :: "[i=>i,i] => i" (\<open>(_^\<omega> '(_'))\<close> [60,1000] 60) where
"F^\<omega> (x) == \<Union>n\<in>nat. F^n (x)"
lemma iterates_triv:
"[| n\<in>nat; F(x) = x |] ==> F^n (x) = x"
by (induct n rule: nat_induct, simp_all)
lemma iterates_type [TC]:
"[| n \<in> nat; a \<in> A; !!x. x \<in> A ==> F(x) \<in> A |]
==> F^n (a) \<in> A"
by (induct n rule: nat_induct, simp_all)
lemma iterates_omega_triv:
"F(x) = x ==> F^\<omega> (x) = x"
lemma Ord_iterates [simp]:
"[| n\<in>nat; !!i. Ord(i) ==> Ord(F(i)); Ord(x) |]
==> Ord(F^n (x))"
by (induct n rule: nat_induct, simp_all)
lemma iterates_commute: "n \<in> nat ==> F(F^n (x)) = F^n (F(x))"
by (induct_tac n, simp_all)
subsection\<open>Transfinite Recursion\<close>
text\<open>Transfinite recursion for definitions based on the
three cases of ordinals\<close>
definition
transrec3 :: "[i, i, [i,i]=>i, [i,i]=>i] =>i" where
"transrec3(k, a, b, c) ==
transrec(k, \<lambda>x r.
if x=0 then a
else if Limit(x) then c(x, \<lambda>y\<in>x. r`y)
else b(Arith.pred(x), r ` Arith.pred(x)))"
lemma transrec3_0 [simp]: "transrec3(0,a,b,c) = a"
by (rule transrec3_def [THEN def_transrec, THEN trans], simp)
lemma transrec3_succ [simp]:
"transrec3(succ(i),a,b,c) = b(i, transrec3(i,a,b,c))"
by (rule transrec3_def [THEN def_transrec, THEN trans], simp)
lemma transrec3_Limit:
"Limit(i) ==>
transrec3(i,a,b,c) = c(i, \<lambda>j\<in>i. transrec3(j,a,b,c))"
by (rule transrec3_def [THEN def_transrec, THEN trans], force)
declaration \<open>fn _ =>
Simplifier.map_ss (Simplifier.set_mksimps (fn ctxt =>
map mk_eq o Ord_atomize o Variable.gen_all ctxt))
\<close>
end
```
| 810
| 2,249
|
{"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
| 3
|
CC-MAIN-2022-33
|
latest
|
en
| 0.551594
|
https://uva.onlinejudge.org/board/search.php?author_id=2474&sr=posts&
| 1,563,630,379,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-30/segments/1563195526517.67/warc/CC-MAIN-20190720132039-20190720154039-00427.warc.gz
| 582,936,680
| 8,791
|
Search found 80 matches
Thu Aug 30, 2018 12:15 pm
Forum: Volume 2 (200-299)
Topic: 207 - PGA Tour Prize Money
Replies: 30
Views: 6287
Re: 207 - PGA Tour Prize Money
I think the uDebug code is still slightly off when it comes to printing prize amount, at least based on my reading of the statement (there's a difference between winning \$0.00 and not winning anything IMHO). Which I guess means the judge data is also a bit lacking since my AC code disagrees on this ...
Mon Aug 27, 2018 1:17 am
Forum: Volume 127 (12700-12799)
Topic: 12734 - Guess the String
Replies: 1
Views: 754
Re: 12734 - Guess the String
It seems like the judge for this problem is broken? Can someone check it please?
Perhaps submission for this problem should be disabled until it can be fixed.
Tue Feb 14, 2017 4:01 am
Forum: Volume 100 (10000-10099)
Topic: 10069 - Distinct Subsequences
Replies: 26
Views: 11196
Re: 10069 - Distinct Subsequences
To clarify, the reason big int is required is because the statement is supposed to say 10^100, not 10100
Also the description of "subsequence" is cribbed directly & without credit from Intro to Algorithms, which is shameful to say the least.
Tue Nov 29, 2016 12:17 pm
Forum: Volume 122 (12200-12299)
Topic: 12287 - Network Flow
Replies: 1
Views: 887
Re: 12287 - Network Flow
It seems to me there's something wrong with the data for this problem. Ignoring the part about optimizing the rotation in the flow, I'm having difficulty understanding how to justify the TRA computation used to get ACC (which I just got). Consider the following cases, which all specify the same pump...
Thu Dec 17, 2015 5:33 am
Forum: Volume 108 (10800-10899)
Topic: 10840 - Multi-stage Compressor
Replies: 4
Views: 6488
Re: 10840 - Multi-stage Compressor
Thanks to uDebug I finally got AC on this problem. There is a discrepancy between the data and problem statement. The statement says to output p_i, but actually what works is to output p_i / p_1. In other words we want not the output pressure after stage i but the compression ratio after stage i. Th...
Mon Mar 18, 2013 3:01 am
Forum: Bugs and suggestions
Topic: 597 broken input
Replies: 3
Views: 1930
Re: 597 broken input
I know I can't get AC. I thought I read somewhere that red checkmarks could mean no I/O or could mean the OJ has input but not a verified output. Not that I could find anywhere that explains what the checkmarks mean (do you have a link for that?) Anyway, the judge is definitely providing non-empty i...
Fri Mar 15, 2013 1:39 pm
Forum: Bugs and suggestions
Topic: 511 Sample output erroneous
Replies: 0
Views: 1207
511 Sample output erroneous
It seems the issue mentioned in the forum thread:
http://acm.uva.es/board/viewtopic.php?f=6&t=42698
has not been addressed (probably it wasn't reported directly?).
Please take a look.
Thanks!
Fri Mar 15, 2013 1:26 pm
Forum: Bugs and suggestions
Topic: 597 broken input
Replies: 3
Views: 1930
597 broken input
I realise this problem has a red checkmark (I didn't at first since I accessed it via http://uva.onlinejudge.org/external/5/597.html directly), but it seems the input doesn't follow the specification (giving me runtime errors until I figured out the problem). I confirmed there aren't any empty lines...
Sun Jul 08, 2012 1:10 pm
Forum: Bugs and suggestions
Topic: 10679-I Love String!!! - Shallow judge data
Replies: 3
Views: 4642
Re: 10679-I Love String!!! - Shallow judge data
Has this been fixed? I don't want to submit to find out since it would surely overwrite my current (legitimate) ranking. I couldn't find any post by Carlos noting that this issue was addressed.
Thu Jun 21, 2012 7:57 am
Forum: Volume 1 (100-199)
Topic: 176 - City Navigation
Replies: 20
Views: 7710
Re: 176 - City Navigation
Hi kurtdz,
My AC program gives the following. Thanks for your cases, they helped me track down my bug(s)!
Code: Select all
``````213
49
129
197
164
176
1
197
198
0
1
49
100
``````
Sat Mar 31, 2012 4:05 am
Forum: Bugs and suggestions
Topic: Slow judge
Replies: 0
Views: 1632
Slow judge
I haven't submitted to this judge in a while, but it seems excessively slow. Is it related to a brief downtime earlier today? Or perhaps someone ("Lee Wei") making a huge number of submissions over a short period?
Sat Jan 26, 2008 7:41 am
Forum: Volume 101 (10100-10199)
Topic: 10136 - Chocolate Chip Cookies
Replies: 6
Views: 4087
Careful Igor -- unless the two points are a full diameter apart, they actually determine two circles with a given radius (or none, if they are further apart than a diameter), not a unique one.
Tue Aug 07, 2007 7:29 am
Forum: C++
Topic: Initialize a Queue Empty
Replies: 5
Views: 2745
You could also make your queue variable local to the while loop, since that seems to be the only place you use it.
Sun Apr 22, 2007 12:50 am
Forum: Volume 102 (10200-10299)
Topic: 10282 - Babelfish
Replies: 48
Views: 18973
I agree. Your vm.push_back(m) in particular -- you're making a copy of the dictionary so far and pushing it into the vector...so at the end you end up with a vector with O(n^2) string pairs inside...
Thu Apr 19, 2007 7:39 am
Forum: Algorithms
Topic: arctan (1/u)
Replies: 2
Views: 2222
Sorry, you're not even close.... Why do you assume "k" has to be an integer? There is no reason that k^2-4uk-4 should be a perfect square, you only need it to be positive. If this is homework, have you done Lagrange multipliers? Or any calculus at all?? I can tell you that you'll probably need a der...
| 1,565
| 5,479
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.578125
| 3
|
CC-MAIN-2019-30
|
latest
|
en
| 0.915894
|
https://community.deeplearning.ai/t/mse-cost-function/23349
| 1,721,224,685,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514771.72/warc/CC-MAIN-20240717120911-20240717150911-00323.warc.gz
| 161,772,652
| 6,278
|
# Mse Cost function
Hi team,
Why don’t we get the convex function ,if we use MSE as cost function in Logistic Regression.
It turns out that distance based cost functions do not perform well on classifications. To MSE, the difference between 0.49 and 0.51 is the same as the distance from 0.89 to 0.91, right? But in a classification problem where the label is True, those two changes do not have the same effect, right? So giving them both the same reward or punishment is not a good strategy.
My previous reply gives a way to think about why traditional distance metrics don’t work well for classification problems, but it may also help to see a visual demonstration. Here is a graph of what the loss surface looks like if you use the MSE cost function with the dataset from Prof Ng’s original Stanford Machine Learning course in the Logistic Regression assignment there:
For comparison, here is what you get with the standard cross entropy or “log loss” cost function that is used for Logistic Regression:
A classic example of the traditional maxim: “A picture is worth a thousand words.”
These plots are courtesy of Olivier Philip who was a mentor for Stanford Machine Learning a few years back when I took that course.
Yeah thanks for that clarification. But still the idea behind the distance between 0.91,0.89 and 0.51 and 0.49.the idea is like the distance is calculated between actual y and y hat but the the ys will be only 0 and 1 right?
Hey,
Can you please tell whether I made you clearly understand my query.
Yes, you’re right that the loss is calculated between the label (y) and the prediction (\hat{y}). But the same argument still applies: Euclidean distance is not a good metric for a classification problem using the intuition that I gave above.
| 381
| 1,772
|
{"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-2024-30
|
latest
|
en
| 0.938906
|
https://popflock.com/learn?s=Games_behind
| 1,627,929,026,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-31/segments/1627046154356.39/warc/CC-MAIN-20210802172339-20210802202339-00265.warc.gz
| 472,518,457
| 21,585
|
Games Behind
Get Games Behind essential facts below. View Videos or join the Games Behind discussion. Add Games Behind to your PopFlock.com topic list for future reference or share this resource on social media.
Games Behind
A partial view of the Green Monster at Fenway Park during the 2007 MLB season, with the final regular season standings for the American League East division, including a "GB" column
In most North American sports, the phrase games behind or games back (often abbreviated GB) is a common way to reflect the gap between a leading team and another team in a sports league, conference, or division.
## Example
In the below standings from the 1994 Major League Baseball season, the Atlanta Braves are six games behind the Montreal Expos. Atlanta would have to win six games, and Montreal would have to lose six games, to tie for first. The leading team is zero games behind itself, and this is indicated in standings by a dash, not a zero.
NL East W L Pct. GB Home Road
Montreal Expos 74 40 0.649 -- 32-20 42-20
Atlanta Braves 68 46 0.596 6 31-24 37-22
New York Mets 55 58 0.487 18½ 23-30 32-28
Philadelphia Phillies 54 61 0.470 20½ 34-26 20-35
Florida Marlins 51 64 0.443 23½ 25-34 26-30
## Computing games behind
Games behind is calculated by using either of the following formulas, in which Team A is a leading team, and Team B is a trailing team. Example math in this section uses the above standings, with Montreal as Team A and Atlanta as Team B.
${\displaystyle {\text{Games Behind}}={\frac {({\text{Team A's wins - Team A's losses}})-({\text{Team B's wins - Team B's losses}})}{2}}}$
${\displaystyle {\text{Games Behind}}={\frac {({\text{74 - 40}})-({\text{68 - 46}})}{2}}={\frac {\text{34 - 22}}{2}}={\frac {12}{2}}=6}$
Alternately:
${\displaystyle {\text{Games Behind}}={\frac {({\text{Team A's wins - Team B's wins}})+({\text{Team B's losses - Team A's losses}})}{2}}}$
${\displaystyle {\text{Games Behind}}={\frac {({\text{74 - 68}})+({\text{46 - 40}})}{2}}={\frac {\text{6 + 6}}{2}}={\frac {12}{2}}=6}$
Notes:
• It can alternately be said that Montreal is six games ahead of Atlanta.
• A games behind situation can change rapidly when two teams contesting for the lead play each other. For example, Atlanta could cut Montreal's lead in half (to three games) by sweeping a three-game head-to-head series.
• The leading team, in terms of games behind, is the team with the best won-loss difference. This is not always the team with the most wins. For example, a team with an 80-70 record (10 more wins than losses) would be one game behind a team with a 79-67 record (12 more wins than losses).
## Anomalies
A games behind calculation can be misleading when attempting to compare teams that have played an unequal number of games. This is because the games behind calculation simply computes the difference between wins and losses for each team, and then averages those two numbers. Essentially, this treats each unplayed game as being a 12 win and a 12 loss.
In an extreme example, attempting to compare the records of the 2007 New England Patriots (16-0; 1.000 winning percentage) and the 1972 Detroit Tigers (86-70; .551 winning percentage) finds that the teams are equivalent per a games behind calculation, as each team won 16 more games than it lost. However, the Tigers played 140 more games than the Patriots. The Patriots' 140 "unplayed" games are essentially treated as 70-70; indeed, if the 16-0 Patriots had 70 more wins and 70 more losses, their 86-70 record would match that of the Tigers.
In reality, teams in an actual sports league can have an unequal number of games played due to various scheduling anomalies, postponements, or cancellations. This can result in:
• Two teams with different winning percentages may be tied in terms of games behind. For example, Team A at 6-4 would be tied with Team B at 4-2, in terms of games behind. However, Team B has the better winning percentage, at .667 compared to .600 for Team A.
• A team with a lower winning percentage may lead (in terms of games behind) a team with a higher winning percentage. For example, Team A at 6-4 would lead Team B at 2-1 by a half-game when calculating games behind. However, Team B has the better winning percentage at .667, compared to .600 for Team A.
Such conditions have occurred multiple times in major sports leagues, examples include:
Date League Division Teams W-L Win Pct. GB Ref.
May 17, 2018 MLB AL East New York Yankees 28-13 .683 12 [1]
Boston Red Sox 30-14 .682 --
December 28, 2018 NBA Eastern Conference Milwaukee Bucks 24-10 .706 12 [2]
Toronto Raptors 26-11 .703 --
August 24, 2020 MLB AL East New York Yankees 16-9 .640 12 [3]
Tampa Bay Rays 19-11 .633 --
Leagues generally use winning percentage to order teams in official standings; however, standings appearing in newspapers or online may order teams based on games behind.
## Usage
NBA standings in November 1965 as published in The Minneapolis Star
The games behind calculation is often used in professional baseball and basketball, where tie games are not permitted.[a] Standings for these sports appearing in print or online during a season usually will have teams ordered by winning percentages, with a "GB" column provided as a convenience to the reader. Games behind is used less often in American football, where ties are possible but relatively uncommon. Games behind is rarely used in ice hockey and soccer, where ties are or were traditionally common and standings points are typically used.
### Major League Baseball
Major League Baseball (MLB) defines games behind as "the average of the differences between the leading team wins and the trailing team wins, and the leading teams losses and the trailing team losses."[4] A games behind column almost always appears in MLB standings for each five-team division.
#### Wild card race
In the 1994 MLB season, the American League and National League each split into three divisions, and each added a wild card team to the playoffs. Following this change, it became common for the media to publish an additional set of standings for the wild card race. It included all teams from a league, with the exception of the division leaders, and games behind was calculated with respect to the team with the highest standing in the wild card race.
In the 2012 MLB season, both leagues added a second wild card team. Now, games behind in the wild card race is calculated with respect to the team with second highest standing in the wild card race. MLB's website distinguishes this statistic as wild card games behind, abbreviated WCGB. Assuming that teams are not tied for first place in the wild card race, this results in the team leading the wild card race being shown as some number of "games ahead" of the second place team, indicated by a plus sign ("+") in the standings. As an example, see the 2012 NL Wild Card standings, which shows the Atlanta Braves six games ahead of the St. Louis Cardinals.
National Basketball Association (NBA) standings typically report games behind within each five-team division. However, it is not as closely followed as in baseball, because more teams qualify for the NBA playoffs, and the divisional statistics are not as important for playoff qualification. Sometimes, especially nearing the end of the regular season, games behind will be given with respect to the eighth position in the Eastern Conference and Western Conference, as the eighth position is the last to qualify for the playoffs in each conference.
### National Football League
NFL standings in October 1972 as published in the Tampa Bay Times
National Football League (NFL) standings sometimes report games behind, although the statistic is not emphasized; winning percentage is used, computed from each team's win-loss-tie record. This is especially true since the introduction of the bye week in 1990, exacerbating differences in the number of games that teams have played at various points in time, and since tied games (while highly uncommon since the introduction of overtime in the regular season starting in 1974) do still occur on occasion. Games behind is omitted from standings on the NFL's website and is absent from most published standings.
### Other sports
The games behind statistic is eschewed in sports where tie games are traditionally common, such as ice hockey and soccer. Leagues in these sports typically rank teams by awarding a certain number of points for each win or tie. In competitions where ties have been abolished (especially in hockey), points are still awarded for an "overtime loss" such that they are often (but not always) the same value as ties previously were, while in soccer the traditional value of two points for a win has been replaced by three points, while ties are still worth one point. These changes would make calculating a "games behind" statistic even more complicated compared to if it were to be used under the traditional system in which a tie was effectively worth a "half-win."
The Canadian Football League (CFL) also does not use games behind, and awards standings points. However, unlike leagues such as the National Hockey League (NHL) the CFL does not award points for overtime losses, although it experimented with such a system in the early 21st century. Also, unlike most other football codes that use a point system, the CFL still uses the traditional values of two points for a win and one for a tie. Therefore, a tie in the CFL is still effectively worth a "half-win" as it always has been in Canadian football (and also as it has been in the NFL since 1972).
### Related usage
Teams are sometimes referred to as being over or under "five hundred", in comparison to a .500 winning percentage. The calculation for this is simple subtraction. For example, a team at 29-19 is "10 games over five hundred",[5] as they could lose their next 10 games and still have a .500 record, while a team at 12-17 would be "five games under five hundred",[6] as the quickest they could reach .500 would be by winning their next five games. "Above" and "below" can be substituted for "over" and "under", respectively.
## Notes
1. ^ Historically, various MLB games have ended in a tie; such games are excluded from league standings, while statistics for individual players are counted.
## References
1. ^ "MLB Scores and Standings". Baseball-Reference.com. May 17, 2018. Retrieved 2018.
2. ^ "Conference Standings". basketball-reference.com. December 28, 2018. Retrieved 2020.
3. ^ "MLB Scores and Standings". Baseball-Reference.com. August 24, 2020. Retrieved 2020.
4. ^ "Standings". MLB.com. April 5, 2010. Archived from the original on April 5, 2010 – via Wayback Machine.
5. ^ McManaman, Bob (May 24, 2017). "Don't pop the bubbly yet, but Diamondbacks are 10 games above .500 for 1st time since 2011". azcentral.com. Retrieved 2021.
6. ^ "Nationals drop third straight, sink to five games under .500". NBC Sports. May 1, 2019. Retrieved 2021.
| 2,587
| 10,982
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "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-2021-31
|
latest
|
en
| 0.844548
|
https://www.deepdyve.com/lp/ou_press/erratum-a-review-on-the-systematic-formulation-of-3-d-multiparameter-VkBkznydW0
| 1,548,123,444,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-04/segments/1547583823140.78/warc/CC-MAIN-20190122013923-20190122035923-00577.warc.gz
| 786,103,464
| 22,140
|
# Erratum: A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium
Erratum: A review on the systematic formulation of 3-D multiparameter full waveform inversion in... Erratum of the paper ‘A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium’, by Yang et al., published in Geophys. J. Int. (2016) 207, 129–149. The following equations were erroneously displayed in this paper and should be read as follow. The gradient of the misfit function with respect to model parameters m is the same as the gradient of the Lagrangian at the saddle points considering w and m are independent variables when performing derivatives: \begin{eqnarray} \frac{\partial \mathbb {L}}{\partial \mathbf {m}} = \left\langle \bar{\mathbf {w}},\frac{\partial F(\mathbf {m},\mathbf {w})}{\partial \mathbf {m}}\right\rangle _T \Leftrightarrow \frac{\partial \chi }{\partial \mathbf {m}} = \left\langle \bar{\mathbf {w}},\frac{\partial F(\mathbf {m},\mathbf {w})}{\partial \mathbf {m}}\right\rangle _T \end{eqnarray} (61) \begin{eqnarray} && {\left\langle \frac{\partial \chi }{\partial \mathbf {m}},\delta \mathbf {m} \right\rangle _\Omega =\int _\Omega \mathrm{d}\mathbf {x} \delta \rho \left(\int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v} \right)}\nonumber\\ && {\qquad + \sum _{I=1}^6 \sum _{J=I}^6\int _\Omega \mathrm{d}\mathbf {x} \delta C_{IJ} \left(\int _0^T \mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger \frac{\partial C^{-1}}{\partial C_{IJ}} \left(\partial _t\boldsymbol{\sigma }-\mathbf {f}_\sigma + (C:: \Gamma)\sum^L_{\ell=1}y_\ell{\boldsymbol \xi_\ell}\right)\right) + \sum^6_{I=1}\sum^6_{J=I}\int_\Omega {\rm d}{\bf x}\delta C_{IJ}\left(\int^T_0{\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell\right)}\nonumber\\ && {\qquad +\sum _{\ell =1}^L\sum _{I=1}^6\sum _{J=I}^6 y_\ell \int _{\Omega }\mathrm{d}\mathbf {x}\delta Q_{IJ}^{-1} \left(\int _0^T\mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger C^{-1} \left(C::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \boldsymbol{\xi }_\ell \right),} \end{eqnarray} (66) \begin{eqnarray} \frac{\partial \chi }{\partial \rho } &=& \int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v}, \nonumber \\ \frac{\partial \chi }{\partial C_{IJ}}&=& \int _0^T \mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger \frac{\partial C^{-1}}{\partial C_{IJ}} \left(\partial _t\boldsymbol{\sigma } -\mathbf {f}_\sigma + (C::\Gamma)\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell\right) + \int^T_0{\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell, \nonumber \\ \frac{\partial \chi }{\partial Q_{IJ}^{-1}} &=& \int _0^T\mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger C^{-1}\left(C::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \left(\sum _{\ell =1}^L y_\ell \boldsymbol{\xi}_\ell \right), \quad {\rm with}\ \left(\frac{\partial C::\Gamma}{\partial C_{IJ}}\right)_{ij} =\left\{\begin{array}{l@{\quad}l} \left(Q^{-1}_{IJ}\right)_{ij}, & {\rm if}\ \ ij=IJ, JI\\ 0, & {\rm otherwise}. \end{array}\right. \end{eqnarray} (69) \begin{eqnarray} \frac{\partial \chi }{\partial \rho } &=& \int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v}, \nonumber \\ \frac{\partial \chi }{\partial C_{IJ}} &=&-\int _0^T \mathrm{d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial C}{\partial C_{IJ}} C^{-1} D^T {\mathbf {v}} + \int^T_0 {\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1} \frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell,\nonumber\\ \frac{\partial \chi }{\partial Q_{IJ}^{-1}} &=& \int _0^T\mathrm{d}t \left( D^T \bar{\mathbf {u}} \right)^\dagger \left(C ::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \left(\sum _{\ell =1}^L y_\ell \boldsymbol{\xi}_\ell \right), \end{eqnarray} (70) \begin{eqnarray} \Gamma= \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & 0 & 0 &0\\ \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & 0 & 0 & 0\\ \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & 0& 0 & 0\\ 0& 0 & 0 & \frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} & 0 &0\\ 0& 0 & 0 & 0 &\frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} &0\\ 0& 0 & 0 & 0 & 0 &\frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} \end{array}\right] \end{eqnarray} (86) \begin{eqnarray} \frac{\partial\Gamma}{\partial Q^{-1}_\alpha}= \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} 1 & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 0 & 0 &0\\ \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 1 & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 0 & 0 &0\\ \frac{\alpha^2}{\alpha^2 - 2\beta^2} & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 \end{array} \right],\ \frac{\partial \Gamma}{\partial Q^{-1}_\beta} = \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} 0 & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0\\ \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0\\ \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 \end{array} \right] \end{eqnarray} (87) $$\partial _t\xi _\ell ^{ij}+\omega _\ell \xi _\ell ^{ij}=\omega _\ell \dot{\epsilon }_{ij}\Rightarrow \xi _\ell ^{ij}=-\frac{1}{\omega _\ell }\partial _t \xi _\ell ^{ij} + \dot{\epsilon }_{ij},$$ (B8) The online version of this paper has been corrected. The publisher apologise for these errors. © The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press
# Erratum: A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium
Geophysical Journal International, Volume 212 (3) – Mar 1, 2018
2 pages
/lp/ou_press/erratum-a-review-on-the-systematic-formulation-of-3-d-multiparameter-VkBkznydW0
Publisher
Oxford University Press
© The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggx493
Publisher site
See Article on Publisher Site
### Abstract
Erratum of the paper ‘A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium’, by Yang et al., published in Geophys. J. Int. (2016) 207, 129–149. The following equations were erroneously displayed in this paper and should be read as follow. The gradient of the misfit function with respect to model parameters m is the same as the gradient of the Lagrangian at the saddle points considering w and m are independent variables when performing derivatives: \begin{eqnarray} \frac{\partial \mathbb {L}}{\partial \mathbf {m}} = \left\langle \bar{\mathbf {w}},\frac{\partial F(\mathbf {m},\mathbf {w})}{\partial \mathbf {m}}\right\rangle _T \Leftrightarrow \frac{\partial \chi }{\partial \mathbf {m}} = \left\langle \bar{\mathbf {w}},\frac{\partial F(\mathbf {m},\mathbf {w})}{\partial \mathbf {m}}\right\rangle _T \end{eqnarray} (61) \begin{eqnarray} && {\left\langle \frac{\partial \chi }{\partial \mathbf {m}},\delta \mathbf {m} \right\rangle _\Omega =\int _\Omega \mathrm{d}\mathbf {x} \delta \rho \left(\int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v} \right)}\nonumber\\ && {\qquad + \sum _{I=1}^6 \sum _{J=I}^6\int _\Omega \mathrm{d}\mathbf {x} \delta C_{IJ} \left(\int _0^T \mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger \frac{\partial C^{-1}}{\partial C_{IJ}} \left(\partial _t\boldsymbol{\sigma }-\mathbf {f}_\sigma + (C:: \Gamma)\sum^L_{\ell=1}y_\ell{\boldsymbol \xi_\ell}\right)\right) + \sum^6_{I=1}\sum^6_{J=I}\int_\Omega {\rm d}{\bf x}\delta C_{IJ}\left(\int^T_0{\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell\right)}\nonumber\\ && {\qquad +\sum _{\ell =1}^L\sum _{I=1}^6\sum _{J=I}^6 y_\ell \int _{\Omega }\mathrm{d}\mathbf {x}\delta Q_{IJ}^{-1} \left(\int _0^T\mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger C^{-1} \left(C::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \boldsymbol{\xi }_\ell \right),} \end{eqnarray} (66) \begin{eqnarray} \frac{\partial \chi }{\partial \rho } &=& \int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v}, \nonumber \\ \frac{\partial \chi }{\partial C_{IJ}}&=& \int _0^T \mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger \frac{\partial C^{-1}}{\partial C_{IJ}} \left(\partial _t\boldsymbol{\sigma } -\mathbf {f}_\sigma + (C::\Gamma)\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell\right) + \int^T_0{\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell, \nonumber \\ \frac{\partial \chi }{\partial Q_{IJ}^{-1}} &=& \int _0^T\mathrm{d}t \bar{\boldsymbol{\sigma }}^\dagger C^{-1}\left(C::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \left(\sum _{\ell =1}^L y_\ell \boldsymbol{\xi}_\ell \right), \quad {\rm with}\ \left(\frac{\partial C::\Gamma}{\partial C_{IJ}}\right)_{ij} =\left\{\begin{array}{l@{\quad}l} \left(Q^{-1}_{IJ}\right)_{ij}, & {\rm if}\ \ ij=IJ, JI\\ 0, & {\rm otherwise}. \end{array}\right. \end{eqnarray} (69) \begin{eqnarray} \frac{\partial \chi }{\partial \rho } &=& \int _0^T \mathrm{d}t \bar{\mathbf {v}}^\dagger \partial _t\mathbf {v}, \nonumber \\ \frac{\partial \chi }{\partial C_{IJ}} &=&-\int _0^T \mathrm{d}t\bar{\boldsymbol\sigma}^\dagger C^{-1}\frac{\partial C}{\partial C_{IJ}} C^{-1} D^T {\mathbf {v}} + \int^T_0 {\rm d}t\bar{\boldsymbol\sigma}^\dagger C^{-1} \frac{\partial(C::\Gamma)}{\partial C_{IJ}}\sum^L_{\ell=1}y_\ell{\boldsymbol\xi}_\ell,\nonumber\\ \frac{\partial \chi }{\partial Q_{IJ}^{-1}} &=& \int _0^T\mathrm{d}t \left( D^T \bar{\mathbf {u}} \right)^\dagger \left(C ::\frac{\partial \Gamma }{\partial Q_{IJ}^{-1}}\right) \left(\sum _{\ell =1}^L y_\ell \boldsymbol{\xi}_\ell \right), \end{eqnarray} (70) \begin{eqnarray} \Gamma= \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & 0 & 0 &0\\ \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & 0 & 0 & 0\\ \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q^{-1}_\beta}{\rho\alpha^2 - 2\rho\beta^2} & \frac{\rho\alpha^2 Q^{-1}_\alpha - 2\rho\beta^2 Q_\beta^{-1}}{\rho\alpha^2 - 2\rho \beta^2} & \frac{\rho\alpha^2Q^{-1}_\alpha}{\rho\alpha^2} & 0& 0 & 0\\ 0& 0 & 0 & \frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} & 0 &0\\ 0& 0 & 0 & 0 &\frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} &0\\ 0& 0 & 0 & 0 & 0 &\frac{\rho\beta^2 Q^{-1}_\beta}{\rho\beta^2} \end{array}\right] \end{eqnarray} (86) \begin{eqnarray} \frac{\partial\Gamma}{\partial Q^{-1}_\alpha}= \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} 1 & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 0 & 0 &0\\ \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 1 & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 0 & 0 &0\\ \frac{\alpha^2}{\alpha^2 - 2\beta^2} & \frac{\alpha^2}{\alpha^2 - 2\beta^2} & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 \end{array} \right],\ \frac{\partial \Gamma}{\partial Q^{-1}_\beta} = \left[\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} 0 & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0\\ \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0\\ \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & \frac{-2\beta^2}{\alpha^2 - 2\beta^2} & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 \end{array} \right] \end{eqnarray} (87) $$\partial _t\xi _\ell ^{ij}+\omega _\ell \xi _\ell ^{ij}=\omega _\ell \dot{\epsilon }_{ij}\Rightarrow \xi _\ell ^{ij}=-\frac{1}{\omega _\ell }\partial _t \xi _\ell ^{ij} + \dot{\epsilon }_{ij},$$ (B8) The online version of this paper has been corrected. The publisher apologise for these errors. © The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.
### Journal
Geophysical Journal InternationalOxford University Press
Published: Mar 1, 2018
## You’re reading a free preview. Subscribe to read the entire article.
### DeepDyve is your personal research library
It’s your single place to instantly
discover and read the research
that matters to you.
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year
Save searches from
PubMed
Create lists to
Export lists, citations
| 5,858
| 14,485
|
{"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": 3, "x-ck12": 0, "texerror": 0}
| 2.71875
| 3
|
CC-MAIN-2019-04
|
latest
|
en
| 0.558848
|
https://math.answers.com/other-math/16_miles_in_82_minutes_is_what_mph
| 1,723,572,533,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641082193.83/warc/CC-MAIN-20240813172835-20240813202835-00674.warc.gz
| 304,373,350
| 48,666
|
0
# 16 miles in 82 minutes is what mph?
Updated: 4/28/2022
Wiki User
14y ago
1 hour = 60 minutes.
So 16 miles in 82 minutes = 60*16/82 = 11.71 mph
Wiki User
14y ago
| 67
| 172
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.96875
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.834051
|
https://graphscope.io/docs/reference/networkx/generated/graphscope.nx.generators.degree_seq.random_degree_sequence_graph.html
| 1,659,999,127,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-33/segments/1659882570879.1/warc/CC-MAIN-20220808213349-20220809003349-00612.warc.gz
| 286,399,352
| 5,341
|
# graphscope.nx.generators.degree_seq.random_degree_sequence_graph
graphscope.nx.generators.degree_seq.random_degree_sequence_graph(sequence, seed=None, tries=10)[source]
Returns a simple random graph with the given degree sequence.
If the maximum degree \$d_m\$ in the sequence is \$O(m^{1/4})\$ then the algorithm produces almost uniform random graphs in \$O(m d_m)\$ time where \$m\$ is the number of edges.
Parameters
• sequence (list of integers) – Sequence of degrees
• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
• tries (int, optional) – Maximum number of tries to create a graph
Returns
G – A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in the sequence.
Return type
Graph
Raises
• NetworkXUnfeasible – If the degree sequence is not graphical.
• NetworkXError – If a graph is not produced in specified number of tries
`is_graphical`, `configuration_model`
Notes
The generator algorithm 1 is not guaranteed to produce a graph.
References
1
Moshen Bayati, Jeong Han Kim, and Amin Saberi, A sequential algorithm for generating random graphs. Algorithmica, Volume 58, Number 4, 860-910, DOI: 10.1007/s00453-009-9340-1
Examples
```>>> sequence = [1, 2, 2, 3]
>>> G = nx.random_degree_sequence_graph(sequence, seed=42)
>>> sorted(d for n, d in G.degree())
[1, 2, 2, 3]
```
| 367
| 1,436
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.671875
| 3
|
CC-MAIN-2022-33
|
latest
|
en
| 0.745036
|
https://forum.arduino.cc/t/how-to-set-19-5hz-pwm-frequency/126798
| 1,653,828,801,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662644142.66/warc/CC-MAIN-20220529103854-20220529133854-00461.warc.gz
| 328,841,530
| 6,164
|
How to set 19.5Hz PWM frequency?
Hi there,
I am trying to control some solenoids and the pwm frequency has to be 19.5Hz!!! I have searched the forum and the tables say that the minimum frequency that i can set is around 30Hz. I have an arduino UNO board and i only need one output!
Set up a timer that interrupts at your duty cycle (say 500us). Once that timer trips, set it up for another interrupt for 51582us-500us. This provides a total period of 51582us -> 19.5hz.
On a resource rich system, you can implement a two-timer solution, with one setting the pin and another clearing it.
psyche: I am trying to control some solenoids and the pwm frequency has to be 19.5Hz!!!
At that low of a frequency you could just use blink-without-delay.
psyche: I am trying to control some solenoids and the pwm frequency has to be 19.5Hz!!!
That seems a very odd requirement. Are you quite sure it has to be exactly 19.5Hz, rather than at least 19.5Hz? Can you provide a link to the solenoid datasheet?
Although timer/counters 0 and 2 are limited to approximately 30Hz and above on a standard 16MHz Arduino, you should be able to get a single 19.5Hz PWM signal from TC1. Set the prescaler to 64, register OCR1A to 6409, and OCR1B to 0-6409 to get the required on/off ratio. That will give you a frequency of 16000000/(64*(6409+1)*2) = 19.5008Hz.
psyche: I am trying to control some solenoids and the pwm frequency has to be 19.5Hz!!!
That is sloooow. You can use as dumb an algorithm to control that as you want. It barely needs more than the Blink example, as long as you are not careless calculating the transition times.
You can do it with a hardware timer, but the last time someone wanted such a slow PWM frequency they were trying to change traffic lights from red to green on-the-fly. I don’t suppose this is anything to do with that?
Hehehehe! Nick what i want to do is control a solenoid from a car! People have reported the 19.5Hz frequency to be the correct one to control it! I haven't measured the output of the car's ECU but if everyone says that the frequency is 19.5Hz then this is it!
Any code examples to get an idea? Or a guide?
If i change the pwm frequency in this sketch, will i have to change it if i build a new sketch? Do i have to set it back to default?
Thanx guys
1000000 / 19.5 = 51282.0512821 microseconds. Let's call it 51282. I doubt the extra precision is going to matter with a solenoid.
This might work...
``````const uint8_t SOLENOID_PIN = 13;
const unsigned long PulseWidth = 51282UL;
static unsigned long CurrentHighWidth;
void setup( void 0
{
pinMode( SOLENOID_PIN, OUTPUT );
CurrentHighWidth = (PulseWidth / 2) /* some fraction of PulseWidth */;
}
void loop( void )
{
unsigned long Now;
Now = micros();
if ( Now - PreviousLeadingEdge >= PulseWidth )
{
digitalWrite( SOLENOID_PIN, HIGH );
| 760
| 2,841
|
{"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-2022-21
|
latest
|
en
| 0.954914
|
http://wilydubudifejumig.billsimas.com/teacher-made-students-write-arabic-numbers-3299932999.html
| 1,542,247,488,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-47/segments/1542039742338.13/warc/CC-MAIN-20181115013218-20181115035218-00187.warc.gz
| 362,263,637
| 5,111
|
# Teacher made students write arabic numbers
If your students are struggling with certain numbers, feel free to also write the numeral on the board but be sure to say it first. Continuously, several students teacher made students write arabic numbers first language is Arabic write endless sentences with no periods and infinite commas! Smaller classes can engage in play-acting and dialogues in a way that larger classes can not.
When you say a word aloud, the student whose turn it is should run to the board and write the numeral. Secondly, I will discuss the main differences between reading in L1 and L2.
Teach them to yourself now before you go on. Have each student choose and write in symbols a number from eleven to nineteen and take that many sticks.
Likewise, the transition from a non-alphabetic system e. Some erroneously think that learning Arabic means converting to Islam. When you call out a number, the first student to say and smack the appropriate card gets to keep it.
Taking a middle stance on the issue, they believe that while some strategies can be taught, others e. The next section moves to a more specific account of the major challenges, problems, and issues faced by Arabic-speaking students by virtue of their L1.
If the tens frames and word card match they keep the matching pair and the winner is the student with the most pairs. Then look at the Arabic answers. Many students tend to literally translate from their first language to English. Students should record with pictures, words and an equation what they did and what their result is.
Understand that in a teen number the 1 represents one group of ten Activity 1 Have students sit with a partner. This is a good opportunity for them to practice letter and word spacing.
A group activity will get your students on their feet. Write the numbers 11 — 19 in symbols and words on chart paper, highlighting the inconsistencies of the language and exploring for fun alternative forms of some of the teen numbers, for example, eleven oneteentwelve twoteenthirteen threeteenfifteen fiveteen.
Generally, the more distant the writing system in L1, the less smooth the transition to reading in L2 is, regardless of how many strategies are used previously Bassetti, Have them fill in the grid with letters and then say letters at random until one or more students have gotten bingo. How many beans are left to plant in the second row?
The three stages of a holistic reading approach as modeled on Swaffar and Arens Model one more example then have the students individually draw and write about three of their favourite teen numbers. For example, the root KTB which has the basic meaning of write can be combined with different patterns of vowels to give, among other words, kataba he wroteyaktubu he writeskitab bookmaktab officeand maktaba library.
Words like teacher, student, book, pencil, and desk would all be appropriate. Introduce students to plastic beans and containers. Depending on the writing system of the L1, there seems to be a permanent effect on the reading habits of the individual, impacting several variables including reading fluency, word recognition, and language processing.
Session 4 Understand and apply a ten for one exchange. Students may be confused or hesitant due to lack of understanding but will often be unwilling or unable to ask for help.
Recognise and record words and symbols for teen numbers. Plus, the teacher should give them solutions to over come this problem out like adding periods then starting new sentences and using connectors.
The question then becomes:How to Teach Numbers. some new vocabulary so choose words that will be used often in your classroom and words where the plural form is made by simply adding -s. Words like teacher the student whose turn it is should run to the board and write the numeral. If your students do very well, tell them they have to spell out the word and maybe.
Arabic Numbers. 27 comments. So if you want to be able to read the numbers correctly (and write them correctly), you need to be familiar with the material below. Furthermore, since you may not know any colloquial Arabic, you will need the rules and pronunciation from the standard when you wish to use numbers in speech.
Some students of. Lina Gomaa is a language instructor having taught Arabic to students at Beloit College in Wisconsin and English to students at Misr International University in Cairo. She holds a BA in Creative Writing from Beloit College and obtained a BA in Arabic-English Translation and English Literature from Ain Shams University, Cairo.
1. A different alphabet makes reading and writing difficult. As Arabic is written from right to left, English looks backwards to Arabic speakers, meaning they can find course books overwhelming.
Adults, in particular, may be slower in the initial stages of studying English than learners whose first language uses the same alphabet as English. We offer Arabic Worksheets, Books, Videos, Songs and Software. Find this Pin and more on Arabic Resources by Raki's Rad Language Resources.
Write the number after Find this Pin and more on Arabic Numbers Worksheets by Arabic Worksheets. Daughter Teaching Students Products Arabic Lessons Learning Arabic Arabic Language Image Bingo Cards.
Find this Pin and more on Arabic & numbers: Teaching kids by mona rajab. For Parents: 7 Things You Should Be Doing as You’re Reading to Your Child 7 helpful tips for reading to your child.
I especially like the last one, "really enjoy the book with your child." I'm forever grateful that my mom read to .
Teacher made students write arabic numbers
Rated 5/5 based on 60 review
| 1,144
| 5,669
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2018-47
|
longest
|
en
| 0.944852
|
https://math.answers.com/Q/Convert_240_square_yard_in_square_feet
| 1,708,862,520,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474595.59/warc/CC-MAIN-20240225103506-20240225133506-00893.warc.gz
| 378,582,744
| 46,863
|
0
# Convert 240 square yard in square feet?
Updated: 12/17/2022
Shivashish
Lvl 1
15y ago
9 cubic feet = 1 cubic yard.
Therefore: 240 cubic yards = 9*240 cubic feet = 2160 cubic feet.
Wiki User
15y ago
| 72
| 208
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.828125
| 3
|
CC-MAIN-2024-10
|
latest
|
en
| 0.771574
|
https://wwwmpa.mpa-garching.mpg.de/gadget/gadget-list/0551.html
| 1,670,526,356,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446711360.27/warc/CC-MAIN-20221208183130-20221208213130-00758.warc.gz
| 1,119,686,901
| 3,564
|
# <A timestep of size zero was assigned on the integer timeline!> Checked smoothing lengths are non-zero
From: DIXON J.B. <jonathan.dixon_at_durham.ac.uk>
Date: Mon, 7 Jan 2013 09:56:59 -0000
All,
I am having a problem I hope you can help me with..
I'm running a basic simulation of a disc galaxy forming with 100,000 particles and getting the following error:
Begin Step 0, Time: 0, Systemstep: 0
domain decomposition...
NTopleaves= 344
domain decomposition done.
begin Peano-Hilbert order...
Peano-Hilbert done.
Start force computation...
Tree construction.
Tree construction done.
Begin tree force.
tree is done.
Begin tree force.
tree is done.
Start density computation...
ThisTask=0: Need to do a second neighbour loop for (0.0514353|-0.225033|-0.00548556) hsml=0.7 no=36679
ThisTask=0: Need to do a second neighbour loop for (0.0486755|-0.226033|-0.00132951) hsml=0.7 no=36725
ThisTask=0: Need to do a second neighbour loop for (0.0443219|-0.230982|-0.00975273) hsml=0.7 no=36717
ThisTask=0: Need to do a second neighbour loop for (0.0387366|-0.238146|-0.00368765) hsml=0.7 no=36659
ThisTask=0: Need to do a second neighbour loop for (0.0436788|-0.238358|-0.00278879) hsml=0.7 no=97435
.
.
. (Lots more output here)
.
ThisTask=0: Need to do a second neighbour loop in hydro-force for (0.0421819|-0.239535|0.00401269) hsml=0.7 no=90617
ThisTask=0: Need to do a second neighbour loop in hydro-force for (0.0457042|-0.226046|0.000454599) hsml=0.7 no=25608
ThisTask=0: Need to do a second neighbour loop in hydro-force for (0.0457325|-0.229131|0.00956516) hsml=0.7 no=25610
force computation done.
Error: A timestep of size zero was assigned on the integer timeline!
We better stop.
Task=1 Part-ID=54529 dt=9.09641e-09 tibase=1.86265e-08 ti_step=0 ac=6.04269e+14 xyz=(0.101498|-2.55188|-0.00968288) tree=(-2.53342e+13|6.0373e+142.9378e+12)
hydro-frc=(-197733|59003.1|-17028.6)
task 1: endrun called with an error level of 818
Error: A timestep of size zero was assigned on the integer timeline!
We better stop.
Task=0 Part-ID=1050 dt=1.62322e-08 tibase=1.86265e-08 ti_step=0 ac=1.89764e+14 xyz=(-0.269647|-4.84833|-0.00568618) tree=(1.03536e+13|1.89481e+142.57818e+11)
hydro-frc=(-13511.4|4029.45|-121.305)
task 0: endrun called with an error level of 818
--------------------------------------------------------------------------
MPI_ABORT was invoked on rank 0 in communicator MPI_COMM_WORLD
with errorcode 818.
I have had a look at some previous entries to this list and they suggest checking that the smoothing lengths are all non-zero: this I have done and all the relevant smoothing lengths are indeed non-zero.
Any help much appreciated! All the best,
Jono
| 873
| 2,678
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.515625
| 3
|
CC-MAIN-2022-49
|
longest
|
en
| 0.736972
|
http://www.codeproject.com/script/Answers/List.aspx?tab=active&tags=960&pgnum=8
| 1,454,801,624,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-07/segments/1454701148402.62/warc/CC-MAIN-20160205193908-00250-ip-10-236-182-209.ec2.internal.warc.gz
| 341,887,272
| 16,657
|
12,064,498 members (47,368 online)
# Algorithms Questions
13-Oct-13 7:28am - updated 13-Oct-13 10:50am
, +
### Divide students in groups based on preferences
29-Sep-13 1:00am - updated 29-Sep-13 1:31am
### Logarithmic scaling algo by x, not y
26-Sep-13 5:37am - updated 26-Sep-13 15:12pm
### How to improve this RemoveAt
26-Sep-13 2:00am - updated 26-Sep-13 3:13am
### What Algorithm is used to tile Mdi Forms in c#'s LayoutMdi(MdiLayout.TileVertical)
22-Sep-13 11:23am - updated 22-Sep-13 17:14pm
17-Sep-13 6:17am - updated 17-Sep-13 6:27am
### Robust Point Matching Algorithm Implementation
15-Sep-13 18:29pm
### Algorithm for random polygon generation
10-Sep-13 20:27pm - updated 11-Sep-13 9:44am
### I need a simple and working algorithm for finding out the squareroot of a number (preferably a 4 digit number)
27-Jul-13 20:08pm - updated 28-Jul-13 21:14pm
### how to convert Computer Calender To Hijri Calender in JAVA
16-Jul-13 7:35am - updated 16-Jul-13 8:36am
### How to make an Android Ocr a[pp? Please
12-Jul-13 13:22pm
30-Jun-13 6:00am
### Path finding algorithm to maximise points of interest along the route
22-Jun-13 23:43pm - updated 23-Jun-13 21:40pm
### Algoritm for checking one gate's output to be stuck-at-1 or stuck-at-0?
22-Jun-13 15:57pm - updated 22-Jun-13 20:59pm
### Sort large Unicode textfile
19-Jun-13 5:51am - updated 19-Jun-13 6:45am
### using BFS and DFS to GENERATE graph
17-Jun-13 13:48pm - updated 17-Jun-13 13:56pm
### maximum flow , Ford_Fulkerson
6-Jun-13 9:54am - updated 6-Jun-13 10:05am
23-May-13 0:49am
### Finding cycle in 2 dimensional array
11-May-13 8:21am - updated 11-May-13 13:14pm
### I want to make static lib in Microsoft Visual C++ with External headers and sources files
1-May-13 7:37am
Page 8 of 19
To narrow down your search try filtering by tags using the Filter box at the top right.
| 637
| 1,879
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.703125
| 3
|
CC-MAIN-2016-07
|
latest
|
en
| 0.623937
|
https://papers-gamma.link/paper/60/Representation%20Learning%20on%20Graphs:%20Methods%20and%20Applications
| 1,709,467,128,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947476374.40/warc/CC-MAIN-20240303111005-20240303141005-00721.warc.gz
| 434,044,915
| 9,267
|
Uploaded by: Maximimi
Upload date: 2018-05-28 17:47:21
Comments:
## Great overview of graph embedding methods ### The encoder, decoder and loss function formalism is very well designed! ### Similarity matrix: In Table 1, maybe there are methods dedicated to the case where the similarity matrix is required to be a positive semidefinite (SDP) matrix. Indeed, (i) there are plenty of such relevant SDP matrices (such as "$D+A$", "$A*A$" or "the cosine similarity" which are all SDP) and (ii) the optimal embedding minimizing the L2 loss function is easy to find using the eigenvectors associated with the largest eigenvalues. It thus makes this kind of method very handy. This kind of [kernel PCA](https://en.wikipedia.org/wiki/Kernel_principal_component_analysis)-like method does not work if the similarity matrix (somehow the kernel here) is not SDP. ### Shallow embedding VS autoencoder-based embedding: Limitations of "shallow embedding methods" are highlighted on page 9 and it seems that autoencoder-based methods answer some of them. But this part is not totally clear to me. From what I understand, the major difference between the two kinds of methods is that: - for the methods referred to as "shallow embedding methods", if you want to reconstruct the entry $s(i,j)$ of the input similarity matrix, then you need the learned feature vectors of both nodes $i$ and $j$ and then the reconstruction of $s(i,j)$ is often simple, e.g. the scalar product between the two feature vectors (cf. equation (5)) or sometimes a softmax (cf. equation (10)) is added on top of the scalar product; - while in the case of autoencoder-based embedding methods, you only need the learned feature vector of a single node $i$ to reconstruct the full column $s_i$ of the input similarity matrix and the reconstruction is more elaborated. We can notice that no parameters are shared between nodes in the decoder for the shallow methods, while some parameters can be shared in the case of autoencoder-based methods. There thus can be fewer parameters in autoencoder-based methods and thus it could be in principle faster and have some regularisation. In addition, if a previously unseen node arrives, an autoencoder-based method could in principle still give a feature vector for that node, while it does not seem to be the case for shallow methods (they are referred to as "inherently transductive" methods). "Shallow embedding also fails to leverage node attributes during encoding". I think that it is possible to adapt both shallow methods and autoencoder-based methods to take into account this additional information on node attributes. I didn't get this point. As noted in the survey, it seems that current autoencoder-based methods (SDNE and DNGR) are not scalable and are inherently transductive: "the input dimension to the autoencoder is fixed at $|V|$, which can be extremely costly and even intractable for graphs with millions of nodes. In addition, the structure and size of the autoencoder is fixed, so SDNE and DNGR are strictly transductive and cannot cope with evolving graphs, nor can they generalize across graphs." The scalability issue has also been noted in [VERSE](https://papers-gamma.link/paper/48/): "Works such as [12, 48] investigate deep learning approaches for graph embeddings. Their results amount to complex models that require elaborate parameter tuning and computationally expensive optimization, leading to time and space complexities unsuitable for large graph" where [12] and [48] are SDNE and DNGR. ### Neighborhood aggregation and convolutional encoders: This part seems important. In particular, Algorithm 1 seems important as it is referred to in subsequent parts. However, I found this section very hard to understand. ### Incorporating task-specific supervision: Even though this section is short, I find it very interesting. ### Typos: - "they found the the more complex aggregators" - In equation (24) $h_j^{k-1}$ - End of page 20. What is $\Epsilon$ in $O(|\Epsilon|)$? - "(e.g. , using..." - "[8] J. Bruna, W. Zaremba, and Y. Szlam, A.and LeCun. Spectral networks and locally connected networks on graphs..."
Maximimi at 2018-05-29 18:46:15
Edited by Maximimi at 2018-05-30 15:37:52
| 958
| 4,219
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.75
| 3
|
CC-MAIN-2024-10
|
latest
|
en
| 0.888079
|
https://www.mecharithm.com/dynamics-and-control-of-a-quadrotor/
| 1,652,752,079,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662515466.5/warc/CC-MAIN-20220516235937-20220517025937-00758.warc.gz
| 1,049,391,560
| 31,802
|
Blog Post
# Implementing Dynamics and Control of a Quadrotor in MATLAB
In this post, we will implement the dynamics and control of a quadrotor in MATLAB and Simulink. Stabilizing and tracking controllers are simulated and implemented on Quadcopter. A square trajectory is specified for the tracking controller.
The reference of the simulation equations is the paper “Modeling and control of quadcopter” by Teppo Luukkonen. You can download the paper HERE! It has a table of values that we will use for the simulation.
The objective is to implement a simulation of the quadcopter dynamics by implementing the equations of motion given in the paper. We will then:
a) Implement the stabilizing controller using the gains given in the paper.
b) Implement a controller to follow a square trajectory with the body-fixed x-axis aligned with the direction of travel.
The following stabilizing controller and tracking controller are implemented in Simulink:
The main program to get the outputs for stabilizing controller and tracking controller for the quadcopter is as follows:
%the main program
clc
clear
close all
% parameters of the system
g = 9.81; % gravity constant m/s^2
m = 0.468; % mass of helicopter kg
l = 0.225; % distance between a rotor and the center of quadcopter (m)
k = 2.98e-6; % lift constant
b = 1.14e-7; % drag constant
I_M = 3.357e-5; % rotational moment of inertia kg.m^2
% drag force coefficients
A_x = 0.25; % kg/s
A_y = 0.25;
A_z = 0.25;
% inertia matrix
I_xx = 4.856e-3; %kgm^2
I_yy = 4.856e-3;
I_zz = 8.801e-3;
% parameters of the PD controller
KpT = 3.5;
KdT = 4.5;
KpR = 1;
KdR = 3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% simulation parameters
T_f = 0.01; % simulation interval
% AT = 1e-6; % absolute tolerance
% RT = 1e-6; % relative tolerance
% RF = 4; % Refine factor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% start simulation
figure
h1 = plot(Time, x, 'b', 'linewidth',2);
hold on
h2 = plot(Time, y, 'r', 'linewidth',2, 'LineStyle', '--');
h3 = plot(Time, z, 'g', 'linewidth',2, 'LineStyle', '-.');
legend([h1 h2 h3], 'x', 'y', 'z')
grid on
xlabel('Time (sec.)');
figure
h1 = plot(Time, phi, 'b', 'linewidth',2);
hold on
h2 = plot(Time, theta, 'r', 'linewidth',2, 'LineStyle', '--');
h3 = plot(Time, psi, 'g', 'linewidth',2, 'LineStyle', '-.');
legend([h1 h2 h3], '\phi', '\theta', '\psi')
grid on
xlabel('Time (sec.)');
%%
% figure
% plot3(xd,yd,1*ones(length(xd)), 'b', 'linewidth', 2);
% hold on
% plot3(x,y,1*ones(length(x)), 'r', 'linewidth',2);
% xlabel('x')
% ylabel('y')
% zlabel('z')
% grid on
figure
h1 = plot(xd, yd, 'b', 'linewidth',2);
hold on
h2 = plot(x, y, 'r', 'linewidth', 2, 'LineStyle', '--');
legend([h1 h2], 'Desired trajectory', 'Quadrotor trajectory', 'Location', 'best')
axis([-1 11 -1 11])
grid on
xlabel('x');
ylabel('y');
By running this code we will get the following results for stabilizing controller, and tracking controller of the quadcopter as follows:
You can see the other posts on Mechatronics and Robotics in the link below:
https://www.mecharithm.com/category/learning-robotics-mechatronics/
If you enjoyed this post, please consider contributing to help us with our mission to make robotics and mechatronics available for everyone. We deeply thank you for your generous contribution!
Be sure to let us know your thoughts and questions about this post, as well as the other posts on the website. You can either contact us through the βContactβ tab on the website or email us at support[at]mecharithm.com.
Send us your work/ research on Robotics and Mechatronics to have a chance to get featured in Mecharithm’s Robotics News/ Learning.
Follow Mecharithm in the following social media too:
| 1,053
| 3,687
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.09375
| 3
|
CC-MAIN-2022-21
|
longest
|
en
| 0.754462
|
https://brainmass.com/math/linear-algebra/linear-algebra-wronskian-16068
| 1,718,447,115,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198861586.40/warc/CC-MAIN-20240615093342-20240615123342-00277.warc.gz
| 132,683,311
| 6,716
|
Purchase Solution
# Linear Algebra : Wronskian
Not what you're looking for?
Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: x^2 - x, x^2 + x, x^2, all x
##### Solution Summary
The Wronskian is computed for a set of functions. Linear dependence is determined.
##### Solution Preview
We need to find the Wronskian= ...
##### Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
##### Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
##### Probability Quiz
Some questions on probability
##### Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
| 184
| 887
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.546875
| 3
|
CC-MAIN-2024-26
|
latest
|
en
| 0.769903
|
https://socratic.org/questions/is-5-7-a-rational-irrational-number-natural-whole-or-integer
| 1,579,286,736,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-05/segments/1579250590107.3/warc/CC-MAIN-20200117180950-20200117204950-00001.warc.gz
| 679,157,707
| 5,982
|
Is 5/7 a rational, irrational number, natural, whole or integer?
$\frac{5}{7} = 0 , \textcolor{b l u e}{714285} 714285714285714285. \ldots$
the block: $\textcolor{b l u e}{714285}$ repets itself forever!!!
| 73
| 206
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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}
| 2.5625
| 3
|
CC-MAIN-2020-05
|
longest
|
en
| 0.365491
|
http://www.livingmath.net/Reviews/Reviews-TeenPre-Teen/Planiverse/tabid/1083/Default.aspx
| 1,495,989,405,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-22/segments/1495463610342.84/warc/CC-MAIN-20170528162023-20170528182023-00007.warc.gz
| 694,965,081
| 12,925
|
## Planiverse
Review of The Planiverse by A. K. Dewdney
The Planiverse: Computer Contact with a Two-Dimensional World by A. K. Dewdney. Review by Troy, age 12.
The Planiverse is about computer contact with a 2 dimensional (2D) world. It all starts when a lab professor creates a program called 2DWORLD that simulates a 2D world. His students, while running and modifying the program, discover that they have created a link to a 2D world that is inhabited by strange creatures called Nsana. They spend several months studying a certain Nsana called Yndrd ("Yendred"). They learn many things about what could happen in a 2D world such as magnetism, chemistry, astronomy and even religion. After following Yendred for one month, disaster strikes - they must work at night because the populace of the university thinks that a 2D world could invade theirs and the link is dangerous.
The story is told so creatively you could think it is real. The artist's drawings help you picture things that might be impossible otherwise. There's an action sequence where there's this thing that can fly in the air, by trapping air pockets underneath its body, and it falls on top of Yendred and his traveling buddy, kills his traveling buddy, but Yendred takes a bottle of "hrabx" (2D helium) and fills the monster's stomach with it so that it explodes. Yendred then goes on with a wounded hand and gets rescued by an elderly Nsana couple. They nurse him back to health and send him on his way. He then meets a Nsana that can transcend into the 3rd dimension, and adapts his religion. The link then breaks up because Yendred wishes it to. Meanwhile word gets out and the students and professor get a lot of publicity.
I recommend the book for ages 9 to adults because it uses some scientific language and has some intense action sequences. I rate it 9 out of 10 because there are some boring spots, but overall it is extremely interesting.
Reviewed 5/25/04 Also see reviews at http://math.cofc.edu
A Gebra Named Al Planiverse Marvels of Math Haven
| 471
| 2,039
|
{"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-2017-22
|
longest
|
en
| 0.95921
|
https://math.stackexchange.com/questions/2753210/when-can-we-say-that-a-mathrm-t-b-b-mathrm-t-a
| 1,721,512,813,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763517541.97/warc/CC-MAIN-20240720205244-20240720235244-00528.warc.gz
| 347,241,521
| 37,302
|
# When can we say that $A^{\mathrm T} B = B^{\mathrm T} A$?
I was looking at the derivation of the normal equation from here.
Now, the author has used the fact that $$A^{\mathrm T} B = B^{\mathrm T} A$$ to reach the step shown in the below image. Can anyone provide some information like, when is it true, or how we can prove it?
$$J(\theta) = ((X\theta)^{\mathrm T} -y^{\mathrm T})(X\theta -y)$$ $$J(\theta) = (X\theta)^{\mathrm T} X\theta -\color{blue}{(X\theta)^{\mathrm T} y \color{black}{-} y^{\mathrm T} (X\theta)} +y^{\mathrm T} y$$ Note that $$X\theta$$ is a vector, and so is $$y$$. So when we multiply one by another, it doesn't matter what the order is (as long as the dimensions work out). So we can further simplify: $$J(\theta) = \theta^{\mathrm T} X^{\mathrm T} X \theta -\color{blue}{2(X\theta)^{\mathrm T} y} +y^{\mathrm T} y$$
• $(AB)^T=B^TA^T$ Commented Apr 25, 2018 at 13:51
Note that $(A^{\rm T} B)^{\rm T} = B^{\rm T} (A^{\rm T})^{\rm T} = B^{\rm T} A$, so if you are constraining $A^{\rm T} B = B^{\rm T} A$, that implies $(A^{\rm T} B)^{\rm T} = A^{\rm T} B$, meanining $A^{\rm T} B$ is symmetric.
• Got the symmetric part...So does it mean that $(X\theta)^Ty$ will always be a symmetric matrix?...how to prove that w.r.t normal equation derivation? Commented Apr 25, 2018 at 14:30
• Is $X$ a matrix and both $\theta$ and $y$ are column vectors? If so, then $(X\theta)^{\rm T} y$ will always be symmetric because $X\theta$ is a vector and $(X\theta)^{\rm T} y$ is a scalar (a $1\times 1$ matrix), and scalars are always symmetric. Commented Apr 25, 2018 at 14:35
Let's call $$C=AB$$ Then we have that $$C_{ij}=A_{ik}B_{kj}$$ We know that $$(M^T)_{ab}=M_{ba}$$ So we have that: $$(C^T)_{ij}=C_{ji}$$ $$(C^T)_{ij}=A_{jk}B_{ki}$$ $$(C^T)_{ij}=B_{ki}A_{jk}$$ $$(C^T)_{ij}=(B^T)_{ik}(A^T)_{kj}$$ And finally: $$C^T=B^TA^T$$ $$(AB)^T=B^TA^T$$
| 706
| 1,867
|
{"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": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.125
| 4
|
CC-MAIN-2024-30
|
latest
|
en
| 0.684414
|
http://www.coursehero.com/file/1298866/MasterPhysics-8-soln/
| 1,412,187,621,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-41/segments/1412037663551.47/warc/CC-MAIN-20140930004103-00285-ip-10-234-18-248.ec2.internal.warc.gz
| 505,679,748
| 15,528
|
This preview has intentionally blurred parts. Sign up to view the full document
View Full Document
Unformatted Document Excerpt
PHYS-408 Fall 2008 Mastering Physics Assignment #8 Solutions Problem 26.35 Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released, they begin to accelerate at 150 m/s 2 . (a) What is the magnitude of the charge on each sphere? From the acceleration, we can find the force r F = m r a F = 0.001 kg ( ) 150 m / s 2 ( ) = 0.150 N This must equal the electrostatic force F = 1 4 q 1 q 2 r 2 = 1 4 q 2 r 2 q 2 = 4 r 2 F = 4 8.85 10 12 C 2 / Nm 2 ( ) 0.02 m ( ) 2 0.150 N ( ) = 6.67 10 15 C 2 q = 6.67 10 15 C 2 = 8.17 10 8 C = 81.7 nC Problem 26.17 (a) What is the magnitude of the net electric force on charge A in the figure? The charge A is repelled by B with a magnitude F 1 = 1 4 q 1 q 2 r 2 = 8.99 10 9 Nm 2 / C 2 ( ) 1.0 10 9 C 2.0 10 9 C 0.02 m ( ) 2 = 4.50 10 5 N The charge A is attracted by C with a magnitude F 2 = 1 4 q 1 q 2 r 2 = 8.99 10 9 Nm 2 / C 2 ( ) 1.0 10 9 C 2.0 10 9 C 0.03 m ( ) 2 = 2.00 10 5 N So, F = F 1 F 2 = 4.50 10 5 N 2.00 10 5 N = 2.5 10 5 N (b) What is the direction of the net electric force on charge A in the figure?What is the direction of the net electric force on charge A in the figure?... View Full Document
End of Preview
| 528
| 1,312
|
{"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}
| 3.875
| 4
|
CC-MAIN-2014-41
|
latest
|
en
| 0.811336
|
https://gmatclub.com/forum/if-ab-is-not-equal-to-ab-is-a-b-1-a-b-3-2-a-2-b-278848.html
| 1,571,285,284,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570986672548.33/warc/CC-MAIN-20191017022259-20191017045759-00373.warc.gz
| 512,579,738
| 142,701
|
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 16 Oct 2019, 21:08
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# If |ab| is not equal to ab, is a > b ? (1) |a| > b^3 (2) a^2 < b
Author Message
TAGS:
### Hide Tags
Director
Joined: 02 Oct 2017
Posts: 720
If |ab| is not equal to ab, is a > b ? (1) |a| > b^3 (2) a^2 < b [#permalink]
### Show Tags
Updated on: 12 Oct 2018, 06:33
3
00:00
Difficulty:
45% (medium)
Question Stats:
67% (01:55) correct 33% (01:48) wrong based on 103 sessions
### HideShow timer Statistics
If |ab| is not equal to ab, is a > b ?
(1) |a| > b^3
(2) a^2 < b
_________________
Give kudos if you like the post
Originally posted by push12345 on 12 Oct 2018, 06:26.
Last edited by Bunuel on 12 Oct 2018, 06:33, edited 1 time in total.
Renamed the topic and edited the question.
Director
Joined: 19 Oct 2013
Posts: 518
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If |ab| is not equal to ab, is a > b ? (1) |a| > b^3 (2) a^2 < b [#permalink]
### Show Tags
12 Oct 2018, 11:34
push12345 wrote:
If |ab| is not equal to ab, is a > b ?
(1) |a| > b^3
(2) a^2 < b
From the question stem |ab| does not equal ab means a or b is minus.
Try a = 2 and b = -1
a > b yes
Try a = -2 and b = 1
a > b no.
Insufficient.
Statement 2)
a^2 < b
This means b is positive.
a > b no.
Posted from my mobile device
Re: If |ab| is not equal to ab, is a > b ? (1) |a| > b^3 (2) a^2 < b [#permalink] 12 Oct 2018, 11:34
Display posts from previous: Sort by
| 660
| 1,965
|
{"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}
| 3.703125
| 4
|
CC-MAIN-2019-43
|
latest
|
en
| 0.851027
|
https://powerclues.com/does-a-circuit-need-a-battery-to-work/
| 1,702,155,109,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100972.58/warc/CC-MAIN-20231209202131-20231209232131-00486.warc.gz
| 527,722,378
| 25,121
|
# Does a Circuit Need a Battery to Work? (What is a Battery in a Circuit)
Published on: January 2, 2023
Written by Nolan Miles / Fact-checked by Porimol Sorkar
A battery is not necessary for a circuit to work. A circuit is created when there is a complete path for electrons to flow from one point to another. When you connect a power source, such as a battery, to two points in a circuit, it provides the electrons with the potential energy they need to flow from one point to the other.
The battery creates a difference in voltage between the two points, and this voltage difference is what gives the electrons the push they need to flow through the wires and create an electric current.
A circuit needs a battery to work because the battery provides the power needed to make the circuit work. Without a battery, the circuit would not be able to function.
## How Does a Battery Work in a Circuit?
In a circuit, there are three main components: the power source (battery), the load (light bulb), and the wires connecting them. The battery provides the energy to flow through the load and create light. The load resistance determines how much current flows through it.
The wire connects the two together and allows current to flow from one point to another. The battery has two terminals, positive and negative. The positive terminal is connected to the load and the negative terminal is connected to the ground.
When you connect the battery to a circuit, electrons flow from the negative terminal of the battery through your wires to the positive terminal of the battery. This creates a loop or circuit that electrons can travel in. As electrons travel through the wire they bump into atoms which makes them slow down.
This happens because electrons are negatively charged and atoms are positively charged so they attract each other. The more collisions an electron has with atoms, the slower it will go. When an electron bumps into an atom it also causes that atom to vibrate which we feel as heat!
## What is a Battery in a Circuit?
A battery is an electrical device that provides power to a circuit. It consists of one or more cells that convert chemical energy into electrical energy. Each cell has two terminals, positive and negative, that are connected to the load.
The load may be a light bulb (the most common type of light bulb is the incandescent light bulb), a resistor, or another device that uses electrical energy. The cell produces a voltage difference between its terminals. This voltage difference is caused by the chemical reaction that takes place inside the cell when it is in use.
The voltage difference drives a current through the circuit. The current flows from the positive terminal to the negative terminal of the cell. As the current flows through the circuit, it does work on devices in the circuit.
For example, if the circuit includes a light bulb, the current flowing through the light bulb will cause it to emit light. The size of the voltage produced by a cell depends on its type. The most common types of cells used in batteries are lead-acid cells and lithium-ion cells.
## How Does Battery Work?
Batteries are one of the most common devices in our lives—they power everything from our cell phones to our cars. But how do they work? A battery is made up of two electrodes, separated by an electrolyte.
The electrodes are made of different materials, which makes them chemically incompatible. When the battery is connected to a circuit, electrons flow from the negative electrode to the positive electrode through the electrolyte. This creates a current that can be used to power devices.
The chemical reaction that powers the battery also produces heat and waste products like water and carbon dioxide. Eventually, the electrodes will degrade and the battery will no longer be able to hold a charge.
## How Does a Rechargeable Battery Work?
A rechargeable battery is a type of battery that can be reused multiple times. These batteries are made with materials that allow them to be charged again and again. Rechargeable batteries are found in many common devices, such as cell phones, laptops, and digital cameras.
How do rechargeable batteries work? Charging a rechargeable battery is similar to charging a cell phone or laptop—it’s all about electrical current. When you plug your device into the wall socket, an electrical current flows from the outlet through the cord and into your device.
This flow of electricity charges up the cells inside the battery. The charging process reverses when you use your device. As you operate your electronics, the electrical current flows from the battery out through the cord and back into whatever it is you’re using (say, your laptop).
This depletes the energy stored in the cells and eventually causes your device to shut off or die until it can be recharged again. Rechargeable batteries are becoming increasingly popular as people look for ways to save money and reduce their environmental impact.
## How Do Lithium Batteries Work?
Lithium batteries are a type of battery that uses lithium metal as an anode. Lithium batteries have a higher energy density than other types of batteries, making them ideal for use in computer applications where weight and size are important considerations. The way lithium batteries work is by using the electrolyte to allow electrons to flow between the electrodes, creating a current.
The amount of current that can be generated is determined by the number of lithium ions present in the electrolyte. When the battery is discharged, the lithium ions flow back into the anode, where they are stored until the battery is recharged again. One advantage of lithium batteries over other types of batteries is that they have a higher power density, meaning they can generate more power per unit volume.
This makes them ideal for use in portable electronic devices such as laptops and cell phones, where space is limited. Lithium batteries also have a longer lifespan than other types of batteries, which makes them more cost-effective in the long run.
## How Do Batteries Produce Electricity?
Batteries produce electricity through a process called electrolysis. Electrolysis is the process of using an electric current to break down water molecules into their component parts, oxygen, and hydrogen. The oxygen and hydrogen are then drawn off by electrodes placed in the water, leaving behind electrically charged ions.
These charged ions are what allow the battery to store and release electrical energy.
## The Function of a Battery
A battery is an electrical device that converts chemical energy into electrical energy. It is composed of one or more electrochemical cells. The term “battery” originates from the fact that early batteries consisted of multiple cells connected in series, or “stacked” together.
The function of a battery is to store and provide electricity. Batteries are used in many devices, including cell phones, laptops, and cars.
## Do You Need a Battery in a Circuit?
If you want your circuit to do anything, you’ll need a power source. The most common power source is a battery. Batteries come in all shapes and sizes, from small watch batteries to giant batteries in cars.
Even if your circuit is just a light bulb, it will still need a battery to power it.
## Why Does a Circuit Need a Battery?
A battery is a device that converts chemical energy into electrical energy. In a circuit, the battery provides the power needed to run the devices in the circuit. The battery does this by providing electrons to flow through the circuit.
## What are the 3 Things a Circuit Needs to Work?
In order for a circuit to work, it needs three things: a power source, conductors, and a load.
### The Power Source
The power source provides the energy needed to make the circuit work. This can be a battery, solar panel, or another type of energy source.
### The Conductors
The conductors are what carry the electricity from the power source to the load. They can be made of metal, carbon, or other materials that allow electricity to flow through them easily.
The load is what uses the electricity from the power source to do work. This could be a light bulb, motor, or another device that uses electrical energy to function.
### Note It
If any one of these three elements is missing, then the circuit will not work properly. For example, if there is no load for the electricity to flow through, then the circuit will not do anything.
Similarly, if there is no power source or no conductors connecting the power source to the load, then again the circuit will not work correctly. All three elements are necessary for a functioning circuit.
## What Must a Circuit Have to Work?
In order for a circuit to work, it must have a complete path for the current to flow. The current will flow from the negative terminal of the power source, through the load, and back to the positive terminal of the power source. If there is any break in this path, the current will not be able to flow and the circuit will not work.
You have to know that 9V batteries are not a good power source for Arduino. The voltage is too low and the current is too high. The Arduino will not be able to run on a 9V battery.
## Summary
No, a circuit does not need a battery to work. A circuit can be powered by a variety of sources, including a generator, solar panel, or windmill.
Rate this post
| 1,886
| 9,440
|
{"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}
| 3.328125
| 3
|
CC-MAIN-2023-50
|
latest
|
en
| 0.953174
|
https://designatedderiver.com/2015/12/07/linear-functions-practice-with-stations/
| 1,679,381,838,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00439.warc.gz
| 242,841,716
| 34,134
|
# Linear Functions Practice with Stations
My algebra 1 class only has 11 students who all work at very different paces. I don’t really like doing traditional stations because they tend to talk and not do their work, especially if the answers are at their table. I arranged this activity based off of math sprints from I love Math. I changed the activity to focus on everything we’ve focused on this unit.
Each student started off with sheet #1. . I had all of the answers for all four sheets glued on the inside of a folder that I kept upfront with me. When students finished the first sheet they came to me to check their answers. When they got one incorrect I would circle it and send them back to their seats. When students came to me with a completed and correct sheet they were able to get the next sheet. I personally thought the sheets became slightly harder as class went on.
Because students were checking their answers with me, I was able to see what each student understood and how they improved throughout the class.Because every student worked at their own pace I was able to help every student. I was also able to see what the class as a whole was struggling on. I’m not sure how this would work in a larger class, but in my class of 11 very hyperactive students it was perfect! They loved getting to move around and get instant feedback on their work.
At the end of class I had them staple all four sheets together and told them this was their Linear Equation Book (so far). I’ve found that they also love having practice problems and notes all in one place (the more compact the better). I teach very interactive, so students tend not to take detailed notes in my class. I’d rather them be engaged all during class and have this small book of practice problems to refresh their memories.
Sheet #1: Finding slope between two coordinate points
Sheet #2: Graphing Linear Equations
Sheet #3: Finding the equation of a line when given a graph
Sheet #4: Finding Equations of Lines given two coordinate points
I taught students how to find equations of lines given two coordinate points during the beginning of class using a Writing an Equation from 2 Points Template from the Algebra Toolbox Blog. Every student had a template in a sheet protector and a dry erase marker. We did a few together and I walked them through the template. I then put coordinates on the board and had students create equations by themselves. After every equation, we would check them! My students love to compete against each other so they would race to see who finished first. They love the template, but it’s been difficult weaning them off of it. I plan to have them journal quickly at the beginning of class about what they are actually doing in the template to gage their understanding.
| 590
| 2,792
|
{"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}
| 3.5625
| 4
|
CC-MAIN-2023-14
|
latest
|
en
| 0.985065
|
https://oeis.org/A119423
| 1,632,836,354,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780060803.2/warc/CC-MAIN-20210928122846-20210928152846-00212.warc.gz
| 467,514,815
| 3,940
|
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119423 Denominators of coefficients in a continued fraction expansion of the Gamma function. 2
2021, 125896643, 4596084813365743279, 20539143739435534417826656817767471, 154187684682287395130815676867766056654304274786409523983, 53758055914442388300525602657237655353613236528990789014340068307611233396794963869, 582235181033697130010052826698193975503732624065579606751772525345364278965643722001124189437614592415486167547436141091 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS David W. Cantrell, Table of n, a(n) for n = 1..18 David W. Cantrell, A new convergent expansion for the gamma function, sci.math.num-analysis, Nov 05, 2001 EXAMPLE For Re(z) > 0, Gamma(z + 1/2) = sqrt(2*pi)*(z/e)^z / [1 + 1/( 24*z - 1/2 + CF(z) )] where continued fraction CF(z) = 1/(c_1*z + 1/(c_2*z + 1/(c_3*z + ...))) with c_1 = 1440/2021, c_2 = 686186088/125896643, c_3 = 1521596612992267104/4596084813365743279, ... MATHEMATICA See A119422. CROSSREFS Numerators given in A119422. Sequence in context: A252327 A252326 * A176913 A013687 A257766 A126821 Adjacent sequences: A119420 A119421 A119422 * A119424 A119425 A119426 KEYWORD frac,nonn AUTHOR David W. Cantrell (DWCantrell(AT)sigmaxi.net), May 18 2006 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)
| 572
| 1,761
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.984375
| 3
|
CC-MAIN-2021-39
|
latest
|
en
| 0.558815
|
https://physics.stackexchange.com/questions/658256/determine-lens-system-for-known-magnification-and-available-space
| 1,642,402,451,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00432.warc.gz
| 476,110,134
| 33,746
|
# Determine lens system for known magnification and available space
I'm trying to create a system of two lenses with a set magnification in a limited space for the setup, i.e. the distance from the object to the first lens $$g_1$$ has a minimum ($$152\,$$cm) and the whole lens setup is limited ($$40\,$$cm). The defined length of the setup $$L$$ is defined below. For a sketch see image:
In total there are the following important parameters:
• object size $$G=4.136\,$$mm, is known
• magnification $$V\simeq0.2579$$
• focal length $$f_i$$ of each lens (should be reasonable so one can buy it)
• distance to objects $$g_i$$ (where $$g_1$$ has a minimum of $$g_{min}=152\,$$cm)
• distance to image $$b_i$$
• image size $$B_i$$ ($$B_2$$ is set due to the magnification)
• distance between lenses $$d=b_1+g_2$$
where $$i\in\{1,2\}$$ and the setup distance $$L=(g_1-g_{min})+d+b_2\overset{!}{<}40\,$$cm. Since the image is captured by a camera in position $$B_2$$ the image distance of the second lens is required as $$b_2>0$$.
My question is, whether there is an elegant way of finding the best possible fit of lenses and positions that I don't know of or if is this only solvable by calculating the whole system for varying $$f_i,g_i,d$$?
• Does the "lens setup" refer to distance (d)? Is lens (2) the lens of your camera? Aug 9 '21 at 14:21
• I updated the question to clarify, that the setup distance is given by $L$ (so not the total length of all parameters, but a reduced length due to $g_{min}$. No, the camera is in the focal plane of the second lens or in other words at the position of $B_2$. Aug 9 '21 at 14:27
• I haven't looked closely at this question, but I'll share that I've had success getting large magnifications in small distances using negative focal length lenses. Aug 9 '21 at 14:44
You can start with a single lens to achieve the magnification you want. This will give you a range of values for the focal length. If the orientation of $$B_2$$ does not matter, then you would get two intervals for the focal length: $$f = \frac{g_1}{1 \pm \frac{1}{V}}$$
| 589
| 2,082
|
{"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": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.40625
| 3
|
CC-MAIN-2022-05
|
latest
|
en
| 0.914255
|
https://ru.scribd.com/document/268622693/alg-notes-2-15
| 1,582,471,630,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-10/segments/1581875145774.75/warc/CC-MAIN-20200223123852-20200223153852-00441.warc.gz
| 527,426,877
| 84,299
|
Вы находитесь на странице: 1из 15
# UNIVERSITY OF NEW SOUTH WALES
## SCHOOL OF MATHEMATICS AND STATISTICS
MATH 1131
MATHEMATICS 1A ALGEBRA.
Section 2: - Vector Geometry.
In Chapter 1, see looked at the rudiments of vector geometry. We now have enough machinery to study this subject in greater depth.
Distances and Lengths:
We saw earlier that: in higher
lows:
a1
a2
Definition: A vector x = ..
.
an
## The distance between two points A and B in Rn will be
as the length of the vec defined
a1
a2
tor AB, in other words, if A has position vector a = .. and B has position vector
.
an
b1
b2
## b = .. , then the length of AB is
.
bn
| AB | = |b a| =
p
(b1 a1 )2 + + (bn an )2 .
A vector which has unit length is called a unit vector. Any vector can be made into a unit
vector by dividing by its length.
a1
b1
Dot Product: We define the dot product of two vectors a = a2 and b = b2
a3
b3
by
a b = a1 b1 + a2 b2 + a3 b3 .
Note that this is a scalar, and so the
called a scalar product.
dot
product isoften
1
1
Ex: Find the dot product of a = 2 and b = 7
3
3
1
## The dot product also has a geometric interpretation in R2 and R3 .
Indeed for non-parallel vectors a and b in R3 , we consider the following triangle.
a
c
b
We can write c = a b and so taking lengths, we have
|c|2 = (a1 b1 )2 + (a2 b2 )2 + (a3 b3 )2 = |a|2 + |b|2 2(a1 b1 + a2 b2 + a3 b3 )
= |a|2 + |b|2 2 a b.
Also, if we write down the cosine rule for this triangle, we have |c|2 = |a|2 +|b|2 2|a||b| cos ,
where is the angle between the vectors a and b. Comparing the two expressions we see
that
a1 b1 + a2 b2 + a3 b3 = a b = |a||b| cos .
This formula is fundamental and should be committed to memory.
Notice that if the angle between a and b is 90 we have
a b = a1 b1 + a2 b2 + a3 b3 = 0.
## Ex: Find the
dot product
and hence the acute angle between the vectors a and b if
1
2
a = 1 and b = 1 .
2
1
2
## Definition: The dot product of two vectors a and b in Rn is given by
a b = a1 b1 + + an bn .
## The dot product has the following properties:
1. a a = |a|2 and so |a| =
a a.
2. a b is a scalar (which is why the dot product is sometimes called the scalar product).
3. a b = b a. (Commutative law).
4. a (b) = (a b).
5. a (b + c) = a b + a c. (Distributive law).
The proofs of these are easy.
Ex: Prove that the diagonals of a rhombus are perpendicular.
In higher dimensions we can define the angle between two vectors a and b by
cos =
ab
.
|a||b|
Orthogonality:
Two vectors a and b are said to be orthogonal if a b = 0.
3
In two and three dimensions, this is the same as saying that the two vectors are perpendicular.
2
3
Ex: Show that 5 is orthogonal to 1 .
1
11
2
4
Ex: Write down a unit vector which is perpendicular to both 6 and 3 .
3
1
## A set of vectors which are mutually orthogonal is called an orthogonal set.
1
1
1
1 , 1 ,
1
For example the set of vectors
is an orthogonal set.
1
0
2
A set of vectors which each have length 1 and are also orthogonal is called an orthonormal
set.
0
0
1
3
0 , 1 , 0 form an orthonormal
For example the 3 basis vectors in R ,
0
0
1
set.
1
1
1
1
,
is an orthonormal set in R2 .
The set
2 1
2 1
4
## Ex: Suppose that {a1 , a2 , a3 } is an orthonormal set in Rn , (with n 3) and
b = c1 a1 + c2 a2 + c3 a3 .
Find the scalars c1 , c2 , c3 .
Projections:
In the diagram, we are given two (non-zero) vectors a and b.
A
a
projb a
ab
|b|
## using the properties of dot product.
b
OP = |OP| |b|
and so, in two and three-dimensional space,
projb a =
5
ab
|b|2
b.
Also
## In higher dimensions we will take this for
a1
Note that 0 is the projection of
0
2
Ex: Find the projection of 3 onto
1
## our definition of the projection of a onto b.
a1
a2 onto the unit vector e1 and so on.
a3
2
3 .
6
2
3
onto
5
6
.
## The Cross Product:
There is another way in which we can define vector multiplication. This product only makes
sense in R3 and is known as the cross product.
a1
b1
Given two (non-zero) vectors a = a2 and b = b2 , we seek a third vector
a3
b3
x1
## x2 which is perpendicular to both of these. From the dot product we know
x =
x3
that such a vector must satisfy each of the equations
a1 x1 + a2 x2 + a3 x3 = 0
b1 x1 + b2 x2 + b3 x3 = 0.
6
where is real.
a2 b3 a3 b2
x = a3 b1 a1 b3
a1 b2 a2 b1
## We put = 1 and define the cross product of a and b by
a2 b3 a3 b2
a b = a3 b1 a1 b3 .
a1 b2 a2 b1
This is also sometimes known as the vector product of a and b. It is quite difficult to
remember, but can be written mnemonically using what is called the determinant notation:
i
j
k
a b = a1 a2 a3
b1 b2 b3
where, recall,
i = 0 ,
0
j = 1 ,
0
## We can expand the determinant and write
a
a2 a3
j 1
i
b1
b2 b3
k = 0 .
1
a
a3
+ k 1
b1
b3
a2
.
b2
Each subdeterminant is then evaluated to give the three co-ordinates of the cross product,
using the rule
a b
2
6
Ex: Use the determinant formula to find the cross product of 1 and 2 .
2
3
7
## Suppose a, b and c are vectors in R3 . Then
(i) a a = 0.
(ii) b a = a b.
(Note then that the cross product is NOT commutative. Changing the order changes the
sign.)
(iii) a (b) = (a b) and (a) b = (a b) for R.
(iv) From (i) and (iii) we have a (a) = 0. In other words, the cross product of parallel vectors is the zero vector.
(v) a (b + c) = a b + a c and (a + b) c = a c + b c. (Distributive law).
(vi) For the three standard basis vectors in R3 we have
e1 e2 = e3 ,
e2 e3 = e1 ,
e3 e1 = e2 .
(vii) |a b| = |a||b| sin , where is the angle between the two vectors.
All of these may be proven by writing out the co-ordinates. Some of the proofs are given in
the Algebra notes.
Example: Suppose we have three vectors a, b, c which form the sides of a triangle,
i.e. a + b + c = 0. By taking cross products derive the sine rule for this triangle.
## Note in particular result (vii). We can use this to find:
Area of a Parallelogram: Given a parallelogram S in R3 , defined by
S = {a + b : 0 1,
0 1},
Area = |a b|
## But by (vii) above, this is simply |a b|.
2
1
Ex: Find the area of the parallelogram spanned by 3 and 3 .
1
7
## Scalar Triple Product:
The scalar triple product of three vectors is defined by
a (b c).
We will see shortly that it also has a geometric interpretation.
Note that in the evaluation of the triple
product,
you must
perform
the cross product first.
2
3
5
Ex: Find the scalar triple product of 1 , 1 , 2 .
3
4
1
## Theorem: For a, b, c we have
(i) a (b c) = (a b) c
(ii) a (b c) = a (c b)
(iii) a (a b) = (a a) b = 0
(iv) The scalar triple product can be written as a
a1 a2
a (b c) = b1 b2
c1 c2
determinant, viz:
a3
b3 .
c3
There is also a vector triple product which arises in Physics. The vector triple product of
three vectors a, b, c is given by a (b c). Note that cross product is NOT associative so
a (b c) 6= (a b) c.
10
Volume of a Parallelepiped:
A
C
a
n
O
c
b
## A parallelepiped is the 3-dimensional analogue of a parallelogram.
(The word comes literally from the Greek o meaning that (the top) is
parallel to () the base (literally plane)).
Suppose we have three non-coplanar vectors a, b and c, which form the edges of the
parallelepiped. The parallelepiped is said to be spanned by these three vectors.
To find the volume, we must multiply the area of the base by the perpendicular height.
Let n be a normal to the base given by n = b c. The perpendicular height then, is given
by the length of the projection of a onto n which is simply
|projn a| =
|a n|
|a (b c)|
=
.
|n|
|b c|
Now the denominator of this expression is simply the area of the base parallelogram, and so
the volume is given by the magnitude of the scalar triple product, i.e. |a (b c)|.
2
3
3
Ex: Find the volume of the parallelepiped spanned by 4 , 4 , 2 .
1
6
5
11
Note that if the three vectors are coplanar then the volume of the parallelepiped that they
span will be zero, and conversely, so this gives us:
Theorem: Three vectors in R3 are co-planar if and only if their scalar triple product is zero.
More on Planes:
We can use the dot product to give an alternate formula for the equation of a plane.
Suppose we know a point A on the plane and a vector n which is perpendicular to the
plane.
n
X
A
a
x
b
Take any general point X on the plane. Then AX and n are perpendicular and so their dot
product is zero. Hence n. AX= 0. If we let x be the position vector of X and a be the
position vector of A, then
n (x a) = 0.
This is called the point normal form of the plane.
Ex: Find the
pointnormal form and
hence
the (Cartesian) equation of the plane pass2
1
ing through 1 with normal 2 .
3
1
12
n1
Observe that if n = n2 , then when we use the point-normal form of the equation, the
n3
co-efficients in the Cartesian equation are precisely the components of this vector. We can
exploit this idea to convert a plane from vector form to cartesian form.
Ex: Find
the
cartesian
form
of the
plane
whose equation is
2
1
3
x = 1 + 2 + 4 .
2
4
2
## Ex: Convert to point-normal form, the plane with equation 2x 3y + 4z = 12.
13
Ex: Convert
to point-normal
form,
theplane with vector equation
2
3
0
5
0
1 .
x=
+
+
3
2
2
## Distances between lines, points and planes:
1. Distance of a point to a line:
0
Ex: Find the shortest distance from the point B = 3 to the line
8
1
1
x = 2 + 1 .
3
4
1
Let A = 2 and P be the foot of the perpendicular from B to the line. Then AP is the
3
projection of AB onto the direction vector of the line. We can then find the length of BP
using the length of AB and Pythagoras.
14
## 2. Distance of a point to a Plane:
1
Find the shortest distance from the point B = 2 to the plane
3
2
1
1
x=
0
+ 1
+
0 .
0
0
2
2
## 0 and P be the foot of the perpendicular from B to the plane.
Let A be the point
0
Then BP is simply the length of the projection of AB onto the normal n to the plane.
15
| 3,225
| 9,816
|
{"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}
| 4.65625
| 5
|
CC-MAIN-2020-10
|
latest
|
en
| 0.908387
|
https://en.wikipedia.org/wiki/Divergence_operator
| 1,524,738,002,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-17/segments/1524125948125.20/warc/CC-MAIN-20180426090041-20180426110041-00583.warc.gz
| 609,482,355
| 26,534
|
# Del
(Redirected from Divergence operator)
Del operator,
represented by
the nabla symbol
Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol . When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), it may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.
Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, a dot product, and a cross product, respectively, of the del "operator" with the field. These formal products do not necessarily commute with other operators or products. These three uses, detailed below, are summarized as:
• Gradient: ${\displaystyle \operatorname {grad} f=\nabla f}$
• Divergence: ${\displaystyle \operatorname {div} {\vec {v}}=\nabla \cdot {\vec {v}}}$
• Curl: ${\displaystyle \operatorname {curl} {\vec {v}}=\nabla \times {\vec {v}}}$
## Definition
In the Cartesian coordinate system Rn with coordinates ${\displaystyle (x_{1},\dots ,x_{n})}$ and standard basis ${\displaystyle \{{\vec {e}}_{1},\dots ,{\vec {e}}_{n}\}}$, del is defined in terms of partial derivative operators as
${\displaystyle \nabla =\left({\partial \over \partial x_{1}},\ldots ,{\partial \over \partial x_{n}}\right)=\sum _{i=1}^{n}{\vec {e}}_{i}{\partial \over \partial x_{i}}}$
In three-dimensional Cartesian coordinate system R3 with coordinates ${\displaystyle (x,y,z)}$ and standard basis ${\displaystyle \{{\vec {e}}_{x},{\vec {e}}_{y},{\vec {e}}_{z}\}}$, del is written as
${\displaystyle \nabla =\left({\partial \over \partial x},{\partial \over \partial y},{\partial \over \partial z}\right)={\vec {e}}_{x}{\partial \over \partial x}+{\vec {e}}_{y}{\partial \over \partial y}+{\vec {e}}_{z}{\partial \over \partial z}}$
Del can also be expressed in other coordinate systems, see for example del in cylindrical and spherical coordinates.
## Notational uses
Del is used as a shorthand form to simplify many long mathematical expressions. It is most commonly used to simplify expressions for the gradient, divergence, curl, directional derivative, and Laplacian.
The vector derivative of a scalar field ${\displaystyle f}$ is called the gradient, and it can be represented as:
${\displaystyle \operatorname {grad} f={\partial f \over \partial x}{\vec {e}}_{x}+{\partial f \over \partial y}{\vec {e}}_{y}+{\partial f \over \partial z}{\vec {e}}_{z}=\nabla f}$
It always points in the direction of greatest increase of ${\displaystyle f}$, and it has a magnitude equal to the maximum rate of increase at the point—just like a standard derivative. In particular, if a hill is defined as a height function over a plane ${\displaystyle h(x,y)}$, the 2d projection of the gradient at a given location will be a vector in the xy-plane (visualizable as an arrow on a map) pointing along the steepest direction. The magnitude of the gradient is the value of this steepest slope.
In particular, this notation is powerful because the gradient product rule looks very similar to the 1d-derivative case:
${\displaystyle \nabla (fg)=f\nabla g+g\nabla f}$
However, the rules for dot products do not turn out to be simple, as illustrated by:
${\displaystyle \nabla ({\vec {u}}\cdot {\vec {v}})=({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}+{\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})}$
### Divergence
The divergence of a vector field ${\displaystyle {\vec {v}}(x,y,z)=v_{x}{\vec {e}}_{x}+v_{y}{\vec {e}}_{y}+v_{z}{\vec {e}}_{z}}$ is a scalar function that can be represented as:
${\displaystyle \operatorname {div} {\vec {v}}={\partial v_{x} \over \partial x}+{\partial v_{y} \over \partial y}+{\partial v_{z} \over \partial z}=\nabla \cdot {\vec {v}}}$
The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately, it is a measure of that field's tendency to converge toward or repel from a point.
The power of the del notation is shown by the following product rule:
${\displaystyle \nabla \cdot (f{\vec {v}})=f(\nabla \cdot {\vec {v}})+{\vec {v}}\cdot (\nabla f)}$
The formula for the vector product is slightly less intuitive, because this product is not commutative:
${\displaystyle \nabla \cdot ({\vec {u}}\times {\vec {v}})={\vec {v}}\cdot (\nabla \times {\vec {u}})-{\vec {u}}\cdot (\nabla \times {\vec {v}})}$
### Curl
The curl of a vector field ${\displaystyle {\vec {v}}(x,y,z)=v_{x}{\vec {e}}_{x}+v_{y}{\vec {e}}_{y}+v_{z}{\vec {e}}_{z}}$ is a vector function that can be represented as:
${\displaystyle \operatorname {curl} {\vec {v}}=\left({\partial v_{z} \over \partial y}-{\partial v_{y} \over \partial z}\right){\vec {e}}_{x}+\left({\partial v_{x} \over \partial z}-{\partial v_{z} \over \partial x}\right){\vec {e}}_{y}+\left({\partial v_{y} \over \partial x}-{\partial v_{x} \over \partial y}\right){\vec {e}}_{z}=\nabla \times {\vec {v}}}$
The curl at a point is proportional to the on-axis torque to which a tiny pinwheel would be subjected if it were centered at that point.
The vector product operation can be visualized as a pseudo-determinant:
${\displaystyle \nabla \times {\vec {v}}=\left|{\begin{matrix}{\vec {e}}_{x}&{\vec {e}}_{y}&{\vec {e}}_{z}\\[2pt]{\frac {\partial }{\partial x}}&{\frac {\partial }{\partial y}}&{\frac {\partial }{\partial z}}\\[2pt]v_{x}&v_{y}&v_{z}\end{matrix}}\right|}$
Again the power of the notation is shown by the product rule:
${\displaystyle \nabla \times (f{\vec {v}})=(\nabla f)\times {\vec {v}}+f(\nabla \times {\vec {v}})}$
Unfortunately the rule for the vector product does not turn out to be simple:
${\displaystyle \nabla \times ({\vec {u}}\times {\vec {v}})={\vec {u}}\,(\nabla \cdot {\vec {v}})-{\vec {v}}\,(\nabla \cdot {\vec {u}})+({\vec {v}}\cdot \nabla )\,{\vec {u}}-({\vec {u}}\cdot \nabla )\,{\vec {v}}}$
### Directional derivative
The directional derivative of a scalar field ${\displaystyle f(x,y,z)}$ in the direction ${\displaystyle {\vec {a}}(x,y,z)=a_{x}{\vec {e}}_{x}+a_{y}{\vec {e}}_{y}+a_{z}{\vec {e}}_{z}}$ is defined as:
${\displaystyle {\vec {a}}\cdot \operatorname {grad} f=a_{x}{\partial f \over \partial x}+a_{y}{\partial f \over \partial y}+a_{z}{\partial f \over \partial z}={\vec {a}}\cdot (\nabla f)}$
This gives the rate of change of a field ${\displaystyle f}$ in the direction of ${\displaystyle {\vec {a}}}$. In operator notation, the element in parentheses can be considered a single coherent unit; fluid dynamics uses this convention extensively, terming it the convective derivative—the "moving" derivative of the fluid.
Note that ${\displaystyle ({\vec {a}}\cdot \nabla )}$ is an operator that takes scalar to a scalar. It can be extended to operate on a vector, by separately operate on each of its components.
### Laplacian
The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; for cartesian coordinate systems it is defined as:
${\displaystyle \Delta ={\partial ^{2} \over \partial x^{2}}+{\partial ^{2} \over \partial y^{2}}+{\partial ^{2} \over \partial z^{2}}=\nabla \cdot \nabla =\nabla ^{2}}$
and the definition for more general coordinate systems is given in vector Laplacian.
The Laplacian is ubiquitous throughout modern mathematical physics, appearing for example in Laplace's equation, Poisson's equation, the heat equation, the wave equation, and the Schrödinger equation.
### Tensor derivative
Del can also be applied to a vector field with the result being a tensor. The tensor derivative of a vector field ${\displaystyle {\vec {v}}}$ (in three dimensions) is a 9-term second-rank tensor – that is, a 3×3 matrix – but can be denoted simply as ${\displaystyle \nabla \otimes {\vec {v}}}$, where ${\displaystyle \otimes }$ represents the dyadic product. This quantity is equivalent to the transpose of the Jacobian matrix of the vector field with respect to space. The divergence of the vector field can then be expressed as the trace of this matrix.
For a small displacement ${\displaystyle \delta {\vec {r}}}$, the change in the vector field is given by:
${\displaystyle \delta {\vec {v}}=(\nabla \otimes {\vec {v}})\cdot \delta {\vec {r}}}$
## Product rules
For vector calculus:
{\displaystyle {\begin{aligned}\nabla (fg)&=f\nabla g+g\nabla f\\\nabla ({\vec {u}}\cdot {\vec {v}})&={\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})+({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}\\\nabla \cdot (f{\vec {v}})&=f(\nabla \cdot {\vec {v}})+{\vec {v}}\cdot (\nabla f)\\\nabla \cdot ({\vec {u}}\times {\vec {v}})&={\vec {v}}\cdot (\nabla \times {\vec {u}})-{\vec {u}}\cdot (\nabla \times {\vec {v}})\\\nabla \times (f{\vec {v}})&=(\nabla f)\times {\vec {v}}+f(\nabla \times {\vec {v}})\\\nabla \times ({\vec {u}}\times {\vec {v}})&={\vec {u}}\,(\nabla \cdot {\vec {v}})-{\vec {v}}\,(\nabla \cdot {\vec {u}})+({\vec {v}}\cdot \nabla )\,{\vec {u}}-({\vec {u}}\cdot \nabla )\,{\vec {v}}\end{aligned}}}
For matrix calculus (for which ${\displaystyle {\vec {u}}\cdot {\vec {v}}}$ can be written ${\displaystyle {\vec {u}}^{\text{T}}{\vec {v}}}$):
{\displaystyle {\begin{aligned}(\mathbf {A} \nabla )^{\text{T}}{\vec {u}}&=\nabla ^{\text{T}}(\mathbf {A} ^{\text{T}}{\vec {u}})-(\nabla ^{\text{T}}\mathbf {A} ^{\text{T}}){\vec {u}}\end{aligned}}}
## Second derivatives
DCG chart: A simple chart depicting all rules pertaining to second derivatives. D, C, G, L and CC stand for divergence, curl, gradient, Laplacian and curl of curl, respectively. Arrows indicate existence of second derivatives. Blue circle in the middle represents curl of curl, whereas the other two red circles (dashed) mean that DD and GG do not exist.
When del operates on a scalar or vector, either a scalar or vector is returned. Because of the diversity of vector products (scalar, dot, cross) one application of del already gives rise to three major derivatives: the gradient (scalar product), divergence (dot product), and curl (cross product). Applying these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v; the use of the scalar Laplacian and vector Laplacian gives two more:
{\displaystyle {\begin{aligned}\operatorname {div} (\operatorname {grad} f)&=\nabla \cdot (\nabla f)\\\operatorname {curl} (\operatorname {grad} f)&=\nabla \times (\nabla f)\\\Delta f&=\nabla ^{2}f\\\operatorname {grad} (\operatorname {div} {\vec {v}})&=\nabla (\nabla \cdot {\vec {v}})\\\operatorname {div} (\operatorname {curl} {\vec {v}})&=\nabla \cdot (\nabla \times {\vec {v}})\\\operatorname {curl} (\operatorname {curl} {\vec {v}})&=\nabla \times (\nabla \times {\vec {v}})\\\Delta {\vec {v}}&=\nabla ^{2}{\vec {v}}\end{aligned}}}
These are of interest principally because they are not always unique or independent of each other. As long as the functions are well-behaved, two of them are always zero:
{\displaystyle {\begin{aligned}\operatorname {curl} (\operatorname {grad} f)&=\nabla \times (\nabla f)=0\\\operatorname {div} (\operatorname {curl} {\vec {v}})&=\nabla \cdot \nabla \times {\vec {v}}=0\end{aligned}}}
Two of them are always equal:
${\displaystyle \operatorname {div} (\operatorname {grad} f)=\nabla \cdot (\nabla f)=\nabla ^{2}f=\Delta f}$
The 3 remaining vector derivatives are related by the equation:
${\displaystyle \nabla \times \left(\nabla \times {\vec {v}}\right)=\nabla (\nabla \cdot {\vec {v}})-\nabla ^{2}{\vec {v}}}$
And one of them can even be expressed with the tensor product, if the functions are well-behaved:
${\displaystyle \nabla (\nabla \cdot {\vec {v}})=\nabla \cdot (\nabla \otimes {\vec {v}})}$
## Precautions
Most of the above vector properties (except for those that rely explicitly on del's differential properties—for example, the product rule) rely only on symbol rearrangement, and must necessarily hold if the del symbol is replaced by any other vector. This is part of the value to be gained in notationally representing this operator as a vector.
Though one can often replace del with a vector and obtain a vector identity, making those identities mnemonic, the reverse is not necessarily reliable, because del does not commute in general.
A counterexample that relies on del's failure to commute:
{\displaystyle {\begin{aligned}({\vec {u}}\cdot {\vec {v}})f&\equiv ({\vec {v}}\cdot {\vec {u}})f\\(\nabla \cdot {\vec {v}})f&=\left({\frac {\partial v_{x}}{\partial x}}+{\frac {\partial v_{y}}{\partial y}}+{\frac {\partial v_{z}}{\partial z}}\right)f={\frac {\partial v_{x}}{\partial x}}f+{\frac {\partial v_{y}}{\partial y}}f+{\frac {\partial v_{z}}{\partial z}}f\\({\vec {v}}\cdot \nabla )f&=\left(v_{x}{\frac {\partial }{\partial x}}+v_{y}{\frac {\partial }{\partial y}}+v_{z}{\frac {\partial }{\partial z}}\right)f=v_{x}{\frac {\partial f}{\partial x}}+v_{y}{\frac {\partial f}{\partial y}}+v_{z}{\frac {\partial f}{\partial z}}\\\Rightarrow (\nabla \cdot {\vec {v}})f&\neq ({\vec {v}}\cdot \nabla )f\\\end{aligned}}}
A counterexample that relies on del's differential properties:
{\displaystyle {\begin{aligned}(\nabla x)\times (\nabla y)&=\left({\vec {e}}_{x}{\frac {\partial x}{\partial x}}+{\vec {e}}_{y}{\frac {\partial x}{\partial y}}+{\vec {e}}_{z}{\frac {\partial x}{\partial z}}\right)\times \left({\vec {e}}_{x}{\frac {\partial y}{\partial x}}+{\vec {e}}_{y}{\frac {\partial y}{\partial y}}+{\vec {e}}_{z}{\frac {\partial y}{\partial z}}\right)\\&=({\vec {e}}_{x}\cdot 1+{\vec {e}}_{y}\cdot 0+{\vec {e}}_{z}\cdot 0)\times ({\vec {e}}_{x}\cdot 0+{\vec {e}}_{y}\cdot 1+{\vec {e}}_{z}\cdot 0)\\&={\vec {e}}_{x}\times {\vec {e}}_{y}\\&={\vec {e}}_{z}\\({\vec {u}}x)\times ({\vec {u}}y)&=xy({\vec {u}}\times {\vec {u}})\\&=xy{\vec {0}}\\&={\vec {0}}\end{aligned}}}
Central to these distinctions is the fact that del is not simply a vector; it is a vector operator. Whereas a vector is an object with both a magnitude and direction, del has neither a magnitude nor a direction until it operates on a function.
For that reason, identities involving del must be derived with care, using both vector identities and differentiation identities such as the product rule.
| 4,578
| 14,834
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 47, "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-2018-17
|
latest
|
en
| 0.859964
|
https://netlib.org/lapack/explore-html-3.6.1/d2/d54/cblat2_8f_a79d49aeeff7537ed123dda585c238f18.html
| 1,726,768,392,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00475.warc.gz
| 394,409,949
| 3,833
|
LAPACK 3.6.1 LAPACK: Linear Algebra PACKage
complex function cbeg ( logical RESET )
Definition at line 3131 of file cblat2.f.
3131 *
3132 * Generates complex numbers as pairs of random numbers uniformly
3133 * distributed between -0.5 and 0.5.
3134 *
3135 * Auxiliary routine for test program for Level 2 Blas.
3136 *
3137 * -- Written on 10-August-1987.
3138 * Richard Hanson, Sandia National Labs.
3139 * Jeremy Du Croz, NAG Central Office.
3140 *
3141 * .. Scalar Arguments ..
3142 LOGICAL reset
3143 * .. Local Scalars ..
3144 INTEGER i, ic, j, mi, mj
3145 * .. Save statement ..
3146 SAVE i, ic, j, mi, mj
3147 * .. Intrinsic Functions ..
3148 INTRINSIC cmplx
3149 * .. Executable Statements ..
3150 IF( reset )THEN
3151 * Initialize local variables.
3152 mi = 891
3153 mj = 457
3154 i = 7
3155 j = 7
3156 ic = 0
3157 reset = .false.
3158 END IF
3159 *
3160 * The sequence of values of I or J is bounded between 1 and 999.
3161 * If initial I or J = 1,2,3,6,7 or 9, the period will be 50.
3162 * If initial I or J = 4 or 8, the period will be 25.
3163 * If initial I or J = 5, the period will be 10.
3164 * IC is used to break up the period by skipping 1 value of I or J
3165 * in 6.
3166 *
3167 ic = ic + 1
3168 10 i = i*mi
3169 j = j*mj
3170 i = i - 1000*( i/1000 )
3171 j = j - 1000*( j/1000 )
3172 IF( ic.GE.5 )THEN
3173 ic = 0
3174 GO TO 10
3175 END IF
3176 cbeg = cmplx( ( i - 500 )/1001.0, ( j - 500 )/1001.0 )
3177 RETURN
3178 *
3179 * End of CBEG.
3180 *
complex function cbeg(RESET)
Definition: cblat2.f:3131
Here is the caller graph for this function:
| 614
| 1,595
|
{"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-2024-38
|
latest
|
en
| 0.337635
|
https://knoji.com/article/fishers-equation-of-exchange/
| 1,585,998,496,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-16/segments/1585370521876.48/warc/CC-MAIN-20200404103932-20200404133932-00190.warc.gz
| 551,933,540
| 8,520
|
GuidesFitness Gear & Equipment
# Fisher's Equation of Exchange
Knoji reviews products and up-and-coming brands we think you'll love. In certain cases, we may receive a commission from brands mentioned in our guides. Learn more.
Fisher's Equation of Exchange Fisher, who developed the theory, tried to put it in the form of the following algebraic equation of exchange:
Fisher's Equation of Exchange
Fisher, who developed the theory, tried to put it in the form of the following algebraic equation of exchange:
P= M/ T or, (Price level is equal to money divided by trade or goods exchanged)
Where P stands for price level, M is money, and T stands for trade or goods exchanged.
This simple equation can be true only of a small isolated community,
(a) where the number of transactions is small,
(b) where there are no barter transactions,
(c) where, except coins, there are no other types of money like notes and cheques in use, and
(d) Where every piece of money changes hands but once. Such isolated communities are not found now-a-days, however.
We observe that in modern communities a coin changes hands a number of times. The butcher takes it to the baker and the grocer and he again to some other person. The work done by a coin which is circulated five times is equal to that done by five coins which change hands only once each. As slated earlier, this speed is called the velocity of circulation.
Hence, to find out the effective amount of money in a country, we have to multiply the total number of coins by their velocity. Out equation would then be:
P= MV/ T or, (Price level is equal to money multiplied by velocity of money divided by trade or goods exchanged)
Where V is the velocity of circulation of money
But in addition to metallic money, in every modern country, there is a large amount of paper money which helps in the exchange of goods. Instruments of credit like cheques, drafts and bills also serve the same purpose. There velocity of circulation has also to be taken into consideration. So our equation finally develops into: —
P= MV+M'V’/ T 0r (or, (Price level is equal to money multiplied by velocity of money plus credit money multiplied by velocity of circulation divided by trade or goods exchanged)
Where M' stands for credit money, and V for its rapidity or velocity of circulation. The equation signifies that the price level (P) changes when the quantity of money (M) or quantity of credit money (M') changes or when their velocities (V and V’) change. Of course, P will also change if the quantity of goods (T) required to be exchanged changes.
| 562
| 2,597
|
{"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}
| 3.875
| 4
|
CC-MAIN-2020-16
|
longest
|
en
| 0.961609
|
http://github-pages.ucl.ac.uk/rsd-engineeringcourse/ch05construction/08objects.html
| 1,638,948,371,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964363445.41/warc/CC-MAIN-20211208053135-20211208083135-00598.warc.gz
| 39,448,083
| 364,852
|
Close
MPHY0021: Research Software Engineering With Python
Home
## Class design¶
The concepts we have introduced are common between different object oriented languages. Thus, when we design our program using these concepts, we can think at an architectural level, independent of language syntax.
In Python:
In [1]:
class Particle:
def __init__(self, position, velocity):
self.position = position
self.velocity = velocity
def move(self, delta_t):
self.position += self.velocity * delta_t
In C++:
class Particle {
std::vector<double> position;
std::vector<double> velocity;
Particle(std::vector<double> position, std::vector<double> velocity);
void move(double delta_t);
}
In Fortran:
type particle
real :: position
real :: velocity
contains
procedure :: init
procedure :: move
end type particle
### UML¶
UML is a conventional diagrammatic notation used to describe "class structures" and other higher level aspects of software design.
Computer scientists get worked up about formal correctness of UML diagrams and learning the conventions precisely. Working programmers can still benefit from using UML to describe their designs.
### YUML¶
We can see a YUML model for a Particle class with position and velocity data and a move() method using the YUML online UML drawing tool (example).
http://yuml.me/diagram/boring/class/[Particle|position;velocity|move%28%29]
Here's how we can use Python code to get an image back from YUML:
In [2]:
import requests
from IPython.display import Image
def yuml(model):
result = requests.get("http://yuml.me/diagram/boring/class/" + model)
return Image(result.content)
In [3]:
yuml("[Particle|position;velocity|move()]")
Out[3]:
The representation of the Particle class defined above in UML is done with a box with three sections. The name of the class goes on the top, then the name of the member variables in the middle, and the name of the methods on the bottom. We will see later why this is useful.
### Information Hiding¶
Sometimes, our design for a program would be broken if users start messing around with variables we don't want them to change.
Robust class design requires consideration of which subroutines are intended for users to use, and which are internal. Languages provide features to implement this: access control.
In python, we use leading underscores to control whether member variables and methods can be accessed from outside the class:
• single leading underscore (_) is used to document it's private but people could use it if wanted (thought they shouldn't);
• double leading underscore (__) raises errors if called.
In [4]:
class MyClass:
def __init__(self):
self.__private_data = 0
self._private_data = 0
self.public_data = 0
def __private_method(self): pass
def _private_method(self): pass
def public_method(self): pass
def called_inside(self):
self.__private_method()
self._private_method()
self.__private_data = 1
self._private_data = 1
MyClass().called_inside()
In [5]:
MyClass()._private_method() # Works, but forbidden by convention
In [6]:
MyClass().public_method() # OK
print(MyClass()._private_data)
0
In [7]:
print(MyClass().public_data)
0
In [8]:
MyClass().__private_method() # Generates error
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/tmp/ipykernel_14474/347243643.py in <module>
----> 1 MyClass().__private_method() # Generates error
AttributeError: 'MyClass' object has no attribute '__private_method'
In [9]:
print(MyClass().__private_data) # Generates error
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/tmp/ipykernel_14474/2056773552.py in <module>
----> 1 print(MyClass().__private_data) # Generates error
AttributeError: 'MyClass' object has no attribute '__private_data'
### Property accessors¶
Python provides a mechanism to make functions appear to be variables. This can be used if you want to change the way a class is implemented without changing the interface:
In [10]:
class Person:
def __init__(self):
self.name = "Graham Chapman"
assert(Person().name == "Graham Chapman")
becomes:
In [11]:
class Person(object):
def __init__(self):
self._first = "Graham"
self._second = "Chapman"
@property
def name(self):
return f"{self._first self._second}"
assert(Person().name == "Graham Chapman")
File "<fstring>", line 1
(self._first self._second)
^
SyntaxError: invalid syntax
Making the same external code work as before.
Note that the code behaves the same way to the outside user. The implementation detail is hidden by private variables. In languages without this feature, such as C++, it is best to always make data private, and always access data through functions:
In [12]:
class Person(object):
def __init__(self):
self._name = "Graham Chapman"
def name(self): # an access function
return self._name
assert(Person().name() == "Graham Chapman")
But in Python this is unnecessary because the @property capability.
Another way could be to create a member variable name which holds the full name. However, this could lead to inconsistent data. If we create a get_married function, then the name of the person won't change!
In [13]:
class Person(object):
def __init__(self, first, second):
self._first = first
self._second = second
self.name = f"{self._first} {self._second}"
def get_married(self, to):
self._second = to._second
graham = Person("Graham", "Chapman")
david = Person("David", "Sherlock")
assert(graham.name == "Graham Chapman")
graham.get_married(david)
assert(graham.name == "Graham Sherlock")
---------------------------------------------------------------------------
AssertionError Traceback (most recent call last)
/tmp/ipykernel_14474/3625705027.py in <module>
12 assert(graham.name == "Graham Chapman")
13 graham.get_married(david)
---> 14 assert(graham.name == "Graham Sherlock")
AssertionError:
This type of situation could makes that the object data structure gets inconsistent with itself. Making variables being out of sync with other variables. Each piece of information should only be stored in once place! In this case, name should be calculated each time it's required as previously shown. In database design, this is called Normalisation.
#### UML for private/public¶
We prepend a +/- on public/private member variables and methods:
In [14]:
yuml("[Particle|+public;-private|+publicmethod();-privatemethod]")
Out[14]:
### Class Members¶
Class, or static members, belong to the class as a whole, and are shared between instances.
This is an object that keeps a count on how many have been created of it.
In [15]:
class Counted:
number_created = 0
def __init__(self):
Counted.number_created += 1
@classmethod
def howMany(cls):
return cls.number_created
Counted.howMany() # 0
x = Counted()
Counted.howMany() # 1
z = [Counted() for x in range(5)]
Counted.howMany() # 6
Out[15]:
6
The data is shared among all the objects instantiated from that class. Note that in __init__ we are not using self.number_created but the name of the class. The howMany function is not a method of a particular object. It's called on the class, not on the object. This is possible by using the @classmethod decorator.
## Inheritance and Polymorphism¶
### Object-based vs Object-Oriented¶
So far we have seen only object-based programming, not object-oriented programming.
Using Objects doesn't mean your code is object-oriented.
To understand object-oriented programming, we need to introduce polymorphism and inheritance.
### Inheritance¶
• Inheritance is a mechanism that allows related classes to share code.
• Inheritance allows a program to reflect the ontology) of kinds of thing in a program.
### Ontology and inheritance¶
• A bird is a kind of animal
• An eagle is a kind of bird
• A starling is also a kind of bird
• All animals can be born and die
• Only birds can fly (Ish.)
• Only eagles hunt
• Only starlings flock
### Inheritance in python¶
In [16]:
class Animal:
def beBorn(self):
print("I exist")
def die(self):
print("Argh!")
class Bird(Animal):
def fly(self):
print("Whee!")
class Eagle(Bird):
def hunt(self):
print("I'm gonna eatcha!")
class Starling(Bird):
def flew(self):
print("I'm flying away!")
Eagle().beBorn()
Eagle().hunt()
I exist
I'm gonna eatcha!
### Inheritance terminology¶
Here are two equivalents definition, one coming from C++ and another from Java:
• A derived class derives from a base class.
• A subclass inherits from a superclass.
These are different terms for the same thing. So, we can say:
• Eagle is a subclass of the Animal superclass.
• Animal is the base class of the Eagle derived class.
Another equivalent definition is using the synonym child / parent for derived / base class:
• A child class extends a parent class.
### Inheritance and constructors¶
To use implicitly constructors from a superclass, we can use super as shown below.
In [17]:
class Animal:
def __init__(self, age):
self.age = age
class Person(Animal):
def __init__(self, age, name):
super().__init__(age)
self.name = name
Read Raymond Hettinger's article about super to see various real examples.
### Inheritance UML diagrams¶
UML shows inheritance with an open triangular arrow pointing from subclass to superclass.
In [18]:
yuml("[Animal]^-[Bird],[Bird]^-[Eagle],[Bird]^-[Starling]%")
Out[18]:
### Aggregation vs Inheritance¶
If one object has or owns one or more objects, this is not inheritance.
For example, the boids example we saw few weeks ago, could be organised as an overall Model, which it owns several Boids, and each Boid owns two 2-vectors, one for position and one for velocity.
#### Aggregation in UML¶
The Boids situation can be represented thus:
In [19]:
yuml("[Model]<>-*>[Boid],[Boid]position++->[Vector],[Boid]velocity++->[Vector]%")
Out[19]:
The open diamond indicates Aggregation, the closed diamond composition. (A given boid might belong to multiple models, a given position vector is forever part of the corresponding Boid.)
The asterisk represents cardinality, a model may contain multiple Boids. This is a one to many relationship). Many to many relationship) is shown with * on both sides.
#### Refactoring to inheritance¶
Smell: Repeated code between two classes which are both ontologically subtypes of something
Before:
In [20]:
class Person:
def __init__(self, age, job):
self.age = age
self.job = job
def birthday(self):
self.age += 1
class Pet:
def __init__(self, age, owner):
self.age = age
self.owner = owner
def birthday(self):
self.age += 1
After:
In [21]:
class Animal:
def __init__(self, age):
self.age = age
def birthday(self):
self.age += 1
class Person(Animal):
def __init__(self, age, job):
self.job = job
super().__init__(age)
class Pet(Animal):
def __init__(self, age, owner):
self.owner = owner
super().__init__(age)
### Polymorphism¶
In [22]:
class Dog:
def noise(self):
return "Bark"
class Cat:
def noise(self):
return "Miaow"
class Pig:
def noise(self):
return "Oink"
class Cow:
def noise(self):
return "Moo"
animals = [Dog(), Dog(), Cat(), Pig(), Cow(), Cat()]
for animal in animals:
print(animal.noise())
Bark
Bark
Miaow
Oink
Moo
Miaow
This will print "Bark Bark Miaow Oink Moo Miaow"
If two classes support the same method, but it does different things for the two classes, then if an object is of an unknown class, calling the method will invoke the version for whatever class the instance is an instance of.
### Polymorphism and Inheritance¶
Often, polymorphism uses multiple derived classes with a common base class. However, duck typing in Python means that all that is required is that the types support a common Concept (Such as iterable, or container, or, in this case, the Noisy concept.)
A common base class is used where there is a likely default that you want several of the derived classes to have.
In [23]:
class Animal:
def noise(self):
return "I don't make a noise."
class Dog(Animal):
def noise(self):
return "Bark"
class Worm(Animal):
pass
class Poodle(Dog):
pass
animals = [Dog(), Worm(), Pig(), Cow(), Poodle()]
for animal in animals:
print(animal.noise())
Bark
I don't make a noise.
Oink
Moo
Bark
### Undefined Functions and Polymorphism¶
In the above example, we put in a dummy noise for Animals that don't know what type they are.
Instead, we can explicitly deliberately leave this undefined, and we get a crash if we access an undefined method.
In [24]:
class Animal:
pass
class Worm(Animal):
pass
In [25]:
Worm().noise() # Generates error
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/tmp/ipykernel_14474/2760045235.py in <module>
----> 1 Worm().noise() # Generates error
AttributeError: 'Worm' object has no attribute 'noise'
### Refactoring to Polymorphism¶
Smell: a function uses a big set of if statements or a case statement to decide what to do:
Before:
In [26]:
class Animal:
def __init__(self, animal_kind):
self.animal_kind = animal_kind
def noise(self):
if self.animal_kind == "Dog":
return "Bark"
elif self.animal_kind == "Cat":
return "Miaow"
elif self.animal_kind == "Cow":
return "Moo"
which is better replaced by the code above.
### Interfaces and concepts¶
In C++, it is common to define classes which declare dummy methods, called "virtual" methods, which specify the methods which derived classes must implement. Classes which define these methods, but which cannot be instantiated into actual objects, are called "abstract base" classes or "interfaces".
Python's Duck Typing approach means explicitly declaring these is unnesssary: any class concept which implements appropriately named methods will do. These as user-defined concepts, just as "iterable" or "container" are built-in Python concepts. A class is said to "implement an interface" or "satisfy a concept".
### Interfaces in UML¶
Interfaces implementation (a common ancestor that doesn't do anything but defines methods to share) in UML is indicated thus:
In [27]:
yuml("[<<Animal>>]^-.-[Dog]")
Out[27]:
| 3,371
| 14,215
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.640625
| 3
|
CC-MAIN-2021-49
|
longest
|
en
| 0.782476
|
https://merithub.com/quiz/game-of-shapes-a-fun-quiz-on-problems-related-to-various-shapes-c7p97t1nuvt9smd84m50
| 1,723,447,810,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641036271.72/warc/CC-MAIN-20240812061749-20240812091749-00195.warc.gz
| 316,580,396
| 8,467
|
Game of Shapes, a fun quiz on problems related to various shapes
In this quiz game, you will learn about the perimeter and area of various shapes like squares, rectangles, pentagons, etc. You will find lengths of the side of many shapes, their perimeter, and area. We have included pictures of different shapes to make you feel the questions and understand the solutions.
Start Quiz
Find the value of X in the figure. Given the area of the shape and one of the side lengths are 21 and 7 respectively.
18
7
3
6
If the perimeter of a rectangle is 20 units and its length is given 7 units. Then find the width of the given rectangle.
13
3
7
27
Match the following shapes with their respective perimeters correctly.
Scarlett decided to hang the fairy lights around all the walls of his room. So she measured the total length and found she needs 24 meters of fairy lights. What measurement did Scarlett measure?
Area
Perimeter
Side length
Volume
Peter’s grandfather has a small garden that is square in shape. His grandfather told him that the garden is 100 sq. ft and he wants to build a boundary around that garden. He asked him to calculate the total length of the boundary. So, help Peter in finding the length of the boundary.
30 ft.
20 ft.
100 ft.
40 ft.
The perimeter of the given rectangle is 24 units. Find its width.
5 units
6 units
4 units
3 units
Find the area of the given square.
20
25
15
10
Find the perimeter of the given pentagon.
18
12
15
10
Find the perimeter of the given shape.
36
26
28
26
Find the perimeter of the rectangle.
11
22
24
48
Quiz/Test Summary
Title: Game of Shapes, a fun quiz on problems related to various shapes
Questions: 10
Contributed by:
| 406
| 1,723
|
{"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-2024-33
|
latest
|
en
| 0.940546
|
https://forum.ansys.com/forums/reply/64718/
| 1,680,171,802,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296949181.44/warc/CC-MAIN-20230330101355-20230330131355-00472.warc.gz
| 293,055,873
| 24,120
|
peteroznewman
Subscriber
Did you set Share Topology to Share so that the two bodies share nodes at the circular edge?
When you do that, the mesh aligns.
If you have a left edge Temperature Boundary condition of 100 C, an internal heat generation, and a convection BC on the right edge, then heat will flow out of the left edge with the 100 C edge to maintain the 100 C. You can see this if you plot Heat Flux. You can plot arrows of a fixed length to show direction, or you can plot the arrow length to be proportional to the magnitude of the heat flux so a point where the heat flux is large gets a long arrow and a point where the heat flux is small gets a short arrow. The plots below have fixed length arrows.
If you make the left edge Temperature BC 500 C then for the SS solution, the heat will flow in from the left edge.
And if you make the left edge Temperature BC 300 C, then the SS solution is the the heat flow changes direction from out to in on the left edge as you look from the top to the bottom.
The above were all Steady State Thermal analysis results. You should look at a Steady State result before you develop Transient models. For one thing, they solve a lot faster. Why do you think the Transient solution is important?
3. Convection is a common BC because solid objects are usually touching some fluid, often air, that is at some bulk temperature, say room temperature of 22 C. Heat can flow out of a hot solid and into the room air by means of convection. Or heat can flow into a cold solid from the warmer room air by means of convection. The convection film coefficient defines the heat flux as a function of the temperature difference between the solid and the air.
| 381
| 1,704
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2023-14
|
latest
|
en
| 0.900473
|
https://codingskyscrapers.com/get-sum-of-array-of-numbers-in-javascript/
| 1,679,514,996,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00770.warc.gz
| 229,432,004
| 20,694
|
# How to get the Sum of an Array of Numbers in JavaScript
## Get the Sum of an Array of Numbers using Array.reduce() method.
To get the sum of an array of numbers:
1. Use the `reduce()` method to iterate over an array.
2. To get started, set the initial value in the reduce method to 0.
3. On each iteration, add the current number to the sum of all previous numbers.
Example –
``````
const theArray = [2, 55, 100];
const sum = theArray.reduce((accumulator, value) => {
return accumulator + value;
}, 0);
console.log(sum);
``````
Here’s what the above code is doing:
1. The `reduce()` method takes two arguments: a callback function and an initial value.
2. The callback function takes two arguments: an accumulator and the current value.
3. The accumulator is like a total that `reduce()` keeps track of after each operation.
4. The current value is just the next element in the array that `reduce()` is iterating over.
5. The initial value sets the accumulator to `0`.
6. The callback function adds the current value to the accumulator.
7. The `reduce()` method returns the final value of the accumulator.
## Get the Sum of an array of numbers using a for…of loop.
To get the sum of an array of numbers:
1. Declare a `sum` variable and set it to `0`.
2. Use the for…of loop to iterate over the array.
3. On each iteration, add the value of the current element to the sum variable.
Example –
``````
const theArray = [2, 55, 100];
let sum = 0;
for (const value of theArray) {
sum += value;
}
console.log(sum);
``````
Here’s what the above code is doing:
1. We create an array called `theArray`.
2. We create a variable called `sum` and set it to `0`.
3. We use a `for...of` loop to loop over `theArray`.
4. We add the value of the current element to `sum`.
5. We log the value of sum to the console.
âšī¸ The for…of loop is a great way to loop over arrays.
## Get the sum of an array of numbers using a `for` loop.
To get the `sum` of an array of numbers:
1. Declare a `sum` variable and set it to `0`.
2. Use the `for` loop to iterate over the array.
3. On each iteration, add the value of the current element to the `sum` variable.
Example –
``````
const theArray = [2, 55, 100];
let sum = 0;
for (let index = 0; index < theArray.length; index++) {
sum += theArray[index];
}
``````
Here’s what the above code is doing:
1. We create a variable called `sum` and set it equal to `0`.
2. We create a `for` loop that will run as long as the index is less than the length of the array.
3. We add the value of the current index to the `sum` variable.
4. We increment the index by `1`.
5. We repeat steps 2-4 until the index is no longer less than the length of the array.
6. We log the `sum` variable to the console.
`đī¸ The `reduce()` method is the best way to get the sum of an array of numbers in JavaScript. A `for...of` or `for` loop would be less efficient.`
| 772
| 2,895
|
{"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-2023-14
|
latest
|
en
| 0.710059
|
https://techlurker.com/using-the-quadratic-formula-to-solve-7x2-x-7-what-are-the-values-of-x/
| 1,709,503,954,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947476399.55/warc/CC-MAIN-20240303210414-20240304000414-00377.warc.gz
| 556,637,740
| 19,776
|
# Using The Quadratic Formula To Solve 7×2 – X = 7, What Are The Values Of X?
• Puzzle
The quadratic formula can be a powerful tool in the right hands. It can be applied to solve any situation where you need to find the value of an even number in a specific amount of time.
For example, let’s say you need to solve 7×2 – X = 7, where X is a whole number. You have a limited amount of time and don’t know what the even numbers are.
The quadratic formula can be used to give you the values of X in the given time! This is called numerical solution and is what most computer programs offer.
## Calculate the roots of 7×2 – x = 7
The quadratic formula can be used to calculate the roots of a square matrix, or the values of an unknown quantity in a rectangular matrix. The quadratic formula has two parts: the fundamental theorem and the linear equa-tion.
The fundamental theorem states that if you know the value of one variable in one row and one column of a square matrix, then you can find its equivalent in another row and another column.
For example, if we know that the weight of an orange is equal to 6 ounces, we can find its equivalent in another row and another column with an orange having a weight of 8 ounces.
The linear equation states that if you know one variable in one place in a vector, then you can find it in another place using it as an input. For example, let’s say we want to find the value of x at point (1 , 1) using x = 4 . Then our linear equation would be x = 4 + 5 , so we could substitute (1 , 1) into this equation and get 5 + 5 = 7 .
## Find all the possible solutions
The quadratic formula can be used to solve any number of squared equations. This includes the equation 7×2 – x = 7, where x is the value of one of the variables.
Using the quadratic formula, we can find all the possible solutions to any square equation. This is helpful when trying to determine why one solution was not a good fit for the original problem.
Many students do not learn this formula in high school or college, so it is important to know how to use it. Luckily, we can show you how in this article!
This article will go through some tips on how to use the quadratic formula to solve problems. However, first we will give you a basic tip on how to use it.
## Put everything in order
The most important thing to know about the quadratic formula is that it does not place order in your hands. All it can do is find the closest value to a given value of X, and give you those values.
That’s it!
That’s also what you have to do when solving equations!
So, no, you cannot just plug in a number and have your answer appear. You have to put something in order of what you want it to be, and then give it a number and see what happens.
This applies even when X is very small — for example, when X = 1 or 2 – because then the answer will appear very quickly. With larger numbers, there is more time for order to come into place.
## Solve using a calculator
When you need to solve a quadratic equation, the best way to do it is using a calculator. A calculator can help you determine the value of each variable on the equation, as well as provide the closest solution.
Many calculators have a quadratic function that can be used. Just plug in your numbers and try entering different values for x to find other solutions. Many times, this is more accurate than using a computer because your fingers may not be able to match up the buttons and fields on a computer.
A good way to learn how to use the quadratic formula is by trying. First, choose an easy problem to solve- say, find the average of three numbers with an average of 7,000 units between them.)
Subtracting both sides of the equation will yield your first number in the parentheses (x). Subtracting that number from both sides of the equation will yield your second number in the parentheses (x2). d/dx = x2 so solving this two-line equation will yield x = 2 and d/dx = 2 which equals x2. Now choose one number in your solution and solve for x! Try these steps out until you have found your unique value for x.
## Solve by hand using algebra
Using the quadratic formula is not a precise way to solve for x in many cases. There are ways to do it by hand, however!
Using the quadratic formula at a glance is not very helpful when trying to calculate cost savings. That depends on your goal. For example, if you want cost savings as a method of teaching improvement, then using the quadratic formula is not going to help that more effectively.
But if you only wanted x in order to determine if the lesson was worth doing again then by hand? Then yes! By checking the value of x with and without the calculator you can figure out which one works best for you.
## What is the quadratic formula?
The quadratic formula is a very useful math equation that can be used to solve for any number of things. The quadratic formula can be used to find the value of any algebraic expression.
The quadratic formula was developed in the nineteenth century by scholars studying polynomial equations. These equations can have several variables, and when combined together, produce a single variable.
An example of a polynomial equation with two variables is:
2x + 5 = 7, where x = 5, 7, and 15. In this case, the value of the polynomial depends on the values of the two other variables.
However, many times we do not know which variables are being used to solve an equation.
Most algebraic equations have a variable variable, called the x-variable. The y-variable does not appear to be variable, but it is actually called the factor or factor component.
The x- and y-factors are called factors because they come from variables in an equation. For example, when we say that lukewarm water will cool a frozen waterball down, we are saying that the waterball contains some of the variable lukewarm water + some of the variable temperature + the factor component of the time.
To solve an equation with more than one term, you always separate out the ones that have different variables. For example, in the above equation, we would take away lukewarm and frozen so that we had only warm water and ice to solve for our frozen waterball.
## Example Using Quadratic Equation Formulas
An example of using the Quadratic Formula to solve an equation is finding the value of a variable in an equation.
For example, say you have an equation that has a variable in it, as the only information. The variable wants to change when the equation has a equal-to-equal-to clause.
Using the Quadratic Formula, you can find the value of the variable in this case. If it is seven, then your solution has a value of seven!
The value of the variable can be found by changing one side of the equation to be equal to something else. In this case, changing the equal-to clause to be seven times makes one side of the original equation become seven times what it was before.
#### Harry Potter
Harry Potter, the famed wizard from Hogwarts, manages Premier Children's Work - a blog that is run with the help of children. Harry, who is passionate about children's education, strives to make a difference in their lives through this platform. He involves children in the management of this blog, teaching them valuable skills like writing, editing, and social media management, and provides support for their studies in return. Through this blog, Harry hopes to inspire others to promote education and make a positive impact on children's lives. For advertising queries, contact: support@techlurker.comView Author posts
| 1,643
| 7,572
|
{"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}
| 4.75
| 5
|
CC-MAIN-2024-10
|
latest
|
en
| 0.913537
|
https://physics.stackexchange.com/questions/508758/error-estimation-with-missed-data
| 1,722,762,402,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640393185.10/warc/CC-MAIN-20240804071743-20240804101743-00366.warc.gz
| 361,466,139
| 40,596
|
# Error estimation with missed data
When I need to find an error in the value of some real physical quantity and I can have as many number of measurements as needed, then it is clear. For example, I have a metal rod 10 cm length and 1 cm diameter and I need to measure it's length. I take this tool, make 10, 20, 50 whatever measurements. Write it down, calculate average, standard deviation, etc and I will get the average length error estimation somehow in this form $$10.2cm\pm0.3cm$$.
But how to calculate error in case if I cannot make enough measurements? For example, I have 100 meters length and 5 cm diameter rod and I need to measure the average diameter of this rod. Because it is very long (100 m) ideally I need to measure it every millimeter many times (at least 10) and do it over whole it's length. In this case, it will be 100000*10 = 1 million measurements. If I do these 1 million measurements, then I can use the same method to calculate the error. But I cannot do 1 million measurements in real life.
What if I have only 5 measurements after every meter, which in total gives me 500 measurements. How to calculate the error and how to take into account that it is possible, that when I do the measurement after 1 meter, in the middle can be a very big deviation from average and my error will be very very high.
Rod is just an example, because it is just a theoretical question, do not spend you time to explain, that it is not possible to make this rod, invent some clever technic, etc.
Just simple case, I have:
1. 100m rod.
2. This tool with 0.1mm precision.
3. Piece of paper or Excel to write it all down.
4. 500 measurements of the diameter of this rod, 5 per each meter.
Questions: What will be the precision of this experiment? How to calculate the precision of diameter and average diameter? In other words how to get the answer in this form: $$50.1mm\pm0.5mm$$?
Another example can be like this. I have a piece of land 10x10 km (area $$10^8 m^2$$) and I need to measure "Metres above sea level". Let say I will do it with GPS sensor and let's assume GPS "Metres above sea level" is very precise. If I divide this piece for 100x100m squares and make 1 measurement in the middle of this square, then it will be 10000 measurements which is realistic. But what if in between this 100x100m will be some hill or hole? and I want to be more precise, then I need to make a measurement inside every 1x1m square and it will be $$10^8$$ (10 million) measurements, which is not realistic.
My question: Is there well known scientific method to estimate the error in the cases described above?
| 641
| 2,619
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.96875
| 4
|
CC-MAIN-2024-33
|
latest
|
en
| 0.926343
|
https://customwriting.studyace.net/2020/10/08/fin-591-before-var-and-es-have-become-important-risk-measures-to-manage-portfolio-financial-risk-management-assignment-uon/
| 1,722,725,920,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640380725.7/warc/CC-MAIN-20240803214957-20240804004957-00400.warc.gz
| 151,991,761
| 23,127
|
# FIN 591: Before VaR and ES have Become Important Risk Measures to Manage Portfolio: Financial Risk Management Assignment, UoN
Questions 1. Conceptual Questions about Risk Measures. Before VaR and ES have become important risk measures to manage portfolio risk, the volatility of the portfolio returns was the main risk measure. In this context, explain what VaR is and why it is an interesting alternative measure of risk when compared to the traditional volatility benchmark. …
Continue reading “FIN 591: Before VaR and ES have Become Important Risk Measures to Manage Portfolio: Financial Risk Management Assignment, UoN”
The post FIN 591: Before VaR and ES have Become Important Risk Measures to Manage Portfolio: Financial Risk Management Assignment, UoN appeared first on Assignment Help Singapore No 1 : Essay & Dissertation Writers, SG.
Questions
1. Conceptual Questions about Risk Measures.
• Before VaR and ES have become important risk measures to manage portfolio risk, the volatility of the portfolio returns was the main risk measure. In this context, explain what VaR is and why it is an interesting alternative measure of risk when compared to the traditional volatility benchmark.
• Explain the main conceptual di erences between the Riskmetrics VaR and the VaR obtained with a traditional Historical Simulation.
• Explain what Expected Shortfall is and why it is a more appropriate measure of risk than VaR. Illustrate the appropriateness of ES as compared to VaR with an example.
2. Properties of Measures of Risk and their use.
Consider the following DGP for the returns: Rt+1 = t+1zt+1, with zt+1 i.i.d. Fz.
• Show that VaR satis es the positive homogeneity axiom of coherent measures of risk. Then, obtain an explicit formula for the V aRtp+1 of Rt+1. Finally, explain the importance of the positive homogeneity axiom in your calculation of V aRtp+1.
• Let X be a random variable representing the potential losses of a portfolio, with existing moment generating function MX ( ) = E[e X ]; 8 0. De ne the following risk measure, that we denominate the moment generating risk measure, for a con dence level 1 p:
p(X) = inf >0 ln( ) . Show that (:) is a Coherent Measure of Risk. p
Note: If you can’t show sub-additivity with general Xi’s you can assume that the Xi’s are independent to show the validity of this axiom under this simpler hypothesis. In this case, I will discount 1 point from the 10.
Knowing that the DGP for the returns is given by Rt+1 = t+1zt+1, we will estimate the risk measure of 2.2 for the shocks’ losses X = zt+1 in two ways. First, non-parametrically directly from data. Second, parametrically, assuming that Fz N( ; 2), but with the Gaussian parameters estimated from data.
• Use the leveraged GARCH(1,1) model for the volatility: t2+1 = ! + (Rt t)2 + t2. Take the AppleMidtermFall2020.xls worksheet (adjusted close prices), calculate the historical returns fRt+1gTt=1, and normalize those returns by the leveraged GARCH(1,1) estimated volatility t+1 to obtain the sequence of shocks fzt+1g. Show the values of the estimated parameters f!; ;; g and plot a graph of the leveraged GARCH(1,1) volatility.
• Using the innovation terms zt+1’s obtained in 2.3, create a grid with 1000 observations ranging from 0.01 to 100 and, for each j, estimate the sample value of the moment generating function of X: M^X ( j) = Pi=1T. Plot the values of against 1ln( ) . p Estimate ^p(X) by minimizing this function, for p = 2:5% (that is, the 2:5% highest losses of your n o portfolio).
• Obtain an analytical solution for ^p(X) when X N( ; 2) as a function of p; ; . Compare the results of this item with those in 2.4 and also with a leveraged GARCH(1,1) Gaussian V aRp with p = 2:5%. Comment on your comparisons. In other words, I am asking you to compare the results of three risk measures here: the nonparametric moment generating risk measure of item 2.4, the parametric moment generating risk measure of this item, and the leveraged GARCH(1,1) Gaussian VaR risk measure.
Note: A leveraged GARCH(1,1) Gaussian VaR that considers the following DGP for the returns: t2+1 = ! + (Rt t)2 + t2 is simply a variation of the RiskMetrics model Rt+1t+1zt+1, with zt+1 i.i.d. N(0; 1) and t2+1 = ! + (Rt t)2 + t2.
Write My Assignment
#### Hire a Professional Essay & Assignment Writer for completing your Academic Assessments
Native Singapore Writers Team
• 100% Plagiarism-Free Essay
• Highest Satisfaction Rate
• Free Revision
• On-Time Delivery
3. VaR and ES with the t-student(d) distribution and with Filtered Historical Simulation.
• Consider a t-student(d) random variable with density ft(d)(x; d) = x2 (1+d) d ) . Show that its variance is given by .
• Fit a standard t-student to the shocks zt’s of the IBM stock. To that end, rst estimate the variance of the returns with a t-student GARCH(1,1) model and normalize the returns Rt’s with the square root of this variance, that is: zt = Rt . Then, if the GARCH software hasn’t tGARCH given you the degrees of freedom of the implied t-student distribution for the z’s, use the obtained z’s to estimate the degrees of freedom parameter d of the t distribution, either by Maximum Likelihood or by the trick of matching moments learned in class. Finally, use the QQ-plot to inform you about the quality of the approximation of the distribution of the z’s by the standard t-student distribution.
Note: The GARCH can alternatively be estimated with QMLE (assuming that the z’s are Gaussian even though they are not).
• Calculate, for three di erent values of p = 1%; 2:5%; 5%, the ratio of ES to VaR for the tted standard t-distribution of item 3.2 using the formulas from pages 24 and 25 of the slides of Lectures 9 10 and 11.pdf” on Non-normal distributions. Compare them to the ratio that you would obtain by using the corresponding nonparametric estimates of ES and VaR for the shocks fztg’s (that is, using the Filtered Historical Simulation). If you wanted to minimize the chances of underestimating the risk of your portfolio, which method would you choose, the GARCH with parametric standard t or the Filtered Historical Simulation (GARCH with nonparametric distribution for z)?
4. Risk estimation based on the GPD via EVT
Let Lt+1 be a random variable representing the portfolio loss for tomorrow, and FLt+1 (y) its cumula-tive distribution function. In class we saw that the tail of the distribution FLt+1 (y) (observations that exceed a certain threshold u), here represented by the conditional distribution Fu(y) = P (Lt+11yjLt+1 > u), is well approximated by a Pareto Distribution (PD) Fu(y) = 1 cy , with y > u and > 0.
Use the Excel le spxlongFall2020.xls” that contains a long dataset of S&P 500 prices and sup-pose that you are long one unit of the index. Calculate log returns, normalize the returns using a GARCH(1,1) variance to obtain the sequence of shocks fztg, and switch the sign of these shocks to obtain the corresponding sequence of losses yt = zt. You should set the threshold u in two ways and then compare the results of each solution: First, use the 95% quantile of the loss distribution. Second, use a QQ-plot against a standard Gaussian distribution and choose the threshold such that the positive losses that deviate from the 45-degree line should appear in the tail. For each case, use the Hill estimator described in the slides of Lectures 9, 10, and 11.pdf” to estimate the parameter and the Equation on page 43 to estimate the parameter c.
Estimate VaR and ES for = 95; 99; 99:5; 99:9% using the PD and compare to the standard Risk-Metrics VaR and ES. The goal of this exercise is to observe and contrast what happens on a usual region of the tail (95%) compared to a very extreme area of the tail (99:9%). Comment your results.
The post FIN 591: Before VaR and ES have Become Important Risk Measures to Manage Portfolio: Financial Risk Management Assignment, UoN appeared first on Assignment Help Singapore No 1 : Essay & Dissertation Writers, SG.
| 1,988
| 8,025
|
{"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}
| 3.53125
| 4
|
CC-MAIN-2024-33
|
latest
|
en
| 0.878315
|
https://getrevising.co.uk/forums/topics/what_two_numbers_added_together_make_11_and_multiplied_make_6
| 1,547,903,194,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-04/segments/1547583667907.49/warc/CC-MAIN-20190119115530-20190119141530-00160.warc.gz
| 514,679,923
| 15,860
|
# What two numbers added together make -11 and multiplied make 6?
Thank you
Posted Mon 3rd December, 2012 @ 18:18 by Emily
if it's a quadratic equation then can you give the whole equation??
Answered Mon 3rd December, 2012 @ 18:20 by Diya
Its 3p^2-11p+6=o
Thanks :)
Answered Mon 3rd December, 2012 @ 18:50 by Emily
im not sure how u were taught but this is how i do it when the x^2 is a prime factor..
first.. u do 3 * 6 = 18
then u find two numbers.. that add to give -11 and times to 18
so the two numbers should be -9 and -2
makes sense ?? or shld i explain the steps properly. coz i knw its a bit vauge..
hope it helps :)
Answered Mon 3rd December, 2012 @ 19:45 by ? Secret - Team GR
Thanks :)
Answered Mon 3rd December, 2012 @ 20:05 by Emily
your welcome :) if it doesnt make sense feel free to ask.. i dont mind
Answered Mon 3rd December, 2012 @ 20:06 by ? Secret - Team GR
| 281
| 897
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.46875
| 3
|
CC-MAIN-2019-04
|
longest
|
en
| 0.930627
|
http://www.talkstats.com/threads/transforming-the-data.279/
| 1,585,419,185,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-16/segments/1585370492125.18/warc/CC-MAIN-20200328164156-20200328194156-00323.warc.gz
| 314,214,235
| 10,394
|
Transforming the data
AlexKom
New Member
Hello!
I can't understand: In order to transform the data to make it appear more linear, how can I choose what transformation to use, if I don't have any data, but just scatterplot in front of me....(I hope, you understand me)
Thank you!
JohnM
TS Contributor
There are certain transformations that work better, depending on the original relationship between x and y. Your text probably has a table that shows the appropriate or "recommended" transformation, based on the approximate equation between x and y.
AlexKom
New Member
I have a task in test, where the image of scatterplot is given and then 4 possible types of transformation. I know how to transform the data by the method of trying different combinations (log x, log y, y2 etc.) on graphic calculator. But what if they don't give any data, but just the image of scatterplot with a certain pattern and then they ask what method of transformation to use?
JohnM
TS Contributor
From the scatterplot, you should be able to estimate the relationship between x and y. Such as y = x^2 or y = ln(x) etc.
From this, does your text discuss what transformation works the best based on the original relationship between x and y?
AlexKom
New Member
I am sorry, but how can I estimate what is the relationship between x and y? I know that if it lookslike a curve, than exponential or logarithmic model is used. I am sorry, can you explain it to me?
JohnM
TS Contributor
If the scatterplot includes the x and y axis marks with numbers, then you should be able to sketch a "best fit" line through it and estimate the equation of the best fit line by picking a few values of x and seeing what y would be. This is normally done in algebra --> given a few data pairs (x,y), determine the slope and y-intercept of the line.
In your example, I imagine it would be a pretty simple relationship even though it won't be linear...
Does it look something like y = x^2 or y = ln(x) or y = n^x ?
| 454
| 1,984
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.703125
| 4
|
CC-MAIN-2020-16
|
latest
|
en
| 0.937674
|
https://brainmass.com/math/algebra/desalination-exponential-equation-324617
| 1,576,130,882,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-51/segments/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00274.warc.gz
| 300,077,178
| 11,878
|
Explore BrainMass
Share
# Equations
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
1. Desalination. More cities are supplying some of their fresh water through desalination, the process of removing the salt from the ocean water. The worldwide desalination capacity has grown exponentially from 15 million m^3 per day in 1990 to 55 million m^3 per day in 2007.
a) Find the exponential growth rate k and write an equation for an exponential function that can be used to predict the worldwide desalination capacity D(t) in millions of cubic meters per day, t years after 1990.
b) Predict the worldwide desalination capacity in 2012.
c) In what year will the worldwide desalination capacity reach 100 million m^3 per day?
4.y=-log2(x/4)
Evaluate the equation for 1, 2, 3, 4, 0.5 ,0.33,& 0.25
Graph.
| 225
| 861
|
{"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-2019-51
|
longest
|
en
| 0.859988
|
https://www.accountingdetails.com/economic_order_quantity_eco.htm?replytocom=462068
| 1,590,476,880,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00017.warc.gz
| 554,846,269
| 47,050
|
# Economic Order Quantity (EOQ) Destination , formula and Example
Learning Objective:
1. Definite and explain economic order quantity (EOQ).
2. How is economic order quantity (EOQ) calculated?
1. economic order quantity Formula (EOQ formula)
2. ## Definition and Explanation:
Economic order quantity (EOQ) is that size of the order which gives maximum economy in purchasing any material and ultimately contributes towards maintaining the materials at the optimum level and at the minimum cost.
In other words, the economic order quantity (EOQ) is the amount of inventory to be ordered at one time for purposes of minimizing annual inventory cost.
The quantity to order at a given time must be determined by balancing two factors: (1) the cost of possessing or carrying materials and (2) the cost of acquiring or ordering materials. Purchasing larger quantities may decrease the unit cost of acquisition, but this saving may not be more than offset by the cost of carrying materials in stock for a longer period of time.
The carrying cost of inventory may include:
• Interest on investment of working capital
• Property tax and insurance
• Storage cost, handling cost
• Deterioration and shrinkage of stocks
• Obsolescence of stocks.
## Formula of Economic Order Quantity (EOQ):
The different formulas have been developed for the calculation of economic order quantity (EOQ). The following formula is usually used for the calculation of EOQ.
• A = Demand for the year
• Cp = Cost to place a single order
• Ch = Cost to hold one unit inventory for a year
• * = ×
## Example:
Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit is \$2.50 and the cost to place an order is \$50.
Calculate economic order quantity (EOQ)
## Underlying Assumptions of Economic Order Quantity:
1. The ordering cost is constant.
2. The rate of demand is constant
3. The lead time is fixed
4. The purchase price of the item is constant i.e no discount is available
5. The replenishment is made instantaneously, the whole batch is delivered at once.
None Found
| 470
| 2,135
|
{"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}
| 3.984375
| 4
|
CC-MAIN-2020-24
|
latest
|
en
| 0.87849
|
https://www.cscodehelp.com/%E7%A7%91%E7%A0%94%E4%BB%A3%E7%A0%81%E4%BB%A3%E5%86%99/cs%E4%BB%A3%E8%80%83%E8%AE%A1%E7%AE%97%E6%9C%BA%E4%BB%A3%E5%86%99-fprintf-n/
| 1,726,850,442,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725701419169.94/warc/CC-MAIN-20240920154713-20240920184713-00220.warc.gz
| 651,353,177
| 12,845
|
# CS代考计算机代写 fprintf( ‘————————————- ’ );
fprintf( ‘————————————-
’ );
fprintf( ‘Q 1
’ );
fprintf( ‘————————————-
’ );
nx = 640;
ny = 480;
T_cann_from_screen = [ 2/nx 0 -(1-1/nx);
0 -2/ny (1-1/ny);
0 0 1 ]
ptA = [ 10 35 1 ]’;
ptB = [ 50 340 1 ]’;
ptA_cann = T_cann_from_screen * ptA;
ptB_cann = T_cann_from_screen * ptB;
fprintf( ‘Click A =
’)
fprintf( ‘[ %5.2f %5.2f ]^T
’, ptA_cann(1:2) );
fprintf( ‘Click B =
’)
fprintf( ‘[ %5.2f %5.2f ]^T
’, ptB_cann(1:2) );
% Try this to convince yourself that its is correct:
% inv(T_cann_from_screen)
clear all;
fprintf( ‘————————————-
’ );
fprintf( ‘Q 2
’ );
fprintf( ‘————————————-
’ );
eyeVec = [ 5 1 3 ]’;
atVec = [ -1 -1 -6 ]’;
upVec = [ 0 0 1]’;
gazeVec = atVec-eyeVec;
w = -gazeVec/norm(gazeVec,2);
u = cross( upVec, w )/norm(upVec,2);
v = cross( w, u );
fprintf( ‘u =
’)
fprintf( ‘[ %5.2f %5.2f %5.2f ]^T
’, u );
fprintf( ‘v =
’)
fprintf( ‘[ %5.2f %5.2f %5.2f ]^T
’, v );
fprintf( ‘w =
’)
fprintf( ‘[ %5.2f %5.2f %5.2f ]^T
’, w );
fprintf( ‘
’)
M_v = [ u’ -dot(u,eyeVec);
v’ -dot(v,eyeVec);
w’ -dot(w,eyeVec);
0 0 0 1 ];
fprintf( ‘Therefore M_v =
’)
fprintf( ‘%5.2f %5.2f %5.2f %5.2f
’, (M_v)’ );
fprintf( ‘
’)
clear all;
fprintf( ‘————————————-
’ );
fprintf( ‘Q 3
’ );
fprintf( ‘————————————-
’ );
% Viewing frustum from question
n_p = -5;
l_p = -3;
b_p = -1;
r_p = l_p + 5;
t_p = b_p + 5;
f_p = n_p – 10;
% Open GL projection matrix set with glFrustum
MOpenGLProj = [ 2*abs(n_p)/(r_p-l_p) 0 (r_p+l_p)/(r_p-l_p) 0;
0 2*abs(n_p)/(r_p-l_p) (t_p+b_p)/(t_p-b_p) 0;
0 0 (abs(n_p)+abs(f_p))/(abs(n_p)-abs(f_p)) 2*abs(n_p)*abs(f_p)/(abs(n_p)-abs(f_p));
0 0 -1 0 ];
% Scene points to be projected
a1 = transpose([ 2 -1 -5 1 ]);
a2 = transpose([ -9 12 -15 1 ]);
% Points in homogenous canonical volume coordinates
a1Proj_homogeneous = MOpenGLProj * a1;
a2Proj_homogeneous = MOpenGLProj * a2;
% Points in cartesian canonical volume coordinates
a1Proj = a1Proj_homogeneous(1:3)/a1Proj_homogeneous(4);
a2Proj = a2Proj_homogeneous(1:3)/a2Proj_homogeneous(4);
fprintf( ‘Points in cartesian canonical viewing volume:
’)
fprintf( ‘[ %5.2f %5.2f %5.2f ]^T
’, a1Proj );
fprintf( ‘[ %5.2f %5.2f %5.2f ]^T
’, a2Proj );
fprintf( ‘
’)
clear all;
| 938
| 2,191
|
{"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-2024-38
|
latest
|
en
| 0.252335
|
http://mathhelpforum.com/discrete-math/157239-can-t-prove-proposition-about-transitive-trees.html
| 1,527,394,170,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-22/segments/1526794867995.55/warc/CC-MAIN-20180527024953-20180527044953-00302.warc.gz
| 190,947,533
| 10,487
|
1. can't prove proposition about transitive trees.
I need to prove: (T,S) is a transitive tree iff (T, S<) is a tree (where S< represents the immediate predecessor relation given by s S< t iff s S t and moreover s S v and v S t for holds for no v in T).
I proved the ==> direction by its contrapositive, but I'm thinking the <== direction is false. What happens if S< simply equals S. We know S< isn't transitive from the definition - so (T,S) wouldn't be a transitive tree. If this isn't a counterexample, let me know what I'm missing here.
2. Originally Posted by jimbob11
I need to prove: (T,S) is a transitive tree iff (T, S<) is a tree (where S< represents the immediate predecessor relation given by s S< t iff s S t and moreover s S v and v S t for holds for no v in T).
I proved the ==> direction by its contrapositive, but I'm thinking the <== direction is false. What happens if S< simply equals S. We know S< isn't transitive from the definition - so (T,S) wouldn't be a transitive tree. If this isn't a counterexample, let me know what I'm missing here.
I guess I am not the only one not familiar with the terminology.
Obviously the OP uses book Modal logic By Patrick Blackburn, Maarten de Rijke, Yde Venema
- it is exercise 1.1.4 from this book.
I think your counterexample works, but if you change the claim to:
"Let S be a SPO on T. (T,S) is a transitive tree if (T,S<) is a tree."
then it should work.
3. Yes. I guess in this case the pf is trivial since a strict partial ordering is already transitive by defn. I'm extremely impressed that you found the reference. I should've included it, but didn't realize their terminology was idiosyncratic.
4. Originally Posted by jimbob11
Yes. I guess in this case the pf is trivial since a strict partial ordering is already transitive by defn. I'm extremely impressed that you found the reference. I should've included it, but didn't realize their terminology was idiosyncratic.
It wasn't that difficult to find - I've just searched for "transitive tree" in google books.
BTW as far as this book is concerned, here's a part of a review by by Manuel Bremer SpringerLink - Minds and Machines, Volume 15, Number 1
Further on, given the abstract approach, the book – although mostly clearly written – is not easy. The exercises are often far from trivial, and no solutions are provided. So this is not – as again the back cover has it – ‘‘both for novices and for more experienced readers’’ or ‘‘ideal for anyone wanting to learn modern modal logic’’. Novices will likely be frustrated if they try the book on their own. Crucial lemmas (like Lindenbaum’s Lemma) are left as an ‘‘exercise to the reader’’ and having not come up with the proof the overall picture may have gaps.
| 689
| 2,740
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.296875
| 3
|
CC-MAIN-2018-22
|
latest
|
en
| 0.971293
|
https://www.convertunits.com/from/stere/day/to/cubic+inch/day
| 1,631,920,513,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780055808.78/warc/CC-MAIN-20210917212307-20210918002307-00373.warc.gz
| 760,462,990
| 12,916
|
››Convert stere/day to cubic inch/day
stere/day cubic inch/day
How many stere/day in 1 cubic inch/day? The answer is 1.6387064236111E-5.
We assume you are converting between stere/day and cubic inch/day.
You can view more details on each measurement unit:
stere/day or cubic inch/day
The SI derived unit for volume flow rate is the cubic meter/second.
1 cubic meter/second is equal to 86400 stere/day, or 5272451413.8174 cubic inch/day.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between steres/day and cubic inches/day.
Type in your own numbers in the form to convert the units!
››Quick conversion chart of stere/day to cubic inch/day
1 stere/day to cubic inch/day = 61023.74322 cubic inch/day
2 stere/day to cubic inch/day = 122047.48643 cubic inch/day
3 stere/day to cubic inch/day = 183071.22965 cubic inch/day
4 stere/day to cubic inch/day = 244094.97286 cubic inch/day
5 stere/day to cubic inch/day = 305118.71608 cubic inch/day
6 stere/day to cubic inch/day = 366142.45929 cubic inch/day
7 stere/day to cubic inch/day = 427166.20251 cubic inch/day
8 stere/day to cubic inch/day = 488189.94572 cubic inch/day
9 stere/day to cubic inch/day = 549213.68894 cubic inch/day
10 stere/day to cubic inch/day = 610237.43215 cubic inch/day
››Want other units?
You can do the reverse unit conversion from cubic inch/day to stere/day, or enter any two units below:
Enter two units to convert
From: To:
››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!
| 504
| 1,957
|
{"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-2021-39
|
latest
|
en
| 0.797799
|
https://www.findstuff1.com/coffee/okuyucular-soruyor-how-to-make-coffee-at-work.html
| 1,638,144,272,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964358673.74/warc/CC-MAIN-20211128224316-20211129014316-00546.warc.gz
| 863,070,823
| 11,762
|
# Okuyucular soruyor: How To Make Coffee At Work?
## How do you make coffee manually?
HOW TO BREW IT
1. Pour water into your pan.
2. Stir the coffee grounds right into the water.
3. Set a burner to medium-high and bring your coffee to a boil.
4. Boil your coffee uncovered for two minutes.
5. Remove the pot from the heat and let it sit for four minutes.
## How do you make coffee in 10 steps?
10 Steps from Seed to Cup
1. Planting. A coffee bean is actually a seed.
2. Harvesting the Cherries.
3. Processing the Cherries.
4. Drying the Beans.
5. Milling the Beans.
6. Exporting the Beans.
7. Tasting the Coffee.
8. Roasting the Coffee.
## How do you make creamy coffee?
Instructions
1. Place the instant coffee, sugar and water in a bowl.
2. Use a whisk, hand mixer or frother to combine. It will take about 5-15 minutes depending on the type of whisk you use. Look for a thickened consistency that’s much lighter in color.
3. Serve it as a creamy topping over any milk of choice – iced or hot.
## How much coffee do you add per cup?
The standard ratio for brewing coffee is 1-2 tablespoons of ground coffee per 6 ounces of water – 1 tablespoon for lighter coffee and 2 for stronger coffee. That 6-ounce measure is equivalent to one “cup” in a standard coffeemaker, but keep in mind that the standard mug size is closer to 12 ounces or larger.
You might be interested: Hızlı Cevap: Does Bicarbonatre In Coffee Reduce Acidity?
## How much coffee do you put in a coffee maker?
Measure Your Grounds: Add the desired amount of grounds to the filter: about 1 tablespoon per 5 to 6 fluid ounces of cold water for regular coffee, and 2 tablespoons per 5 to 6 fluid ounces for strong coffee. Or check out our helpful Measurement Chart and Cups Calculator.
## How much coffee do I use for 6 cups?
Weigh or measure the amount of whole bean coffee for the desired number of cups. For this brew, we measured 7 Tablespoons or ~40 grams of light roasted, whole bean coffee (1 Tablespoon ≈ 6 grams). For making 6 cups, we recommend 10 Tablespoons or ~ 60 grams of coffee.
## What is the best coffee making method?
From the drip method to the pour over technique, these are of some of the best ways to make coffee.
• Drip Coffee. Drip Coffee Pros. Set it and forget it.
• French Press Coffee. French Press Pros. It makes a rich, full-bodied cup.
• Pour Over Coffee. Pour Over Pros.
• AeroPress Coffee. AeroPress Pros.
• Coffee Dripper. Coffee Dripper Pros.
## Is instant coffee bad for you?
Instant coffee contains slightly less caffeine and more acrylamide than regular coffee, but it contains most of the same antioxidants. Overall, instant coffee is a healthy, low-calorie beverage that is linked to the same health benefits as other types of coffee.
## Can you use ground coffee as instant?
Thankfully, you can easily turn regular coffee into instant coffee if that’s all you have at home. One way is to grind your coffee beans into a fine powder. Another way you can use ground coffee like instant coffee is by putting ground coffee in a cup and adding hot water to it.
You might be interested: Sık sorulan: When Was The Coffee Maker Invented?
## How do you make coffee in 7 steps?
7 Steps to Making that Perfect Cup of Blaze Coffee
1. Step 1: The Coffee Beans.
2. Step 2: The Ratio of Water to Coffee.
3. Step 3: The Type of Grind.
4. Step 4: Your Preferred Brewing Method or Equipment.
5. Step 5: Proper Brewing Technique/Operation.
6. Step 6: The Quality of your Water.
7. Step 7: Your Chosen Filtering Type.
## How do you make a cup of coffee with milk?
Pour the coffee in a tall, thick glass, and in a gentle but quick stream, pour the milk in. This will cool down the coffee/milk mixture, it will form a layer of foam at the top of the glass. After this, add sugar to sweeten and enjoy your Coffee with milk!
## How do you make tea in 10 steps?
How to Make the Perfect Cup of Tea.
1. Step 1: Choose Your Brewing Vessel.
2. Step 2: Warm Your Teaware.
3. Step 3: Disgard the Hot Water.
| 997
| 4,013
|
{"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-2021-49
|
latest
|
en
| 0.891314
|
https://mathlair.allfunandgames.ca/postcards.php
| 1,709,018,069,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474671.63/warc/CC-MAIN-20240227053544-20240227083544-00526.warc.gz
| 392,278,666
| 3,098
|
# Postcards
Math Lair Home > Topics > Postcards
Here's an interesting exercise to test your estimation skills. Before World War I or so, postcards typically were printed to the edge of the postcard, with the picture filling the entire card. During World War I and for a while afterwards, postcard publishers tended to leave a white border around the edge of the card, to save on ink. For example, below you can view an example of a postcard from 1913 (top) and an example of a postcard from the 1920s (bottom):
Now for the mathematics part. What percentage of ink do you think was saved by leaving a white border instead of printing on the entire area of the card? Before reading on, have a look at the cards above and estimate what percentage of ink would be saved.
Measuring the cards, we find that each card is 5½ inches wide and 3½ inches high. The picture on the bottom card is 5 inches wide and 3 inches high. So, the area covered with ink on the top card is:
3½ × 5½ = 19¼in²
The area covered with ink on the bottom card is:
3 × 5 = 15in²
The savings is
1 − 1519¼ ≅ 22%
So, the savings in ink is 22%; in other words, the border consumes more than 15 of the area of the card. Surprising, isn't it? Our intuition can sometimes deceive us about areas when they are displayed like this. It is a good idea to be alert in the real world for things like this.
If you want to print the cards out and measure for yourself, the images are scaled to 100 pixels per inch. Here's a scale ruler:
If you're interested in more information on the postcards depicted: The top postcard, entitled "Zavikon (The House is in Canada and the Island with the Flagpole in the United States), Thousand Islands, St. Lawrence River," was published by The Valentine & Sons Publishing Co., Ltd., and the card that I scanned was postmarked August 9, 1913. It is numbered 108358 in their series. The bottom postcard, entitled "Zavikon, Thousand Islands (showing the smallest international bridge in the world)", was published by Valentine-Black Co., Ltd., the successor company to Valentine & Sons, and is not postmarked. According to this page, Valentine-Black was active between 1922 and 1933, so sometime in the 1920s seems a reasonable guess for the latter card. The two views appear to be based on the exact same photograph. Note that both islands are actually in Canada; there is a boundary marker on the smaller island but the border actually runs slightly to the south and east.
If you're interested in other pages on this site that are illustrated with vintage postcards, see also "The Mathematics of the Lost Chord" and The Expanding Bridge. If you're looking for more images of old postcards, you can see postcards on Canadian Transport Sourcebook.
| 644
| 2,746
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.53125
| 5
|
CC-MAIN-2024-10
|
latest
|
en
| 0.954176
|
https://fr.mathworks.com/matlabcentral/cody/problems/730-how-many-trades-represent-all-the-profit/solutions/517037
| 1,590,705,606,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00526.warc.gz
| 371,171,498
| 15,767
|
Cody
# Problem 730. How many trades represent all the profit?
Solution 517037
Submitted on 27 Oct 2014 by Yalong Liu
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
trades = 1 3 -4 2 -1 2 3 ans = 2
2 Pass
trades = 1 2 3 -5 ans = 1
3 Pass
trades = 1 2 3 4 5 6 ans = 6
4 Pass
%% trades = [-2 3 -4 5 -6 1 2 3 4 5] y_correct = 3; assert(isequal(trade_profit(trades),y_correct))
trades = -2 3 -4 5 -6 1 2 3 4 5 ans = 3
| 213
| 549
|
{"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-2020-24
|
latest
|
en
| 0.667394
|
http://www.dailyfreecode.com/Code/flood-fill-algorithm-698.aspx
| 1,568,557,351,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-39/segments/1568514571506.61/warc/CC-MAIN-20190915134729-20190915160729-00380.warc.gz
| 237,625,775
| 11,014
|
Search:
# C++ Programming Articles
Submit Article
RSS Feeds
# Program of Flood fill algorithm
Posted By: Easy Tutor Category: C++ Programming Views: 54924
## Code for Program of Flood fill algorithm in C++ Programming
```# include <stdio.h>
# include <dos.h>
# include <iostream.h>
# include <conio.h>
# include <stdlib.h>
# include <graphics.h>
void FloodFill(int,int,int,int);
void MidPoint(int);
void main()
{
int xCenter=320;
int yCenter=240;
int gDriver = DETECT, gMode, errorcode;
initgraph(&gDriver, &gMode, "c:\\tc\\bgi");
cleardevice();
MidPoint(49);
FloodFill(xCenter+1,yCenter+1,0,8);
getch();
return;
}
void MidPoint(int Radius)
{
int iCntr, x, y,p0;
x=0;
y=Radius;
int xCenter=320;
int yCenter=240;
p0=(5/4)-Radius;
putpixel(xCenter+x,yCenter+y,15);
putpixel(xCenter-x,yCenter+y,15);
putpixel(xCenter+x,yCenter-y,10);
putpixel(xCenter-x,yCenter-y,10);
putpixel(xCenter+y,yCenter+x,12);
putpixel(xCenter-y,yCenter+x,12);
putpixel(xCenter+y,yCenter-x,9);
putpixel(xCenter-y,yCenter-x,9);
while(x<=y)
{
if(p0 < 0)
{
p0=p0 + 2*(x+1) + 1;
x=x+1;
}
else
{
p0=p0 + 2*(x+1) + 1 - 2*(y-1);
x=x+1;
y=y-1;
}
putpixel(xCenter+x,yCenter+y,15);
putpixel(xCenter-x,yCenter+y,15);
putpixel(xCenter+x,yCenter-y,10);
putpixel(xCenter-x,yCenter-y,10);
putpixel(xCenter+y,yCenter+x,12);
putpixel(xCenter-y,yCenter+x,12);
putpixel(xCenter+y,yCenter-x,9);
putpixel(xCenter-y,yCenter-x,9);
}
}
void FloodFill(int pointx,int pointy,int OldColor,int NewColor)
{
int Intensity=getpixel(pointx,pointy);
if(Intensity==OldColor)
{
putpixel(pointx,pointy,NewColor);
FloodFill(pointx+1,pointy,OldColor,NewColor);
FloodFill(pointx-1,pointy,OldColor,NewColor);
FloodFill(pointx,pointy+1,OldColor,NewColor);
FloodFill(pointx,pointy-1,OldColor,NewColor);
}
}```
Share:
Didn't find what you were looking for? Find more on Program of Flood fill algorithm Or get search suggestion and latest updates.
Easy Tutor author of Program of Flood fill algorithm is from United States. Easy Tutor says Hello Friends,I am Free Lance Tutor, who helped student in completing their homework. I have 4 Years of hands on experience on helping student in completing their homework. I also guide them in doing their final year projects.I have share many programs on this website for everyone to use freely, if you need further assistance, than please contact me on easytutor.2ya [at the rate] gmail [dot] comI have special discount scheme for providing tutor services. I am providing tutor service to students from various contries, currently most of my students are from United States, India, Australia, Pakistan, Germany, UK and Canada. I am also here to expand my technical network to receive more opportunity in my career, make friends to help them in resolving their technical problem, learn and share my knowledge, If you like to be my friend, Please send me friend request.Thanks,Happy Programming :) View All Articles
Please enter your Comment
• Comment should be atleast 30 Characters.
• Please put code inside [Code] your code [/Code].
Jeena Raghavan from Australia Comment on: Jan 18 dos.h: No such file or directory # include ^compilation terminated.I got this error during compilation :-(
Anisha Amir from Taiwan Comment on: Nov 05 I get errors and one of my error is: graphics.h: No such file or directory. Do I have to download any additional library?
View All Comments
| 933
| 3,376
|
{"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-2019-39
|
longest
|
en
| 0.592643
|
https://www.ibpsguide.com/sbi-po-prelims-reasoning-ability-questions-day-05/
| 1,627,196,956,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-31/segments/1627046151638.93/warc/CC-MAIN-20210725045638-20210725075638-00600.warc.gz
| 837,664,009
| 73,337
|
# SBI PO Prelims Reasoning (Day-05)
Dear Aspirants, Our IBPS Guide team is providing new series of Reasoning Questions for SBI PO 2020 Prelims so the aspirants can practice it on a daily basis. These questions are framed by our skilled experts after understanding your needs thoroughly. Aspirants can practice these new series questions daily to familiarize with the exact exam pattern and make your preparation effective.
Start Quiz
Order and ranking
Directions (1-3):Â Study the following information carefully and answer the questions given below:
Seven cities – V, L, P, R, G, D and X have different number of lakes. City P has more number of lakes than City V but less number of lakes than City R. Only one city has less number of lakes than City D. City L has less number of lakes than City X but more number of lakes than City V. City X has more number of lakes than City R. City V does not have the least number of lakes. City R has more number of lakes than L.
1) Which of the following city has maximum number of lake?
A) P
B) L
C) R
D) X
E) None of these
2) How many cities have more number of lake than City P?
A) One
B) Two
C) Three
D) Four
E) Cannot be determined
3) Which are the two cities have less number of lakes than City V?
A) P, L
B) R, P
C) X, P
D) G, D
E) None of these
Misc
4) How many meaningful English words can be formed with the letter D, P, A, U, E, T using each letter only once in each word?
A) One
B) Two
C) Three
D) Four
E) None of these
Inequality
Directions (5-6): In each question, relationships between different elements are shown in the statements. The statements are followed by some conclusions. Study the conclusions based on the given statements and select the appropriate answer.
5) Statements:
L ≥ M = N > G ≤ H = J;        B ≥ C = N < O ≤ P < I;
Conclusions:
I) C < L
II) J > I
III) I > G
IV) M=J
A) Only I follow
B) Only III follow
C) Either I or IV follows
D) Only III and Neither II nor IV follows
E) None of these
6) Statements:
R > N = W ≤ D < K; V < H ≥ O = T;  S ≤ N = H > A
Conclusions:
I) R > T
II) S < K
III) V < D
IV) T ≤ D
A) Only III follow
B) Only II and III follow
C) All follows
D) Only I and III follow
E) None follows
Alphanumeric series
Directions (7-10): Study the given information and answer the questions:
7) How many symbols are there which is immediately followed by vowels and preceded by consonants?
A) None
B) 1
C) 2
D) 3
E) None of these
8) If all the numbers from the above sequence are dropped, which of the following element is 8th to the right of the 15th from the left end?
A) 1
B) 5
C) C
D) L
E) None of these
9) How many consonants are there immediately followed by number and preceded by consonant?
A) None
B) 1
C) 2
D) 3
E) None of these
10) If all the symbols from the above sequence are dropped, which of the following element is 19th from the right end?
A) Q
B) W
C) F
D) 4
E) None of these
Directions (1-3) :
X > R>P/L>P/L>V>D>G
X > R>P/L>P/L>V>D>G
X > R>P/L>P/L>V>D>G
UPDATE
Directions (5-6) :
Directions (7-10) :
I J K 3 9 ( ! F W Q 4 8 # ^ M Z VÂ G @ AÂ \$ ) S O P % 1 5 C L E 2 6
I J KÂ ( ! F W QÂ # ^ M Z V G @ A \$ ) S O P %Â Â CÂ L E
| 1,013
| 3,256
|
{"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-2021-31
|
latest
|
en
| 0.894994
|
https://www.mathcelebrity.com/community/threads/deon-opened-his-account-starting-with-650-and-he-is-going-to-take-out-40-per-month-mai-opened-up.4510/
| 1,721,503,745,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763517515.18/warc/CC-MAIN-20240720174732-20240720204732-00321.warc.gz
| 755,557,371
| 9,305
|
# Deon opened his account starting with \$650 and he is going to take out \$40 per month. Mai opened up
Discussion in 'Calculator Requests' started by math_celebrity, Oct 25, 2021.
Tags:
1. ### math_celebrityAdministratorStaff Member
Deon opened his account starting with \$650 and he is going to take out \$40 per month. Mai opened up her account with a starting amount of \$850 and is going to take out \$65 per month. When would the two accounts have the same amount of money?
We set up a balance equation B(m) where m is the number of months.
Set up Deon's Balance equation:
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m
Set up Mai's Balance equation:
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m
When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m
Solve for m in the equation 650 - 40m = 850 - 65m
Step 1: Group variables:
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m
Step 2: Cancel -65m on the right side:
25m + 650 = 850
Step 3: Group constants:
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650
Step 4: Cancel 650 on the left side:
25m = 200
Step 5: Divide each side of the equation by 25
25m/25 = 200/25
m = 8
| 449
| 1,512
|
{"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}
| 4.5
| 4
|
CC-MAIN-2024-30
|
latest
|
en
| 0.917103
|
https://www.whizwriters.com/mathematics-1734/
| 1,606,655,409,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-50/segments/1606141198409.43/warc/CC-MAIN-20201129123729-20201129153729-00396.warc.gz
| 896,924,687
| 11,793
|
# Mathematics
398
Chapter Preview Now that we have some basic techniques for evaluating integrals, we turn our attention to the uses of integration, which are virtually endless. We first illus- trate the general rule that if the rate of change of a quantity is known, then integration can be used to determine the net change or the future value of that quantity over a certain time interval. Next, we explore some rich geometric applications of integration: comput- ing the area of regions bounded by several curves, the volume and surface area of three- dimensional solids, and the length of curves. A variety of physical applications of integration include finding the work done by a variable force and computing the total force exerted by water behind a dam. All of these applications are unified by their use of the slice-and- sum strategy. We end this chapter by revisiting the logarithmic function, exploring the many applications of the exponential function, and introducing hyperbolic functions.
6.1 Velocity and Net Change In previous chapters, we established the relationship between the position and velocity of an object moving along a line. With integration, we can now say much more about this relationship. Once we relate velocity and position through integration, we can make analogous observations about a variety of other practical problems, which include fluid flow, population growth, manufacturing costs, and production and consumption of natu- ral resources. The ideas in this section come directly from the Fundamental Theorem of Calculus, and they are among the most powerful applications of calculus.
Velocity, Position, and Displacement Suppose you are driving along a straight highway and your position relative to a reference point or origin is s1t2 for times t Ú 0. Your displacement over a time interval 3a, b4 is the change in the position s1b2 – s1a2 (Figure 6.1). If s1b2 7 s1a2, then your displacement is positive; when s1b2 6 s1a2, your displacement is negative.
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Surface Area
6.7 Physical Applications
6.8 Logarithmic and Exponential Functions Revisited
6.9 Exponential Models
6.10 Hyperbolic Functions
Applications of Integration
6
s(b)s ! 0 s(a) s (line of motion)
Position at t ! a Position at t ! b ” a
Displacement ! s (b) # s (a) ” 0
s(a)s ! 0 s(b) s (line of motion)
Position at t ! b ” a Position at t ! a
Displacement ! s (b) # s (a) \$ 0Figure 6.1
M06_BRIG7345_02_SE_C06.1.indd 398 21/10/13 9:20 PM
6.1 Velocity and Net Change 399
Now assume that v1t2 is the velocity of the object at a particular time t. Recall from Chapter 3 that v1t2 = s′1t2, which means that s is an antiderivative of v. From the Funda- mental Theorem of Calculus, it follows that
L b
a v1t2 dt = Lba s′1t2 dt = s1b2 – s1a2 = displacement.
We see that the definite integral 1ba v1t2 dt is the displacement (change in position) be- tween times t = a and t = b. Equivalently, the displacement over the time interval 3a, b4 is the net area under the velocity curve over 3a, b4 (Figure 6.2a).
Not to be confused with the displacement is the distance traveled over a time interval, which is the total distance traveled by the object, independent of the direction of motion. If the velocity is positive, the object moves in the positive direction and the displacement equals the distance traveled. However, if the velocity changes sign, then the displacement and the distance traveled are not generally equal.
QUICK CHECK 1 A police officer leaves his station on a north-south freeway at 9 a.m., trav- eling north (the positive direction) for 40 mi between 9 a.m. and 10 a.m. From 10 a.m. to 11 a.m., he travels south to a point 20 mi south of the station. What are the distance trav- eled and the displacement between 9 a.m. and 11 a.m.?
To compute the distance traveled, we need the magnitude, but not the sign, of the velocity. The magnitude of the velocity ” v1t2 ” is called the speed. The distance traveled over a small time interval dt is ” v1t2 ” dt (speed multiplied by elapsed time). Summing these dis- tances, the distance traveled over the time interval 3a, b4 is the integral of the speed; that is,
distance traveled = L b
a ” v1t2 ” dt.
As shown in Figure 6.2b, integrating the speed produces the area (not net area) bounded by the velocity curve and the t-axis, which corresponds to the distance traveled. The distance traveled is always nonnegative.Figure 6.2
y
t
t
a b
a
b
y
O
O
y ! v(t)
Area ! A1
Area ! A1
Area ! A2
Area ! A2
Displacement ! A1 ” A2 ! ! v(t) dt a
b
Distance traveled ! A1 # A2 ! ! “v(t)” dt a
b
y ! “v(t)”
(a)
(b)
DEFINITION Position, Velocity, Displacement, and Distance
1. The position of an object moving along a line at time t, denoted s1t2, is the loca- tion of the object relative to the origin.
2. The velocity of an object at time t is v1t2 = s′1t2. 3. The displacement of the object between t = a and t = b 7 a is
s1b2 – s1a2 = Lba v1t2 dt. 4. The distance traveled by the object between t = a and t = b 7 a is
L b
a ” v1t2 ” dt,
where ” v1t2 ” is the speed of the object at time t. QUICK CHECK 2 Describe a possible motion of an object along a line for 0 … t … 5 for which the displacement and the distance traveled are different.
M06_BRIG7345_02_SE_C06.1.indd 399 21/10/13 11:29 AM
400 Chapter 6 Applications of Integration
EXAMPLE 1 Displacement from velocity A jogger runs along a straight road with velocity (in mi/hr) v1t2 = 2t2 – 8t + 6, for 0 … t … 3, where t is measured in hours. a. Graph the velocity function over the interval 30, 34. Determine when the jogger moves
in the positive direction and when she moves in the negative direction.
b. Find the displacement of the jogger (in miles) on the time intervals 30, 14, 31, 34, and 30, 34. Interpret these results. c. Find the distance traveled over the interval 30, 34. SOLUTION
a. By solving v1t2 = 2t2 – 8t + 6 = 21t – 121t – 32 = 0, we find that the velocity is zero at t = 1 and t = 3; these values are the t-intercepts of the graph of v, which is an upward-opening parabola with a v-intercept of 6 (Figure 6.3a). The velocity is posi- tive on the interval 0 … t 6 1, which means the jogger moves in the positive s direc- tion. For 1 6 t 6 3, the velocity is negative and the jogger moves in the negative s direction.
b. The displacement (in miles) over the interval 30, 14 is s112 – s102 = L10 v1t2 dt
= L 1
0 12t2 – 8t + 62 dt Substitute for v.
= a2 3
t3 – 4t2 + 6tb ` 1 0
= 8 3
. Evaluate integral.
A similar calculation shows that the displacement over the interval 31, 34 is s132 – s112 = L31 v1t2 dt = – 83.
Over the interval 30, 34, the displacement is 83 + 1-832 = 0, which means the jogger returns to the starting point after three hours.
c. From part (b), we can deduce the total distance traveled by the jogger. On the interval 30, 14, the distance traveled is 83 mi; on the interval 31, 34, the distance traveled is also 8 3 mi. Therefore, the distance traveled on 30, 34 is 163 mi. Alternatively (Figure 6.3b), we can integrate the speed and get the same result:
L 3
0 ! v1t2 ! dt = L10 12t2 – 8t + 62 dt + L31 1-12t2 – 8t + 622 dt Definition of ! v1t2 !
= a 2 3
t3 – 4t2 + 6tb ` 1 0
+ a – 2 3
t3 + 4t2 – 6tb ` 3 1
Evaluate integrals.
= 16 3
. Simplify.
Related Exercises 7–14
Figure 6.3
6
4
2
!2
310
v
t
6
4
2
!2
321
!v!
t0
0
1
1
3
0
3
v (t) ” 2t2 ! 8t # 6 !v (t)! ” !2t2 ! 8t # 6! Displacement
” ” v(t) dt ” Displacement
” ” v(t) dt ”
Distance traveled from t ” 0 to t ” 3
is ” !v (t)! dt ” Displacement from t ” 0to t ” 3 is ” 0.
Area ”
Area ”
Area ”
Area ”
(a) (b)
6
4
2
!2
310
v
t
6
4
2
!2
321
!v!
t0
0
1
1
3
0
3
v (t) ” 2t2 ! 8t # 6 !v (t)! ” !2t2 ! 8t # 6! Displacement
” ” v(t) dt ” Displacement
” ” v(t) dt ”
Distance traveled from t ” 0 to t ” 3
is ” !v (t)! dt ” Displacement from t ” 0to t ” 3 is ” 0.
Area ”
Area ”
Area ”
Area ”
(a) (b)
M06_BRIG7345_02_SE_C06.1.indd 400 21/10/13 11:29 AM
6.1 Velocity and Net Change 401
Future Value of the Position Function To find the displacement of an object, we do not need to know its initial position. For ex- ample, whether an object moves from s = -20 to s = -10 or from s = 50 to s = 60, its displacement is 10 units. What happens if we are interested in the actual position of the object at some future time?
Suppose we know the velocity of an object and its initial position s102. The goal is to find the position s1t2 at some future time t Ú 0. The Fundamental Theorem of Calculus gives us the answer directly. Because the position s is an antiderivative of the velocity v, we have
L t
0 v1x2 dx = L t0 s′1×2 dx = s1x2 ` t0 = s1t2 – s102.
Rearranging this expression leads to the following result.
➤ Note that t is the independent variable of the position function. Therefore, another (dummy) variable, in this case x, must be used as the variable of integration.
➤ Theorem 6.1 is a consequence (actually a statement) of the Fundamental Theorem of Calculus.
THEOREM 6.1 Position from Velocity Given the velocity v1t2 of an object moving along a line and its initial position s102, the position function of the object for future times t Ú 0 is
s1t2 = s102 + L t0 v1x2 dx.
position initial displacement
at t position
over 30, t4dee Theorem 6.1 says that to find the position s1t2, we add the displacement over the interval 30, t4 to the initial position s102. QUICK CHECK 3 Is the position s1t2 a number or a function? For fixed times t = a and t = b, is the displacement s1b2 – s1a2 a number or a function?
There are two equivalent ways to determine the position function:
Using antiderivatives (Section 4.9)
Using Theorem 6.1
The latter method is usually more efficient, but either method produces the same result. The following example illustrates both approaches.
Order now and get 10% discount on all orders above \$50 now!!The professional are ready and willing handle your assignment.
ORDER NOW »»
| 2,966
| 10,088
|
{"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}
| 4.46875
| 4
|
CC-MAIN-2020-50
|
latest
|
en
| 0.909069
|
https://git.llvm.org/klaus/llvm/commit/5b52f6d655e34de5c6fedbb71b6c94775cc10032/
| 1,568,706,992,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-39/segments/1568514573053.13/warc/CC-MAIN-20190917061226-20190917083226-00373.warc.gz
| 502,785,700
| 3,737
|
llvm.org GIT mirror
Add an (interleave A, B, ...) SetTheory operator. This will interleave the elements from two or more lists. git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@148824 91177308-0d34-0410-b5e6-96231b3b80d8 Jakob Stoklund Olesen 7 years ago
3 changed file(s) with 29 addition(s) and 0 deletion(s).
199 199 // 200 200 // (decimate GPR, 2) - Pick every N'th element, starting with the first. 201 201 // 202 // (interleave A, B, ...) - Interleave the elements from each argument list. 203 // 202 204 // All of these operators work on ordered sets, not lists. That means 203 205 // duplicates are removed from sub-expressions. 204 206 205 207 // Set operators. The rest is defined in TargetSelectionDAG.td. 206 208 def sequence; 207 209 def decimate; 210 def interleave; 208 211 209 212 // RegisterTuples - Automatically generate super-registers by forming tuples of 210 213 // sub-registers. This is useful for modeling register sequence constraints
164 164 // CHECK: S9b = [ e7 e6 e5 e4 e3 ] 165 165 // CHECK: S9c = [ e0 ] 166 166 // CHECK: S9d = [ a b c d e0 e3 e6 e9 e4 e5 e7 ] 167 168 // The 'interleave' operator is almost the inverse of 'decimate'. 169 def interleave; 170 def T0a : Set<(interleave S9a, S9b)>; 171 def T0b : Set<(interleave S8e, S8d)>; 172 // CHECK: T0a = [ e3 e7 e4 e6 e5 ] 173 // CHECK: T0b = [ e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 ]
135 135 throw "Positive stride required: " + Expr->getAsString(); 136 136 for (unsigned I = 0; I < Set.size(); I += N) 137 137 Elts.insert(Set[I]); 138 } 139 }; 140 141 // (interleave S1, S2, ...) Interleave elements of the arguments. 142 struct InterleaveOp : public SetTheory::Operator { 143 void apply(SetTheory &ST, DagInit *Expr, RecSet &Elts) { 144 // Evaluate the arguments individually. 145 SmallVector Args(Expr->getNumArgs()); 146 unsigned MaxSize = 0; 147 for (unsigned i = 0, e = Expr->getNumArgs(); i != e; ++i) { 148 ST.evaluate(Expr->getArg(i), Args[i]); 149 MaxSize = std::max(MaxSize, unsigned(Args[i].size())); 150 } 151 // Interleave arguments into Elts. 152 for (unsigned n = 0; n != MaxSize; ++n) 153 for (unsigned i = 0, e = Expr->getNumArgs(); i != e; ++i) 154 if (n < Args[i].size()) 155 Elts.insert(Args[i][n]); 138 156 } 139 157 }; 140 158 210 228 addOperator("rotl", new RotOp(false)); 211 229 addOperator("rotr", new RotOp(true)); 212 230 addOperator("decimate", new DecimateOp); 231 addOperator("interleave", new InterleaveOp); 213 232 addOperator("sequence", new SequenceOp); 214 233 } 215 234
| 836
| 2,497
|
{"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-2019-39
|
latest
|
en
| 0.357475
|
http://www.mathisfunforum.com/viewtopic.php?pid=248954
| 1,397,945,330,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00607-ip-10-147-4-33.ec2.internal.warc.gz
| 556,547,764
| 7,385
|
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
## #2026 2013-01-16 08:23:41
anonimnystefy
Real Member
Offline
### Re: What do you think?
Hi
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
## #2027 2013-01-16 08:31:29
bobbym
Offline
### Re: What do you think?
Hi;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2028 2013-01-16 08:36:08
anonimnystefy
Real Member
Offline
### Re: What do you think?
A 2x2 matrix? How?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
## #2029 2013-01-16 08:40:02
bobbym
Offline
### Re: What do you think?
Hi;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2030 2013-01-16 08:46:06
anonimnystefy
Real Member
Offline
### Re: What do you think?
Hi bobbym
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
## #2031 2013-01-16 08:52:34
bobbym
Offline
### Re: What do you think?
Hi;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2032 2013-01-16 21:28:23
gAr
Star Member
Offline
### Re: What do you think?
Hi bobbym,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2033 2013-01-16 23:55:08
bobbym
Offline
### Re: What do you think?
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2034 2013-01-17 00:17:37
gAr
Star Member
Offline
### Re: What do you think?
Hi bobbym,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2035 2013-01-17 00:35:12
bobbym
Offline
### Re: What do you think?
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2036 2013-01-17 01:25:11
phrontister
Real Member
Offline
### Re: What do you think?
Hi Bobby,
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
## #2037 2013-01-17 01:26:56
bobbym
Offline
### Re: What do you think?
Hi phrontister;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2038 2013-01-17 01:34:49
gAr
Star Member
Offline
### Re: What do you think?
Hi bobbym,
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2039 2013-01-17 01:42:42
bobbym
Offline
### Re: What do you think?
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2040 2013-01-17 01:56:44
phrontister
Real Member
Offline
### Re: What do you think?
Hi Bobby,
Howdy!
The spreadsheet (which I've deleted by mistake ) gave the answer after about 25 to 30 iterations, depending on the starting volume of water in the urns. I tried it with the same volume in each urn and also with different volumes in each urn, with not much change to the number of iterations.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
## #2041 2013-01-17 01:56:45
gAr
Star Member
Offline
### Re: What do you think?
You're welcome!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2042 2013-01-17 01:58:24
phrontister
Real Member
Offline
### Re: What do you think?
Hi gAr,
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
## #2043 2013-01-17 02:02:39
bobbym
Offline
### Re: What do you think?
Hi phrontister;
Yes the naswer is independent of the volumes of the urns and the starting amounts of water.
Hi gAr;
The Feller books have a lot of stuff in them!
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2044 2013-01-17 02:24:31
gAr
Star Member
Offline
### Re: What do you think?
Hi phrontister,
I did not see that you had written up there, I actually replied to bobbym!
Hi bobbym,
Yes, you're right, he has covered a lot of topics.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2045 2013-01-17 02:46:54
bobbym
Offline
### Re: What do you think?
Hi;
Thanks for both of you looking at the problem.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2046 2013-01-17 02:52:09
gAr
Star Member
Offline
### Re: What do you think?
Hi bobbym,
I have a question on numerical methods:
How do we test whether a huge integer is a perfect square, if I'm to implement it in a language like C?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2047 2013-01-17 03:01:42
bobbym
Offline
### Re: What do you think?
How big is the integer?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2048 2013-01-17 03:09:49
gAr
Star Member
Offline
### Re: What do you think?
A number which fits "long" data type, taking 64 bits..
I'll take a break, see you later..
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
## #2049 2013-01-17 03:22:43
bobbym
Offline
### Re: What do you think?
Hi gAr;
Comparing floating point numbers like the routine sqr in C++ does and integers can be tricky.
I assume you want unsigned 64 bit numbers you will be testing numbers from 0 to 18446744073709551616. The roots would range from 0 to 4294967296.
Are your arguments going to be integers or floating point numbers?
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
## #2050 2013-01-17 03:57:28
gAr
Star Member
Offline
### Re: What do you think?
In particular, I'm trying to find values of n for which a polynomial like n*(5*n+14)+1 are perfect squares..
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
| 2,657
| 9,487
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.78125
| 3
|
CC-MAIN-2014-15
|
longest
|
en
| 0.914173
|
https://byjus.com/question-answer/the-moment-of-inertia-of-a-hollow-cylinder-of-radius-r-and-mass-m-about/
| 1,716,127,350,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971057788.73/warc/CC-MAIN-20240519132049-20240519162049-00635.warc.gz
| 129,275,707
| 28,757
|
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question
# The moment of inertia of a hollow cylinder of radius R and mass M about an axis passing through the outer circumference along the height of the hollow cylinder is
A
MR2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
MR22
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4MR2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2MR2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
## The correct option is D 2MR2 Let Icom be the moment of inertia of the hollow cylinder about the axis passing through its C.O.M. Applying parallel axis theorem, I=Icom+Md2 [∵ here d=R] =MR2+MR2 [∵Icom=MR2 for hollow cylinder] ⇒I=2 MR2
Suggest Corrections
1
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
| 280
| 901
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.831788
|
https://www.onlinemath4all.com/ratio-and-proportion-in-geometry.html
| 1,638,656,421,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00173.warc.gz
| 1,014,826,136
| 17,639
|
# RATIO AND PROPORTION IN GEOMETRY
## Computing Ratios
If a and b are two quantities that are measured in the same units, then the ratio of a to b is
a / b
The ratio of a to b can also be written as a : b. Because a ratio is a quotient, its denominator cannot be zero.
Ratios are usually expressed in simplified form. For instance, the ratio of 9 : 6 is usually simplified as 3 : 2.
## Simplifying Ratios
Example 1 :
Simplify the ratio :
16 cm / 4 m
Solution :
To simplify ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible.
16 cm / 4 m = 16 cm / 4 ⋅ 100 cm
16 cm / 4 m = 16 cm / 400 cm
16 cm / 4 m = 16 / 400
16 cm / 4 m = 1 / 25 or 1 : 25
Example 2 :
Simplify the ratio :
12 ft / 24 in.
Solution :
The given two quantities are in different units.
That is, the first one is in feet and the second in inches.
As we did in the first example, we can convert them into like units and then simplify the fraction, if possible.
12 ft / 24 in. = 12 12 in. / 24 in.
12 ft / 24 in. = 144 in. / 24 in.
12 ft / 24 in. = 144 / 24
12 ft / 24 in. = 6 / 1 or 6 : 1
## Using Ratio
Example 1 :
The perimeter of rectangle PQRS shown below is 60 centimeters. The ratio of PQ : QR is 3 : 2. Find the length and width of the rectangle.
Solution :
Because the ratio of PQ : QR is 3 : 2, we can represent the length PQ as 3x and the width QR as 2x.
2l + 2w = p
Substitute l = 3x and w = 2x.
2(3x) + 2(2x) = 60
Simplify.
6x + 4x = 60
10x = 60
Divide both sides by 10.
x = 6
So, we have
length = 3 ⋅ 6 = 18 cm
width = 2 ⋅ 6 = 12 cm
Hence, rectangle PQRS has a length of 18 centimeters and a width of 12 centimeters.
Example 2 :
The ratios of the side lengths of ΔABC to the corresponding side lengths of ΔPQR are 2 : 1. Find the unknown lengths.
Solution :
From the given information and the diagram shown above, we can consider the following points.
• AB is twice PQ and AB = 8, so PQ = 1/2 ⋅ 8 = 4 in.
• Using the Pythagorean Theorem, we can determine that QR = 5.
• AC is twice PR and PR = 3, so AC = 2 ⋅ 3 = 6 in.
• BC is twice QR and QR = 5, so BC = 2 ⋅ 5 = 10 in.
## Using Extended Ratios
Example 3 :
The measure of the angles in ABC are in the extended ratio of 1 : 2 : 3. Find the measures of the angles.
Solution :
Begin by sketching a triangle. Then use the extended ratio of 1 : 2 : 3 to label the measures of the angles as x°, 2x°, and 3x°.
By Triangle Sum Theorem,
x° + 2x° + 3x° = 180°
x + 2x + 3x = 180
Simplify.
6x = 180
Divide both sides by 6.
x = 30
So, we have
x° = 30°
2x° = 2 ⋅ 30° = 60°
3x° = 3 ⋅ 30° = 90°
Hence, the angle measures are 30°, 60° and 90°.
## Proportions
An equation that equates two ratios is a proportion.
For instance, if the ratio a/b is equal to the ratio c/d, then the following proportion can be written :
The numbers a and d are the extremes of the proportion.
The numbers b and c are the means of the proportion.
## Properties of Proportions
1. Cross Product Property :
The product of the extremes equals the product of the means.
If a/b = c/d, then ad = bc.
2. Reciprocal Property :
If two ratios are equal, then their reciprocals are also equal.
If a/b = c/d, then b/a = d/c.
## Solving Proportions
Example 1 :
Solve the proportion :
6 / x = 12 / 5
Solution :
Write the original proportion.
6 / x = 12 / 5
By reciprocal property, we have
x / 6 = 5 / 12
Multiply each side by 6.
⋅ (x / 6) = (5 / 12) ⋅ 6
Simplify.
x = 5 / 2
Example 2 :
Solve the proportion :
3 / (p + 2) = 2 / p
Solution :
Write the original proportion.
3 / (p + 2) = 2 / p
By cross product property, we have
3p = 2(p + 2)
3p = 2p + 4
Subtract 2p from both sides.
p = 4
## Using Proportions in Real Life
Example :
The photo below shows a painting. The actual painting is 12 inches high. How wide is it ?
Solution :
We can reason that in the photograph all measurements of the artist’s painting have been reduced by the same ratio.
That is, the ratio of the actual width to the reduced width is equal to the ratio of the actual height to the reduced height.
The photograph is 1¼ inches by 4inches.
Problem Solving Strategy :
Multiply each side by 4.375
4.375 ⋅ (x / 4.375) = (12 / 1.25) ⋅ 4.375
Simplify.
x = (12 / 1.25) ⋅ 4.375
Using calculator, we have
x = 42
So, the actual painting is 42 inches wide.
Apart from the stuff given above if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Algebra word problems
Word problems on trains
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on unit price
Word problems on unit rate
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Double facts word problems
Trigonometry word problems
Percentage word problems
Profit and loss word problems
Markup and markdown word problems
Decimal word problems
Word problems on fractions
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Word problems on ages
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Profit and loss shortcuts
Percentage shortcuts
Times table shortcuts
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
| 2,069
| 6,958
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.78125
| 5
|
CC-MAIN-2021-49
|
longest
|
en
| 0.780249
|
https://resources.quizalize.com/view/quiz/combination-84455c1c-abeb-4a10-a1c5-ad19ea9f55f7
| 1,708,920,453,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474650.85/warc/CC-MAIN-20240226030734-20240226060734-00361.warc.gz
| 503,857,946
| 16,530
|
COMBINATION
Quiz by Alma Ventura
Mathematics
Feel free to use or edit a copy
includes Teacher and Student dashboards
M10SP-IIIc-1
M10SP-IIIa-1
M10SP-IIId-e-1
Track each student's skills and progress in your Mastery dashboards
• edit the questions
• save a copy for later
• start a class game
• automatically assign follow-up activities based on students’ scores
• assign as homework
• share a link with colleagues
• print as a bubble sheet
### Our brand new solo games combine with your quiz, on the same screen
Correct quiz answers unlock more play!
10 questions
• Q1
It is an arrangement/selection where order does not matter.
Permutation
Combination
Fundamental Counting
Probability
30s
M10SP-IIIc-1
• Q2
Opening a combination lock like the one at the right is an example of ___________.
Fundamental Counting
Permutation
Probability
Combination
30s
M10SP-IIIc-1
• Q3
Assembling jigsaw puzzle is an example of ___________.
Combination
Probability
Fundamental Counting
Permutation
30s
M10SP-IIIa-1
• Q4
Find the value of P(7,4).
840
35
1260
70
30s
M10SP-IIIc-1
• Q5
Find the value of C(4,2).
12
24
48
6
30s
M10SP-IIIc-1
• Q6
Find the value of C(5,5)+ C(5,1).
1
125
5
6
30s
M10SP-IIIc-1
• Q7
Find the value of P(5,5) + P(5,1).
125
5
6
1
30s
M10SP-IIIc-1
• Q8
What is the permutation of 5 objects taken three at a time?
10
60
120
20
30s
M10SP-IIIc-1
• Q9
What is the combination of 10 objects taken five at a time?
15, 120
504
30, 240
252
30s
M10SP-IIIc-1
• Q10
Hezekiah would like to invite 8 friends to Marikina Hotel but the available room is only 5. In how many ways can they be chosen?
28
6,720
56
3,360
30s
M10SP-IIId-e-1
Teachers give this quiz to your class
| 577
| 1,738
|
{"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}
| 3.328125
| 3
|
CC-MAIN-2024-10
|
latest
|
en
| 0.764622
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.