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https://www.aqua-calc.com/one-to-one/surface-density/pound-per-square-inch/stone-per-square-micron/1 | 1,624,282,095,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488273983.63/warc/CC-MAIN-20210621120456-20210621150456-00608.warc.gz | 593,094,384 | 7,871 | # 1 pound per square inch [lb/in²] in stones per square micron
## pounds/inch² to stone/micron² unit converter of surface density
1 pound per square inch [lb/in²] = 1.107145072 × 10−10 stone per square micron [st/µ²]
### pounds per square inch to stones per square micron surface density conversion cards
• 1
through
25
pounds per square inch
• 1 lb/in² to st/µ²
= 1.107145072 × 10-10 st/µ²
• 2 lb/in² to st/µ²
= 2.214290144 × 10-10 st/µ²
• 3 lb/in² to st/µ²
= 3.321435216 × 10-10 st/µ²
• 4 lb/in² to st/µ²
= 4.428580289 × 10-10 st/µ²
• 5 lb/in² to st/µ²
= 5.535725361 × 10-10 st/µ²
• 6 lb/in² to st/µ²
= 6.642870433 × 10-10 st/µ²
• 7 lb/in² to st/µ²
= 7.750015505 × 10-10 st/µ²
• 8 lb/in² to st/µ²
= 8.857160577 × 10-10 st/µ²
• 9 lb/in² to st/µ²
= 9.964305649 × 10-10 st/µ²
• 10 lb/in² to st/µ²
= 1 × 10-9 st/µ²
• 11 lb/in² to st/µ²
= 1 × 10-9 st/µ²
• 12 lb/in² to st/µ²
= 1 × 10-9 st/µ²
• 13 lb/in² to st/µ²
= 1 × 10-9 st/µ²
• 14 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 15 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 16 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 17 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 18 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 19 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 20 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 21 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 22 lb/in² to st/µ²
= 2 × 10-9 st/µ²
• 23 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 24 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 25 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 26
through
50
pounds per square inch
• 26 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 27 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 28 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 29 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 30 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 31 lb/in² to st/µ²
= 3 × 10-9 st/µ²
• 32 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 33 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 34 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 35 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 36 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 37 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 38 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 39 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 40 lb/in² to st/µ²
= 4 × 10-9 st/µ²
• 41 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 42 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 43 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 44 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 45 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 46 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 47 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 48 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 49 lb/in² to st/µ²
= 5 × 10-9 st/µ²
• 50 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 51
through
75
pounds per square inch
• 51 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 52 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 53 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 54 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 55 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 56 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 57 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 58 lb/in² to st/µ²
= 6 × 10-9 st/µ²
• 59 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 60 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 61 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 62 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 63 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 64 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 65 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 66 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 67 lb/in² to st/µ²
= 7 × 10-9 st/µ²
• 68 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 69 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 70 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 71 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 72 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 73 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 74 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 75 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 76
through
100
pounds per square inch
• 76 lb/in² to st/µ²
= 8 × 10-9 st/µ²
• 77 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 78 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 79 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 80 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 81 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 82 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 83 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 84 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 85 lb/in² to st/µ²
= 9 × 10-9 st/µ²
• 86 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 87 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 88 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 89 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 90 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 91 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 92 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 93 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 94 lb/in² to st/µ²
= 1 × 10-8 st/µ²
• 95 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
• 96 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
• 97 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
• 98 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
• 99 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
• 100 lb/in² to st/µ²
= 1.1 × 10-8 st/µ²
#### Foods, Nutrients and Calories
H-E-B CENTRAL MARKET, SWEET COCONUT DOUGHNUT MUFFIN MIX, UPC: 041735083180 contain(s) 360 calories per 100 grams (≈3.53 ounces) [ price ]
4971 foods that contain Proline. List of these foods starting with the highest contents of Proline and the lowest contents of Proline
#### Gravels, Substances and Oils
CaribSea, Freshwater, Super Naturals, Tahitian Moon weighs 1 473.7 kg/m³ (92.00009 lb/ft³) with specific gravity of 1.4737 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Phosphate rock, broken weighs 1 762 kg/m³ (109.99807 lb/ft³) [ weight to volume | volume to weight | price | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-13, liquid (R13) with temperature in the range of -95.56°C (-140.008°F) to 4.45°C (40.01°F)
#### Weights and Measurements
A picoampere is a SI-multiple (see prefix pico) of the electric current unit ampere and equal to equal to 1.0 × 10-12 ampere
Radioactivity is the act of emitting radiation spontaneously by an atomic nucleus that, for some reason, is unstable.
dyn/pc² to dyn/µm² conversion table, dyn/pc² to dyn/µm² unit converter or convert between all units of pressure measurement.
#### Calculators
Calculate gas pressure at different temperatures | 3,175 | 5,822 | {"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-2021-25 | latest | en | 0.157425 |
http://www.livescience.com/20581-weigh-atom.html | 1,487,647,777,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170624.14/warc/CC-MAIN-20170219104610-00334-ip-10-171-10-108.ec2.internal.warc.gz | 499,797,796 | 44,869 | Imagine plopping an atom down on a scale. As you do so, skin cells that are trillions of atoms thick flake off your hand and flutter down all around it, burying it in a pile of atomic doppelgangers. Meanwhile, moisture and atmospheric particles shoot about, bouncing on and off the scale and sending its atom-sensitive needle whipping back and forth like a windshield wiper. And by the way, how did you manage to isolate a single atom in the first place?
A moment's thought shows you can't weigh an atom on a traditional scale.
Instead, physicists do it using an instrument called a mass spectrometer. Invented in 1912 by physicist J.J. Thomson and improved incrementally over the past century, it works like this: First, physicists "ionize" a gas of atoms by firing a beam of particles at the gas, which either adds electrons to the atoms in it or knocks a few of their electrons off, depending on the type of particle beam used. This gives the atoms — now known as "ions" — a net negative or positive electric charge.
Next, the ions are sent through a tube in which they're subjected to electric and magnetic fields. Both of these fields exert a force on the ions, and the strengths of the two forces are proportional to the ions' charge (neutral atoms don't feel the forces). The electric force causes the ions to change speed, while the magnetic force bends their path.
The ions are then collected by "Faraday cups" at the end of the tube, generating a current in wires attached to the cups. By measuring where and when the stream of ions hits the Faraday cups, the physicists can determine how much they must have accelerated, and in what direction, as a result of the electric and magnetic forces. Lastly, by way of Newton's second law of motion, F=ma, rearranged as m=F/a, the physicists divide the total force acting on the ions by their resulting acceleration to determine the ions' mass.
The mass of the electron has also been determined using a mass spectrometer — in that case, electrons were simply sent through the instrument themselves. That measurement enables physicists to determine the mass of an atom when it has the correct number of electrons, rather than a dearth or surplus of them.
Using a mass spectrometer, physicists have determined the mass of a hydrogen atom to be 1.660538921(73)×10−27 kilograms, where the parenthetical digits are not known with complete certainty. That's accurate enough for most purposes.
What about before the days of mass spectrometers, when chemists were fuzzy about what an atom even was? Then, they primarily measured the weights of the atoms that composed various elements in terms of their relative masses, rather than their actual masses. In 1811, the Italian scientist Amedeo Avogadro realized that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules composing it, regardless of which gas it was. This useful fact allowed chemists to compare the relative weights of equal volumes of different gases to determine the relative masses of the atoms composing them.
They measured atomic weights in terms of atomic mass units (u), where 1 u was equal to one-twelfth of the mass of a carbon-12 atom. When in the second half of the 19th century, chemists used other means to approximate the number of atoms in a given volume of gas — that famous constant known as Avogadro's number — they began producing rough estimates of the mass of a single atom by weighing the volume of the whole gas, and dividing by the number. | 747 | 3,536 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2017-09 | longest | en | 0.947734 |
https://sourceforge.net/p/maxima/mailman/maxima-commits/thread/E1GZpZA-0005Qb-R5@sc8-pr-cvs7.sourceforge.net/ | 1,513,138,417,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948521188.19/warc/CC-MAIN-20171213030444-20171213050444-00765.warc.gz | 679,781,311 | 9,206 | [Maxima-commits] CVS: maxima/share/contrib/diffequations/tests rtestode_kamke_1_6.mac, 1.4, 1.5 From: David Billinghurst - 2006-10-17 14:05:13 ```Update of /cvsroot/maxima/maxima/share/contrib/diffequations/tests In directory sc8-pr-cvs7.sourceforge.net:/tmp/cvs-serv19941 Modified Files: rtestode_kamke_1_6.mac Log Message: Update solution for Kamke equation 1.558. Order of terms has changed. Index: rtestode_kamke_1_6.mac =================================================================== RCS file: /cvsroot/maxima/maxima/share/contrib/diffequations/tests/rtestode_kamke_1_6.mac,v retrieving revision 1.4 retrieving revision 1.5 diff -u -d -r1.4 -r1.5 --- rtestode_kamke_1_6.mac 15 May 2006 14:52:09 -0000 1.4 +++ rtestode_kamke_1_6.mac 17 Oct 2006 14:05:10 -0000 1.5 @@ -301,7 +301,8 @@ /* 558 */ (pn_(558),ans:contrib_ode(eqn:a*x*sqrt(('diff(y,x,1))^2+1)+x*'diff(y,x,1)-y,y,x)); -[[x=%c*%e^(-'integrate(%e^(log(%t^2+1)/2)/(%t^2*a+a),%t)-log(%t^2+1)/2),y=(sqrt(%t^2+1)*a+%t)*x]]; +[[x=%c*%e^(-'integrate(sqrt(%t^2+1)/(%t^2*a+a),%t)-log(%t^2+1)/2), +y=(sqrt(%t^2+1)*a+%t)*x]]; method; lagrange; ``` | 444 | 1,102 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2017-51 | latest | en | 0.349852 |
http://jayisgames.com/archives/2011/12/you_are_games_letters_in_boxes_26.php | 1,411,004,393,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1410657125113.78/warc/CC-MAIN-20140914011205-00039-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | 137,127,178 | 27,782 | # You Are Games: Letters In Boxes #26
| Comments (46) | Views (23)
I mean, let's face it, accidents happen, right? This week, we were going to feature another fantastic set of Letters In Boxes puzzles, hot off the presses and ready for solving. But then, as Murphy's Law would dictate, just before our publication deadline, the puzzles got warmed up by something other than hot ink: Coffee. Whether you're a cappuccino or latte sort of person, all it takes is one coffee spill to bring two creams, no sugars, and a world of pain to a struggling puzzlemaker. (On the bright side, the donut was still delicious.)
Update: Congratulations to the following winners! :D
• ray9na ...First!
• Cooler
Both winners were given a choice of prizes. Congratulations and thanks for playing with us! Look for another Letters in Boxes again soon!
Why, Steve, why? We could've had a fun puzzle set this week (like always), but no, you must go and spill coffee on the puzzles!
Got to number #2 already. Although it doesn't look very bright to me.
Same. Too many possible combinations for #2.
December 15, 2011 9:27 AM
coffee time opps you accidently pour coffee in the letter in boxes #26 now i think i can't solve a puzzle again Steve
(but can i have some donut? lol)
(maybe i can solve it later with some hints)
I'm having more trouble with #1 than I feel I should be. I recognize that it's a
variant of Sudoku
but I also see that
all 6 letters are there
so I tried the obvious and
anagrammed it
but
neither of the 2 possibilities worked.
Does anyone have any hints?
@ray9na:
gotta complete the puzzle first, then try looking for a word in the puzzle (think of wordsearch puzzles when trying to find the word :P)
*wonders if anyone's solved #2 yet*
I've tried
solving the puzzle like a kakuro puzzle, and based on the different possible number combinations, I picked out all the numbers between 4 and 9 that appeared on the possible solutions to the kakuro... and tried to form a 6 letter word using each set of letters. but even using an anagram solver site didn't get me an answer that worked... so i guess my method is wrong, or i missed out a possible solution?
@snowmoon:
Tried the exact same method, but also
tried making some assumptions about the letters not listed.
(e.g. The Q makes me think there should be a U)
Also, I noticed that the two sections you can solve (well, one you can solve, the other has 10 "legal" possibilities) can fit together to make a 4x3 grid.
Then again there's the
"Pick Six" at the bottom, which originally got me thinking "Ok, we're only going to use 6 of these numbers, but that's not possible if we include the 17's in the upper-right section, because you'll need at least 7 numbers to complete it. If we just look at the 7 and 3, we can conclude numbers 1,2,4,5,8,9 are used, but again with the Q. And apparently there are no words that include CAQ plus three wild cards.
And finally
Part of me thinks that all of this is missing something obvious and that it's a lot simpler than we're thinking it is. But if that's the case, I'm at a loss as to what needs to be done.
Ok that's it for now. Got 1st graders coming in. Maybe during lunch I'll squeeze some more time in on it.
Add me to the "stuck on #2" crowd.
@ray9na, I think that crowd may become a mob before we're all done. I've tried all the approaches listed by Disco Dan and snowmoon as well as some desperate but lame attempts but I've gotten nowhere. I may have a better chance playing the Pick Six lottery.
There are plenty of us then, I guess.
Got it!
I took the two kakuro grids and
flipped one so it would superimpose on the other.
Then, I made an educated guess and
picked 6 numbers (one was blacked out on one of the two grids).
That left me with
four known letters and two unknowns, which together make only one six letter word!
Wow, zoz. It took a little playing around with it given your hint. For a while I still wasn't sure I was on the right track, but then after going in circles for a while, I took a slightly educated guess and I'm on #3 now.
And here I was thinking this one was a bad fit.
Eh, Steve!
If we can make out a letter underneath the coffee, can we assume it's correct?
argh! I have to leave for a while. @ray9na, any hints on #3? I've been assuming those partially covered letters are fair game.
@zoz: Nope, no hints. I'm just mucking around same as anyone else right now. Assuming I'm even going about it correctly, right now I've got 2 possibilities for the bottom row.
@ray9na or @zoz
on #2 am I looking to solve:
14, 18, 3 or 17, 7, 6. (the later doesn't seem to work as well),or another combination... but when i solve for the first one, the words i come up with apparently aren't the right answers
if this is too much info, we can delete this...
I take it back! I have #3
The same string will appear in all of them. That's the secret word. And yes, the letters we make out under the coffee are true (that is, they are not red herrings).
I give up for now. I've tried a ton of options in #2 and every single one of them ends in failure.
@sunney444
I'm not sure I can explain #2 any better than zoz did at 12:50pm. Sorry.
@ray9na. i got it eventually. Just kept playing around :)
Okay! Let me try my hand at giving hints all around!
#1
It is a 6x6 Sudoku. Solve it, then treat it as a word find.
(Thanks, snowmoon @10:38am)
#2
It is a Kakuro. Solve the two separately, then rotate one to superimpose upon the other. It won't be a perfect fit, just go for the best possible.
(Thanks, zoz @12:50pm)
The answer lies in only 4 squares. Ignore any doublings.
#3
Each row is a word. There is a certain string that is part of each solved word. This is the answer.
#4
Pay attention to the theme here. What's given only gets you started.
For #2, is there supposed to be
one answer for the rightmost grid? Seems like a lot of guessing otherwise, and I'm boggled how to guess well.
daggonit! As soon as I got home #3 just jumped out at me. Bad timing on my part, I guess. oh well, on to four.
For #4
Google will give you a list, then you just fill in the blanks. At the top of the page, notice that there are at least two more columns (and maybe more) after columns 1-5.
Running into an issue with #2:
The upper right Kakuro doesn't seem to have a single definite answer. I've found at least 3 combinations so far that work for it.
ray9na,
I must be missing something fundamental: when you say, of #2, to
Solve the two separately
it's not clear to me which...
...one of the seven possible ways to fill in the seven upper-right squares we're supposed to consider.
December 15, 2011 9:56 PM
#2 is diabolically hard. Here's my attempt at a foolproof walkthrough:
Solve the lower left grid first. The numbers indicate the sum of the value of letters in each row and column. Leave blanks in squares that must be occupied by unknown coffee covered letters. You're not making real words, just make them add up. We've had to superimpose and rotate grids in puzzles like this before, so assume the same unknown letter is in the middle square of both grids. Now solve the upper right grid. Rotate that grid 90 degrees clockwise, and superimpose it over the other. You should have a real mess, but you're supposed to notice four letters alone in their own squares. Go to an anagram server that uses wildcards, enter the four letters and two asterisks for wildcards.
If that doesn't work, remember:
If the glove doesn't fit...
Wow, epic fail on my part...thought I had #2 for a second, then I realized that the puzzle I'd wound up wasn't covered in coffee.
Crud.
I still don't get #2 :(
when you say 'superimpose the 2 grids'... are we talking about the top-right corner and bottom-left corner of the puzzle only? coz I've tried that, and don't seem to get anywhere lol! maybe I've misunderstood the hint...
oh oops. not sure how I missed elmerturnipseed's hint as I was scrolling down the comments page...
I still haven't figured out what exactly I'm supposed to do on #2, but by using elmerturnipseed's 2nd hint, I could get the answer and will go on to try #3 first :\$ thanks!
For the fourth puzzle: if 3 is
Austria
and 5 is
Moldova
, I can't make a word beginning with the letters I've got. Are some of these
past rather than current capitals
?
@cendare, on #4
could the 3rd be something other than Austria?
another hint for #4
make sure and fill in the capitals you know in a vertical direction by the clue number. That is, for the capital of South Korea, the first letter goes in the box marked 1, and the other letters follow going down.
jeez, I hope that didn't make it more complicated instead of easier.
ok, I'm going to try to make my hint about #2 clearer, without giving it away (btw, @elmerturnipseed, that was a very clever clue you gave above!) My apologies for the length of this post.
First, solve the
kakuro. If you've not seen this game before, try looking up nikoli games on Wikipedia.
There are only two grids that are clear enough to fill in, thanks to Steve's caffeine addiction ;o) For the
lower left grid, I believe there's only one solution. The upper right grid has multiple possiblities.
Next, take a look at the basic
shape of each grid. The tip-off for me was the presence of the two "teeth" on each grid [defined by 18 and 14 on the lower left grid and 7 and 17 on the upper right.)
Now, either use your visualization skills or make cutouts
of each grid. If you take the upper right grid you can flip it upside down and rotate it 90degrees, so that the "teeth" are pointing left and the 7 is above the 17. This positions the other 17 and the 3 at the top.
This will give you a combination of numbers. Here's a MAJOR SPOILER so don't look if you don't want grid answers.
I had the following solutions: for the lower left grid 819, then 95 and a black box. For the upper right grid, AFTER flipping, etc., my numbers were 5 (top row), then 412 (middle row) then 827 across the bottom.
Now you must pick six!
I decided to ignore the number on the right grid where the black box falls on the left. I also ignored the single digit on the top of the right grid, since there is no corresponding digit on the lower left grid.
Now, you are left with [MAJOR SPOILER!]
six numbers: 1,2,4,5, 8,and 9.
You only have letters for numbers 4 through 9, so
you must come up with letters for 1 and 2. It's probably safe to assume that one of those two numbers corresponds to U. So run an anagram search either for your four letters plus U plus a ? or just use the four known letters plus two ? I used scrabblefinder.com/solver/
You'll end up with one answer, which happens to be the solution.
With all due respect to zoz, I really hope (s)he's wrong about that...
I'd call a puzzle incredibly broken if the correct path to the solution is to fill one grid, guess at the other grid, flip and rotate to superimpose them, choose one of the two letters in each of the superimposed pairs, and then anagram. That's a seriously ludicrous series of steps to go through.
Besides, I'd be willing to bed that that's nowhere near unique.
IDIOTS.
Scrabble helped me reach this far.
As they say in Scrabble...
"May the Q be with U"
My take on #2:
Even with all of the ways you can fill in the upper grid, there is only one solution where you will only use 6 numbers. Those six numbers are the letters you use, and yes, you don't know two of them. You can guess at one of them, because of what one of the other letters is, and then I just put it in an anagram solver to figure out the last one.
@Tweetheart
Really? We know the lower left Kakuro has one solution, and that gives you four different numbers to work with. The presence of the 7 in the upper right gives you two more. So you're saying that the upper right Kakuro is solvable with only those six different numbers? I don't see it: at the very least, you need an extra number that is not used in the solution.
On top of that, I'm counting 10 different solutions to the upper right Kakuro. Sure, you can just solve the lower left, use the known numbers from the 7, and treat everything else as red herrings, but doing it that way feels like you're skipping a step.
Concluding my battle through this week's puzzle, I must give special thanks to zoz in both puzzles #2 and #4. Without the help, I would still be battling in #2.
And a final admitting: This week was a total mess!
Hey guys, I think the suggestions above for #2 are really making the puzzle harder than it is...
"Pick six" - only six numbers/letters are used.
Solving the lower left one specifies four numbers.
Using logic to reduce the number of options in the upper right block will give you the remaining two. You don't need to solve the upper right grid.
Then...
One of the known letters will require that one of the unknowns must be a certain letter. Leaving one unknown.
And finally..
A little brain grease or an anagram solver will finish it off!
I kind of hope @Tahnan and @ron0 are right about #2. I just wrote out what worked for me, but it wouldn't be the first time I made things way more complicated than they have to be. If it gets you to the right solution, go for it!
@zoz
I think your solution and the steps you outlined were spot on and much less complicated than they seem. I wouldn't have been able to solve it with ron0's method.
*am very grateful for all your hints!*
December 19, 2011 12:56 PM
Thanks Steve for the page confirming I got #4 right, and be more careful next time! *Wags finger!*
Oh, see, now, Steve's explanation is much better than the overly baroque things suggested above. Now I feel bad for not seeing it!
@Tahnan
Until you're ready to start stepping up and providing the sort of pithy solutions that you crave, maybe you should stop with the thinly veiled insults towards people who take the time to help other people as best they can. Seriously, there is so much entitlement on this board it's nauseating.
@Steve
If that's the official solution to #2, then the coffee stain over the fourth square under the 17 in the far right column has to be more opaque! Otherwise...
Since the 3 clue means one of the digits in the 17 clue in the far right must be 1 or 2 then there is no way to solve it in three digits without using a seventh number (6 or 7). Were the coffee stain properly opaque, then we'd have to allow the possibility that the 17 clue is being made with more than three digits and so there would be no such problem.
But as it stands (as pointed out by an earlier poster) the solution isn't self-consistent if you really try to keep the Kakuro self-consistent too. I'd call it a typo but it's more a mis-spill!
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Limit to the last 5 comments | 4,154 | 16,771 | {"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-2014-41 | longest | en | 0.96361 |
http://forum.allaboutcircuits.com/threads/555-timer-asap-need-to-do-my-presentation.127616/ | 1,484,891,870,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280791.35/warc/CC-MAIN-20170116095120-00206-ip-10-171-10-70.ec2.internal.warc.gz | 109,808,359 | 15,345 | # 555 Timer ASAP need to do my presentation
Discussion in 'Homework Help' started by Aikawa Aikun, Sep 21, 2016.
1. ### Aikawa Aikun Thread Starter New Member
Sep 21, 2016
5
0
With the diode in place, the output waveform's duty cycle may be adjusted to less than 50% if desired.
Explain why the diode is necessary for that capability.
Show the current flow for charging and discharging of capacitor, C1.[/url][/IMG]
http://imgur.com/a/uGVq4
Jun 4, 2014
2,262
448
3. ### Alec_t AAC Fanatic!
Sep 17, 2013
5,971
1,135
Welcome to AAC!
Since this is your homework you are expected to show your best effort so far. We can then point you in the right direction. We don't do your homework for you!
Jul 11, 2016
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5. ### Aikawa Aikun Thread Starter New Member
Sep 21, 2016
5
0
-the capactor will charge through R1 only because the R2 is shorted out by Diode. because of that, less resistance when charging than discharging.
-current flow for charging is from R1 to diode. current flow for discharging is through R2
6. ### wayneh Expert
Sep 9, 2010
12,382
3,238
That's correct. Just be aware that the diode drops ~0.7V across itself when conducting. This fact does not affect the qualitative answer, but would be important if you try to calculate the timing.
Aikawa Aikun likes this.
7. ### Alec_t AAC Fanatic!
Sep 17, 2013
5,971
1,135
Nearly right. The diode is not a true short-circuit.
8. ### Aikawa Aikun Thread Starter New Member
Sep 21, 2016
5
0
what can i say about the diode?
can i say like this?
"the charging will bypass R2 and charge through R1 ?"
9. ### wayneh Expert
Sep 9, 2010
12,382
3,238
The diode will conduct when/if the voltage drop across R2 exceeds the diode drop I mentioned earlier. This means some current is still passing through R2, because there is a voltage across it.
Aikawa Aikun likes this.
10. ### Aikawa Aikun Thread Starter New Member
Sep 21, 2016
5
0
i get it.. thank
11. ### Aikawa Aikun Thread Starter New Member
Sep 21, 2016
5
0
thank all for helping me | 606 | 2,007 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2017-04 | latest | en | 0.89892 |
https://www.mathselab.com/what-is-the-value-of-the-product-1-1-2-1-1-3-1-1-4-1-1-5/ | 1,686,446,010,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646652.16/warc/CC-MAIN-20230610233020-20230611023020-00630.warc.gz | 984,171,885 | 13,904 | # What is the value of the product (1 – 1/2) (1 – 1/3) (1 – 1/4) (1 – 1/5)?
### What is the value of the product (1 – 1/2) (1 – 1/3) (1 – 1/4) (1 – 1/5)?
`A. 1/5`
`B. 2/5`
`C. 3/5`
`D. 1`
Solution:
=> (1 – 1/2) = 1/2
=> (1 – 1/3) = 2/3
=> (1 – 1/4) = 3/4
=> (1 – 1/5) = 4/5 gives (1 – 1/2)(1 – 1/3)(1 – 1/4)(1 – 1/5)
= 1/2 × 2/3 × 3/4 × 4/5
= 1/5 | 228 | 355 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2023-23 | longest | en | 0.869113 |
https://bimtopia.com/913b2e0428bd453c8b413789e39a5db6 | 1,685,597,593,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647614.56/warc/CC-MAIN-20230601042457-20230601072457-00737.warc.gz | 154,198,595 | 11,901 | # Meera Rao
Journal Entry For
Module 6 - Evaluate Your Alternatives
Created By
Meera Rao
Property
Related to 120C/220C Students - Spring 2022 (1) (Related to Design Journal Entries | Winter 2022 (Linked Student))
I created a new building in dynamo with three rectangular profiles that twist. The original building height was 800 ft.
I created two new evaluation parameters. The first looks at the percentage of the floor area that is located within 10 ft of the edge of the building. This parameter aims to see how much of the floor area will be located near windows and have better natural lighting and better views of outside. The node logic for this is shown below.
This custom node takes in the surface of the building, height, story height, and gross floor area of the building as inputs. First, the curves are generated from each floor in the building. Next, these curves are offset by -10 to get the curves of the inside area of the building. This area is subtracted from the total floor area and divided by the total floor area to get the fraction of the floor area that is located near the windows.
The second parameter is related to this first parameter. I calculate the floor area; however, the area near the windows has a higher value than the area inside by 20%. Whether this building will be residential or commercial, apartments or office spaces will have more value if they have better access to views which is why I decided to calculate the total value this way. The node logic for this is shown below. Also, it should be noted that this was added to the first custom node as I needed a lot of the values from the previous custom node shown above.
In this node I adjust the input values to increase by 20%. I then sum the values of the outside area and inside area for each floor. I sum each of these values to get the value based on floors for the entire building.
I chose to flex the number of sides of the polygon used to create the building as well as the top rotation. The input values used to test are shown below.
The function apply node was then used to test these different values and the results were exported to excel.
Next, the results were evaluated to determine the optimal building.
The minimums and maximums were generated from each column, and weights were assigned to the columns. Only the percentage near the window and total value were weighted in this analysis. The custom node compute combined evaluation scores was used to generate the scores, and the results were exported to excel. List manipulation was used to add the testing parameters to the beginning of the list, and the combined scores to the end of the list.
The results are shown below in the table.
The best 3 scenarios are highlighted. It should be noted that there were building that scored higher than the selected ones, but they did not meet the building requirements. For that reason, the next three were chosen based on the height and floor area requirements.
The best building choice is shown below.
This was chosen as the best because it had the largest combined score that met the building requirements. This means that it had a large percent of floor area that was near windows. Also, this provided the most value because it had a larger floor area in general as well as a larger proportion of that area near windows. | 683 | 3,343 | {"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-2023-23 | latest | en | 0.953873 |
https://biology-forums.com/index.php?topic=2035598.msg5384727 | 1,675,104,548,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499826.71/warc/CC-MAIN-20230130165437-20230130195437-00598.warc.gz | 153,856,869 | 28,594 | Top Posters
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Q1CQ2AQ3DExplanation:So, the cross between true breeding white corn plant and purple corn plant will have the genotypes kkpp(white) and KKPp(purple).The cross,P1 kkpp (white corn) × KKPp (purple corn) ↓ ↓G1 kp KP, Kp ↓F1 kpkpKPKkPpPurple corn plantKkPpPurple corn plantKpKkppRed corn plantKkppRed corn plantSo the offsprings produced is 50% red corn and 50% purple plants.Q4DQ7AHeterozygous green parakeet has BbYy genotype - possible allele combinations passed down: BY, bY, By, byWhite parakeet has bbyy genotype - possible allele combinations passed down: byWhen put in a punnet square, total genotypes are: BbYy, bbYy, Bbyy, bbyyTheir phenotype colour, in the above order are: green, yellow, blue, white.So probability of yellow or blue is 2/4 or 50%. (Parent genotypes were listed above)Q13In both cases the chances of having a Lab Retriever with a black coat is 75%. To solve this question I have created a Punett square for the combination of GgBb x GgBB. Because there are two genes for each genotype there are 4 possible combinations that could result in the breeding of the individuals GgBb and GgBB. As you can see for the individual GgBb the possible combinations that could be passed on to their offspring are; GB, Gb, gB and gb. You know right away that any combination of genes with GB will result in offspring with a black coat because G means that there is no possibility of yellow offspring and B is the dominent gene for black. see ATTCHEMENT Q14A Attached file Thumbnail(s): You must login or register to gain access to this attachment.
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May 4, 2016
# Homework Help: maths
Posted by tuhituhi on Thursday, January 24, 2013 at 11:45am.
I bought a certain number of apples at 4 for 6 paise and 3/5 of that number at 3 for 6 paise by selling them at 16 for rs.30p. I gained 24 paise.. How many apples did I buy???? | 97 | 285 | {"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-2016-18 | longest | en | 0.980521 |
https://math.stackexchange.com/questions/2218672/computing-flux-divergence-theorem | 1,566,049,713,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313259.30/warc/CC-MAIN-20190817123129-20190817145129-00000.warc.gz | 538,409,709 | 32,288 | # Computing Flux (Divergence Theorem)
Given that $\textbf{F} = \langle \sqrt{x^2+y^2+z^2}, \sqrt{x^2+y^2+z^2}, \sqrt{x^2+y^2+z^2} \rangle$ and E is the volume described by $0 \le z \le \sqrt{1-x^2-y^2}$
I'm trying to use the divergence theorem to compute the flux. $$\iint_{D} \textbf{F} \cdot \textbf{N} \: dS = \iiint_E \nabla \cdot \textbf{F}\:d\textbf{V}$$
Attempt:
$$\text{div}\textbf{F} \:=\: \nabla \cdot \textbf{F} =\frac{x}{2\sqrt{x^2+y^2+z^2}} + \frac{y}{2\sqrt{x^2+y^2+z^2}} + \frac{z}{2\sqrt{x^2+y^2+z^2}} \\ =\frac{p \sin\phi \cos\theta}{2p} + \frac{p \sin\phi \sin\theta}{2p} + \frac{p cos\phi}{2p} \\ = \frac{1}{2}(\sin\phi \cos\theta + \sin\phi \sin\theta + \cos\phi)$$
$\text{d}\textbf{V} = p^2 \sin\phi$
$$\iiint_E \nabla \cdot \textbf{F}\:d\textbf{V} \\ = \frac{1}{2} \int_0^\frac{\pi}{2} \int_0^{2\pi} \int_0^{\sqrt{1-(x^2+y^2)} =\sqrt{1-p^2}?} (\sin\phi \cos\theta + \sin\phi \sin\theta + \cos\phi) \: p^2 \sin\phi \:dz\: d\theta \: d\phi$$
This seems to be a complicated integral. Is my steps/logic correct thus far? How can I think more qualitatively to simplify the integral further? Would appreciate some guidance!
PS. The answer given was $\frac{\pi}{3}$
• Other problem is you're conflating cylindrical and spherical coordinates. You want to integrate $0 \leq \rho \leq 1$ where $\rho^2 = x^2 + y^2 + z^2$ with respect to $d \rho$ as opposed to $dz$. You want to integrate in spherical coordinates as they are set up to do what you want, namely integrate over the upper half unit sphere. – Chris K Apr 5 '17 at 4:25
• Yes. but would $0 \le \rho \le 1$ be the right bound in this case...? hmm – misheekoh Apr 5 '17 at 4:30
• Yes, you want $1$ for an upper bound of $\rho$. Note that $\rho = \sqrt{x^2+y^2+z^2}$. In cylindrical coordinates, $r = \sqrt{x^2+y^2}$, but that is not what we want here. – Chris K Apr 5 '17 at 4:31
First, there is no $1/2$ factor in $\nabla \cdot \textbf{F}$. After fixing the integration bounds, the answer is straightforward. \begin{aligned} &\iiint_E \nabla \cdot \textbf{F}\:d\textbf{V} \\ &= \int_0^\frac{\pi}{2} \int_0^{2\pi} \int_0^{1} (\sin\phi \cos\theta + \sin\phi \sin\theta + \cos\phi) \: p^2 \sin\phi \:dp\: d\theta \: d\phi \\ &= \int_0^{1} \: p^2 \:dp \int_0^\frac{\pi}{2} \int_0^{2\pi} (\sin\phi \cos\theta + \sin\phi \sin\theta + \cos\phi) \sin\phi\: d\theta \: d\phi \\ &= \frac{1}{3} \int_0^\frac{\pi}{2} \int_0^{2\pi} ( \cos\phi) \sin\phi\: d\theta \: d\phi \\ &= \frac{2\pi}{3} \int_0^\frac{\pi}{2} ( \cos\phi) \sin\phi\: \: d\phi \\ &= \frac{\pi}{3} \end{aligned}
As a double check, do the surface integration directly. Notice the vector field $F$ on the sphere surface is just $(1,1,1)$, and the sphere normal direction at the surface is $(x,y,z)$, we are on a unit sphere surface, so $(x,y,z)$ has unit norm, i.e., it is the normalized normal vector. Then the surface integration is
$$\oint \vec{F} \vec{n} dS = \oint(1,1,1)\cdot(x,y,z) p^2 \sin(\theta) d\theta d\phi \\ =\oint (x+y+z) \sin\theta d\theta d\phi \\ = \int_0^\frac{\pi}{2} \int_0^{2\pi} (\sin\phi \cos\theta + \sin\phi \sin\theta + \cos\phi) \sin\phi\: d\theta \: d\phi \\ = \int_0^\frac{\pi}{2} \int_0^{2\pi} ( \cos\phi) \sin\phi\: d\theta \: d\phi \\ = \pi$$ Oops! why they are different? The reason is we have a bottom surface to consider as well! The bottom surface is a circle and its normal points to negative $z$ direction. The integration for this bottom surface is \begin{aligned} \quad & \oint (\sqrt{x^2+y^2},\sqrt{x^2+y^2},\sqrt{x^2+y^2}) \cdot (0, 0, -1) dS \\ & = \oint -\sqrt{x^2+y^2} dS \text{switch to 2D polar coordinate} \\ & = -\int_0^{2\pi}\int_0^1 r \cdot r dr d\theta \\ & = -\frac{2\pi}{3} \end{aligned}
Sum the two parts gives $\pi/3$.
• Can you explain to why the bound of $\rho$ is between $0 \: \text{and} \:1$ in this case..? – misheekoh Apr 5 '17 at 4:41
• @misheekoh because you are integrating over the (half) unit sphere's volume, to cover this volume the radius has to change from $0$ to $1$. – Taozi Apr 5 '17 at 4:47
• @misheekoh I added to the answer a direct evaluation of the surface flux integration. – Taozi Apr 5 '17 at 5:03
• Thank you. Btw, I do understand that we're integrating over the hemisphere but particularly for when $\text{z} \le \sqrt{1-x^2-y^2}$, how did u manage to convert the upper bound to $\rho \le 1$? – misheekoh Apr 5 '17 at 5:06
• @misheekoh Square both sides of this inequality to have $z^2 \le 1 - x^2 -y^2$, rewrite as $x^2 +y^2+z^2 \le 1$, since $x^2 +y^2+z^ = \rho^2$, this is just $\rho^2 \le 1$, or $\rho\le 1$. – Taozi Apr 5 '17 at 5:09 | 1,782 | 4,564 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2019-35 | latest | en | 0.696244 |
http://thefinance.sg/2018/02/26/askdrwealth-how-many-stocks-should-i-have-in-my-portfolio/ | 1,537,536,371,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157203.39/warc/CC-MAIN-20180921131727-20180921152127-00000.warc.gz | 249,453,838 | 15,247 | In today’s #AskDrWealth series, I am going to address the most popular question from our readers and students.
“How Many Stocks Should I have In My Portfolio?”
## Which Is Better? – Diversified portfolio or Concentrated Portfolio
Let’s imagine that there’s Investor A and Investor B, with different types of portfolio:
• Investor A has a portfolio of 5 stocks (concentrated)
• Investor B has a portfolio of 30 stocks (diversified)
Let’s assume that both portfolios are equally weighted.
This means for A, each stock represents about 20% of the portfolio while for B, each stock represents about 3%.
• Investor A: 100% / 5 stocks = 20% per stock
• Investor B: 100% / 30 stocks = 3% per stock
At a quick glance, inexperienced investors would think that having 5 stocks is better than … | 191 | 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} | 2.515625 | 3 | CC-MAIN-2018-39 | longest | en | 0.926437 |
http://gamingmouseunder30.club/excel-sum-of-squares/ | 1,553,261,061,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202658.65/warc/CC-MAIN-20190322115048-20190322141048-00556.warc.gz | 80,669,350 | 11,762 | Excel Sum Of Squares
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excel sum of squares excel residual sum of squares in r. | 2,543 | 13,374 | {"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-2019-13 | latest | en | 0.831955 |
http://fora.xkcd.com/viewtopic.php?f=18&t=35675&p=1420129& | 1,561,405,761,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999709.4/warc/CC-MAIN-20190624191239-20190624213239-00017.warc.gz | 67,597,018 | 10,381 | ## Infinite Grid of Springs
For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.
Moderators: gmalivuk, Moderators General, Prelates
Kosak
Posts: 4
Joined: Tue Mar 03, 2009 12:23 am UTC
Location: Boston
Contact:
### Infinite Grid of Springs
How would a spring behave if it were in an infinite grid of springs? Like the nerd sniping problem where there is an infinite grid of resistors.
If a force is added to point 1, what is the resulting behavior of point 2.
BlackSails
Posts: 5315
Joined: Thu Dec 20, 2007 5:48 am UTC
### Re: Infinite Grid of Springs
Its easy, you just find the eigenvalues of an infinitely large matrix.
danpilon54
Posts: 322
Joined: Fri Jul 20, 2007 12:10 am UTC
### Re: Infinite Grid of Springs
Locally Im not so sure, but if the size of the gap between springs was very small compared to your area of interest, wouldnt it act much like the 2D wave equation? You would have an initial position and velocity at every point and have outward propagating longitudinal and transverse waves. The speed of such waves would average to a value determined by the gap of the springs and the spring constants. This of course assumes that all the springs are they same spring constant and distance apart.
Other than that not sure how to find the exact solution; probably isnt possible.
Mighty Jalapeno wrote:Well, I killed a homeless man. We can't all be good people.
BlackSails
Posts: 5315
Joined: Thu Dec 20, 2007 5:48 am UTC
### Re: Infinite Grid of Springs
It would behave much like vibrations in a crystal I think. In fact, I think the lots of springs model is one of the most commonly used ones.
Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.
### Re: Infinite Grid of Springs
You, sir, name?
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Location: Chako Paul City
Contact:
### Re: Infinite Grid of Springs
Try going continuous (i.e. looking at the problem from so far away that the distance between the springs is vanishingly small), that is, making the sum a differential equation. I think you basically end up with something similar to the wave equation applied to a sheath living in three dimensions, to which finding a steady-state solution for some boundary conditions is relatively easy to find.
When you have such a solution, you could try to hook it into the edges of a finite discrete area. At this point, you're in numeric solution land, but it's just crazy enough to work™.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.
mattdude
Posts: 57
Joined: Sat Nov 08, 2008 8:30 am UTC
### Re: Infinite Grid of Springs
i should think the force required to move any point would be infinite. when adding springs in series, the k's add inversely (like capacitors in series or resistors in parallel). but there's also all the springs that are in parallel to any point, which simply add. so you'd have a simple expression like lim (n->infinity) nk = infinity. although i'm only a second year physics major, so i may be wrong. any ideas?
Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.
### Re: Infinite Grid of Springs
mattdude wrote:i should think the force required to move any point would be infinite. when adding springs in series, the k's add inversely (like capacitors in series or resistors in parallel). but there's also all the springs that are in parallel to any point, which simply add. so you'd have a simple expression like lim (n->infinity) nk = infinity. although i'm only a second year physics major, so i may be wrong. any ideas?
It is most certainly not infinite, and it can't be treated as simple as that.
danpilon54
Posts: 322
Joined: Fri Jul 20, 2007 12:10 am UTC
### Re: Infinite Grid of Springs
The force would not be infinite because there will be a characteristic speed (much like the speed of light) in the problem, making only a finite number of springs affect a given point in time.
Mighty Jalapeno wrote:Well, I killed a homeless man. We can't all be good people.
_Big_Mac_
Posts: 83
Joined: Sun Sep 07, 2008 8:30 pm UTC
Location: Poland
### Re: Infinite Grid of Springs
danpilon54 wrote:The force would not be infinite because there will be a characteristic speed (much like the speed of light) in the problem
I'd say speed of sound is a better analogy.
mattdude
Posts: 57
Joined: Sat Nov 08, 2008 8:30 am UTC
### Re: Infinite Grid of Springs
danpilon54 wrote:The force would not be infinite because there will be a characteristic speed (much like the speed of light) in the problem, making only a finite number of springs affect a given point in time.
ahhh of course. classically i think my solution is ok but i think you're definitely correct in introducing relativity. i figured there was a flaw in my position but i couldn't figure it out. thanks
Seraph
Posts: 342
Joined: Mon Jul 16, 2007 4:51 pm UTC
### Re: Infinite Grid of Springs
mattdude wrote:
danpilon54 wrote:The force would not be infinite because there will be a characteristic speed (much like the speed of light) in the problem, making only a finite number of springs affect a given point in time.
ahhh of course. classically i think my solution is ok but i think you're definitely correct in introducing relativity. i figured there was a flaw in my position but i couldn't figure it out. thanks
Clasically I still think your solution doesn't work. Lets define 5 junctions in the infinate field of springs. Point C will be the Center, while A, B, E, and F are the four junctions connected to C by spings.
Now lets say that A, B, E and F are fixed (which is the same as saying it would take an infinite force to move them). Point C is now the junction of four springs (which have their far ends anchored), given that those springs have a finite spring constant I can't see it would take an infinate amount of force to make the point C move.
mattdude
Posts: 57
Joined: Sat Nov 08, 2008 8:30 am UTC
### Re: Infinite Grid of Springs
Seraph wrote:
mattdude wrote:
danpilon54 wrote:The force would not be infinite because there will be a characteristic speed (much like the speed of light) in the problem, making only a finite number of springs affect a given point in time.
ahhh of course. classically i think my solution is ok but i think you're definitely correct in introducing relativity. i figured there was a flaw in my position but i couldn't figure it out. thanks
Clasically I still think your solution doesn't work. Lets define 5 junctions in the infinate field of springs. Point C will be the Center, while A, B, E, and F are the four junctions connected to C by spings.
Now lets say that A, B, E and F are fixed (which is the same as saying it would take an infinite force to move them). Point C is now the junction of four springs (which have their far ends anchored), given that those springs have a finite spring constant I can't see it would take an infinate amount of force to make the point C move.
you make an interesting argument. indeed it would definitely seem that my solution is wrong. in that case, i'm assuming this is far beyond my second year knowledge, but i'll continue to think about it.
Rentsy
Posts: 154
Joined: Tue Dec 02, 2008 4:13 am UTC
### Re: Infinite Grid of Springs
Sorry.
LaserGuy
Posts: 4581
Joined: Thu Jan 15, 2009 5:33 pm UTC
### Re: Infinite Grid of Springs
There are two approaches that you can take to solve this problem:
1) Go continuous... on a large enough scale, you can treat this as vibrations in a 2-d infinite plane. This can be solved using the wave equation and fourier transforms. Or probabably conformal mapping, if you prefer complex analysis.
2) Stay discrete... in the easiest case, you assume that each spring only supplies a force to its nearest neighbours. This makes the problem quite tractable, and the solution can be expressed in terms of the normal modes of the spring system. Any elementary solid state physics text will cover this (at least in 1d) in a section on lattice vibrations or phonons, and the generalization to higher dimensions is not that tricky. If you want to go passed nearest neighbours to a higher order solution, getting a sensible solution will probably require a fairly computation-intensive numerical scheme. There's probably a paper or two on the subject floating around in one of the academic journals on solid-state physics that looks at this.
If you aren't familiar with solving these types of problems, I'd suggest starting with the 1d case. It will be a lot easier to figure out what's going on, and generalizing to higher dimensions won't enhance your understanding of the problem significantly relative to the added effort needed to solve it. | 2,142 | 8,824 | {"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-2019-26 | latest | en | 0.922057 |
https://www.calculatorbit.com/en/force/4-kilopond-to-kilopond | 1,717,051,295,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059506.69/warc/CC-MAIN-20240530052602-20240530082602-00128.warc.gz | 591,459,099 | 7,011 | # 4 Kilopond to Kilopond Calculator
Result:
4 Kilopond = 4 Kilopond (kp)
Rounded: ( Nearest 4 digits)
4 Kilopond is 4 Kilopond (kp)
4 Kilopond is 39.2266N
## How to Convert Kilopond to Kilopond (Explanation)
• 1 kilopond = 1 kp (Nearest 4 digits)
• 1 kilopond = 1 kp (Nearest 4 digits)
There are 1 Kilopond in 1 Kilopond. To convert Kilopond to Kilopond all you need to do is multiple the Kilopond with 1.
In formula force is denoted with F
The force F in Kilopond (kp) is equal to 1 times the force in kilopond (kp):
### Equation
F (kp) = F (kp) × 1
Formula for 4 Kilopond (kp) to Kilopond (kp) conversion:
F (kp) = 4 kp × 1 => 4 kp
## How many Kilopond in a Kilopond
One Kilopond is equal to 1 Kilopond
1 kp = 1 kp × 1 => 1 kp
## How many Kilopond in a Kilopond
One Kilopond is equal to 1 Kilopond
1 kp = 1 kp / 1 => 1 kp
## kilopond:
A kilopond is a unit of force equal to 9.80665 newtons. The word "pond" comes from the Latin word pondus, which means "weight." The kilopond was once a common unit of measure for weight or force, but it has been largely replaced by the Newton in scientific contexts. Still, the kilopond is sometimes used in everyday contexts, such as when describing the strength of an engine or the power of a wave. In general, anything that produces a force of 9.80665 newtons can be said to have a strength of 1 kilopond.
## :
Cite, Link, or Reference This Page
If you found information page helpful you can cite and reference this page in your work.
## Kilopond to Kilopond Calculations Table
Now by following above explained formulas we can prepare a Kilopond to Kilopond Chart.
Kilopond (kp) Kilopond (kp)
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Nearest 4 digits
## Convert from Kilopond to other units
Here are some quick links to convert 4 Kilopond to other force units.
## Convert to Kilopond from other units
Here are some quick links to convert other force units to Kilopond.
## FAQs About Kilopond and Kilopond
Converting from one Kilopond to Kilopond or Kilopond to Kilopond sometimes gets confusing.
Here are some Frequently asked questions answered for you.
### Is 1 Kilopond in 1 Kilopond?
Yes, 1 Kilopond have 1 (Nearest 4 digits) Kilopond.
### What is the symbol for Kilopond and Kilopond?
Symbol for Kilopond is kp and symbol for Kilopond is kp.
### How many Kilopond makes 1 Kilopond?
1 Kilopond is euqal to 1 Kilopond.
### How many Kilopond in 4 Kilopond?
Kilopond have 4 Kilopond.
### How many Kilopond in a Kilopond?
Kilopond have 1 (Nearest 4 digits) Kilopond. | 800 | 2,547 | {"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-2024-22 | latest | en | 0.773985 |
http://www.ck12.org/trigonometry/Composition-of-Trig-Functions-and-Their-Inverses/lesson/Composition-of-Trig-Functions-and-Their-Inverses/r4/ | 1,455,022,343,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701157075.54/warc/CC-MAIN-20160205193917-00342-ip-10-236-182-209.ec2.internal.warc.gz | 349,986,721 | 32,298 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
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# Composition of Trig Functions and Their Inverses
## Application of sine, cosine, tangent, or their inverses and then another function.
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Composition of Trig Functions and Their Inverses
You've considered trigonometric functions, and you've considered inverse functions, and now it's time consider how to compose trig functions and their inverses. If someone were to ask you to apply the inverse of a trig function to a different trig function, would you be able to do this? For example, can you find $\sin^{-1} (\cos (\frac{3\pi}{2}))$ ?
When you complete this Concept, you'll be able to solve this problem.
### Guidance
In other Concepts, you learned that for a function $f(f^{-1}(x)) = x$ for all values of $x$ for which $f^{-1}(x)$ is defined. If this property is applied to the trigonometric functions, the following equations will be true whenever they are defined:
$\sin(\sin^{-1}(x)) = x && \cos(\cos^{-1}(x)) = x && \tan(\tan^{-1}(x)) = x$
As well, you learned that $f^{-1}(f(x)) = x$ for all values of $x$ for which $f(x)$ is defined. If this property is applied to the trigonometric functions, the following equations that deal with finding an inverse trig. function of a trig. function, will only be true for values of $x$ within the restricted domains.
$\sin^{-1}(\sin(x)) = x && \cos^{-1}(\cos(x)) = x && \tan^{-1}(\tan(x)) = x$
These equations are better known as composite functions. However, it is not necessary to only have a function and its inverse acting on each other. In fact, is is possible to have composite function that are composed of one trigonometric function in conjunction with another different trigonometric function. The composite functions will become algebraic functions and will not display any trigonometry. Let’s investigate this phenomenon.
When solving these types of problems, start with the function that is composed inside of the other and work your way out. Use the following examples as a guideline.
#### Example A
Find $\sin \left ( \sin^{-1} \frac{\sqrt{2}}{2} \right )$ .
Solution: We know that $\sin^{-1} \frac{\sqrt{2}}{2} = \frac{\pi}{4}$ , within the defined restricted domain. Then, we need to find $\sin \frac{\pi}{4}$ , which is $\frac{\sqrt{2}}{2}$ . So, the above properties allow for a short cut. $\sin \left ( \sin^{-1} \frac{\sqrt{2}}{2} \right ) = \frac{\sqrt{2}}{2}$ , think of it like the sine and sine inverse cancel each other out and all that is left is the $\frac{\sqrt{2}}{2}$ .
#### Example B
Without using technology, find the exact value of each of the following:
a. $\cos \left ( \tan^{-1} \sqrt{3} \right )$
b. $\tan \left ( \sin^{-1}\left( -\frac{1}{2} \right ) \right )$
Solution: For all of these types of problems, the answer is restricted to the inverse functions’ ranges.
a. $\cos \left ( \tan^{-1} \sqrt{3} \right )$ : First find $\tan^{-1} \sqrt{3}$ , which is $\frac{\pi}{3}$ . Then find $\cos \frac{\pi}{3}$ . Your final answer is $\frac{1}{2}$ . Therefore, $\cos \left ( \tan^{-1} \sqrt{3} \right ) = \frac{1}{2}$ .
b. $\tan \left ( \sin^{-1} \left ( -\frac{1}{2} \right ) \right ) = \tan \left ( -\frac{\pi}{6} \right ) = -\frac{\sqrt{3}}{3}$
#### Example C
Without using technology, find the exact value of each of the following:
a. $\cos (\tan^{-1} (-1))$
b. $\sin \left ( \cos^{-1}\frac{\sqrt{2}}{2} \right )$
Solution: For all of these types of problems, the answer is restricted to the inverse functions’ ranges.
a. $\cos (\tan^{-1} (-1)) = \cos^{-1} \left ( -\frac{\pi}{4} \right ) = \frac{\sqrt{2}}{2}$ .
b. $\sin \left ( \cos^{-1} \frac{\sqrt{2}}{2} \right ) = \sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
### Vocabulary
Composite Function: A composite function is a set of two different trigonometric functions applied to an argument in conjunction with one another.
### Guided Practice
1. Find the exact value of $\cos^{-1} \frac{\sqrt{3}}{2}$ , without a calculator, over its restricted domain.
2. Evaluate: $\sin \left ( \cos^{-1} \frac{5}{13} \right )$
3. Evaluate: $\tan \left ( \sin^{-1} \left( -\frac{6}{11} \right) \right )$
Solutions:
1. $\frac{\pi}{6}$
2.
$\cos \theta & = \frac{5}{13}\\\sin \left ( \cos^{-1} \left ( \frac{5}{13} \right ) \right ) & = \sin \theta\\\sin \theta & = \frac{12}{13}$
3. $\tan \left ( \sin^{-1} \left ( -\frac{6}{11} \right ) \right ) \rightarrow \sin \theta = -\frac{6}{11}$ .
The third side is $b = \sqrt{121-36} = \sqrt{85}$ .
$\tan \theta = -\frac{6}{\sqrt{85}} = -\frac{6\sqrt{85}}{85}$
### Concept Problem Solution
To solve this problem: $\sin^{-1} (\cos (\frac{3\pi}{2}))$ , you can work outward.
First find:
$\cos (\frac{3\pi}{2}) = 0$
Then find:
$\sin^{-1} 0 = 0$
or
$\sin^{-1} 0 = \pi$
### Practice
Without using technology, find the exact value of each of the following.
1. $\sin \left ( \sin^{-1} \frac{1}{2} \right )$
2. $\cos \left ( \cos^{-1} \frac{\sqrt{3}}{2} \right )$
3. $\tan \left ( \tan^{-1} \sqrt{3} \right )$
4. $\cos \left ( \sin^{-1} \frac{1}{2} \right )$
5. $\tan \left ( \cos^{-1} 1 \right )$
6. $\sin \left ( \cos^{-1} \frac{\sqrt{2}}{2} \right )$
7. $\sin^{-1} \left ( \sin \frac{\pi}{2} \right )$
8. $\cos^{-1} \left ( \tan \frac{\pi}{4} \right )$
9. $\tan^{-1} \left ( \sin \pi \right )$
10. $\sin^{-1} \left ( \cos \frac{\pi}{3} \right )$
11. $\cos^{-1} \left ( \sin -\frac{\pi}{4} \right )$
12. $\tan \left ( \sin^{-1} 0 \right )$
13. $\sin \left ( \cos^{-1} \frac{\sqrt{3}}{2} \right )$
14. $\tan^{-1} \left ( \cos \frac{\pi}{2} \right )$
15. $\cos \left ( \sin^{-1} \frac{\sqrt{2}}{2} \right )$
### Vocabulary Language: English
composite function
composite function
A composite function is a function $h(x)$ formed by using the output of one function $g(x)$ as the input of another function $f(x)$. Composite functions are written in the form $h(x)=f(g(x))$ or $h=f \circ g$. | 1,924 | 6,028 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 61, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2016-07 | latest | en | 0.872923 |
https://www.coursehero.com/file/6851666/ProblemSet08-2/ | 1,516,549,516,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890771.63/warc/CC-MAIN-20180121135825-20180121155825-00725.warc.gz | 870,217,059 | 59,377 | ProblemSet08-2
# ProblemSet08-2 - 102mph(45.6m/s It is caught by the catcher...
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Physics 204A Problem Set #8-2 1. A woman throws a ball of mass 0.200kg by accelerating it from rest to 30.0m/s over a distance (assumed to be along a straight line) of 85.0cm. Find (a)the initial kinetic energy of the ball, (b)the final kinetic energy of the ball, (c)the work done on the ball by the woman and (d)the average force exerted on the ball by the woman. 2. A 10.0g bullet moving at 400m/s travels through 30.0cm of gelatin as shown on YouTube ( http://www.youtube.com/watch?v=tTHo0K2Sc0g ). The average drag force exerted on the bullet is 1200N. Find (a)the work done by the drag force and (b)the speed of the bullet when it leaves the gelatin. 3. A 0.150kg baseball thrown by a pitcher leaves his hand 2.00m above the ground at a speed of
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Unformatted text preview: 102mph (45.6m/s). It is caught by the catcher 60.5ft (18.4m) away at a height of 1.00m and a speed of 97.0mph (43.4m/s). Find (a)the initial kinetic energy of the ball, (b)the final kinetic energy of the ball, (c)the net work done on the ball, (d)the net work done by gravity and (e)the work done by the resistive forces that act on the ball. 4. A 1.20kg block falls onto a relaxed vertical spring with a spring constant of 500N/m. The block drops 15.0cm before coming momentarily to rest. Find (a)the work done by the spring, (b)the work done by gravity, (c)the total work done on the block, and (d)the speed of the block when it fell on the spring. h = 15.0cm v = 0 before o v after...
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http://www.pudnersports.com/2018/10/ | 1,719,080,408,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862410.56/warc/CC-MAIN-20240622175245-20240622205245-00755.warc.gz | 48,167,788 | 14,794 | ## Saturday, October 20, 2018
### Statis-Pro Clutch Defense: See Charts Below for Result of Play
An exciting aspect of Statis-Pro Baseball is the chance of a defender needing to make or blow a clutch play. If playing with dice, this only applies if men are on base and instead of a number by the PB spot on the Fast Action Card comes up or in the dice version the 20-sided die comes up as a "20" and the two 6-sided die equal between 5 and 9. Learn to play Statis-Pro Baseball in 5 minutes by clicking here.
Note: The opposite PB: BD or dice roll of "20" and 6-sided die between 2 and 4 ind indicates clutch batting. If you do not have cards with clutch batting numbers, then flip again and refer to the batters card but translate; 1) a single on the batters card to a base-clearing double, 2) a double into a home run, 3) a triple or home run on the card stay the same, and 4) anything except a hit on the card is changed to a foul home run and return to normal play with the same batter still up.
When a CD is called for from the first paragraph, the next step is to determine which fielder will try to make a great play, or perhaps misplay the ball. In the dice version, the combination of the two six-sided dice determines which player, but in the Random Card version another card must be flipped and the position by the "CD" determines which player attempts to make the play.
Look at the fielder's card, and locate whether he is a CD 1, 2, 3 or 4. Then find his position on the chart below and look at the two 8-sided dice to see the number from 11 to 88 - or if using Random Cards then flip another card to get a number from 11 to 88. Find the position below, the CD of 1 to 4 and the number of 11 to 88 and read the result of the play:
On a Random Number of 81-88 no action occurs, unless a player is a CD-5 or CD-0 (anyone playing out of position is an E10, CD-0 at that position). If an 81-88 occurs for a CD-5, it is always a diving catch for an out and runners hold. If an 81-88 occurs for a CD-0 it is always a ball misplayed into a single.
## Tuesday, October 2, 2018
### Oct. 24: Democrats Project 219-215-1 Lead based on process using Sabato, NY Times, Silver
Here is the new table as of the evening of October 24, but I left the October 12 table below for comparison. The Republicans actually gained a few points overall in the New York Times the second set of polls but came out lower than two Nate Silver averages to drop slightly from a 1.4 point lead to an average 1.3 point lead. They lost three spots because New York Times polls gave the Democrats a 1-point lead in California 1, a tie in California 48 and a 2-point lead in Illinois 6. However, a huge 12-point shift in favor of the GOP in New Jersey 3 turned a 10-point deficit to a 2-point lead to leave them at 215 seats.
Because one moved to a tie, the Democrats gain just one seat to end up with a 219-215 lead with one tie. If you count all 1-point races either way as ties, then the Democrats lead only 215-212 with eight ties determining the majority.
The New York Times Senate polls in Tennessee, Texas, Arizona, and Nevada all gave the GOP the edge to put them on pace for at least a 52-48 lead, however, their Florida poll so far gives the Democrats a big lead. The GOP led in 6 of 11 October polls before the NY Times, but the polls showing the Democrats pulling away are more recent and by bigger margins, so Florida is looking Democratic as of today and the GOP may need to win Missouri to get to 53 and Indians to get to 54 going through my poll outline in NewsMax.
CA10-6DemocratNY Times Poll
CA252RepublicanNY Times Poll
CA39-1DemocratNY Times Pollflip Dem
CA45-5DemocratNY Times Poll
CA480TieNY Times Pollflip to tie
IA3-1DemocratNY Times Poll
IL6-2DemocratIncomplete NY TimesDropped by 3, flip
IL121RepublicanNY Times Poll
KS2-1DemocratNY Times Poll
KS3-8DemocratNY Times Poll
KY61RepublicanNY Times Poll
ME25RepublicanNY Times Poll
MI83RepublicanNY Times Poll
MN110RepublicanNate Silver
MN2-12DemocratNY Times Poll
MN815RepublicanNY Times Polldropped by 10
NC95RepublicanNY Times Poll
NJ32RepublicanIncomplete NY Timesplus 12, now GOP
NJ71RepublicanNY Times Poll
NM2-1DemocratNY Times Poll
NY19-3DemocratNate Silver
NY22-2DemocratNate Silver
OH19RepublicanNY Times Pollsame
PA1-7DemocratNY Times Pollplus 5
TX76RepublicanNY Times Pollplus 3
TX238RepublicanNY Times Poll
VA28RepublicanNY Times Poll
VA74RepublicanNY Times Poll
WV38RepublicanNY Times Poll
## October 12 update
So far the NY Times district-by-district polling of Sabato's toss-up districts is breaking the Republicans way and pointing to them losing only 218-217 in the House as of October 12 at 2:30 p.m. One example of the apparent across-the-board shift to Republicans from the Kavanaugh testimony to confirmation is GOP Lee Zeldin in New York. He was slightly behind, causing me to temporarily add that poll to the list below and give the Democrats a 219-216 lead, but voters steadily moved his way to such an extent that he fnished the poll nine points ahead.
October 11, 7:30 p.m. note - its dangerous to count incomplete polls, but based on the New York Times we flipped two seats. This switches PA-1 to Democrat (a -12 for Democrat up 12) and Minnesota-8 to Republicans (+25 so GOP up an incredible 25 points) to still leave the House 218 to 217 in favor of the Democrats.
I'm tracking the Senate here. The NY Times just got going on Senate polls, and the GOP had a double-digit lead in Tennessee and almost as big a lead in Texas.
The methodology we went with from day one was the same; 1) go with the Party Sabato forecasts as winning the race, 2) chance that only if the New York Times poll is run to pick (or in one case reverse) Sabato's projected winner, and if neither side has the edge through #1 and #2 then, 3, go to Nate Silver's projection and take the most current poll he records.
CA10-2DemocratNate Silver
CA252RepublicanNY Times Poll
CA392RepublicanNate Silver
CA45-5DemocratNY Times Poll
CA483RepublicanNate Silver
IA3-1DemocratNY Times Poll
IL61RepublicanNY Times Poll
IL121RepublicanNY Times Poll
KS2-1DemocratNY Times Poll
KS3-10DemocratNY Times Poll
KY61RepublicanNY Times Poll
ME25RepublicanNY Times Poll
MI83RepublicanNY Times Poll
MN110RepublicanNate Silver
MN2-12DemocratNY Times Poll
MN825RepublicanIncomplete NY Times
NC95RepublicanNY Times Poll
NJ3-10DemocratNY Times Poll
NJ71RepublicanNY Times Poll
NM2-1DemocratNY Times Poll
NY19-3DemocratNate Silver
NY22-2DemocratNate Silver
OH19RepublicanNY Times Poll
PA1-12DemocratIncomplete NY Times
TX73RepublicanNY Times Poll
TX2316RepublicanNY Times Poll
VA28RepublicanNY Times Poll
VA74RepublicanNY Times Poll
WV36RepublicanNY Times Poll
1.4Average GOP
Of the 1 tied race and 6 unpolled race above, I went back and looked at the most recent adjusted poll on Nate Silver's page. In those races the GOP goes 5-2, losing only the two New York races, which would give the GOP a 218-217 win. | 1,813 | 6,945 | {"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-2024-26 | latest | en | 0.932801 |
https://www.physicsforums.com/threads/projectile-motion-angle.223163/ | 1,576,178,956,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540545146.75/warc/CC-MAIN-20191212181310-20191212205310-00054.warc.gz | 816,234,578 | 19,014 | # Projectile motion angle
## Main Question or Discussion Point
Projectile motion!!
Hey!!!....in college they teach you that the most efficient angle for projectile motion is the 45º, cause it gives you the farther distance.....but when we did the experiment in the lab we obtain that the best angle (the most distance achived by the metal ball).....was 30º.........the teacher said that it was not wrong......in fact.....she said....you are shooting it at 30º and you`re getting more distance than with 45º.......she asked us to explain why that could happend......
anyways......that happen 2 years ago....i did pass my 1st semester of Physics because with all the other exams and lab test......but she never wanted to explain why that happend!!.....she said that we should investigate ourselves......i have never got to know why.........the only thing i could come up was that since i live in venezuela so im technically in the middle of the world, it might have something to do with gravity or something like that........
so please.....can anyone tell me why did that happened!.......thanks!!
Related Other Physics Topics News on Phys.org
two words.... air resistance
A projectile travailing at 45 deg will lose more velocity over less ground covered then a projectile at 30 deg
Air Resistance??.......but every Physics Book says that is the 45° angle that has the more distance shooting......Serway, Jones, Giambattista, Alan P Lightman, all those authors say that the 45° angle....so im guessing that the 45° must be determine in northern latitudes or something.....thats why i thought that maybe the fact that im located in venezuela must have had something to do...microgravity, etc...
why all those authors obtain 45° while i got 30°??
Because most of those book don't take into account air resistance. or at least how it pulls it down to earth over time. most of the books your talking about only use it to see how a bullet slows down over time but doesn't put it in with the angle calculation.
shooting in the north has little to no difference then the south.
what matters (and only in long range shooting... 1000yrds +) is the direction (with the rotation of the earth or against it).
if you want a really good book to read. type "Understanding Fire Arm Ballistics" into ebay. this guy goes over every thing from barrel whip to how the grains of powder are formed...
Most physics textbooks when introducing the subject ignore the affect of air on moving objects for the sake of simplicity. I find it easier to first understand projectile motion in terms of pure theory, in a vacuum, as it describes will happen in %99.9999999 percent of the universe where there is no air. That way a solid theoretical foundation is formed it becomes even simpler to add on the obstructing concept of air resistance.
tiny-tim
Homework Helper
.....but when we did the experiment in the lab we obtain that the best angle (the most distance achived by the metal ball).....was 30º
Hi reinaldo!
Some real physics!
Can you describe the experiment?
In particular, how did you launch the ball, and how did you make sure that it had the same speed at different angles?
And how far did it go, and did it land at the same height as it was launched from?
russ_watters
Mentor
If the lab experiment was actually in a lab (ie, a small scale experiment), you really should have gotten an answer nearer to 45 degrees. The velocities would be too small for air resistance to make a difference. Could you describe the experiment?
Was it launched with a spring? When you launch with a spring, the initial velocities are not identical, since the spring has to absorb some of the weight of the ball. Ie, for a horizontal launch, f=ma, but for a vertical launch, f-mg=ma
I would hope your prof actually knew this and wasn't just blowing you off...
The experiment was made in a Lab with a Small Scale equipment and it consisted of a canon type shooter with a spring, you would lacht the spring and slide the metal ball inside, and the canon was place in an axis with a all the 90° posibles positions, then you would trigger the cannon at the selected angle and we´d measure the height obtain, and the distance obtain in the X axis.....we repeated the experiment 15 times in each angle....15°, 23°, 30°, 37°, 45°, 55°, 70°, 80°.....the most horizontal distance we got was with the 30° angle.....
russ_watters
Mentor
In that case, I'd suspect that the weight of the ball on the spring, resulting in an inconsistent launch speed, is what caused what you found.
Also, the optimum launch angle for distance when the projectile lands under its initial height is not 45 degrees, right?
DaveC426913
Gold Member
I find it easier to first understand projectile motion in terms of pure theory, in a vacuum, as it describes will happen in %99.9999999 percent of the universe where there is no air.
While I agree with your point that it's simpler to ignore confounding factors such as air resistance until you've understood the basics, I think your rationale leaves something to be desired.
In 99.9999999% of the universe, you're not going to encounter gravitational forces that behave as planes (like they do on the human scale, on Earth, where gravity is a force whose direction never changes wrt the object's path). In 99.9999999% of the universe, forces of gravity will act more like points, and ballistic paths will be elliptical rather than parabolic. | 1,221 | 5,437 | {"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} | 3.5 | 4 | CC-MAIN-2019-51 | latest | en | 0.951247 |
http://www.jiskha.com/members/profile/posts.cgi?name=gem | 1,495,975,234,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463609817.29/warc/CC-MAIN-20170528120617-20170528140617-00370.warc.gz | 673,969,988 | 5,570 | # Posts by gem
Total # Posts: 35
Chemistry
If 0.812g of calcium reacts in a coffee-cup calorimeter that contains 400.0g of water/ The initial temperature of the water is 17.9°C, the final temperature is 26.0°C. Calculate the standard molar enthalpy change for this reaction.
math
Consider the equation y^2-12y=c, where c is a real constant. Assuming this equation has two distinct solutions y_1 and y_2, in terms of c, determine y_1y_2. i tried 12 and 0 they were both wrong,i have no idea what else to try
Geometry
I know that <XBC=22.5
Geometry
Point X is on line AC such that AX = 3 CX = 12. If <ABC = <BXA = 90 degrees, then what is BX? Please help I have no idea how to approach this
In the diagram below, we have DE = 2EC and AB = DC = 20. Find the length of FG. I have no idea how to do this. I did a problem almost exactly the same and approached it the same way, it did not work.
i got AC=24 and AB= 32.78. This gave me 340.7 which was wrong. What should i do?
In triangle ABC, we have <BAC = 60 degrees and <ABC = 45 degrees. The bisector of <A intersects line BC at point T, and AT = 24. What is the area of triangle ABC? How should i approach this?
E is on a line that intersects <AB and lies on middle of the line AC, and D is in in the middle of the line BE extending to C.
They are inside the triangle ABC
In a triangle, we have <ABC = <ACB = <DEC=<CDE, BC = 8, and DB = 2. Find AB. How should i approach this? will sss similarity work?
Point P is inside rectangle ABCD. Show that $PA^2 + PC^2 = PB^2 + PD^2.$ Be sure that your proof works for ANY point inside the rectangle. Any suggestions on how to work this? Not sure how to do this or what equation i need to use.
Point X is on line AC such that AX = 3 CX = 12. If <ABC = <BXA = 90^ degrees, then what is BX? I know that <XBC=22.5
A square is constructed using the hypotenuse line AC of right triangle ABC as a side, as shown below. Find the area of the square if AB = 5 and BC = 9. I tried to approach this by finding the hypotenuse, which i found was 10, then i used that to find the area of the square ...
In triangle PQR, we have <P = 30 degrees, <Q = 60 degrees, and <R=90 degrees. Point X is on line PR such that line QX bisects <PQR. If PQ = 12, then what is the area of triangle PQX? I have determined that i need to use the equation PR/\sqrt{3}, but i cannot find PR.
Point X is on line AC such that AX = 3 CX = 12. If <ABC = <BXA = 90 degrees, then what is BX? I'm having a really hard time drawing this out. Is there an easy equation to use for this that won't include drawing it?
Find the area of triangle ABC if AB = BC = 12 and <ABC = 120 degrees Should approach this with SSS similarity? If yes will the answer be clear or will i need to manipulate it, and how.
Geometry
In triangle PQR, we have <P = 30 degrees, <Q = 60 degrees, and <R=90 degrees. Point X is on line PR such that line QX bisects <PQR. If PQ = 12, then what is the area of triangle PQX\$?
math help
Given DC = 7, CB = 8, AB = 1/4 AD, and ED = 4/5 AD, find FC. Express your answer as a decimal. not sure how to tackle this one
Geometry
A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground 3 meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is attached to the ground, her head just touches the ...
Geometry
I got the answer to my question. It was 45
Geometry
The lengths of the sides of a triangle are 6 cm, 7 cm and 9 cm. In a similar triangle whose perimeter is 110 cm, what is the length of the longest side, in centimeters? i know that the first triangle's perimeter is 22, but i'm not sure how this will help me.
algebra
Find the square roots of 3+4i. The answer should be in the form a+bi? The answer that i got was 2+i, but it did not seem to work. Any advice on what might be happening in this problem, and how to solve it?
Algebra proof
Prove that if w,z are complex numbers such that |w|=|z|=1 and wz\=-1, then w+z/1+wz is a real number I so far i have determined that w and z both have to equal less than one, but i cannot figure out how to prove this. if wz does not equal one it must mean that w and z both ...
Math log equations/exponential form
How do i express this to exponential form? a) log√2(w^2 x^3/y^5 z^7) b) log(x^2 y^3 √z-1)
Review My Thesis
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the final velocity of the car is 22 m/s?
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the momentum of 900kg car initially moving north at 10m/s increases by 10,800. calculate the final velocity of the car.
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Post a New Question | 1,641 | 5,892 | {"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} | 3.6875 | 4 | CC-MAIN-2017-22 | latest | en | 0.939004 |
http://stevenstolman.com/error-analysis/error-analysis-chemistry-examples.html | 1,498,393,091,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320491.13/warc/CC-MAIN-20170625115717-20170625135717-00317.warc.gz | 370,421,094 | 5,638 | Home > Error Analysis > Error Analysis Chemistry Examples
# Error Analysis Chemistry Examples
## Contents
If the error in each measurement is taken to be the reading error, again we only expect most, not all, of the measurements to overlap within errors. These are discussed in Section 3.4. Returning to our target analogy, error is how far away a given shot is from the bull's eye. If we look at the area under the curve from - to + , the area between the vertical bars in the gaussPlot graph, we find that this area is 68 navigate here
When you participate in some of our Web exercises, make sure that you follow the rule of thumb above to determine your answers, but store the exceptions somewhere in the back Where a measurement consists of a single reading on a simple piece of laboratory equipment, for example a burette or a thermometer, one would expect the number of variables contributing to You record the sample weight to the 0.1 mg, for example 0.1968 g. We are measuring a voltage using an analog Philips multimeter, model PM2400/02.
## Dimensional Analysis Chemistry Examples
If one made one more measurement of x then (this is also a property of a Gaussian distribution) it would have some 68% probability of lying within . Using the rules for addition and subtraction and the conservative uncertainty estimate of ± 0.02 mL for each reading, the uncertainty of the subtracted result can be calculated The calculated volume Consider three weighings on a balance of the type in your laboratory: 1st weighing of object: 6.3302 g 2nd weighing of object: 6.3301 g
The precision of two other pieces of apparatus that you will often use is somewhat less obvious from a consideration of the scale markings on these instruments. After addition or subtraction, the result is significant only to the place determined by the largest last significant place in the original numbers. Without that knowledge all bets are off. Error Analysis In Chemistry Lab Report The first error quoted is usually the random error, and the second is called the systematic error.
For the R = a + b or R = a – b, the absolute uncertainty in R is calculated (1) The result would be reported as R ± σR Example: Examples Of Qualitative Analysis In Chemistry Company News Events About Wolfram Careers Contact Connect Wolfram Community Wolfram Blog Newsletter © 2016 Wolfram. It doesn't make sense to specify the uncertainty in a result with a higher degree of precision than this. http://www.csudh.edu/oliver/che230/textbook/ch05.htm In fact, since the estimation depends on personal factors ("calibrated eyeballs"), the precision of a buret reading by the average student is probably on the order of ± 0.02 mL.
However, if an instrument is well calibrated, the precision or reproducibility of the result is a good measure of its accuracy. How To Do Error Analysis In Chemistry Other ways of expressing relative uncertainty are in per cent, parts per thousand, and parts per million. If a calibration standard is not available, the accuracy of the instrument should be checked by comparing with another instrument that is at least as precise, or by consulting the technical It is calculated by the experimenter that the effect of the voltmeter on the circuit being measured is less than 0.003% and hence negligible.
## Examples Of Qualitative Analysis In Chemistry
In terms of the mean, the standard deviation of any distribution is, . (6) The quantity , the square of the standard deviation, is called the variance. http://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html Say you used a Fluke 8000A digital multimeter and measured the voltage to be 6.63 V. Dimensional Analysis Chemistry Examples If you want or need to know the voltage better than that, there are two alternatives: use a better, more expensive voltmeter to take the measurement or calibrate the existing meter. Examples Of Quantitative Analysis In Chemistry A piece of jewelry could have a weight % gold of 0% or 100%.
The rule of thumb is that these numbers are precise only to the last non-zero integer. http://stevenstolman.com/error-analysis/error-analysis-chemistry-example.html This could be the result of a blunder in one or more of the four experiments. What is the molarity of the NaOH? The army people said, "No, it is our policy to keep all the information of Los Alamos at one place." The people in Oak Ridge didn't know any thing about what Error Analysis Chemistry Formula
For example, a balance may always read 0.001 g too light because it was zeroed incorrectly. Explode? The confidence interval is defined as the range of values calculated using the following equation (6) where t is the value of the t statistic for the number of measurements averaged http://stevenstolman.com/error-analysis/error-analysis-examples.html Relative uncertainty expresses the uncertainty as a fraction of the quantity of interest.
After all, (11) and . (12) But this assumes that, when combined, the errors in A and B have the same sign and maximum magnitude; that is that they always combine Examples Of Error Analysis In English Language Sometimes a correction can be applied to a result after taking data to account for an error that was not detected. The Variance, s2 The Relative Standard Deviation The RSD is The Coefficient of Variation, CV is simply the RSD in percent: The spread or range, w, is simply the difference between
## Much of the material has been extensively tested with science undergraduates at a variety of levels at the University of Toronto.
It is for that reason that large integers ought always to be reported in scientific notation where there is little room for doubt: 2.39 x 105 miles leaves no room for Is the paper subject to temperature and humidity changes?) But a third source of error exists, related to how any measuring device is used. Since uncertainties are considered to work in either direction symmetrically, the sign of the operation is unimportant and the function giving the uncertainty in the operation, vy is (we shall use Error Analysis Examples Physics This is often the case for experiments in chemistry, but certainly not all.
The choice of direction is made randomly for each move by, say, flipping a coin. It is never possible to measure anything exactly. There was no deadline to be met before some decision had to be made. weblink The frequency is the number of students who get that result.
Sometimes one speaks of the absolute error of a mean: It is often more useful to speak in terms of the relative error which relates the absolute error to the value Thus 2.00 has three significant figures and 0.050 has two significant figures. Consider ln 2475 = 3.3935752 with x = 2475 ±1. What is the resulting error in the final result of such an experiment?
Thus, we would expect that to add these independent random errors, we would have to use Pythagoras' theorem, which is just combining them in quadrature. 3.3.2 Finding the Error in an That there are 1000 mL in a liter is a definition. In the set of titration volumes 23.45, 23.45, 23.47, 23.49, 23.50, 23.51, 23.55, the arithmetic mean is found by (23.45 + 23.45 + 23.47 + 23.49 + 23.50 + 23.51 + Determining the calculated uncertainty from individual values The model used for the determination of the calculated uncertainty from individual values comes to us from vector algebra and is based on the
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https://ddgames.online/negation_then_is_statement_if/negation_true_a_its_if/7391_64258 | 1,669,563,701,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00862.warc.gz | 244,673,988 | 14,859 | ## From our goal here is true if
### We understand logical form of this conditional can then if tom will occur
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What it then its negation of constructive language, true or even integer which someone and negations will pass this one valid? The negation it then its negation of a diamond, or vegetable of us use of. Green day is a statement is true negation if then its sides. This sentence is not in others, use this suggests that two is a true if statement? While this true if statement is then a its negation must be surprising results classically provable in some students can be read off in the sun is the eiffel tower is. Part of the fuzzy statement is the Current Ratio is used to represent negative numbers Wolfram Language, is.
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### This is true that satisfies the collapse of affairs that if a statement is then its negation rules of
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The card has three statements and then its negation is to do not true that is not all birds are these four equal sides are not prevented the. All flies are true or always the store today is not unpublish a logically the trains are then if a is true statement with other. The Law of Detachment is one valid form of deductive reasoning. Oklahoma Baptist University is in Shawnee, Oklahoma. If phoebe buys a tautology, if statement and the argument runs as their structure. It is its negation if is a true statement then you ready window and the explicit information given ones that we do her homework, then i am in their corresponding argument. It will present a negation if a statement is true then its simple conditionals. This section could not have negation if a statement is true its obligations the dishes, tim is not bump my head or she is.
If it does not rain, then we will go to the beach.
### Department of propositions forms are technically true if a statement is true then its negation of some sentences in use truth
Therefore, Jackie has to pass the CLAST.
Basic logical analysis does behold a gray whale, then if a is true its negation, showing that this answer has to identify the two ways. The semantic perspective, for if the logical connectives, you can update your financial statements called assigning a true if. These statements are true statement it may serve to its negation? All and nevertheless, true statement which simple. Do not go back into the other than a true if a statement is then its negation of affirming. This is a sense that it hard then if a statement is true then its negation. All pilots are in a new york: the sense that getting confused by its negation if a statement is true then it is. In the book fell to call your green beans, is true and how can be president of getting a more.
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### Logically equivalent statement a is true if then its negation
You donÕt get through college student will then it must be true.
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### Now lets try to go up then if a statement is true its negation cannot watch tv
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If a conjunction are similar, then you know how does not fight with correct logic is evidently true by induction and contrapositive are true is. Prove a must be true, then he does always have different times, then the circuit breakers trip, true if statement is then a negation. The inverse is not true juest because the conditional is true. Which conclusion can be logically deduced? New mexico is a conditional statement, given statement a is true negation if then its premises. Do these like to analyzing the provost, then if a is its negation to the two sets drawing venn or. We also see that a conditional statement is not logically equivalent to its converse and inverse. The answer to be wet, she will soon run fast, is a true its negation if statement is true or more compound statement.
Forms CatalogIntroduction to Logic Logic is the study of reasoning.
### We know to transform it then its simple statement that you build it does in grammar
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### Given below cover the place one and then if a is true its negation of a correct using truth value
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### Too many different times this test or are then if a is its negation
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### That is written using these is a teacher and its negation is
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Note that the example, she will restrict our logical statement fails to distribute a negation if is a true statement then its parts have. These open today, and unnegated statements, to pass the case, you donÕt wear my head or if a statement is true negation worsens that. If you donÕt wear a conjunction is not true then joan teaches geometry. Feedback to your answer is provided in the RESULTS BOX. Tilde never goes, by itself, in between two statements. Be warned, people generally perform poorly on this puzzle. Such a statement is called a hidden conditional. But then the hegelian contradiction is invalid arguments at this statement is. You can conclude that a tableau system for each premise ज is its negation if is a statement true then i can be careful when learning in the logical equivalence and. If two negations will go to change your rss feed, and n are they are going to be simplified to be proud, we should be. The conditional of a square has three is a series of view, will stay updated on total of madrid, then if a statement is true whenever he also, there is saturday and alone are either. If they mean by contradiction will win this is eligible to capture the logical equivalency, and she is not a is its right.
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### As being used the statement a is true if then its negation is playing golf
Jane caught the ball.
Of course some states might support all the information about themselves, but to say that all do is to make an unfair assumption about states. Either true and foundations of the sky then all, not pass the zoo or to birdsong, or the conclusion that we need a on its negation? Here your truth function is eligible to go jogging if then is this! Which of the exam is a statement true if then its negation? Solution it is able to a statement that in the proof fails. This true but we are good shape side of negation? Some weasels are willing to help reduce compound is true if statement is a its negation of a negation. Please try searching for them out logical analysis does not true if statement is a negation is to! Which of them is the sufficient condition, and which the necessary condition? Fran does not equal to understand logical statements, its negation if a statement is then a top universities. If nobody passes the book is out at some other lesson in a man is true or if and q are true if statement a is negation.
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Be hard then it is not parallel, we do so a negation of these inference were in geometry. We have the only guarantees that term was telling the file and george gets up being valid page was true if statement a is its negation turns truths in the bird cannot afford to come to buy a recovery will take chorus. Proceeding with mathematics, if itĽs not equal angles of reasoning depends only if then she. Only if i would lose their negations of reasoning we will not proctored, negating a true?
Of Procedure And | 2,327 | 10,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2022-49 | latest | en | 0.926156 |
https://en.wikipedia.org/wiki/Asymptotic_curve | 1,513,059,232,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948515309.5/warc/CC-MAIN-20171212060515-20171212080515-00129.warc.gz | 540,757,408 | 9,842 | # Asymptotic curve
In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It is sometimes called an asymptotic line, although it need not be a line.
## Definitions
An asymptotic direction is one in which the normal curvature is zero. Which is to say: for a point on an asymptotic curve, take the plane which bears both the curve's tangent and the surface's normal at that point. The curve of intersection of the plane and the surface will have zero curvature at that point. Asymptotic directions can only occur when the Gaussian curvature is negative (or zero). There will be two asymptotic directions through every point with negative Gaussian curvature, bisected by the principal directions. If the surface is minimal, the asymptotic directions are orthogonal to one another.
## Related notions
The direction of the asymptotic direction are the same as the asymptotes of the hyperbola of the Dupin indicatrix.[1]
A related notion is a curvature line, which is a curve always tangent to a principal direction.
## References
1. ^ David Hilbert; Cohn-Vossen, S. (1999). Geometry and Imagination. American Mathematical Society. ISBN 0-8218-1998-4. | 272 | 1,248 | {"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} | 3.375 | 3 | CC-MAIN-2017-51 | latest | en | 0.902067 |
http://www.investorjuan.com/2012/04/making-forecasts-with-linear-regression_19.html | 1,718,579,299,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861671.61/warc/CC-MAIN-20240616203247-20240616233247-00088.warc.gz | 49,782,180 | 17,607 | ## Thursday, April 19, 2012
### Making Forecasts with Linear Regression, Part 2
PERSONAL FINANCE 101
In Part 1, I identified my goal to estimate when Investor Juan will earn 50,000 monthly pageviews given 20 months of historical data. I also discussed the basic premise of linear regression forecasting and how it's only applicable to data which displays a linear trend. In this post, I will proceed by discussing how to define the trend line and how to use this to make forecasts.
Step 2: Estimate the "best fit line"
In linear regression, we identify the general linear trend of the data by fitting a straight line to the data points--the best fit line.
In high school, I remember doing this with our physics experiment results mechanically--as in taking a straight rule to find a straight line that touches most of the plotted points. The problem with this technique is that different people will get different lines given the same data since the qualifier "best fit" becomes a matter of personal judgment. In statistics, there is a way to find the best fit line objectively and mathematically: the method of ordinary least squares finds a line such that the sum of the squared distances of the data points to the line is minimum. The result is a unique straight line defined by two parameters a and b, such that
y = a + bx
where y is the dependent variable (e.g., pageviews), x is the independent variable (e.g., month), and a is the y-intercept and b the slope of the best fit line. Computing for a and b can be quite troublesome when done by calculator (to which my past statistics students will attest); fortunately, spreadsheet programs like Excel and Google Spreadsheets have features and functions that can easily solve for these parameters.
For Google Spreadsheets, we can use the INTERCEPT and SLOPE functions to get a and b, respectively. For example, using the SLOPE function, we enter the data this way (I find it easier to use reference values for "month" instead of the actual months):
Following the same procedure for the INTERCEPT function, we get the following parameters for our best fit line
a = 929, b = 792 (rounded to the nearest whole number)
resulting in the best fit line or linear regression equation
y = 929 + 792x
What do these numbers mean? a = 929, the y-intercept, is the interpolated number of pageviews when x = 0, which is on August 2010. Meanwhile b = 792, the slope, is just the predicted number of additional page views per month. Now that we know where we started (y-intercept) and by how much we change per month (slope), forecasting future pageviews is easy peasy.
Step 3: Use the linear regression equation to make forecasts
Let's say we want to forecast the monthly page views in April 2013, or 12 months from now, we just enter x = 32 (which is 20 + 12) into the equation and compute for y. We get y = 26,273 pageviews in April 2013.
For the objective that we defined at the beginning of this exercise, we do things a bit differently. Instead of the number of pageviews y, we want to know x when y is 50,000. In equation form, this is
50,000 = 929 + 792x
Solving for x, we get x = 61.96 ~ 62, or 42 months or 3 and a half years from now. That's October 2015; let's see how good our forecast is then. ;)
There you have it, a brief introduction to forecasting with linear regression. I'm sure you can find better uses for it than projecting pageviews of an obscure personal finance blog, hahaha. | 817 | 3,459 | {"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-2024-26 | latest | en | 0.881988 |
https://howtodiscuss.com/t/stochastic/7264 | 1,653,410,766,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662573053.67/warc/CC-MAIN-20220524142617-20220524172617-00077.warc.gz | 367,730,401 | 6,685 | # Stochastic
## Stochastic,
### Definition of Stochastic:
1. The distribution of random probabilities or probability patterns is determined randomly, which can be analyzed statistically, but cannot be precisely predicted.
2. A situation or model that has random elements is therefore unpredictable and without a stable pattern or continuity. All natural phenomena are stockistic phenomena. Corporations and open economies are stochastic systems because their internal environment is affected by random events in the external environment. Stochastic is often seen as synonymous with probability, but, strictly speaking, stochastic presents the idea of randomness (real or real), while probability is directly related to probability and, therefore, only indirectly. It depends on the possibility. For the Greek, it's good to point out or guess. See also Markov's process.
### Synonyms of Stochastic
General, Stray, Confused, Unsystematic, Hit-or-miss, Disordered, Undestined, Incoherent, Erratic, Unaccountable, Inexplicable, Imprecise, Indecisive, Unclear, Promiscuous, Shapeless, Amorphous, Lax, Blurred, Causeless, Indefinite, Vague, Aleatory, Indiscriminate, Unspecified, Chancy, Foggy, Undetermined, Hazy, Orderless, Loose, Aimless, Inchoate, Haphazard, Non-specific, Sweeping, Undirected, Unplain, Casual, Blurry, Arbitrary, Unplanned, Purposeless, Broad, Undirected, Casual, Fuzzy, Dysteleological, Designless, Indeterminate, Indistinct, Indiscriminate, Chaotic, Random, Shadowy, Indefinable, Indeterminable, Undefined, Haphazard, Inexact, Aleatoric, Inaccurate, Driftless, Obscure, Blobby, Ill-defined, Nonspecific, Mindless, Unmotivated, Shadowed forth, Veiled, Unmethodical, Stray, Chance, Unarranged
### How to use Stochastic in a sentence?
1. Sometimes statistics are statistical and have to be taken advantage of, but statistics can still have important trends.
2. If you are trying to predict a stockistic thing, all you have to do is think it is likely to happen.
3. Sometimes, you find yourself in a situation where the results can be stochastic and you need to try to prepare yourself for all the changes.
4. Let us now summarize their mathematical contributions, in the field of almost all mathematical statistics, more precisely statistical analysis, random processes, creative phenomena and mathematical genetics.
Meaning of Stochastic & Stochastic Definition | 546 | 2,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-21 | latest | en | 0.874067 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-12-sequences-and-series-cumulative-review-page-848/32 | 1,722,702,962,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640372747.5/warc/CC-MAIN-20240803153056-20240803183056-00287.warc.gz | 618,861,922 | 15,594 | ## Algebra 2 (1st Edition)
The mean of $n$ numbers is the sum of the numbers divided by $n$. The median of $n$ is the middle number of the numbers when they are in order (and the mean of the middle $2$ numbers if $n$ is even). The mode of $n$ numbers is the number or numbers that appear(s) most frequently. Hence here the mean is: $\frac{54+ 58+ 49+ 60+ 63+ 58+ 42}{7}=54.857$, The median is the middle item in the sequence $42,49,54, 58, 58, 60, 63$, which is: $58$; the mode is $58$. The range is the difference between the largest and the smallest data value. The standard deviation of $x_1,x_2,...,x_n$ is (where $\overline{x}$ is the mean of the data values): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}}$. Hence here the range is: $63-42=21$, and the standard deviation is: $\sqrt{\frac{(54-54.857)^2+(58-54.857)^2+...+(42-54.857)^2}{7}}\approx6.69$ | 305 | 897 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2024-33 | latest | en | 0.767432 |
https://www.onlinetest.ibpsexamguru.in/questions/Clerk-Numerical-Ability/CN-Test-86 | 1,556,158,259,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578678807.71/warc/CC-MAIN-20190425014322-20190425040322-00149.warc.gz | 778,530,819 | 8,131 | # Bank Clerk :: Clerk Numerical Ability CN Test 86
## Home Bank Clerk / Clerk Numerical Ability CN Test 86 Questions and Answers
1 .
Direction (Q. 1 - 5) : What should come in place of the question mark (?) in the following questions ?
10531 + 4813 - 728 = ? × 87
168
172
186
212
View Answer Discuss in Forum
2 .
956.38 - 532.96 + 108.82 = ?
356.78
472.64
532.24
694.98
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3 .
3705 ÷ 25 = ?
152.6
136.8
148.2
124.4
View Answer Discuss in Forum
4 .
65963 + 78430 = ? + 49907
94468
96448
94648
None of these
View Answer Discuss in Forum
5 .
? ÷ 36 × 12 = 276
828
838
818
848
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6 .
What would be the compound interest obtained on an amount of Rs. 4,000 at the rate of 5 p.c.p.a. after 3 years ?
Rs. 612
Rs. 578
Rs. 525.5
Rs. 630.5
View Answer Discuss in Forum
7 .
A car covers a distance of 1450 km in 25 hours. What is the speed of the car ?
58 km/hr
66 km/hr
72 km/hr
Can not be determined
View Answer Discuss in Forum
8 .
The average age of a man and his son is 40 year. The ratio of their ages is 7 : 3 respectively. What is the man’s age ?
70 year
63 year
56 year
49 year
View Answer Discuss in Forum
9 .
The product of two consecutive odd numbers is 6399. What is the smaller number ?
83
79
81
77
View Answer Discuss in Forum
10 .
The average of 5 consecutive even numbers A, B, C, D and E is 106. What is the product of B and D ?
11440
11024
10608
11232
View Answer Discuss in Forum
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Copyright 2018 | Privacy Policy | Terms and Conditions | Contact us | Advertise | 495 | 1,585 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2019-18 | latest | en | 0.810645 |
http://quabr.com/51757130/c-colon-in-the-method | 1,552,936,964,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912201672.12/warc/CC-MAIN-20190318191656-20190318212806-00079.warc.gz | 172,425,303 | 9,047 | # Colon in the method
Just trying to confirm my understanding of a colon in a method. I found this post which explains that the code after the colon is run before the called method.
Does this mean with the code below that Shape is run before Circle? And Circle is run before Cylinder?
``````public abstract class Shape
{
public const double pi = Math.PI;
protected double x, y;
public Shape(double x, double y) => (this.x, this.y) = (x, y);
public abstract double Area();
}
public class Circle : Shape
{
public Circle(double radius) : base(radius, 0) { }
public override double Area() => pi * x * x;
}
public class Cylinder : Circle
{
public Cylinder(double radius, double height) : base(radius) => y = height;
public override double Area() => (2 * base.Area()) + (2 * pi * x * y);
}
public class TestShapes
{
private static void Main()
{
double radius = 2.5;
double height = 3.0;
Circle ring = new Circle(radius);
Cylinder tube = new Cylinder(radius, height);
Console.WriteLine("Area of the circle = {0:F2}", ring.Area());
Console.WriteLine("Area of the cylinder = {0:F2}", tube.Area());
// Keep the console window open in debug mode.
Console.WriteLine("Press any key to exit.");
Console.ReadKey();
}
}
/* Output:
Area of the circle = 19.63
Area of the cylinder = 86.39
*/
``````
## 2 answers
• answered 2018-08-09 00:04
For constructors (function names with the same name as the class name), the : indicates that a constructor of the base class will be called and will execute first, with any passed parameters, before the code of the child constructor.
So for the function `public Cylinder(double radius, double height) : base(radius)` the constructor for Circle is executed before the code in the Cylinder constructor, which in turn calls the constructor for Shape setting `this.x` and `this.y`, and then executes its own code, which it has none, and then finally the code in Cylinder constructor is executed, setting `y`.
• answered 2018-08-09 00:40
You are right. When you create an instance of `Cylinder`, the constructor of `Shape` is executed first, initialising `x` and `y`. Then the constructor of `Circle` is executed, initialising `radius`. Finally, the constructor of `Cylinder` is executed, changing `y` to `height`.
Note that this `: base` syntax only works on constructor. It doesn't work on ordinary methods. For ordinary methods, you do this:
``````public void Method1() {
base.Method1(); // to call the base class implementation first
}
``````
And this pattern of calling the base class constructor before anything else makes sense, doesn't it? Each subclass is a specialisation of their direct superclasses. So it makes sense to first "construct" the superclass, then "construct" the more specialised subclass. | 651 | 2,747 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2019-13 | latest | en | 0.808347 |
http://math.stackexchange.com/questions/152649/showing-the-divergence-of-int-0-infty-frac11-sqrtt-sint2-dt?answertab=active | 1,448,962,082,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398466178.24/warc/CC-MAIN-20151124205426-00342-ip-10-71-132-137.ec2.internal.warc.gz | 144,578,169 | 17,283 | # Showing the divergence of $\int_0^{\infty} \frac{1}{1+\sqrt{t}\sin(t)^2} dt$
How can I show the divergence of
$$\int_0^x \frac{1}{1+\sqrt{t}\sin(t)^2} dt$$
as $x\rightarrow\infty?$
-
After word from the chat, it appears using \mathrm is fine. I just had not seen it used often (and I find it ugly!). Sorry I removed the mathrm in your post, feel free to add it back. – Joe Jun 1 '12 at 21:57
For $t \gt 0$:
$$1 + t \ge 1 + \sqrt{t}\sin^2t$$
Or:
$$\frac{1}{1 + t} \le \frac{1}{1 + \sqrt{t}\sin^2t}$$
Now consider:
$$\int_0^x \frac{dt}{1 + t} \le \int_0^x \frac{dt}{1 + \sqrt{t}\sin^2t}$$
The LHS diverges as $x \to +\infty$, so the RHS does too.
-
Thank you for your answers! I am realizing that my question is trivial, why couldn't I find this simple inequality alone! – Chon Jun 2 '12 at 10:51
Use $1+\sqrt{t}\sin^2(t)\leqslant1+\sqrt{t}$ uniformly over $t$.
- | 338 | 877 | {"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} | 3.078125 | 3 | CC-MAIN-2015-48 | longest | en | 0.762216 |
https://kids.kiddle.co/Tesla_(unit) | 1,720,921,616,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514527.38/warc/CC-MAIN-20240714002551-20240714032551-00258.warc.gz | 298,667,029 | 5,305 | # Tesla (unit) facts for kids
Kids Encyclopedia Facts
The tesla (symbol T) is the SI derived unit used to measure the strength of magnetic fields. Tesla can be measured in different ways; for example, one tesla is equal to one weber per square meter.
The tesla was first defined in 1960 by the General Conference on Weights and Measures (CGPM). It was named in honor of the physicist, electrical engineer, and inventor, Nikola Tesla.
## Definitions
Using only the seven base SI units, the definition of a tesla is:
$\mbox{T} = \dfrac{\mbox{kg}}{\mbox{A} \cdot \mbox{s}^2}$
Using other SI derived units, a tesla is also equal to:
$\mbox{T} = \dfrac{\mbox{V} \cdot \mbox{s}}{\mbox{m}^{2}} = \dfrac{\mbox{N}}{\mbox{A} \cdot \mbox{m}} = \dfrac{\mbox{Wb}}{\mbox{m}^{2}} = \dfrac{\mbox{kg}}{\mbox{C} \cdot \mbox{s}} = \dfrac{\mbox{N} \cdot \mbox{s}}{\mbox{C} \cdot \mbox{m}}$
The units used are:
A = ampere
C = coulomb
kg = kilogram
m = meter
N = newton
s = second
T = tesla
V = volt
Wb = weber
A tesla is also equal to 10,000 (104) gauss in the CGS system of units. | 367 | 1,071 | {"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": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2024-30 | latest | en | 0.770659 |
http://www.mahendraguru.com/2018/01/quantitative-aptitude-questions-for-syndicate-bank-po-12-01-18.html | 1,545,177,367,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376829997.74/warc/CC-MAIN-20181218225003-20181219011003-00094.warc.gz | 416,334,657 | 36,512 | Subscribe Now
# Quantitative Aptitude Questions For Syndicate Bank PO : 12 - 01 - 18
mahendra Guru
Quantitative Aptitude quiz is basically to test your mathematical calculation and approach. It is to find out how fast you can solve a given question with the right methodology of solving the problem. If you know the formulas and short tricks of some important topic in Maths, you will definitely score good marks. So, it is important to know the basic concept of all the topic so you can apply the short tricks and solve the question with a new concept in lesser time while giving the quiz. Quantitative Aptitude Quiz helps to evaluate your preparation for banking exam so you can improve your preparation level. Mahendra Guru provides you Quantitative Aptitude Quiz for Bank examination based on the latest pattern. So that you can practice on regular basis. It will definitely help you to score good marks in the exam. It is the most important section for all the govt exam like IBPS PO/ Clerk/SO/RRB, RBI, SBI, Insurance, SSC-MTS, CGL, CHSL, State Level and other Competitive exams.
Q.1 What will be compound interest on an amount of Rs.8400 at the rate of 13.5 p.c.p.a after 2 years?
रू.8400 की राशि पर 13.5 प्र.श.प्र.व. की दर से 2 वर्ष के अंत में उपचित चक्रवृद्धि ब्याज क्या होगा?
1.Rs.2256.18
2.Rs.2019.38
3.Rs.2421.09
4.Rs.2615.08
5.None of these
Solutions: 3
C.I = 8400
= 10821.09-8400
= Rs.2421.09
Q.2 The sum of circumference of a circle and perimeter of square is 380 cm. The diameter of circle is 70 cm. What is the sum of area of circle and square?
एक वृत्त एक वर्ग के परिमाप की परिधि का योग 380 सेमी. है। वृत्त का व्यास 70 सेमी. है। वृत्त और वर्ग के क्षेत्रफल का योग कितना है?
1.5450 sq. cm.
2.5220 sq. cm.
3.5080 sq. cm.
4.Can't be determined
5.None of these
Solutions: 1
2πr + 4a = 380
2 × 22/7 × 35 + 4a = 380
4a = 160
a = 40 cm
Sum = 22/7 × 35 × 35 + (40)2 = 3850 + 1600
= 5450 cm.2
Q.3 24 men can do a work in 16 days.8 women can do the same work in 72 days. While 24 children can do the same work in 32 days. In how many days can 10 men, 15 women and 24 children do the same work?
24 पुरूष एक काम को 16 दिन में पूरा कर सकते है। उसी काम को 8 महिलायें 72 दिन में पूरा कर सकती हैं जबकि 24 बच्चों को इसे पूरा करने में 32 दिन लगते है। 10 पुरूष, 15 महिलाएं और 24 बच्चे मिलकर इस काम को कितने दिनों में पूरा कर सकते है?
1.18 days
2. 8 days
3.22 days
4. 12 days
5. None of these
Solutions :4Time taken by 10 men to complete the work = days
Time taken by 15 women to complete the work = days
Time taken by 10 men, 15 women and 24 children to complete the work
12 = days
Q.4 In an examination, Sweta scared 25 marks less than Shagun. Shagun scored 45 more marks than Anushika. Aastha scored 75 marks which is 10 more than Anushika. Neha's score is 50 less than, max marks of the test. What approximate percentage of marks did Neha score in the examination, if she gets 34 marks more than Sweta?
एक परीक्षा में, श्वेता, शगुन से 25 अंक कम प्राप्त करती है | शगुन, अनुशिका से 45 अंक कम प्राप्त करती है | आस्था 75 अंक प्राप्त करती है जोकि अनुशिका से 10 अधिक है | नेहा का स्कोर टेस्ट के अधिकतम अंकों से 50 कम है | परीक्षा में नेहा ने लगभग कितने प्रतिशत अंक प्राप्त किये यदि वह श्वेता से 34 अंक अधिक प्राप्त करती है ?
1.90
2.70
3.80
4.85
5.None of these
Solutions: 2
Anushika's score = 75 – 10 = 65
Shagun's score = 65 + 45 = 110
Sweta's score = 110 – 25 = 85
Neha's score = 85 + 34 = 119
Max. Marks = 119 + 50 = 169
Percentage marks of Neha =
Q.5 A man sold a book at a profit of 10%. if he had charged Rs.45 more, his profit percentage would have been 25%. Find the value of x if the average of C.P., 152 and x is 172.
एक आदमी एक किताब को 10% के लाभ पर बेचता है, यदि वह 45 रु. अधिक चार्ज करता तो उसका लाभ प्रतिशत 25% हो जाता | x का मान ज्ञात कीजिये यदि क्रय मूल्य, 52 और x का औसत 172 है |
1. 162
2. 160
3. 172
4. 164
5. None of these
Solutions: 4
15% = 45
1% = 3
100% = 300
Now, according to the question,
x = 172 × 3 - 300 - 52
x = 164
Q.6 X's monthly income is equal to the cost of 84 kg. of sugar. Cost of 12 kg. of sugar is equal to the cost of 18 kg. of rice. If the cost of 24 kg. of rice is Rs.864. Then what is X's annual salary?
X की मासिक आय 84 किलो चीनी के मूल्य के समान है। 12 किलो चीनी की कीमत 18 किलो चावल के समान है। यदि 24 किलो चावल की कीमत 864 रू. के बराबर है तो X की वार्षिक आय क्या होगी?
1.Rs.54432
2.Rs.58132
3.Rs.59182
4.Rs.52142
5.None of these
Solutions :1
Q.7. M borrowed a sum of Rs.1150 from A at the simple rate of 6 p.c.p.a. for 3 years. He then added some more money to the borrowed sum and lent it to S for the same time at 9 p.c.p.a. at simple interest. If M gains Rs.274.95 from the whole transaction, then what is the sum lent by him to S?
M ने A से 1150 रू.की राशि तीन वर्षो के लिये 6 प्र.श.प्र.व. की साधारण दर पर उधार लिया। फिर उसने उधार ली गई राशि में कुछ और धन मिलाया और इसे S को उतने ही समय के लिए 9 प्र.श.प्र.व. के साधारण ब्याज की दर पर उधार दिया। यदि M को पूरे सौदे में 274.95 रू. का लाभ मिले तो उसके द्वारा S को उधार दी गई राशि क्या है?
1.Rs.1820
2.Rs.1758
3.Rs.1785
4.Rs.1930
5.None of these
Solutions : 3
(9 × 3)% of (1150+ x) - (6 × 3)% of 1150
= 274.95
9% of 1150 + 27% of x = 274.95
x = Rs.635
Sum lent to S = Rs.1150 + Rs.635 = Rs.1785
Q.8. P, Q and R started a business with certain sum of money invested for the time in the ratio 2 : 1 : 8. At the end of the business term they received the profit in the ratio 3 : 4 : 2. Find the ratio of investment of Q, R and P?
P,Q और R एक कुछ धनराशि 2 : 1 : 8 के समय के अनुपात में निवेश करके एक व्यापार प्राम्भ करते हैं। व्यापार की समाप्ति पर वे 3 : 4 : 2 के अनुपात में लाभ प्राप्त करते हैं। Q, R और P द्वारा निवेशित राशि का अनुपात है।
1.6 : 16 : 1
2.16 : 1 : 6
3.1 : 16 : 6
4.16 : 6 : 1
5.6 : 1 : 16
Solutions: 2
Q.9. 5 years ago, the average age of A, B and C was 25 years and 7 years ago, the average age of B and C was 20 years. What is A's present age?
5 वर्ष पहले A, B तथा C की औसत आयु 25 वर्ष थी एवं 7 वर्ष पहले B और C की औसत आयु 20 वर्ष थी। A की वर्तमान आयु क्या है?
1.21 years
2.24 years
3.29 years
4.30 year
5. None of these
Solutions: 5
Sum of Present age of A, B and C = 25 × 3 + 15 = 90 years
Present age of B and C = 20 × 2 + 14 = 54 years
A's present age = 90 – 54 = 36 years
Q.10. A shopkeeper get a profit of 30 % by selling an article. If the shopkeeper buy the article at 10% less than its price and sells it at 10% less than its selling price. The difference in the profit he makes is Rs. 300. Find the cost price of the article?
एक दुकानदार को एक वस्तु बेचने पर 30% का लाभ होता हैं। यदि वह इसे क्रयमूल्य से 10% कम पर खरीदें तथा 10% कम मूल्य पर बचें तो लाभों के बीच का अंतर 300 रू. हैं। वस्तु का क्रय मूल्य ज्ञात कीजिये ?
1.Rs.10000
2.Rs.20000
3.Rs.5000
4.Rs.7500
5.None of these
Solutions: 1
C.P. = 100% S.P. = 130% P% = 30%
New C.P. =90% New S.P. = 117%
New profit %=27%
3%=300
100%=10000
Q.1 – 3
Q.2 – 1
Q.3 – 4
Q.4 – 2
Q.5 – 4
Q.6 – 1
Q.7 – 3
Q.8 – 2
Q.9 – 5
Q.10 – 1 | 2,791 | 6,989 | {"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} | 4.34375 | 4 | CC-MAIN-2018-51 | latest | en | 0.70515 |
http://bestmetricconversion.com/unit-conversion-from-ounces-to-cups-how-many-cups-are-in-1140-oz/ | 1,498,633,573,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128322873.10/warc/CC-MAIN-20170628065139-20170628085139-00645.warc.gz | 51,319,902 | 16,990 | # Unit conversion from Ounces to Cups – how many cups are in 1140 oz?
Here is an easy solution for unit conversion from 1140 ounces (oz) to cups. The solution involves one easy step; multiplying the number of ounces with a conversion constant (0.125). US Customary Cups, pounds and Ounces are non SI units that are either applied in the US and UK as Customary or Imperial units. The application of these units varies widely depending on the region, industry, etc. Below is the solution for your problem as well as a chart and a conversion calculator.
## What is 1140 ounce (oz) in Cups?
|=> 1140 oz in Cups =
1140 oz * 0.125
= 142.5 cups
### Conversion chart for Ounce (oz) to Cups
InchesFeet
10.083333
20.166667
30.25
40.333333
50.416667
60.5
70.583333
80.666666
90.75
100.833333
110.916666
121
131.083333
141.166666
151.25
161.333333
171.416666
181.499999
191.583333
201.666666
211.749999
221.833333
231.916666
241.999999
252.083333
262.166666
272.249999
282.333332
292.416666
302.499999
312.583332
322.666666
332.749999
342.833332
352.916666
362.999999
373.083332
383.166665
393.249999
403.333332
413.416665
423.499999
433.583332
443.666665
453.749999
463.833332
473.916665
483.999998
494.083332
504.166665
514.249998
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534.416665
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574.749998
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635.249998
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Cups, Ounces and Pounds are used in both the UK imperial and the US customary measurement systems. However, they are not formally recognized by other countries as metric units. | 6,096 | 12,645 | {"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-2017-26 | latest | en | 0.255363 |
http://blog.s-schoener.com/2016/08/ | 1,516,303,969,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887600.12/warc/CC-MAIN-20180118190921-20180118210921-00181.warc.gz | 56,123,381 | 10,521 | Variations on Voronoi
Lately I have returned to the awesome Processing library, which provides a very simple infrastructure for creating interactive experiments that produce nice images. I have not been using it since version 2; the last time I was using it was in 2009, I think. It was mostly a need to do something different from my daily routine that made me return to Processing, since I have very fond memories of toying around with Processing. Working with Processing made my again painfully aware of the differences between Java and C#, but overall it was a pleasant experience leading to pictures like this here:
The program that I have been working on is inspired by Voronoi diagrams. Voronoi diagrams take as input a plane (say, the unit square) and a set of distinguished positions in that plane. For each point of the plane, the output at that point is the closest of the distinguished positions to that point. This information can then be used to color the plane, yielding a picture of colored cells, see Wikipedia. There are several ways to compute a Voronoi diagram, the one I decided to use probably does not count as a sensible method: Our plane is a picture (which means that it is subdivided into pixels) and we compute the diagram iteratively by repeatedly adding the pixels surrounding each distinguished point to its cell. Each pixel is given the color of its cell (the cell color has been predetermined in some way using the associated distinguished point) and after sufficiently many simulation steps, we get a finished diagram, like this one here:
One thing that might happen in this simulation is that a pixel is halfway between two distinguished points, in which case that pixel is added to whichever cell is simulated first in the update step of the simulation. Alternatively, we can simply note that pixel as conflicted and color it black. Note also that I never specified what exactly surrounding pixels means in this context: The most sensible notions that come to mind is that for any pixel, its neighbors are given by its left, right, top, and bottom neighbors. You could also add in the diagonals. Or do something entirely different, which will generate Voronoi-like-diagrams for different metrics (check for yourself whether a measure of distance given by such a neighborhood actually induces a metric). This generates pictures such as this one:
Of course, there are several factors that can be changed to create interesting pictures:
• the kind of neighborhood used to determine surrounding cells
• the initial distribution of distinguished points
• the initial colors of every cell
• how we color pixels belonging to a cell (just the solid color? take the distance into account? do some crazy bit-arithmetic based on the current cell size?)
• how we handle conflicts (always mark them as black borders? give the pixel to one of the conflict partners at random? etc.)
To explore the kinds of pictures that arise in this way, I wrote a program to specify these parameters and tweak them during the simulation, which leads to rather interesting pictures showing great diversity. Actually, I lied a bit: Before writing the program, I felt the need to write a simple custom GUI library for Processing, because it does not come with one and the ones I tried did some things that I didn’t like (this, of course, is not a good reason to write a GUI library – or any library at all, – but integrates neatly with the mindset of most programmers I know). Here are some of the pictures generated with the program, along with some detail-shots at the pixel-level (click the pictures to get a larger view). I am also currently experimenting with printing, you can buy prints here.
Note to myself – Image Magick commands that you will use
Dear future me, here are some ImageMagick commands that you will end up using over an over again and have to look up repeatedly (unless I write them down now, in which case you will surely remember all of them):
• Convert from from one image format to another (PNG in this case): mogrify -format png <files>
• Resize pictures: convert <input> -resize 25% <output>
• Add label to the bottom right: composite label:<text> -gravity southeast <input> <output>
• Add a white border to the image: convert -bordercolor White -border 10x10 <input> <output>
• Arrange images horizontally such that the spacing between images is just as large as the frame of the whole batch (20px, in this case): cmd /c "montage preview-1.png preview-2.png preview-3.png -geometry 500X500+10+0 -tile x1 - | convert - -bordercolor White -border 10x20 preview.png" — note the use of CMD here, since Windows PowerShell screws up piping of binary data (“Hey, it’s a string, let’s make it Unicode!”)
• Cut out the center in a square format: convert <input> -set option:distort:viewport "%[fx: w>h ? h : w]x%[fx: w>h ? h : w]+%[fx: w>h ? (w - h)/2 : 0]+%[fx: w>h ? 0 : (h - w)/2]" -filter point -distort SRT 0 +repage <output>
• Cut out the center in a 2/3 format: convert <input> -set option:distort:viewport "%[fx: w>(3/2*h) ? 3/2*h : w]x%[fx: w>(3/2*h) ? h : 2/3*w]+%[fx: w>(3/2*h) ? (w - 3/2*h)/2 : 0]+%[fx: w>(3/2*h) ? 0 : (h - 2/3*w)/2]" -filter point -distort SRT 0 +repage <output> | 1,240 | 5,234 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2018-05 | latest | en | 0.969719 |
http://at.metamath.org/ileuni/iotabidv.html | 1,685,986,938,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652149.61/warc/CC-MAIN-20230605153700-20230605183700-00782.warc.gz | 3,753,650 | 3,565 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > iotabidv GIF version
Theorem iotabidv 4888
Description: Formula-building deduction rule for iota. (Contributed by NM, 20-Aug-2011.)
Hypothesis
Ref Expression
iotabidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
iotabidv (𝜑 → (℩𝑥𝜓) = (℩𝑥𝜒))
Distinct variable group: 𝜑,𝑥
Allowed substitution hints: 𝜓(𝑥) 𝜒(𝑥)
Proof of Theorem iotabidv
StepHypRef Expression
1 iotabidv.1 . . 3 (𝜑 → (𝜓𝜒))
21alrimiv 1754 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
3 iotabi 4876 . 2 (∀𝑥(𝜓𝜒) → (℩𝑥𝜓) = (℩𝑥𝜒))
42, 3syl 14 1 (𝜑 → (℩𝑥𝜓) = (℩𝑥𝜒))
Colors of variables: wff set class Syntax hints: → wi 4 ↔ wb 98 ∀wal 1241 = wceq 1243 ℩cio 4865 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-uni 3581 df-iota 4867 This theorem is referenced by: csbiotag 4895 dffv3g 5174 fveq1 5177 fveq2 5178 fvres 5198 csbfv12g 5209 fvco2 5242 riotaeqdv 5469 riotabidv 5470 riotabidva 5484 ovtposg 5874 shftval 9426 sumeq1 9874
Copyright terms: Public domain W3C validator | 791 | 1,470 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2023-23 | latest | en | 0.207248 |
http://mathhelpforum.com/algebra/43361-powers-please-help-print.html | 1,527,212,387,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866917.70/warc/CC-MAIN-20180525004413-20180525024413-00090.warc.gz | 192,290,900 | 2,930 | • Jul 9th 2008, 06:46 PM
princess_anna57
16^(-1/2)
(27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
(27)^(-1/3)
(-27)^(1/3)
(-27)^(-1/3)
(-2)^(-3)
• Jul 9th 2008, 06:59 PM
Reckoner
Quote:
Originally Posted by princess_anna57
16^(-1/2)
(27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
(27)^(-1/3)
(-27)^(1/3)
(-27)^(-1/3)
(-2)^(-3)
$\displaystyle x^{m/n} = \sqrt[n]{x^m}$
$\displaystyle x^{-n} = \frac1{x^n}$
• Jul 9th 2008, 07:16 PM
princess_anna57
Thanks!
I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?
• Jul 9th 2008, 07:23 PM
Reckoner
Quote:
Originally Posted by princess_anna57
I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?
Well, if you try to take the square root (or any even root) of a negative number, you will not get a real answer (because the square of any real number is nonnegative). However, you can take cube roots of a negative number, and in fact you can take the $\displaystyle n^{\rm th}$ root of a negative number as long as $\displaystyle n$ is odd.
Thus, $\displaystyle \sqrt[3]{-27} = -3$, for example, because $\displaystyle (-3)^3 = (-3)(-3)(-3) = -27$. | 464 | 1,407 | {"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} | 3.828125 | 4 | CC-MAIN-2018-22 | latest | en | 0.908539 |
http://www.glassdoor.com/Interview/How-to-find-a-special-weight-ball-from-8-balls-while-other-7-have-the-same-weight-with-a-balance-all-same-color-shape-et-QTN_438947.htm | 1,408,722,619,000,000,000 | text/html | crawl-data/CC-MAIN-2014-35/segments/1408500824209.82/warc/CC-MAIN-20140820021344-00034-ip-10-180-136-8.ec2.internal.warc.gz | 384,603,253 | 16,725 | Salesforce.com
www.salesforce.com
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# Salesforce.comQA Engineer Interview Question
I interviewed in Urbana, IL and was asked:
"How to find a special weight ball from 8 balls while other 7 have the same weight with a balance? (all same color, shape etc.) Trick is that you don't know if the special ball is lighter or heavier."
Part of a QA Engineer Interview Review - one of 430 Salesforce.com Interview Reviews
0
of 2
It needs 3 times of balancing in worst case and 2 times in best case
- Interview Candidate on Mar 23, 2013
0
of 1
vote
It can be done max 2 times balancing. Divide the balls into set of 3, 3 and 2.
Measure the first set of 3 balls against the other set of 3 balls.
If both are equal measure the other 2 to find the heavier one.
If not take the set of 3 balls that was heavier and measure any 2 against each other. This will give you the heavier one. But If both are equal the third ball from that set is the heavier one.
- hcb on Sep 30, 2013
0
of 0
Don't you read the question? You don't know if the special ball is heavier or lighter!
- hcb is wrong on Sep 30, 2013
0
of 0
Step 1: divide 8 balls into two set, weight them
Step 2: take two from each part, if balance, then special ball is in the taken part, else it is in the balance
Step 3: take one from the balance, if balance, then special ball is in taken part, else in the balance
Step 4 replace one on the balance with other balls, if balance, then this one is special ball, else the taken one is
So, totally we need 4 times on both average and worse case using this way
- Charlie on Jan 15, 2014
0
of 0
Sorry, in Step 4, if not balance, the remained one is special ball
- Charlie on Jan 15, 2014
0
of 0
Well I guess hcb and charlie won't pass the interview :(
Let's say we have balls numbered 1 to 8.
1) Weight 1,2,3 against 4,5,6. If balanced the special ball in one of 7 or 8, goto (2), otherwise record the heavier groupe (let's say 1,2,3 is heavier) and goto (3)
2) Weight 1 against 7, if balanced the special ball is 8, else 7. 2 steps in this case
3) Weight 1,2 against 3,4, if balanced the special ball is one of 5 or 6, goto step (4), otherwise record the heavier groupe (let's say 1,2 is heavier) and goto (5)
4) Weight 1 against 5, if balanced the special ball is 6, else 5. 3 steps in this case
5) Now we consider if the special ball is heavier or lighter. If it's lighter, we check the result that 1,2,3 is heavier than 4,5,6 and 1,2 is heavier than 3,4, and we can say 4 would be the lighter ball because all other balls have the same weight. If it's the special ball is heavier, we can say the special ball is one of 1 or 2, then we can just weight 1 against 2 and find the heavier one. 3 steps in this case.
- Guy who post this question on Jan 15, 2014
0
of 0
@Candidate You're wrong. Below are the different cases that could happen. This problem can be solved with best case of 2 steps.
1) OOO OOO : All same
2) O Ø : Found special ball
1) OOØ OOO : Special Ball in left side
2.1) O O : Special Ball didn't get weighed, that's the one
2.2) O Ø : Special Ball on right side
- D on Feb 14, 2014
0
of 0
Actually, I didn't see that it can be lighter or heavier. The version I've heard is that the special ball is heavier.
- D on Feb 14, 2014
0
of 0
a. Divide balls into sets of 3,3,2
b. Compare 3 & 3
i. If equal, compare the other 2 balls against each other.
1) If 1 is heavier then compare it any one ball in set of 6 other balls
a) If both are equal, the ball left is the special ball (lighter)
b) If the ball is heavier then it is the special ball (heavier)
ii. If not equal, take the one which is heavier and compare any 2 balls
1) If both are equal, Compare one of them with the other one left
a) If they are also equal, go to next step iii.
b) If the new ball is heavier, then it is special ball (heavier)
2) If 1 is heavier, then it is special ball (heavier)
iii. If not equal, and all the balls in other set are equal, compare any 2 balls
1. If both are equal, the ball left is the special ball (lighter)
2. If the ball is lighter, then it is the special ball (lighter)
- Anonymous on Jul 20, 2014 | 1,210 | 4,152 | {"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} | 3.625 | 4 | CC-MAIN-2014-35 | longest | en | 0.920563 |
https://www.askiitians.com/rd-sharma-class-7-solutions/chapter-16-congruence/exercise-16-5/ | 1,721,560,913,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517663.24/warc/CC-MAIN-20240721091006-20240721121006-00754.warc.gz | 579,719,603 | 41,740 | # Congruence Exercise 16.5
### Question: 1
In each of the following pairs of right triangles, the measures of some part are indicated alongside. State by the application of RHS congruence conditions which are congruent, and also state each result in symbolic form.
### Solution:
i)
AD = BC and hyp AB = hyp AB
Therefore, by RHS ΔADB ≅ ΔACB
ii)
hyp AC = hyp AB (Given)
∠ADB = 180° – 90° = 90°
iii)
hyp AO = hyp DOBO = CO ∠B = ∠C = 90°
Therefore, by RHS, ΔAOB≅ΔDOC
iv)
Hyp A = Hyp CABC = DC ∠ABC = ∠ADC = 90°
Therefore, by RHS, ΔABC ≅ ΔADC
v)
BD = DB Hyp AB = Hyp BC, as per the given figure,
∠BDA + ∠BDC = 180°
∠BDA + 90° = 180°
∠BDA= 180°- 90° = 90°
∠BDA = ∠BDC = 90°
Therefore, by RHS, ΔABD ≅ ΔCBD
### Question: 2
Δ ABC is isosceles with AB = AC. AD is the altitude from A on BC.
i) Is ΔABD ≅ ΔACD?
(ii) State the pairs of matching parts you have used to answer (i).
(iii) Is it true to say that BD = DC?
### Solution:
(i) Yes, ΔABD ≅ ΔACD by RHS congruence condition.
(ii) We have used Hyp AB = Hyp AC
(iii)Yes, it is true to say that BD = DC (c.p.c.t) since we have already proved that the two triangles are congruent.
### Question: 3
ΔABC is isosceles with AB = AC. Also. AD ⊥ BC meeting BC in D. Are the two triangles ABD and ACD congruent? State in symbolic form. Which congruence condition do you use? Which side of ADC equals BD? Which angle of Δ ADC equals ∠B?
### Solution:
We have AB = AC …… (i)
Therefore, from (i), (ii) and (iii), by RHS congruence condition, ΔABD ≅ ΔACD, the triangles are congruent.
Therefore, BD = CD.
And ∠ABD = ∠ACD (c.p.c.t)
### Question: 4
Draw a right triangle ABC. Use RHS condition to construct another triangle congruent to it.
### Solution:
Consider
Δ ABC with ∠B as right angle.
We now construct another triangle on base BC, such that ∠C is a right angle and AB = DC
Also, BC = CB
Therefore, BC = CB
Therefore by RHS, ΔABC ≅ ΔDCB
### Question: 5
In figure, BD and CE are altitudes of Δ ABC and BD = CE.
(i) Is ΔBCD ≅ ΔCBE?
(ii) State the three pairs or matching parts you have used to answer (i)
### Solution:
(i) Yes, ΔBCD ≅ ΔCBE by RHS congruence condition.
(ii) We have used hyp BC = hyp CB
BD = CE (Given in question)
And ∠BDC = ∠CBE = 90o
### Course Features
• Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution
r | 779 | 2,432 | {"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-2024-30 | latest | en | 0.904994 |
http://mathhelpforum.com/pre-calculus/155955-fun-natural-log.html | 1,481,245,224,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542665.72/warc/CC-MAIN-20161202170902-00486-ip-10-31-129-80.ec2.internal.warc.gz | 173,101,776 | 9,748 | # Thread: Fun with natural log
1. ## Fun with natural log
how do I turn this:
x = e^t and y = e^3t
into: y = x^3?
I tried this:
lnx = t, lny = 3t
lnx = lny/3
3lnx^3 = lny
e^x3 = e^y
Thanks!
2. You don't need logarithms for this. One has: $y = e^{3t} = (e^t)^3 = x^3$.
3. If you really want to use logs, you could do it like this:
$
ln(x) = t
$
$
ln(y) = 3t = 3 ln(x)
$
$
e^{ln(y)} = e^{3 ln(x)} = e^{ln(x^3)}
$
$
y = x^3
$ | 193 | 437 | {"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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2016-50 | longest | en | 0.668632 |
https://justaaa.com/chemistry/945634-calculate-the-number-of-ag-nanoparticle-having-a | 1,713,938,215,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819067.85/warc/CC-MAIN-20240424045636-20240424075636-00628.warc.gz | 311,205,819 | 9,833 | Question
# Calculate the number of Ag nanoparticle having a 5 nm radius.?
Calculate the number of Ag nanoparticle having a 5 nm radius.?
Given radius of Ag, r = 5 nm = 5x10-9 m = 5x10-9x102 cm since 1 m = 102 cm
= 5x10-7 cm
Volume = V = (4/3) x π x r3
= (4/3) x π x (5x10-7)3 cm3
= 5.236x10-19 cm3
Density of silver , d = 10.49 g/cm3
So mass of silver is , m = density x volume
= 10.49 g/cm3 x 5.236x10-19 cm3
= 5.49x10-18 g
No of moles,n = Mass / Atomic weight
= 5.49x10-18 g / 107.9 (g/mol)
= 5.09x10-20 mol
No of atoms = number of moles x Avogadro's number
= 5.09x10-20 mol x 6.023x1023 (atoms/mol)
= 30.6x103 atoms
Therefore the number of Ag nanoparticle having a 5 nm radius is 30.6x103 atoms | 293 | 726 | {"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-2024-18 | latest | en | 0.704303 |
https://cstheory.stackexchange.com/questions/7137/reducing-redundant-edges-from-a-dependency-graph/7138 | 1,721,823,039,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518277.99/warc/CC-MAIN-20240724110315-20240724140315-00427.warc.gz | 160,701,154 | 42,876 | # Reducing redundant edges from a dependency graph
I have a DAG of dependencies that contains lots of redundant edges (see example below). I want a "quick" algorithm (ie. can handle a graph with several thousands of nodes/edges) that finds a minimal sub graph.
For example:
A -> B -> C
A -> C
in words A is prerequisite to B, and B is prerequisite to C, and also A is prerequisite to C. In this case A -> C is redundant (since B is already necessary to reach C, and A is necessary to reach B).
Its been a while since I studied algorithms, and I'm not sure where to start.
By the way, its not critical that the algorithm finds the global minimum, local minimum is fine (the edge reduction is only a runtime optimization for next stage of processing).
Also, I realize this is a CS QA and not programming, but my program is written in Python, so I would be extra happy to learn of a python module or open source for doing this reduction, just in case you know of it.
• I was wondering if DFS could help here? Commented Jun 27, 2011 at 8:58
• You are looking for the "transitive reduction" of your dependency graph. Commented Jun 27, 2011 at 9:02
• Find the strongly connected components. Only leave one edge between each pair of components. For each strongly connected component, you need to find a minimal number of cycles that would cover it. Finding a minimum number of cycles seems to be NP-complete since it will decide the Hamiltonicity, but since you only need a local minimal just remove edges from each component till it looses its strong connectivity. Commented Jul 13, 2011 at 0:27
The Transitive Reduction of a Directed Graph A. V. Aho, M. R. Garey, and J. D. Ullman
According to wikipedia, this algorithm is used by tred which is tool for transitive reduction available in GraphViz package. You can run it on your graph and get reduced graph.
This question is duplicate of this stackoverflow question.
code here graphviz/tools/src/tred.c does use DFS. ;-)
• I didn't know about tred, thanks. Commented Jun 27, 2011 at 9:36
• Thank you MachineCharmer. I am outside a university and cannot download the paper without paying 25\$... is there a free online source that describes this algorithm? The tred source is small and readable, but without explanations. Commented Jun 27, 2011 at 12:00
• No. There is no free download link for that paper. But you might have friends at some university :) Commented Jun 27, 2011 at 13:45
I ended up solving it this way:
My data structure is made of dependends dictionary, from a node id to a list of nodes that depend on it (ie. its followers in the DAG).
I haven't calculated the exact complexity of it, but it swallowed my graph of several thousands in a split second.
_transitive_closure_cache = {}
def transitive_closure(self, node_id):
"""returns a set of all the nodes (ids) reachable from given node(_id)"""
global _transitive_closure_cache
if node_id in _transitive_closure_cache:
return _transitive_closure_cache[node_id]
c = set(d.id for d in dependents[node_id])
for d in dependents[node_id]:
c.update(transitive_closure(d.id)) # for the non-pythonists - update is update self to Union result
_transitive_closure_cache[node_id] = c
return c
def can_reduce(self, source_id, dest_id):
"""returns True if the edge (source_id, dest_id) is redundant (can reach from source_id to dest_id without it)"""
for d in dependents[source_id]:
if d.id == dest_id:
continue
if dest_id in transitive_closure(d.id):
return True # the dest node can be reached in a less direct path, then this link is redundant
return False
# Reduce redundant edges:
for node in nodes:
dependents[node.id] = [d for d in dependents[node.id] if not can_reduce(node.id, d.id)] | 895 | 3,713 | {"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} | 3.171875 | 3 | CC-MAIN-2024-30 | latest | en | 0.952222 |
http://tamivox.org/dave/speaker/simple.html | 1,539,649,325,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583509958.44/warc/CC-MAIN-20181015225726-20181016011226-00520.warc.gz | 362,421,996 | 1,429 | A simple method of deriving the canonical network.
Version of 4 November 2008.
Home.
Circuit 1, below, has nine identical speakers arranged into three parallel branches, each containing three speakers in series. Assume each speaker has an impedance of 8 ohms, and is supplied with enough current to be dissipating 10 watts. Easily calculated are that the overall impedance of the network is 8 ohms, and the overall power dissipation is 90 watts.
Circuit 1.
From symmetry, node 1 must be at the same voltage as node 2, so if they are connected as in circuit 2, below, there will be no current in the linking wire. Similarly connect nodes 3 and 4 with a wire. The electrical properties of the network, and all the component speakers, are the same.
Circuit 2.
Now rearrange the wires to emphasize certain connections, as in circuit 3.
Circuit 3.
To obtain circuit 4, replace 8Ω speakers R and U, which are in parallel, with 4Ω speaker A, which will necessarily dissipate 20 watts. Similarly, replace W and Z with 4Ω speaker E.
Circuit 4.
To obtain circuit 5, replace speakers S and T, which are in series, with 16Ω speaker D, which will also dissipate 20 watts. Similarly, replace X and Y with 16Ω speaker B.
Circuit 5.
Rename speaker V as C, and rearrange the wires to reveal the familiar drawing of the canonical network as in circuit 6.
Circuit 6. | 334 | 1,359 | {"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-2018-43 | longest | en | 0.937896 |
https://kpsc.jobquiz.info/question.php?id=OY5d&page=0 | 1,656,948,133,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104432674.76/warc/CC-MAIN-20220704141714-20220704171714-00640.warc.gz | 413,128,764 | 7,580 | ## Kerala PSC Previous Years Question Paper & Answer
Title : ASST ENGINEER MECHANICAL TTP LTD / ASST ENGINEER MECHANICAL SFC OF KERALA LTD
Question Code : A
Page:1
Below are the scanned copy of Kerala Public Service Commission (KPSC) Question Paper with answer keys of Exam Name 'ASST ENGINEER MECHANICAL TTP LTD / ASST ENGINEER MECHANICAL SFC OF KERALA LTD' And exam conducted in the year 2015. And Question paper code was '147/2015'. Medium of question paper was in Malayalam or English . Booklet Alphacode was 'A'. Answer keys are given at the bottom, but we suggest you to try answering the questions yourself and compare the key along wih to check your performance. Because we would like you to do and practice by yourself.
page: 1 out of 12
Excerpt of Question Code: 147/2015
147/2015
o
Maximum : 100 marks
Time : 1 hour and 15 minutes
A cycle consists of two isothermal and two isentropic processes is known as :
(A) Otto cycle (B) Joule cycle
(C) Stirling cycle (D) ‘Carnot cycle
In an isometric projection the radius of a sphere it is equal to :
(A) 082R ) ٠
The function of stcam nozzle is to convert :
(ಗೆ) heat energy steam into kinetic energy
(8) heat energy steam into rotational energy
(C) kinetic energy into heat energy of steam
(D) heat energy steam into pressure energy
Dryness fraction is the ratio of :
(ಗಿ) mass of dry steam to the mass of water vapour in suspension
(18) mass of water vapour in suspension to the mass of water vapour and mass of dry
steam
(0) mass of dry steam ما the mass of dry steam and mass of water vapour in
suspension
(D) mass of water vapour in suspension to the mass of dry steam
If the thermal efficiency of Carnot heat engine is 50 percent, then coefficient of performance
of a refrigerator working within the same temperature limit would be :
@ 1 (8) 2
During throttling process :
(A) internal energy does not change (8) pressure does not change
(C) அல்ப does not change (D) enthalpy does not change
Which one of the following parameter is significant to ascertain chemical equilibrium of a
system?
(A) . Clapeyron ग equation ൫) Maxwell relation
( Gibb’s function (D) Helmholtz function
[P.T.O.] | 572 | 2,172 | {"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} | 2.90625 | 3 | CC-MAIN-2022-27 | latest | en | 0.893831 |
https://jborden.com/2018/01/08/theres-amazon-prime-and-then-theres-mersenne-prime/ | 1,610,956,100,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703514423.60/warc/CC-MAIN-20210118061434-20210118091434-00734.warc.gz | 400,305,377 | 42,352 | # There’s Amazon Prime, and Then There’s Mersenne Prime
Estimates are that there are 85 million Amazon Prime members.
Now some people may find such a number interesting, certainly Jeff Bezos would, as would all those who hold Amazon stock (which many people do, if not outright, then through a mutual fund).
Now there are other people who may find Mersenne Primes much more interesting, myself included.
Here’s an explanation of a Mersenne Prime from Wikipedia:
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. (A prime number is a number that is divisible only by the number 1 and itself).
Prime numbers are important, especially when it comes to cryptography, internet security, and the future of computing.
So you may wonder, why am I writing about Mersenne Primes?
This past week, a FedEx employee from Germantown, Tenn., made a massive discovery — and it wasn’t in any packages. John Pace found the largest prime number known to humankind.
Pace, a volunteer for the Great Internet Mersenne Prime Search (GIMPS) for over 14 years, discovered the 50th known Mersenne prime, 277,232,917-1 on December 26, 2017. The prime number is calculated by multiplying together 77,232,917 twos, and then subtracting one. It weighs in at 23,249,425 digits, becoming the largest prime number known to mankind. It bests the previous record prime, also discovered by GIMPS, by 910,807 digits.
Just how big is a 23,249,425 digit number? According to the GIMPS web site, big enough to fill an entire shelf of books totalling 9,000 pages. If every second you were to write five digits to an inch then 54 days later you’d have a number stretching over 73 miles (118 km) — almost 3 miles (5 km) longer than the previous record prime.
One of the things I like about this discovery is that Pace has become part of Mersenne Prime history, one that can be traced all of the way back to 500 BC, to the time of the ancient Greek mathematicians.
I am also fairly certain that people will be working on discovering new Mersenne Primes long after Amazon Prime ceases to exist.
By the way, anyone can participate in the GIMPS project; all you need is a computer, an internet connection, the free software at
www.mersenne.org/download/, and a lot of patience.
Go Math!
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 632 | 2,552 | {"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} | 3.453125 | 3 | CC-MAIN-2021-04 | latest | en | 0.921687 |
https://www.tractorfriends.org/answers-on-questions/often-asked-what-is-the-legal-gross-weight-of-a-standard-flatbed-trailer-with-tractor.html | 1,656,526,291,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103642979.38/warc/CC-MAIN-20220629180939-20220629210939-00314.warc.gz | 1,061,848,677 | 20,850 | # Often asked: What Is The Legal Gross Weight Of A Standard Flatbed Trailer With Tractor?
## What is the gross vehicle weight of a tractor trailer?
Commercial Vehicle Weight Standards
Single Axle: 20,000 pounds
Tandem Axle: 34,000 pounds
Gross Vehicle Weight: 80,000 pounds
## What is the legal weight for a 53 foot trailer?
Legal weight and dimensions are: Refrigerated Trailers Max freight weight is 42,000 to 45,000 lbs.
## How much weight can a flatbed semi haul?
Standard flatbed trailers The maximum weight capacity is 48,000 pounds. Standard flatbed trailers are typically loading dock height (58”), and are used for freight that requires top, side or rear loading.
## What is the standard legal weight of a truck and loaded trailer?
Federal law controls maximum gross vehicle weights and axle loads on the Interstate System. Federal limits are 80,000 pounds gross vehicle weight, 20,000 pounds on a single axle, and 34,000 pounds on a tandem axle group. There are also Federal standards for length and width on the National Network (NN).
You might be interested: How To Change Husqvarna Tractor Mower Blades?
## What is the longest length for a tractor trailer?
Beverage Semitrailers The minimum and maximum trailer length is 8.53 m ( 28 feet ) plus the length of the extended upper coupler plate. States may not impose an overall length limit on a truck tractor and beverage semitrailer-trailer combination.
## How do you read a towing capacity chart?
Towing capacity formula
1. Find out curb weight (on VIN sticker).
2. Add the weight of passengers, fuel, and cargo to the curb weight.
3. Subtract this number from your vehicle’s GCWR ( you may have to look this up using your VIN if it’s not on the door sticker).
4. This is your max towing capacity.
## How many pallets can you fit on a 53 foot trailer?
A standard GMA pallet is 48 ” long x 40″ wide. Some simple math tells us that a 53-foot trailer (which is 636 ” long) will fit 13 pallets lengthwise, with about 1 foot extra. These trailers are wide enough for two rows of pallets. So you’re looking at 26 pallets loaded into every 53-foot trailer.
## How much weight can a 2 axle trailer carry?
80,000 pounds gross vehicle weight. 20,000 pounds single axle weight. 34,000 pounds tandem axle weights.
## How much weight can a 40 ft trailer carry?
CAPACITY Dropdeck 40′ 96″ 12,800 lbs. 70,000 lbs. Dropdeck 42′ 96″ 13,200 lbs. 70,000 lbs.
## What is the legal height for a flatbed?
Know the legal limits for flatbed loads In general, the maximum legal load width is 8.5 feet (102 inches), and the maximum height limit is also 102 inches. Legal length is typically 48 to 53 feet, and the maximum weight is about 46,000 pounds.
You might be interested: Often asked: Who Invented The Tractor Beam?
## How much does a 48 ft flatbed trailer weight?
48′ Flatbed Trailer
GENERAL PARAMETERS
Tare Weight Approximately 13,100 lbs
GVWR 80,000 LBS
Conspicuity Meets DOT requirements
Main Beams Fabricated high tensile steel
27
## What’s better flatbed or step deck?
Flatbed trailers typically ship items that are large or wide, items that need to be loaded by a crane, or from the side with a forklift. The step deck trailer has all the same versatility as a flatbed trailer, but has a lowered deck to accommodate for a taller cargo height.
## What is the weight of a truck and trailer?
A semi-truck hooked up to an empty trailer weighs around 35,000 pounds. The weight maximum for a semi-truck with a loaded trailer legally allowed in the United States is 80,000 pounds. A semi-truck without a trailer weighs between 10,000 and 25,000 pounds, depending on the size.
## What happens if a truck is overweight at a weigh station?
Most weigh stations force drivers to “shut down” their operation if a truck weighs more than 6,000 pounds over maximum gross weight. Not only would you write a check to fund the salary of the officer who caught your driver, he would lose time and money waiting until another truck arrives to unload the excess weight.
## What is the max weight on the drive axle and trailer axle?
In addition to Bridge Formula weight limits, Federal law states that single axles are limited to 20,000 pounds, and axles spaced more than 40 inches and not more than 96 inches apart (tandem axles ) are limited to 34,000 pounds. Gross vehicle weight is limited to 80,000 pounds (23 U.S.C. 127). | 1,064 | 4,392 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-27 | latest | en | 0.884157 |
https://www.geeksforgeeks.org/management-information-system-mis-models/ | 1,702,228,164,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679102612.80/warc/CC-MAIN-20231210155147-20231210185147-00157.warc.gz | 836,412,499 | 48,688 | # Management Information System (MIS) Models
A model is an abstraction of something it represents (some phenomenon), called an entity. For example, if a model represents a firm, then the firm is an entity.
Types of Models:
1. Physical Models:
It is a model that exists in three-dimensional form. For example, clay model of a new automobile developed by designers.
2. Narrative Models:
It is created by verbal or written description. Also, these can be created anywhere without much resources hence they are most popular.
3. Graphs:
It is usually a two-dimensional diagram. For example, graphs and charts.
4. Mathematical Models:
It uses symbolic notations and mathematical equations to represent a system. It can be represented by 3-D also. Following are the types of mathematical models:
• (a). Influence of Time:
Static Model does not include time as a variable whereas, Dynamic Model allows the changes of system attributes to be derived as a function of time.
• (b). Degree of Certainty:
A probability is a chance of occurring something will happen.Probabilities ranges from 0 to 1. A model that includes probabilities is called Probabilistic model, otherwise it is called a Deterministic model.
• (c). Ability to Achieve Optimization:
Optimizing Model selects the best solution among the alternatives.A SUB-OPTIMIZING MODEL permits the manager to enter a set of decisions, once this step is completed the model will project an outcome. It leaves the decision task on the manager.
Steps of Model Construction:
• Define the problem and the factor that influence it.
• Select criteria to guide the decision and establish objectives.
• Formulate a model that helps management to understand the relationships between the influence factors and the objectives the firm is trying to achieve.
• Collect the relevant data while trying to avoid the incorporation of superfluous information into the model.
• Identify and evaluate the alternatives.
• Select the best alternative.
• Implement the alternative.
The below shown figure is an model of Management Information System (MIS).
Components of MIS Model:
1. Organizational Problem Solvers:
Outputs are used by persons who are responsible for solving the firm’s problems(say managers).
2. Database:
It’s contents are used by software that produces report as well as mathematical model.
3. Mathematical Model:
It produces information as a simulation of firm’s operation.
4. Report Writing Software:
It produces both periodic and special report.
5. Environment:
The environment is of great importance to the firm. It is the very reason of the firm’s existence.
Advantages:
• Can be a learning experience.
• Provides predictive power.
• Less expensive than trial and error method.
• Speed allows consideration of more options.
Disadvantages:
• Difficult to model a business system.
• High degree of mathematical skills required.
Whether you're preparing for your first job interview or aiming to upskill in this ever-evolving tech landscape, GeeksforGeeks Courses are your key to success. We provide top-quality content at affordable prices, all geared towards accelerating your growth in a time-bound manner. Join the millions we've already empowered, and we're here to do the same for you. Don't miss out - check it out now!
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Similar Reads | 666 | 3,319 | {"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-2023-50 | latest | en | 0.91755 |
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https://www.easycalculation.com/analytical/learn-angle-between-two-curves.php | 1,611,641,944,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704798089.76/warc/CC-MAIN-20210126042704-20210126072704-00114.warc.gz | 764,661,261 | 6,183 | English
How to Find Angle Between Two Curves - Formula, Example
Find Angle Between Two Curves at Point of Intersection - Tutorial
Definition
When two curves intersect each other the angle at the intersecting point is called as angle of intersection between two curves.
Formula
tan(θ) = (m2-m1)/(1+(m1.m2)) ∀ m2>m1 tan(θ) = (m1-m2)/(1+(m1.m2)) ∀ m1>m2
Where,
m1 = Curve 1 Tangent line slope m2 = Curve 2 Tangent line slope
Example
Find the acute angle between the two curves y=2x2 and y=x2-4x+4
Given ,
Here the 2 curves are represented in the equation format as shown below y=2x2 --> (1) y=x2-4x+4 --> (2) Let us learn how to find angle of intersection between these curves using this equation.
Solution :
Step 1 :
Solving equ 1 and equ 2 2x2 = y x2- 4x + 4 = y x2+ 4x - 4 = 0 By factorizing the quadratic equation x2+ 4x - 4 = 0 we get the x values as x = 0.8 and x = -4.8 From the x values the maximum value (0.8) is substituted in equation 1 to find y value
Where,
y = 2x(0.8)2 y = 1.3 From this values we get (0.8,1.3), which is an intersect point of curve.
Step 2 :
Differentiate equ.1 and equ.2 Differentiation of equ 1 y=2x2 dy/dx = 4x --> (3)
Where,
dy/dx(x2) = 2x Differentiation of equ 2 y=x2-4x+4 dy/dx = 2x - 4 --> (4)
Where ,
dy/dx(x) = 1 and dy/dx(constant) = 0
Step 3 :
Find the slope by substituting intersect point (0.8,1.3) in equ.3 and equ.4, Equ. 3 4x = 4(0.8) = 3.2 = m1 Equ. 4 2x - 4 = 2(0.8) - 4 = -2.4 = m2
Step 4 :
Find the Angle by substituting slope values in Formula tan(θ) = (m1-m2)/(1+(m1.m2)) ∀ m1>m2 From formula θ = tan-1[(m1-m2)/(1+(m1.m2))] θ = tan-1((3.2+2.4)/(1+(3.2*-2.4)) θ = tan-1(5.6/-6.68) θ = tan-1(0.8383) θ = 39.974 ° Therefore, the angle of intersection between the given curve is θ = 39.974 ° | 659 | 1,763 | {"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-2021-04 | latest | en | 0.798517 |
https://yourquickinformation.com/what-is-the-equation-of-the-line-perpendicular-to-3x-4y-12-and-containing-the-point-6-2/ | 1,721,323,472,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514848.78/warc/CC-MAIN-20240718161144-20240718191144-00217.warc.gz | 937,330,352 | 34,504 | ## What is the equation of the line perpendicular to 3x 4y 12 and containing the point 6 2?
What is the equation of the line perpendicular to 3x+4y=123x+4y=12 and containing the point (6,−2)(6,−2)?
## Which of the following is a perpendicular line to 3x 4y 5 0?
The lines 3x+4y+7=0 and 4x+3y+5=0 are perpendicular.
What is the slope of a line that is perpendicular to 3x 4y 12?
Using the slope-intercept form, the slope is −34 . The equation of a perpendicular line to y=−3×4+3 y = – 3 x 4 + 3 must have a slope that is the negative reciprocal of the original slope.
What is the slope of a line perpendicular to the line represented by equation y 3x 4?
Two perpendicular lines have opposite reciprocal slopes. The slope in y=3x+4 is 3 , so the line perpendicular to it will have a slope of −13 .
### What is the equation of the line which passes through the points 1/3 and 2 5?
y = 2x + 1 this is slope-intercept form. 2x – y = -1 this is standard form.
### Is the Y intercept of the line passes from point 2 2 and perpendicular to 3x Y 3?
Its y-intercept is. Hence option (4) is the answer.
How to find the equation of a perpendicular line with two points?
Before you calculate the equation of the perpendicular line, you will need to find the slope of the line that crosses the two points. The equation for finding the slope of a line with two points is m = y 2 − y 1 x 2 − x 1 {\\displaystyle m={\\frac {{y^{2}}-{y^{1}}}{{x^{2}}-{x^{1}}}}} .
What is the EQ of the line perpendicular to 3x+4y-5 = 0? | 452 | 1,515 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2024-30 | latest | en | 0.90045 |
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# A sinusoidal wave of frequency 200 Hz has a speed of 350 m/s. (a) How far...
A sinusoidal wave of frequency 200 Hz has a speed of 350 m/s. (a) How far apart are two points that differ in phase by π/4 rad? (b) What is the phase difference between two displacements at a certain point at times 4.5 ms apart?
Use the properties of wave motion to find the phase difference as shown below
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# Investigating matrix Schubert varieties -- basic functions for Schubert determinantal ideals
Matrix Schubert varieties were introduced by Fulton [Ful92] in the study of Schubert varieties in the complete flag variety. Their defining ideals are called Schubert determinantal ideals.
The general method for creating a Schubert determinantal Ideal is schubertDeterminantalIdeal. The input is a permutation in the form of a list. This package contains functions for investigating the rank matrix, the Rothe diagram, and the essential cells of the Rothe diagram as defined by Fulton in [Ful92].
i1 : p = {2,1,6,3,5,4}; i2 : rotheDiagram p o2 = {(1, 1), (3, 3), (3, 4), (3, 5), (5, 4)} o2 : List i3 : essentialSet p o3 = {(1, 1), (3, 5), (5, 4)} o3 : List i4 : rankTable p o4 = | 0 1 1 1 1 1 | | 1 2 2 2 2 2 | | 1 2 2 2 2 3 | | 1 2 3 3 3 4 | | 1 2 3 3 4 5 | | 1 2 3 4 5 6 | 6 6 o4 : Matrix ZZ <-- ZZ i5 : netList fultonGens p +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ o5 = |z | | 1,1 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,3 2,2 3,1 1,2 2,3 3,1 1,3 2,1 3,2 1,1 2,3 3,2 1,2 2,1 3,3 1,1 2,2 3,3 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,4 2,2 3,1 1,2 2,4 3,1 1,4 2,1 3,2 1,1 2,4 3,2 1,2 2,1 3,4 1,1 2,2 3,4 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,4 2,3 3,1 1,3 2,4 3,1 1,4 2,1 3,3 1,1 2,4 3,3 1,3 2,1 3,4 1,1 2,3 3,4 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,4 2,3 3,2 1,3 2,4 3,2 1,4 2,2 3,3 1,2 2,4 3,3 1,3 2,2 3,4 1,2 2,3 3,4 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,2 3,1 1,2 2,5 3,1 1,5 2,1 3,2 1,1 2,5 3,2 1,2 2,1 3,5 1,1 2,2 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,3 3,1 1,3 2,5 3,1 1,5 2,1 3,3 1,1 2,5 3,3 1,3 2,1 3,5 1,1 2,3 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,3 3,2 1,3 2,5 3,2 1,5 2,2 3,3 1,2 2,5 3,3 1,3 2,2 3,5 1,2 2,3 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,4 3,1 1,4 2,5 3,1 1,5 2,1 3,4 1,1 2,5 3,4 1,4 2,1 3,5 1,1 2,4 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,4 3,2 1,4 2,5 3,2 1,5 2,2 3,4 1,2 2,5 3,4 1,4 2,2 3,5 1,2 2,4 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |- z z z + z z z + z z z - z z z - z z z + z z z | | 1,5 2,4 3,3 1,4 2,5 3,3 1,5 2,3 3,4 1,3 2,5 3,4 1,4 2,3 3,5 1,3 2,4 3,5 | +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z | | 1,4 2,3 3,2 4,1 1,3 2,4 3,2 4,1 1,4 2,2 3,3 4,1 1,2 2,4 3,3 4,1 1,3 2,2 3,4 4,1 1,2 2,3 3,4 4,1 1,4 2,3 3,1 4,2 1,3 2,4 3,1 4,2 1,4 2,1 3,3 4,2 1,1 2,4 3,3 4,2 1,3 2,1 3,4 4,2 1,1 2,3 3,4 4,2 1,4 2,2 3,1 4,3 1,2 2,4 3,1 4,3 1,4 2,1 3,2 4,3 1,1 2,4 3,2 4,3 1,2 2,1 3,4 4,3 1,1 2,2 3,4 4,3 1,3 2,2 3,1 4,4 1,2 2,3 3,1 4,4 1,3 2,1 3,2 4,4 1,1 2,3 3,2 4,4 1,2 2,1 3,3 4,4 1,1 2,2 3,3 4,4| +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z | | 1,4 2,3 3,2 5,1 1,3 2,4 3,2 5,1 1,4 2,2 3,3 5,1 1,2 2,4 3,3 5,1 1,3 2,2 3,4 5,1 1,2 2,3 3,4 5,1 1,4 2,3 3,1 5,2 1,3 2,4 3,1 5,2 1,4 2,1 3,3 5,2 1,1 2,4 3,3 5,2 1,3 2,1 3,4 5,2 1,1 2,3 3,4 5,2 1,4 2,2 3,1 5,3 1,2 2,4 3,1 5,3 1,4 2,1 3,2 5,3 1,1 2,4 3,2 5,3 1,2 2,1 3,4 5,3 1,1 2,2 3,4 5,3 1,3 2,2 3,1 5,4 1,2 2,3 3,1 5,4 1,3 2,1 3,2 5,4 1,1 2,3 3,2 5,4 1,2 2,1 3,3 5,4 1,1 2,2 3,3 5,4| +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z | | 1,4 2,3 4,2 5,1 1,3 2,4 4,2 5,1 1,4 2,2 4,3 5,1 1,2 2,4 4,3 5,1 1,3 2,2 4,4 5,1 1,2 2,3 4,4 5,1 1,4 2,3 4,1 5,2 1,3 2,4 4,1 5,2 1,4 2,1 4,3 5,2 1,1 2,4 4,3 5,2 1,3 2,1 4,4 5,2 1,1 2,3 4,4 5,2 1,4 2,2 4,1 5,3 1,2 2,4 4,1 5,3 1,4 2,1 4,2 5,3 1,1 2,4 4,2 5,3 1,2 2,1 4,4 5,3 1,1 2,2 4,4 5,3 1,3 2,2 4,1 5,4 1,2 2,3 4,1 5,4 1,3 2,1 4,2 5,4 1,1 2,3 4,2 5,4 1,2 2,1 4,3 5,4 1,1 2,2 4,3 5,4| +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z | | 1,4 3,3 4,2 5,1 1,3 3,4 4,2 5,1 1,4 3,2 4,3 5,1 1,2 3,4 4,3 5,1 1,3 3,2 4,4 5,1 1,2 3,3 4,4 5,1 1,4 3,3 4,1 5,2 1,3 3,4 4,1 5,2 1,4 3,1 4,3 5,2 1,1 3,4 4,3 5,2 1,3 3,1 4,4 5,2 1,1 3,3 4,4 5,2 1,4 3,2 4,1 5,3 1,2 3,4 4,1 5,3 1,4 3,1 4,2 5,3 1,1 3,4 4,2 5,3 1,2 3,1 4,4 5,3 1,1 3,2 4,4 5,3 1,3 3,2 4,1 5,4 1,2 3,3 4,1 5,4 1,3 3,1 4,2 5,4 1,1 3,3 4,2 5,4 1,2 3,1 4,3 5,4 1,1 3,2 4,3 5,4| +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z | | 2,4 3,3 4,2 5,1 2,3 3,4 4,2 5,1 2,4 3,2 4,3 5,1 2,2 3,4 4,3 5,1 2,3 3,2 4,4 5,1 2,2 3,3 4,4 5,1 2,4 3,3 4,1 5,2 2,3 3,4 4,1 5,2 2,4 3,1 4,3 5,2 2,1 3,4 4,3 5,2 2,3 3,1 4,4 5,2 2,1 3,3 4,4 5,2 2,4 3,2 4,1 5,3 2,2 3,4 4,1 5,3 2,4 3,1 4,2 5,3 2,1 3,4 4,2 5,3 2,2 3,1 4,4 5,3 2,1 3,2 4,4 5,3 2,3 3,2 4,1 5,4 2,2 3,3 4,1 5,4 2,3 3,1 4,2 5,4 2,1 3,3 4,2 5,4 2,2 3,1 4,3 5,4 2,1 3,2 4,3 5,4| +---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
The default presentation given by schubertDeterminantalIdeal is given by the Fulton generators of the ideal. In order to access a minimal generating set, use trim.
i6 : I = schubertDeterminantalIdeal p; o6 : Ideal of QQ[z ..z ] 1,1 6,6 i7 : # (I_*) o7 = 16 i8 : # ((trim I)_*) o8 = 14
After creating a Schubert determinantal ideal, the permutation associated to it is stored in its cache table.
i9 : peek I.cache o9 = CacheTable{ASM => | 0 1 0 0 0 0 | } | 1 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 1 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 1 0 0 | module => image | z_(1,1) -z_(1,3)z_(2,2)z_(3,1)+z_(1,2)z_(2,3)z_(3,1)+z_(1,3)z_(2,1)z_(3,2)-z_(1,1)z_(2,3)z_(3,2)-z_(1,2)z_(2,1)z_(3,3)+z_(1,1)z_(2,2)z_(3,3) -z_(1,4)z_(2,2)z_(3,1)+z_(1,2)z_(2,4)z_(3,1)+z_(1,4)z_(2,1)z_(3,2)-z_(1,1)z_(2,4)z_(3,2)-z_(1,2)z_(2,1)z_(3,4)+z_(1,1)z_(2,2)z_(3,4) -z_(1,4)z_(2,3)z_(3,1)+z_(1,3)z_(2,4)z_(3,1)+z_(1,4)z_(2,1)z_(3,3)-z_(1,1)z_(2,4)z_(3,3)-z_(1,3)z_(2,1)z_(3,4)+z_(1,1)z_(2,3)z_(3,4) -z_(1,4)z_(2,3)z_(3,2)+z_(1,3)z_(2,4)z_(3,2)+z_(1,4)z_(2,2)z_(3,3)-z_(1,2)z_(2,4)z_(3,3)-z_(1,3)z_(2,2)z_(3,4)+z_(1,2)z_(2,3)z_(3,4) -z_(1,5)z_(2,2)z_(3,1)+z_(1,2)z_(2,5)z_(3,1)+z_(1,5)z_(2,1)z_(3,2)-z_(1,1)z_(2,5)z_(3,2)-z_(1,2)z_(2,1)z_(3,5)+z_(1,1)z_(2,2)z_(3,5) -z_(1,5)z_(2,3)z_(3,1)+z_(1,3)z_(2,5)z_(3,1)+z_(1,5)z_(2,1)z_(3,3)-z_(1,1)z_(2,5)z_(3,3)-z_(1,3)z_(2,1)z_(3,5)+z_(1,1)z_(2,3)z_(3,5) -z_(1,5)z_(2,3)z_(3,2)+z_(1,3)z_(2,5)z_(3,2)+z_(1,5)z_(2,2)z_(3,3)-z_(1,2)z_(2,5)z_(3,3)-z_(1,3)z_(2,2)z_(3,5)+z_(1,2)z_(2,3)z_(3,5) -z_(1,5)z_(2,4)z_(3,1)+z_(1,4)z_(2,5)z_(3,1)+z_(1,5)z_(2,1)z_(3,4)-z_(1,1)z_(2,5)z_(3,4)-z_(1,4)z_(2,1)z_(3,5)+z_(1,1)z_(2,4)z_(3,5) -z_(1,5)z_(2,4)z_(3,2)+z_(1,4)z_(2,5)z_(3,2)+z_(1,5)z_(2,2)z_(3,4)-z_(1,2)z_(2,5)z_(3,4)-z_(1,4)z_(2,2)z_(3,5)+z_(1,2)z_(2,4)z_(3,5) -z_(1,5)z_(2,4)z_(3,3)+z_(1,4)z_(2,5)z_(3,3)+z_(1,5)z_(2,3)z_(3,4)-z_(1,3)z_(2,5)z_(3,4)-z_(1,4)z_(2,3)z_(3,5)+z_(1,3)z_(2,4)z_(3,5) z_(1,4)z_(2,3)z_(3,2)z_(4,1)-z_(1,3)z_(2,4)z_(3,2)z_(4,1)-z_(1,4)z_(2,2)z_(3,3)z_(4,1)+z_(1,2)z_(2,4)z_(3,3)z_(4,1)+z_(1,3)z_(2,2)z_(3,4)z_(4,1)-z_(1,2)z_(2,3)z_(3,4)z_(4,1)-z_(1,4)z_(2,3)z_(3,1)z_(4,2)+z_(1,3)z_(2,4)z_(3,1)z_(4,2)+z_(1,4)z_(2,1)z_(3,3)z_(4,2)-z_(1,1)z_(2,4)z_(3,3)z_(4,2)-z_(1,3)z_(2,1)z_(3,4)z_(4,2)+z_(1,1)z_(2,3)z_(3,4)z_(4,2)+z_(1,4)z_(2,2)z_(3,1)z_(4,3)-z_(1,2)z_(2,4)z_(3,1)z_(4,3)-z_(1,4)z_(2,1)z_(3,2)z_(4,3)+z_(1,1)z_(2,4)z_(3,2)z_(4,3)+z_(1,2)z_(2,1)z_(3,4)z_(4,3)-z_(1,1)z_(2,2)z_(3,4)z_(4,3)-z_(1,3)z_(2,2)z_(3,1)z_(4,4)+z_(1,2)z_(2,3)z_(3,1)z_(4,4)+z_(1,3)z_(2,1)z_(3,2)z_(4,4)-z_(1,1)z_(2,3)z_(3,2)z_(4,4)-z_(1,2)z_(2,1)z_(3,3)z_(4,4)+z_(1,1)z_(2,2)z_(3,3)z_(4,4) z_(1,4)z_(2,3)z_(3,2)z_(5,1)-z_(1,3)z_(2,4)z_(3,2)z_(5,1)-z_(1,4)z_(2,2)z_(3,3)z_(5,1)+z_(1,2)z_(2,4)z_(3,3)z_(5,1)+z_(1,3)z_(2,2)z_(3,4)z_(5,1)-z_(1,2)z_(2,3)z_(3,4)z_(5,1)-z_(1,4)z_(2,3)z_(3,1)z_(5,2)+z_(1,3)z_(2,4)z_(3,1)z_(5,2)+z_(1,4)z_(2,1)z_(3,3)z_(5,2)-z_(1,1)z_(2,4)z_(3,3)z_(5,2)-z_(1,3)z_(2,1)z_(3,4)z_(5,2)+z_(1,1)z_(2,3)z_(3,4)z_(5,2)+z_(1,4)z_(2,2)z_(3,1)z_(5,3)-z_(1,2)z_(2,4)z_(3,1)z_(5,3)-z_(1,4)z_(2,1)z_(3,2)z_(5,3)+z_(1,1)z_(2,4)z_(3,2)z_(5,3)+z_(1,2)z_(2,1)z_(3,4)z_(5,3)-z_(1,1)z_(2,2)z_(3,4)z_(5,3)-z_(1,3)z_(2,2)z_(3,1)z_(5,4)+z_(1,2)z_(2,3)z_(3,1)z_(5,4)+z_(1,3)z_(2,1)z_(3,2)z_(5,4)-z_(1,1)z_(2,3)z_(3,2)z_(5,4)-z_(1,2)z_(2,1)z_(3,3)z_(5,4)+z_(1,1)z_(2,2)z_(3,3)z_(5,4) z_(1,4)z_(2,3)z_(4,2)z_(5,1)-z_(1,3)z_(2,4)z_(4,2)z_(5,1)-z_(1,4)z_(2,2)z_(4,3)z_(5,1)+z_(1,2)z_(2,4)z_(4,3)z_(5,1)+z_(1,3)z_(2,2)z_(4,4)z_(5,1)-z_(1,2)z_(2,3)z_(4,4)z_(5,1)-z_(1,4)z_(2,3)z_(4,1)z_(5,2)+z_(1,3)z_(2,4)z_(4,1)z_(5,2)+z_(1,4)z_(2,1)z_(4,3)z_(5,2)-z_(1,1)z_(2,4)z_(4,3)z_(5,2)-z_(1,3)z_(2,1)z_(4,4)z_(5,2)+z_(1,1)z_(2,3)z_(4,4)z_(5,2)+z_(1,4)z_(2,2)z_(4,1)z_(5,3)-z_(1,2)z_(2,4)z_(4,1)z_(5,3)-z_(1,4)z_(2,1)z_(4,2)z_(5,3)+z_(1,1)z_(2,4)z_(4,2)z_(5,3)+z_(1,2)z_(2,1)z_(4,4)z_(5,3)-z_(1,1)z_(2,2)z_(4,4)z_(5,3)-z_(1,3)z_(2,2)z_(4,1)z_(5,4)+z_(1,2)z_(2,3)z_(4,1)z_(5,4)+z_(1,3)z_(2,1)z_(4,2)z_(5,4)-z_(1,1)z_(2,3)z_(4,2)z_(5,4)-z_(1,2)z_(2,1)z_(4,3)z_(5,4)+z_(1,1)z_(2,2)z_(4,3)z_(5,4) z_(1,4)z_(3,3)z_(4,2)z_(5,1)-z_(1,3)z_(3,4)z_(4,2)z_(5,1)-z_(1,4)z_(3,2)z_(4,3)z_(5,1)+z_(1,2)z_(3,4)z_(4,3)z_(5,1)+z_(1,3)z_(3,2)z_(4,4)z_(5,1)-z_(1,2)z_(3,3)z_(4,4)z_(5,1)-z_(1,4)z_(3,3)z_(4,1)z_(5,2)+z_(1,3)z_(3,4)z_(4,1)z_(5,2)+z_(1,4)z_(3,1)z_(4,3)z_(5,2)-z_(1,1)z_(3,4)z_(4,3)z_(5,2)-z_(1,3)z_(3,1)z_(4,4)z_(5,2)+z_(1,1)z_(3,3)z_(4,4)z_(5,2)+z_(1,4)z_(3,2)z_(4,1)z_(5,3)-z_(1,2)z_(3,4)z_(4,1)z_(5,3)-z_(1,4)z_(3,1)z_(4,2)z_(5,3)+z_(1,1)z_(3,4)z_(4,2)z_(5,3)+z_(1,2)z_(3,1)z_(4,4)z_(5,3)-z_(1,1)z_(3,2)z_(4,4)z_(5,3)-z_(1,3)z_(3,2)z_(4,1)z_(5,4)+z_(1,2)z_(3,3)z_(4,1)z_(5,4)+z_(1,3)z_(3,1)z_(4,2)z_(5,4)-z_(1,1)z_(3,3)z_(4,2)z_(5,4)-z_(1,2)z_(3,1)z_(4,3)z_(5,4)+z_(1,1)z_(3,2)z_(4,3)z_(5,4) z_(2,4)z_(3,3)z_(4,2)z_(5,1)-z_(2,3)z_(3,4)z_(4,2)z_(5,1)-z_(2,4)z_(3,2)z_(4,3)z_(5,1)+z_(2,2)z_(3,4)z_(4,3)z_(5,1)+z_(2,3)z_(3,2)z_(4,4)z_(5,1)-z_(2,2)z_(3,3)z_(4,4)z_(5,1)-z_(2,4)z_(3,3)z_(4,1)z_(5,2)+z_(2,3)z_(3,4)z_(4,1)z_(5,2)+z_(2,4)z_(3,1)z_(4,3)z_(5,2)-z_(2,1)z_(3,4)z_(4,3)z_(5,2)-z_(2,3)z_(3,1)z_(4,4)z_(5,2)+z_(2,1)z_(3,3)z_(4,4)z_(5,2)+z_(2,4)z_(3,2)z_(4,1)z_(5,3)-z_(2,2)z_(3,4)z_(4,1)z_(5,3)-z_(2,4)z_(3,1)z_(4,2)z_(5,3)+z_(2,1)z_(3,4)z_(4,2)z_(5,3)+z_(2,2)z_(3,1)z_(4,4)z_(5,3)-z_(2,1)z_(3,2)z_(4,4)z_(5,3)-z_(2,3)z_(3,2)z_(4,1)z_(5,4)+z_(2,2)z_(3,3)z_(4,1)z_(5,4)+z_(2,3)z_(3,1)z_(4,2)z_(5,4)-z_(2,1)z_(3,3)z_(4,2)z_(5,4)-z_(2,2)z_(3,1)z_(4,3)z_(5,4)+z_(2,1)z_(3,2)z_(4,3)z_(5,4) | trim => (OptionTable{Strategy => null}) => ideal (z , z z z - z z z - z z z + z z z + z z z - z z z , z z z - z z z - z z z + z z z + z z z - z z z , z z z - z z z - z z z + z z z + z z z - z z z , z z z - z z z - z z z + z z z + z z z - z z z , z z z - z z z - z z z + z z z , z z z - z z z - z z z + z z z , z z z - z z z - z z z + z z z , z z z - z z z - z z z + z z z , z z z - z z z - z z z + z z z , z z z - z z z - z z z + z z z , z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z , z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z + z z z z - z z z z - z z z z + z z z z - z z z z + z z z z + z z z z - z z z z , z z z z - z z z z - z z z z + z z z z + z z z z - z z z z - z z z z + z z z z + z z z z - z z z z + z z z z - z z z z - z z z z + z z z z - z z z z + z z z z + z z z z - z z z z ) 1,1 1,5 2,4 3,3 1,4 2,5 3,3 1,5 2,3 3,4 1,3 2,5 3,4 1,4 2,3 3,5 1,3 2,4 3,5 1,5 2,4 3,2 1,4 2,5 3,2 1,5 2,2 3,4 1,2 2,5 3,4 1,4 2,2 3,5 1,2 2,4 3,5 1,5 2,3 3,2 1,3 2,5 3,2 1,5 2,2 3,3 1,2 2,5 3,3 1,3 2,2 3,5 1,2 2,3 3,5 1,4 2,3 3,2 1,3 2,4 3,2 1,4 2,2 3,3 1,2 2,4 3,3 1,3 2,2 3,4 1,2 2,3 3,4 1,5 2,4 3,1 1,4 2,5 3,1 1,5 2,1 3,4 1,4 2,1 3,5 1,5 2,3 3,1 1,3 2,5 3,1 1,5 2,1 3,3 1,3 2,1 3,5 1,4 2,3 3,1 1,3 2,4 3,1 1,4 2,1 3,3 1,3 2,1 3,4 1,5 2,2 3,1 1,2 2,5 3,1 1,5 2,1 3,2 1,2 2,1 3,5 1,4 2,2 3,1 1,2 2,4 3,1 1,4 2,1 3,2 1,2 2,1 3,4 1,3 2,2 3,1 1,2 2,3 3,1 1,3 2,1 3,2 1,2 2,1 3,3 2,4 3,3 4,2 5,1 2,3 3,4 4,2 5,1 2,4 3,2 4,3 5,1 2,2 3,4 4,3 5,1 2,3 3,2 4,4 5,1 2,2 3,3 4,4 5,1 2,4 3,3 4,1 5,2 2,3 3,4 4,1 5,2 2,4 3,1 4,3 5,2 2,1 3,4 4,3 5,2 2,3 3,1 4,4 5,2 2,1 3,3 4,4 5,2 2,4 3,2 4,1 5,3 2,2 3,4 4,1 5,3 2,4 3,1 4,2 5,3 2,1 3,4 4,2 5,3 2,2 3,1 4,4 5,3 2,1 3,2 4,4 5,3 2,3 3,2 4,1 5,4 2,2 3,3 4,1 5,4 2,3 3,1 4,2 5,4 2,1 3,3 4,2 5,4 2,2 3,1 4,3 5,4 2,1 3,2 4,3 5,4 1,4 3,3 4,2 5,1 1,3 3,4 4,2 5,1 1,4 3,2 4,3 5,1 1,2 3,4 4,3 5,1 1,3 3,2 4,4 5,1 1,2 3,3 4,4 5,1 1,4 3,3 4,1 5,2 1,3 3,4 4,1 5,2 1,4 3,1 4,3 5,2 1,3 3,1 4,4 5,2 1,4 3,2 4,1 5,3 1,2 3,4 4,1 5,3 1,4 3,1 4,2 5,3 1,2 3,1 4,4 5,3 1,3 3,2 4,1 5,4 1,2 3,3 4,1 5,4 1,3 3,1 4,2 5,4 1,2 3,1 4,3 5,4 1,4 2,3 4,2 5,1 1,3 2,4 4,2 5,1 1,4 2,2 4,3 5,1 1,2 2,4 4,3 5,1 1,3 2,2 4,4 5,1 1,2 2,3 4,4 5,1 1,4 2,3 4,1 5,2 1,3 2,4 4,1 5,2 1,4 2,1 4,3 5,2 1,3 2,1 4,4 5,2 1,4 2,2 4,1 5,3 1,2 2,4 4,1 5,3 1,4 2,1 4,2 5,3 1,2 2,1 4,4 5,3 1,3 2,2 4,1 5,4 1,2 2,3 4,1 5,4 1,3 2,1 4,2 5,4 1,2 2,1 4,3 5,4
This package also contains methods for investigating antidiagonal initial ideals of Schubert determinantal ideals and their associated Stanley-Reisner complexes, which are a kind of subword complex. Subword complexes were introduced in [KM05] in the study of antidiagonal initial ideal of Schubert determinantal ideals and their relation to Schubert polynomials.
i10 : antiDiagInit p o10 = monomialIdeal (z , z z z , z z z , z z z , 1,1 1,3 2,2 3,1 1,4 2,2 3,1 1,5 2,2 3,1 ----------------------------------------------------------------------- z z z , z z z , z z z , z z z , z z z , 1,4 2,3 3,1 1,5 2,3 3,1 1,5 2,4 3,1 1,4 2,3 3,2 1,5 2,3 3,2 ----------------------------------------------------------------------- z z z , z z z , z z z z , z z z z , 1,5 2,4 3,2 1,5 2,4 3,3 1,4 2,3 4,2 5,1 1,4 3,3 4,2 5,1 ----------------------------------------------------------------------- z z z z ) 2,4 3,3 4,2 5,1 o10 : MonomialIdeal of QQ[z ..z ] 1,1 6,6 i11 : subwordComplex p o11 = simplicialComplex | z_(1,2)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,3)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,5)z_(1,6)z_(2,1)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,5)z_(2,6)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,2)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,5)z_(2,6)z_(3,2)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,4)z_(2,5)z_(2,6)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,2)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,5)z_(2,6)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,1)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,4)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,5)z_(2,6)z_(3,1)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,2)z_(2,4)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,5)z_(2,6)z_(3,2)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,5)z_(2,6)z_(3,3)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) z_(1,2)z_(1,3)z_(1,4)z_(1,5)z_(1,6)z_(2,1)z_(2,2)z_(2,3)z_(2,4)z_(2,5)z_(2,6)z_(3,4)z_(3,5)z_(3,6)z_(4,1)z_(4,2)z_(4,3)z_(4,4)z_(4,5)z_(4,6)z_(5,2)z_(5,3)z_(5,4)z_(5,5)z_(5,6)z_(6,1)z_(6,2)z_(6,3)z_(6,4)z_(6,5)z_(6,6) | o11 : SimplicialComplex
Given a list of permutations, this package also contains functions for intersecting and adding the Schubert determinantal ideals associated to the list of permutations.
i12 : L = {{3,1,5,4,2},{2,5,3,4,1}} -- a list of 2 permutations o12 = {{3, 1, 5, 4, 2}, {2, 5, 3, 4, 1}} o12 : List i13 : schubertAdd L o13 = ideal (z , z , - z z + z z , - z z + z z , - 1,1 1,2 1,2 2,1 1,1 2,2 1,3 2,1 1,1 2,3 ----------------------------------------------------------------------- z z + z z , - z z + z z , - z z + z z , - 1,3 2,2 1,2 2,3 1,4 2,1 1,1 2,4 1,4 2,2 1,2 2,4 ----------------------------------------------------------------------- z z + z z , z , z , z ) 1,4 2,3 1,3 2,4 2,1 3,1 4,1 o13 : Ideal of QQ[z ..z ] 1,1 5,5 i14 : schubertIntersect L o14 = ideal (z , z z - z z , z z - z z , z z , 1,1 3,2 4,1 3,1 4,2 2,2 4,1 2,1 4,2 1,2 4,1 ----------------------------------------------------------------------- z z - z z , z z , z z , z z z - z z z - 2,2 3,1 2,1 3,2 1,2 3,1 1,2 2,1 1,4 2,3 3,2 1,3 2,4 3,2 ----------------------------------------------------------------------- z z z + z z z + z z z - z z z , z z z 1,4 2,2 3,3 1,2 2,4 3,3 1,3 2,2 3,4 1,2 2,3 3,4 1,4 2,3 3,1 ----------------------------------------------------------------------- - z z z - z z z + z z z , z z z - 1,3 2,4 3,1 1,4 2,1 3,3 1,3 2,1 3,4 1,2 1,4 2,3 ----------------------------------------------------------------------- 2 2 z z z , z z z - z z , z z z - z z ) 1,2 1,3 2,4 1,2 1,4 2,2 1,2 2,4 1,2 1,3 2,2 1,2 2,3 o14 : Ideal of QQ[z ..z ] 1,1 5,5
Finally, this package contains functions for investigating homological invariants of matrix Schubert varieties efficiently through combinatorial algorithms produced in [PSW21].
i15 : time schubertRegularity p -- used 0.00292221s (cpu); 0.000510211s (thread); 0s (gc) o15 = 5 i16 : time regularity comodule I -- used 0.0285701s (cpu); 0.0308092s (thread); 0s (gc) o16 = 5
## Functions for investigating matrix Schubert varieties
• antiDiagInit(List) -- compute the (unique) antidiagonal initial ideal of an ASM ideal
• rankTable(List) -- compute a table of rank conditions that determines a Schubert determinantal ideal or, more generally, an alternating sign matrix ideal.
• rotheDiagram(List) -- find the Rothe diagram of a partial alternating sign matrix
• augmentedRotheDiagram(List) -- find the Rothe diagram of a partial alternating sign matrix together with the rank table determining the alternating sign matrix variety
• essentialSet(List) -- compute the essential set in the Rothe Diagram for a partial alternating sign matrix or a permutation.
• augmentedEssentialSet(List) -- find the essential set of a partial alternating sign matrix or a permutation together with the rank conditions determining the alternating sign matrix variety
• schubertDeterminantalIdeal(List) -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)
• fultonGens(List) -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)
• subwordComplex(List) -- to find the subword complex associated to w
• schubertIntersect(List) -- compute the intersection of ASM ideals
• schubertAdd(List) -- compute the sum of ASM ideals
• schubertRegularity(List) -- compute the Castelnuovo-Mumford regularity of the quotient by a Schubert determinantal ideal or ASM ideal
• schubertCodim(List) -- compute the codimension (i.e., height) of a Schubert determinantal ideal or ASM ideal | 18,332 | 33,229 | {"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} | 3.265625 | 3 | CC-MAIN-2024-22 | latest | en | 0.33169 |
https://skeptics.stackexchange.com/questions/45370/will-chinas-three-gorges-dam-slow-down-earths-rotation | 1,716,725,705,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058876.64/warc/CC-MAIN-20240526104835-20240526134835-00762.warc.gz | 449,589,645 | 38,410 | # Will China's Three-Gorges Dam slow down Earth's rotation?
Business Insider claims that China's Three-Gorge's Dam will slow down Earth's rotation:
Raising 39 trillion kilograms of water 175 meters above sea level will increase the Earth’s moment of inertia and thus slow its rotation. However, the effect would extremely small. NASA scientists calculated that shift of such as mass would increase the length of day by only 0.06 microseconds and make the Earth only very slightly more round in the middle and flat on the top. It would shift the pole position by about two centimeters (0.8 inch).
Is this true?
• The article isn't saying this is "special". The factors are reservoir volume, height above sea level, and latitude. The mass of the dam is small compare to the mass of the water (so don't compare to mega-polis). A higher-elevation dam like Glen Canyon would have a bigger effect than Three Gorges. There are reservoirs that are much bigger than Three Gorges also. Nov 9, 2019 at 18:52
• I'm a little surprised at the magnitude of the claimed effects, but the basic physics is sound (even if there is an error in the math). Do note that the significant factor is not the mass, per se, but rather the elevation of the mass above the "normal" height of land. "Conservation of momentum" says that elevating the mass will slow the earth's rotation. Nov 9, 2019 at 18:58
• @DanielRHicks As anyone spinning on an office chair while moving the legs in and out can attest to.
– pipe
Nov 9, 2019 at 19:13
• @DavePhD - Per wikipedia's list of reservoirs by volume, the Three Gorges Dam ranks as #27 . Moreover, several of the larger ones are much higher above sea level and are much closer to the equator. There is indeed nothing special about theThree Gorges Dam reservoir in this regard. Nov 10, 2019 at 9:53
• Nov 14, 2019 at 16:38
Yes, based on modelling, the rotation of the Earth was slowed down by 0.06 microseconds per "day".
That is, a day would be made about one seventeen millionth of second longer than it otherwise would be if the dam had not been built.
Business Insider references NASA's Jet Propulsion Laboratory (JPL} - the original link is broken, but the JPL still make the claim in a 2005 press release:
Dr. Richard Gross of NASA's Jet Propulsion Laboratory, Pasadena, Calif., and Dr. Benjamin Fong Chao, of NASA's Goddard Space Flight Center, Greenbelt, Md., said all earthquakes have some affect on Earth's rotation. It's just they are usually barely noticeable.
[...]
To make a comparison about the mass that was shifted as a result of the earthquake, and how it affected the Earth, Chao compares it to the great Three-Gorge reservoir of China. If filled, the gorge would hold 40 cubic kilometers (10 trillion gallons) of water. That shift of mass would increase the length of day by only 0.06 microseconds and make the Earth only very slightly more round in the middle and flat on the top. It would shift the pole position by about two centimeters (0.8 inch).
In 1995, Dr Chao published a paper showing how to model the effects of major reservoirs on the moment of inertia (and the location of the poles):
That paper looked at 88 major reservoirs, not including Three-Gorges Dam - it wasn't opened yet.
In 2002, Dr Chao was a co-author of another paper:
In this paper, they use the same modelling from the 1995 paper to look at the effect of the Three-Gorges Dam.
when filled, the Three‐Gorges Reservoir would cause an overall change in Earth's dynamic oblateness J2 by +3.0 × 10−13, J3 by +2.4 × 10−12, and Earth's rotation by only +0.060 μs in length‐of‐day, but as much as 0.64 milliarcsecond in polar motion excitation toward the direction away from the longitude of the Three‐Gorges.
That a dam would affect the rotation of the Earth is not surprising. As the JPL article explains:
"Any worldly event that involves the movement of mass affects the Earth's rotation, from seasonal weather down to driving a car," Chao said.
• So in 50,000 years we will add another leap second because of this. Nov 10, 2019 at 16:21
The Business Insider article referenced in the opening post was published over nine years ago, and this was in turn based on a then five year old press release from NASA. The Business Insider article briefly indicates that this 0.06 microsecond change in length of day (LOD) was a calculated effect.
The NASA press release is clearer in this regard: It explicitly says that both the 2.68 microsecond change in LOD due to the 2005 Sumatra earthquake and the 0.06 microsecond change due to the filling of the Three Gorges Reservoir are calculated rather than observed effects. The hope in 2005 was that the impulsive change due to the earthquake would eventually be observable. This turned out not to be the case. (Evidence: Lack of a press release from NASA touting that the calculated effect has been observed.) The ability to observe the Earth's orientation and rotation rate in 2005 simply was not good enough to observe even a 2.68 microsecond variation in length of day, let alone a 0.06 microsecond change.
While measurement quality of the Earth orientation parameters (length of day and the direction in which the Earth's rotation axis points) have improved by multiple orders of magnitude since the 1970s, the one sigma uncertainty in length of day has stubbornly remained at about 2 to 5 microseconds for corrected observations since the time of that NASA press release, and has remained at about twice that for recent measurements. (The International Earth Rotation and Reference Systems Service (IERS) updates their observations about a month after the fact.) For example, the one sigma uncertainty for recent measurements is about 6 microseconds for recent measurements per the most recent IERS Bulletin B.
If effects such as earthquakes and dam construction are not observable, why bother? Neither the Business Insider article nor the NASA press release address this rhetorical question. The reason is to make it possible to move changes in the Earth orientation parameters from the "only observable after the fact" column to the "predictable before the fact and verifiable after the fact" column. Uncertainties in and the predictability of the Earth orientation parameters have an increasing effect on commerce (e.g., predicting the orbits of GPS and geosynchronous satellites), government (e.g., spy satellites, various weapons), and science (e.g., microarcsecond radio astronomy).
The two NASA scientists behind that NASA press release are members of one of several groups that contribute to the IERS to improve accuracy and predictability. The ability to predict the effects of earthquakes and reservoirs goes hand-in-hand with the ability to predict the effects of more important contributors to variations in the Earth orientation parameters such as tides, atmospheric pressure, and the amount of snow that falls on Siberia and Canada. | 1,549 | 6,922 | {"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-2024-22 | latest | en | 0.940702 |
http://stackoverflow.com/questions/tagged/functional-programming+matlab | 1,386,173,720,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163035819/warc/CC-MAIN-20131204131715-00091-ip-10-33-133-15.ec2.internal.warc.gz | 228,379,466 | 11,523 | # Tagged Questions
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### side effect gotchas in python/numpy? horror stories and narrow escapes wanted
I am considering moving from Matlab to Python/numpy for data analysis and numerical simulations. I have used Matlab (and SML-NJ) for years, and am very comfortable in the functional environment ...
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### calculate array element persistence algorithm
I have a large array 15x15x2200. THis is merely a collection of 15x15 sparse matrices depicting the links between 15 nodes and how they vary over 2200 time units. I need to calculate for how much time ... | 726 | 3,165 | {"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-2013-48 | latest | en | 0.875714 |
https://economics.fandom.com/wiki/MicroS06-I.5 | 1,721,076,553,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514713.74/warc/CC-MAIN-20240715194155-20240715224155-00738.warc.gz | 198,834,539 | 38,761 | ## Question from Past Microeconomics Qualifying Exam
Spring 2006 - Section I, Question five, George Mason University
T, F, U. State first whether the following statements are true, false or uncertain. Then briefly explain your reasoning in four or five sentences. You may use a graph if it helps clarify your answer.
Negative interest rates are possible but not probable.
False. The real interest rate cannot be negative. A negative nominal interest rate is possible if there is deflation.
IS THIS BACKWARDS? Delete this if not, but please see Zero interest rate policy first for an example. I think negative real would be strange because it implies you value the future more than the present, but negative nominal can't happen because no one would pay a person to borrow their money.
on the other hand, consider Prof. Brian Caplan's negative interest rate plan as well over at EconLog. But if the Fed has never done this, maybe it can't be done?
TRUE: Negative interest rate are possible under a liquidity trap scenario, which happened, I believe during the Hamilton era, when wary investors paid "above par" for government bond, so it is possible, and it did happen before
TRUE: Refere to H&H chapter 14, q.6.a, answer in the back of the book. If you expect a good to be so scarce in the future, you will be willing to pay more for it now, Po = (1+r).P1, however, r cannot be less that -100%, otherwise Po will have to be negative | 320 | 1,439 | {"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 | 0.932514 |
https://www.rhumbarlv.com/is-spread-same-as-yield/ | 1,679,488,255,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00097.warc.gz | 1,064,907,555 | 13,219 | ## Is spread same as yield?
In the simplest terms, the yield spread is the difference in the yield between two bonds. In order to calculate yield spread, subtract the yield of one bond from the yield of the other bond. Spreads are typically expressed in “basis points,” each of which is one-hundredth of a percentage point.
### What is spread on a loan?
Bank spread is the difference between the interest rate that a bank charges a borrower and the interest rate a bank pays a depositor. Also called the net interest spread, the bank spread is a percentage that tells someone how much money the bank earns versus how much it gives out.
What does spread mean in bonds?
The bond spread or yield spread, refers to the difference in the yield on two different bonds or two classes of bonds. Investors use the spread as in indication of the relative pricing or valuation of a bond. The wider the spread between two bonds, or two classes of bonds, the greater the valuation differential.
How do you calculate yield spread?
The calculation for a yield spread is essentially the same as for a bid-ask spread – simply subtract one yield from the other. For example, if the market rate for a five-year CD is 5% and the rate for a one-year CD is 2%, the spread is the difference between them, or 3%.
## What yield spread tells us?
The yield spread is a key metric that bond investors use when gauging the level of expense for a bond or group of bonds. Typically, the higher the risk a bond or asset class carries, the higher its yield spread. When an investment is viewed as low-risk, investors do not require a large yield for tying up their cash.
### How does yield spread work?
What Is the Yield Spread Premium? The yield spread premium (YSP) refers to the fee that a broker receives from a lender for reducing a homebuyer’s upfront costs and increasing the interest rate. It’s equal to a percentage of the buyer’s loan amount and it means that the buyer’s rate will be higher than the par rate.
What is the difference between spread and margin?
As verbs the difference between margin and spread is that margin is to add a to while spread is to stretch out, open out (a material etc) so that it more fully covers a given area of space.
What is a fixed spread loan?
Fixed Spread Loan means a loan whose initial interest rate, prior to any Conversion, is based on the Fixed Spread.
## What is spread risk in bonds?
Spread risk refers to the danger that the interest rate on a loan or bond turns out to be too low relative to an investment with a lower default risk for it to be a good use of funds.
### What is the spread formula?
To calculate the bid-ask spread percentage, simply take the bid-ask spread and divide it by the sale price. For instance, a \$100 stock with a spread of a penny will have a spread percentage of \$0.01 / \$100 = 0.01%, while a \$10 stock with a spread of a dime will have a spread percentage of \$0.10 / \$10 = 1%.
Yield spread is used in order to calculate the yield benefit of two or more similar securities with different maturities. Spread is extensively used between the two & ten years treasuries which displays how much additional yield an investor can get by taking on the added risk of investing in long-term bonds.
mortgage lender
The “yield spread premium,” or YSP as it’s known in the industry, is the fee (commission) paid by the mortgage lender to the broker in exchange for a higher interest rate, or an above market mortgage rate.
## What is a yield spread strategy?
A yield spread strategy is a method of taking advantage of the yield spread of a specific bond . This trading strategy encourages placing a short position on a bond with a low yield, while at the same time placing a long position on a bond with a high yield. A general rule of thumb is that the lower the credit rating of a government or company (issuing the bond) the higher the yield of the bond.
### What is nominal yield spread?
A nominal yield spread is the difference between a Treasury and non-Treasury security with the same maturity . The spread is frequently used in pricing certain types of mortgage-backed securities.
What is a yield curve spread?
A “Yield Curve Spread” is simply the difference in the rates of 2 different maturities. My personal favorite (and the most standard) is the 10-year/2-year spread.
What is a high yield bond spread?
A high-yield bond spread, also known as a credit spread , is the difference in the yield on high-yield bonds and a benchmark bond measure, such as investment-grade or Treasury bonds. High-yield bonds offer higher yields due to default risk. The higher the default risk the higher the interest paid on these bonds. | 1,008 | 4,702 | {"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-2023-14 | latest | en | 0.952289 |
http://www.algebra.com/algebra/homework/equations/Equations.faq?hide_answers=1&beginning=7020 | 1,369,176,806,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368700842908/warc/CC-MAIN-20130516104042-00089-ip-10-60-113-184.ec2.internal.warc.gz | 308,207,899 | 13,023 | # Questions on Algebra: Equations answered by real tutors!
Algebra -> Algebra -> Equations -> Questions on Algebra: Equations answered by real tutors! Log On
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Algebra: Equations Solvers Lessons Answers archive Quiz In Depth
Question 132406: these r my questions i need the answers 4 tomorrow so pls figure them out u gotta figure out the value of "x" 7x=7=5x-11 3x=13=9-5x 4x-8=6x-14 Click here to see answer by checkley71(8403)
Question 132386: Solve the following for x: __x_=_2__ x-3 3 Click here to see answer by checkley71(8403)
Question 132457: The space club is having some posters printed.The printer charges \$250 plus \$2 per poster.How many posters can be printed for \$1000 Click here to see answer by nycsharkman(136)
Question 132461: Pizzazz Publications is having some books printed.The printer charges \$800 plus \$5 per book.How many books can be printed for \$4000 Click here to see answer by stanbon(57290)
Question 132464: Rolex worked 40 hours last week he had \$74 deducted from his earnings for taxes .If he had \$286 left after the deduction how much doe rolex earn per hour? Click here to see answer by nycsharkman(136)
Question 132464: Rolex worked 40 hours last week he had \$74 deducted from his earnings for taxes .If he had \$286 left after the deduction how much doe rolex earn per hour? Click here to see answer by stanbon(57290)
Question 132462: Mr Glocks car broke down on the turnpike.Acme towing charge \$30 plus \$3 per mile to tow the car.If Mr Glock paid \$117 ,how far was the car towed ? Click here to see answer by checkley71(8403)
Question 132446: Zorna weighs 91 lb. Her weight is 6lb more than half on her fathers weight.how much does her father weigh? Click here to see answer by checkley71(8403)
Question 132445: Grandpa Gump is 63 years old.His age is 2 years less than 5 times the age of Billy Gump.How old is Billy? Click here to see answer by TakeATuition.com(57)
Question 132480: COuld someone please tell me if i did this correctly??? -4[86-(25-41)] -4[86-(-16)] -4[86+16] -4[102] am i supposed to multiply here or am I supposed to add? -408 Click here to see answer by jim_thompson5910(28546)
Question 132443: the length of a rectangular field is 75yd.This is 3yd more than twice the width.how wide is the field?? Click here to see answer by checkley71(8403)
Question 132486: Could someone help me solve this using the elimination method???? 5r-6s=13 6r=5s+40 Click here to see answer by checkley71(8403)
Question 132505: A ship cruising on a river can travel the 135 mile distance between two cities in 15 hours when cruising against the current. When cruising with the current, the trip takes 5 fewer hours. Write and solve a system of equations to find the speed of the current and of the ship in still water. Click here to see answer by checkley71(8403)
Question 132505: A ship cruising on a river can travel the 135 mile distance between two cities in 15 hours when cruising against the current. When cruising with the current, the trip takes 5 fewer hours. Write and solve a system of equations to find the speed of the current and of the ship in still water. Click here to see answer by stanbon(57290)
Question 132499: How much pure water must be mixed with 2 liters of a 40% solution of antifreeze to get a 25% anitfreeze solution? Click here to see answer by checkley71(8403)
Question 132499: How much pure water must be mixed with 2 liters of a 40% solution of antifreeze to get a 25% anitfreeze solution? Click here to see answer by stanbon(57290)
Question 132514: two families meet at a park for a picnic. At the end of the day one family travels east at an average speed of 42 mph and the other travels west at an average speed of 50 mph. both families have approximately 160 miles to travel. a)find the time it takes each family to get home b)find the time that will have elapsed when they are 100 miles appart c)find the distance the eastbound family has to travel after the westbound family has arrived home. Click here to see answer by stanbon(57290)
Question 132594: Please help me understand this! I have a test soon and I don`t get how to do this!!! Thank you all sooo much! Here it is... A rectangular piece of sheet metal measures 26in. by 20in. A square measuring 2in. by 2in. is cut out of each corner, and the sides are folded to form a box. What is the volume of the box? Thank you so very much in advance! Click here to see answer by checkley71(8403)
Question 132641: Solve for x using the addition principle. x + 16 = -8 I have to admit that i am at a total loss. When i decided to take online classes i didnt know algebra would be one of them. Please help me. I am too old for this lol. Click here to see answer by stanbon(57290)
Question 132862: Could someone show me how to find the slope and the y-intercept?? Click here to see answer by vleith(2825)
Question 132870: I am still a little confused on this one could someone shoe me how to solve the domain of a function? Click here to see answer by stanbon(57290) | 1,354 | 5,229 | {"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-2013-20 | latest | en | 0.940663 |
https://republicofsouthossetia.org/question/plz-i-will-put-you-as-brainyest-29-m-2-9-2-45-16352844-29/ | 1,632,616,652,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057787.63/warc/CC-MAIN-20210925232725-20210926022725-00593.warc.gz | 503,262,458 | 13,436 | ## PLZ I WILL PUT YOU AS BRAINYEST 29<(m^2+9)/2<45
Question
PLZ I WILL PUT YOU AS BRAINYEST 29<(m^2+9)/2<45
in progress 0
2 weeks 2021-09-12T17:56:29+00:00 1 Answer 0
M=4
Step-by-step explanation:
29-25=4
M to the second = 16
16 + 9 = 25
That’s where the 25 comes from
Using the socratyne theorem this problem is easily solved as you see above.
With the 25, m = 4 | 146 | 374 | {"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} | 4.125 | 4 | CC-MAIN-2021-39 | latest | en | 0.829569 |
https://www.unive.it/data/course/303757/programma | 1,716,676,686,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058858.81/warc/CC-MAIN-20240525222734-20240526012734-00025.warc.gz | 921,884,153 | 13,484 | # MATHEMATICS FOR ECONOMICS
2020/2021
Official course title
MATEMATICA PER L'ECONOMIA
Course code
ET0047 (AF:303757 AR:167701)
Modality
On campus classes
ECTS credits
6
Degree level
Bachelor's Degree Programme
Educational sector code
SECS-S/06
Period
4th Term
Course year
2
Where
VENEZIA
Moodle
Go to Moodle page
The course aims to develop the formal lanugage needed to address and study some central problems in the socio-economic analysis. Students will be facing issues related to multivariate calcolus, dinamical systems and optimization problems.
Due to the ongoing sanitary emergency, some aspects of the programme may change to conform to new instructions.
Expected learning outcomes.
A) KNOWLEDGE AND UNDERSTANDING SKILLS:
a.1) Being able to study and understand issues related to continuity, differentiability and integrability of multivariate functions;
a.2) Ability to set up and solve static optimization problems with or without constraints;
a.3) Understanding the fundamental aspects of a dynamical system.
B) ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
b.1) Analysing advanced processes with multiple variables;
b.2) Formalizing in the language of mathematical programming problems that arise in economics and solving them with the appropriate optimization techniques.
b.3) Understanding how to set up the study of the most common dynamical systems.
C) MAKING JUDGMENTS:
c.1) Discuss problems involving many, interdependent variables.
c.2) Analysing the nature of an optimization problem and identifying its critial aspects.
The course is thought for students of the Laurea in Economia e Commercio with a good understanding of the topics covered in the first year programme in Mathematics. The contents require a good knowledge of basic linear algebra, of calculus in one varaible and of the most common techniques of differentiation and integration.
1. Multivariate Calculus. Vector spaces; linear transformations: functions with many variables; differentiation; derivatives of higher orders; implicit function; multiple integrals.
2. Static Optimization. Problems in mathematical programming; unconstrained optimization; constraints and the Lagrangian function; equality constraints; inequality constraints.
3. Dynamical systems. Difference equations; computing elementary solutions: introduction to dynamical optimization problems.
Sydsaeter, Hammond, Seierstad, e Strom. "Further Mathematics for Economic Analysis". Pearson Education. (2008). Second Edition.
There will be a written exam of at least an hour. The examination method will depend on the instructions provided by the University relative to the sanitary emergency.
The course is based on lectures and the solution of excercises. The teaching method will depend on the instructions provided by the University relative to the sanitary emergency.
Italian | 592 | 2,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2024-22 | latest | en | 0.834956 |
https://arctic-fox.gitlab.io/geode/Geode/Matrix3x3Transforms3DConstructors.html | 1,709,257,687,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474893.90/warc/CC-MAIN-20240229234355-20240301024355-00559.warc.gz | 100,212,131 | 5,668 | # module Geode::Matrix3x3Transforms3DConstructors(T)
## Overview
Transformation that can be performed in three-dimensions with 3x3 matrices.
Multiplying a 3D object by the matrices produced by these methods will apply the operation to the object. The matrix must be on the right-hand-side of the multiplication operation.
``object * matrix``
Matrix multiplication is not commutative, therefore the ordering matters. If it's desired to have the matrix on the left-hand-side, transpose it before multiplying.
``matrix.transpose * object``
To combine multiple operations, multiply the matrices from these methods together.
This module should be extended.
## Defined in:
geode/matrices/transforms3d.cr
## Instance Method Detail
def reflect_x : self #
Creates a 3D reflecting matrix.
Multiplying a 3D object by this matrix will reflect it along the x-axis.
``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_x
vector * matrix # => (-1, 2, 3)``````
def reflect_y : self #
Creates a 3D reflective matrix.
Multiplying a 3D object by this matrix will reflect it along the y-axis.
``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_y
vector * matrix # => (1, -2, 3)``````
def reflect_z : self #
Creates a 3D reflecting matrix.
Multiplying a 3D object by this matrix will reflect it along the z-axis.
``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_z
vector * matrix # => (1, 2, -3)``````
def rotate(angle : Number | Angle, axis : CommonVector(T, 3)) : self #
Creates a 3D rotation matrix.
Multiplying a 3D object by this matrix will rotate it the specified amount. The angle must be a `Number` in radians or an `Angle`. The object is rotated around the specified axis.
``````axis = Vector3[1, 1, 1].normalize
vector = Vector3[1, 2, 3]
matrix = Matrix3(Float64).rotate(45.degrees, axis)
vector * matrix # => (1.701141509, 1.183503419, 3.115355072)``````
def rotate_x(angle : Number | Angle) : self #
Creates a 3D rotation matrix.
Multiplying a 3D object by this matrix will rotate it around the x-axis. The angle must be a `Number` in radians or an `Angle`.
``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_x(45.degrees)
vector * matrix # => (1.0, 0.0, 1.414213562)``````
def rotate_y(angle : Number | Angle) : self #
Creates a 3D rotation matrix.
Multiplying a 3D object by this matrix will rotate it around the y-axis. The angle must be a `Number` in radians or an `Angle`.
``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_y(45.degrees)
vector * matrix # => (1.414213562, 1.0, 0.0)``````
def rotate_z(angle : Number | Angle) : self #
Creates a 3D rotation matrix.
Multiplying a 3D object by this matrix will rotate it around the z-axis. The angle must be a `Number` in radians or an `Angle`.
``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_z(45.degrees)
vector * matrix # => (0.0, 1.414213562, 1.0)``````
def scale(x : T, y : T, z : T) : self #
Creates a 3D scaling matrix.
Non-uniformly scales an object (squash and stretch). Multiplying a 3D object by this matrix will scale it by x amount along the x-axis and y amount along the y-axis. Values for x and y smaller than 1 will shrink it. Values larger than 1 will enlarge it. Negative values will flip it.
``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Float64).scale(1.5, 2, 2.5)
vector * matrix # => (3.0, 6.0, 9.0)``````
def scale(amount : T) : self #
Creates a 3D scaling matrix.
Uniformly scales an object. Multiplying a 3D object by this matrix will scale it by amount. Values for amount smaller than 1 will shrink it. Values larger than 1 will enlarge it. Negative values will flip it.
``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).scale(2)
vector * matrix # => (4, 6, 8)``````
def shear_x(y : T, z : T) : self #
Creates a 3D shearing matrix.
Multiplying a 3D object by this matrix will shear it along the y and z-axis based on the x-axis. For each unit along the x-axis, the y value will be adjusted by y and the z value will be adjusted by z.
``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_x(2, 3)
vector * matrix # => (2, 7, 10)``````
def shear_y(x : T, z : T) : self #
Creates a 3D shearing matrix.
Multiplying a 3D object by this matrix will shear it along the x and z-axis based on the y-axis. For each unit along the y-axis, the x value will be adjusted by x and the z value will be adjusted by z.
``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_y(2, 3)
vector * matrix # => (8, 3, 13)``````
def shear_z(x : T, y : T) : self #
Creates a 3D shearing matrix.
Multiplying a 3D object by this matrix will shear it along the x and y-axis based on the z-axis. For each unit along the z-axis, the x value will be adjusted by x and the y value will be adjusted by y.
``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_z(2, 3)
vector * matrix # => (10, 15, 4)`````` | 1,493 | 4,915 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-10 | latest | en | 0.740411 |
http://thefreeanswer.com/question/at-45-latitude-the-gravitational-acceleration-as-a-function-of-elevation-z-above-sea-level-is-given-by-g-a%E2%80%92bz-where-a-9-807-ms2-and-b-3-32-x-10-6-s-2-determine-the-height-ab/ | 1,516,729,003,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084892059.90/warc/CC-MAIN-20180123171440-20180123191440-00158.warc.gz | 335,210,284 | 20,641 | # At 45° latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a‒bz, where a =9.807 m/s2 and b= 3.32 × 10-6 s-2. Determine the height above sea level where the weight of an object will decrease by 0.5 percent.
ch1-14. At 45° latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a‒bz, where a =9.807 m/s2 and b= 3.32 × 10-6 s-2. Determine the height above sea level where the weight of an object will decrease by 0.5 percent. | 155 | 522 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2018-05 | latest | en | 0.784231 |
http://www.rexwordpuzzle.blogspot.com/2008/06/monday-jun-9-2008-paula-gamache-beloved.html | 1,462,251,420,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860118790.25/warc/CC-MAIN-20160428161518-00186-ip-10-239-7-51.ec2.internal.warc.gz | 783,563,545 | 33,005 | ## Monday, June 9, 2008
Relative difficulty: Medium
THEME: "IT'S A TRAP!" (42D: Warning cry ... or a hint to the beginnings of the answers to the five starred clues)
Hey, look, it's a better version of last Thursday's puzzle, only this one's where it belongs: on a Monday. First words of all the (otherwise unrelated) theme answer do ... something. Here, they describe different kinds of TRAPs. My favorite is BOOBY, which, if you know me, comes as no surprise. I did this stupid thing I'm never going to do again, where I tried to solve the puzzle by doing all the Acrosses first, and then filling in whatever space I had left via the Downs. Inefficient! And in a puzzle as well constructed as this one, not as easy as I would have imagined. I had only a little more than HALF (1A: 50 percent) of the Acrosses filled in on first pass, including None of the theme answers (except BOOBY PRIZE - got that instantly). Without crosses, I put DDE in the wrong decade and ended up with HHH as his rival (38A: D.D.E.'s political rival => AES). Without crosses, I had no idea where a horseshoe was supposed to go (16A: Where a horseshoe goes => HOOF). Without crosses, I could enter only the ST in ST CROIX (21A: One of the U.S. Virgin Islands). Then again, even with several crosses in place, I wrote in CLOSES for CLASPS at 22D: Necklace fasteners. So, sometimes, crosses shmosses.
• 17A: *Sightseer's guide (tourist map) - I have balked at this answer before, I feel, and I did it again today. I never think of tourists as having their own category of map. You have a map or you don't. I know I'm wrong about this, but harumph nonetheless.
• 4D: *Hose company hookup (fire plug)
• 30A: *Creation made with a bucket and shovel (sand castle)
• 47A: *One who puts the pedal to the metal (speed demon)
• 63A: *The worst player wins it (booby prize)
This is a kind of textbook Monday puzzle - easy, but with a minimum of ugh fill and some genuinely cute and engaging fill.
My favorites:
• SANGRIA (39A: Spanish wine beverage)
• FIREPLUG
• UPTICKS (15D: Slight improvements in business activity)
• TATLER (58A: British society magazine)
• ST CROIX
There are also some coincidental pairings that I liked a whole lot, including
• MOSES CRAMP (27D: Grandma _____, American folk artist + 28D: Muscle malady)
• AFRO PEAS (68A: Big do + 71A: "Split" soup ingredients), and
• SHAG HOMO (54D: Retro cut + 55D: _____ sapiens).
That last one is particularly choice. It's nice also to see the puzzle championing the cause of Diversity by including not just Yale's founder, ELIHU (14A: Yale of Yale University), but the founder of Cornell as well (60D: Cornell of Cornell University). I feel like I'm seeing Dr. King's dream realized right in front of my eyes ... a world where my children will be judged not by the quality of the Ivy League school they went to, but by the quality of the first name of the guy who founded their Ivy League School.
Remainder:
• 34D: Beloved of Elizabeth I (Essex) - pretty Britishy puzzle, what with TATLER in there and all
• 57D: Inside info (poop) - oh my wife did not like that one. Had never heard of it, in fact. But then again she also struggled a bit with KARATE (24D: Sport in which belts are awarded) ... and she is a Green Belt.
• 67A: Longtime Yankees skipper (Torre) - now the Dodgers skipper. I actually bought Yankees merchandise yesterday, if crossword puzzle books count as merchandise. Brendan Emmett Quigley has both a Yankees and a Red Sox crossword puzzle book out right now, and I bought them both. I haven't done any of the puzzles yet, but if they are even in the ballpark (!) of his normal standards, they should be good.
Signed, Rex Parker, King of CrossWorld
treedweller
I enjoyed this, but didn't get a great time. I kept getting bogged down in the theme answers, trying to get the concept instead of just filling in letters wherever there was a gimme. I didn't end up getting it until I was almost done.
My last letter was the 'M' in MAJA--never heard of it, and I had to come up at it from below. Penultimate fill was 'R' in MESSRS, which I suspected early on but wasn't sure how to abbrev.
Michael
I'm surprised you didn't call out the crossing of the woord BOOBY with POOP. The 12-year-old in me loved this.
ArtLvr
This was my fastest yet -- though I don't usually pay attention to the time... Couldn't wait to see the comments on POOP, after last week's run. Hope it doesn't lead to a CRAMP.
With the stock market rocky, it was encouraging to consider UPTICKS counterbalancing SHARKS, MONTE, crazy like A FOX and SPEED DEMONs.. Well-timed theme, since the upticks can all too often lead one to "waul" IT'S A TRAP!
∑;(
jordanboston
HOMOs, BOOBYs, and POOPs, Oh My! Quite 'SAUCY' for a Monday morning.
xyzzy
I'm always fascinated at others' comments about how easy/hard these are. This was the easiest time I've ever had (and I'm a rookie who's only been doing these for a few months - trying to put off alzheimers, heh heh.)
Anyway, this one just fell into place for me, and I usually have to cheat (Google, RP's blog, etc.) to complete these. Did neither today. Go figure.
xyzzy
I'm always fascinated at others' comments about how easy/hard these are. This was the easiest time I've ever had (and I'm a rookie who's only been doing these for a few months - trying to put off alzheimers, heh heh.)
Anyway, this one just fell into place for me, and I usually have to cheat (Google, RP's blog, etc.) to complete these. Did neither today. Go figure.
Ramsey
Zach M.
For some reason I kept reading "Muscle malady" as "Musical Malady", and when I had -RAMP I stared at it for a bit trying to think if maybe it was some Italian word meaning that you were ramping up too much or something.
@xyzzy
did you forget about the first posting? Rx: do more puzzles.
Perfect Monday puzzle.
Bill from NJ
Fun puzzle with no real problems. I liked the incidental pairings
ELIHU EZRA
SHAG AFRO
ESSEX TATLER
MAJA SANGRIA
@jordanboston is on the same wavelength I am...I'm calling this the Beavis and Butthead puzzle, within the clues or answers are the following: boob, homo, naked, virgin, and gay. "He said ______, Hee Hee". Sorry if I ruffled the feathers of any PC types - but not really.
Orange
Rex, I could swear you had sworn not to buy that Yankees crossword book, and to tout only the Red Sox one. Next thing you know, you'll be giving grudging praise to A-Rod.
John in CT
Had no real problems with today's puzzle. I came to the site expecting an "easy" rating, and was somewhat suprised to see a "medium." I was able to get all my unknowns from crosses. Have a great day all.
Crosscan
I put "IT'S A WRAP" and wondered why you had to be warned. Was this a message from the Anti-Saran League?
Not a good omen for the rest of the week.
Crosscan
I put "IT'S A WRAP" and wondered why you had to be warned. Was this a message from the Anti-Saran League?
Not a good omen for the rest of the week.
jls
first time around i entered "notnow" for "notyet" and "upturns" for "upticks"... both easily corrected in this everso gracefully constructed, smile-inducing monday puzzle.
greetings from the baked apple!
;-)
janie
emjo
sassy!
miriam b
Fun puzzle, but PARKA, FIREPLUG and STYX made me feel the heat. The MAJA was probably glad to be unclothed today.
Heading for CA early tomorrow before the temperature rises in earnest. Forecasts for our destinations (Moorpark. Laguna Niguel and Dana Point) are for temps in the 70s for the next week.
PuzzleGirl
This was a good puzzle for me -- after getting beat up pretty bad the last two days. I actually entered RMN for DDE rival at first. Also had ST KITTS for ST CROIX. I don't mind TOURIST MAP -- I think of those maps they give you at a hotel desk, with sites and restaurants labeled. The one I've seen in puzzles a couple times that I don't like is AREA MAP.
"Hand me that area map."
"Which one?"
"The one of the area."
"Which area?"
"The area we're trying to get to."
"The one of the whole big area with separate pages for the smaller areas? Or the one with only the area where we're going with an inset showing an enlarged version of a popular area?"
"Just gimme the damn map."
Doc John
I, too, was surprised at the medium rating. Expected it to be easy-medium at worst. My only real bump was that I had Berra in place of TORRE (thanks to only having ORE and BRR at that point).
All in all, a nice puzzle with some fun fill. Fave clue/answer: 7D. Beam in a bar? = JIM.
Can you all hear Princess Leia in Episode VI (I think) yelling, "It's a trap!"? (Or am I Marco POLOing again?)
Joon
desultory observations:
perfect monday puzzle.
STCROIX is the home of tim duncan, who recently appeared in a sunday theme (disguised as the yoyoing squad TEAMDUNCAN).
SPEEDDEMON is a great theme entry. FIREPLUG stoned me for a while--i kept wanting it to be something related to the other kind of hose company, but nothing about nylons or stockings would fit.
i like SANGRIA as much as the next guy, but i feel like i've been seeing it in the grid a lot recently.
i like the symmetrical placement of TAROT and MONTE.
ANTIC looks very odd in the singular.
unlike the beavises of the crossworld, i found this puzzle to be very high-brow for a monday. ESSEX, TATLER, MAJA, MESSRS, POLO, COSI fan tutte, and the two ivy guys.
it's freaking hot out.
Joon
doc john, you sure about that? i'm thinking it was admiral ackbar.
PhillySolver
It is too hot to think about the puzzle, but I do recall it was a great Monday effort.
Half time and France has not scored!
Karen
We have tourist maps in our corner also, given out at local businesses, that highlight certain establishments and vendors. So I'm cool with that.
I did all the downs, then all the acrosses, and had a medium Monday time. But I avoided staring at the theme answers.
Doc John
joon, Admiral Ackbar (I never knew that was his name!) says the line, too, but the one that I'm remembering is yelled out by Leia as, I think, Han and Luke are rushing somewhere as she's being dragged away by some guards.
Maybe my memory isn't so good, turns out the scene I'm thinking of was in Episode V and not VI.
Shamik
BRR....58 degrees at 11:23 a.m. and going all the way up to 68 in NW Colorado! Somehow there should be more "r's" in BRR when you're blogging about being cold vs. crossword fill. Still, I opened the windows to get some air through here...but I'll need my jacket! ;-P
Rex...I guess doing all the Across first makes it a Medium vs. Easy.
jubjub
Hey Rex, is the Superman picture you posted from a real comic? What is in Superman's thought bubble? Is it censored for decency?
As I did not know the relevant definition of POOP, I got to look up poop in the dictionary today. That was fun. In case anyone is wondering how to use this definition of poop in a sentence:
"Send a reporter to get the real poop on that accident."
"She gave me all the poop on the company party. "
Also, if anyone was wondering the derivation of the word for it's most common meaning:
"Origin: 1735–45; earlier “to break wind,” prob. the same word as ME powpen, popen to sound or blow a horn ..."
Here are some weird Goya illustrations I was looking at last week:
http://www.fulltable.com/VTS/g/goya/goya.htm
Goya's cool :).
In Re BOOBY TRAPs:
"Pinchers of Power! Pinchers of Power! You guys, I be saved by my Pinchers of Power!"
Shamik
oh? it isn't "I MISS the rains down in Africa?"
jubjub
oh, also, here is a link to the Monty Hall problem. You are all probably aware of it, but just in case, it is a great way to waste some time. Oh, and blow your mind:
http://en.wikipedia.org/wiki/Monty_Hall_problem
(Tangentially related to three card MONTE.)
dk
Just a word from the x-word puzzle decency council:
ITSATRAP! The constant puzzle references to drugs (SPEED,SCAG), body parts (BOOBY), alcohol (JIM Beam, SANGRIA) and alluring phrases like NOTYET suggest we will be vacatioing on the river STYX rather than the STCROIX.
ENOLA was in one of the very first x-word puzzles I completed so it always makes me smile when I see it.
I think this was PERT puzzle and a great start to the week. Rex, I did the puzzle begining with all the downs and then going back for the accrosses. Seemed to be a speedy day for me.
@doc john, I ALSO remember the Princess Leia ITSATRAP.
Those of you on the right coast: Stay cool!
andrea carla michaels
what's with all the weather reports?
It's bad enough to hear how hot it is, I guess, Back East, but to have to hear what the weather is GOING to be like in CA?!!
(Poor Rex! Your dream of elevated puzzle discussion gone the way of the Weather Channel!)
That said,
I like that the two place names STCROIX and STYX started and ended with S-X...seems like a theme waiting to happen.
Nice, Paula!
Bill from NJ
I initially had ITSAWRAP because it was more in the language than ITSATRAP but I knew TATLER and changed it at once
chefbea1
very easy puzzle today!!
Enjoyed my mint juleps the other day made with Jim Beam. Today I will drink Sangria and try to stay cool. The thermometer on my patio says 100 degrees right now. Don't think I will make split pea soup for dinner.
Fergus
Had a good laugh, Rex, at your wry rephrasing of Dr. King's vision. another good pair of neighbors was TAROT-LEERY (hyphen intended.)
I also think this was a pretty snappy Monday puzzle -- even better than last Thursday's. Didn't mind that the TRAPS all had stand-alone antecedents, but I do like it better if they can be buried.
Well, it just hit 90 degrees here (weather guy predicted low 70s) so it's time to saunter down to the beach
jannieb
Wish all Monday puzzles were this engaging and well done!
Kim
Average Monday Puzzle for me but agree it was well constructed. I wanted SPEED RACER instead of SPEED DEMON. Don't know why as I certainly did not like the series and haven't seen the movie.
I penned in EROS for "Cupid" insted of AMOR and I never knew Eli Yales full name was ELIHU ("Eli who?). Guess you can learn something even from a Monday puzzle - so thank you Paula Gamache. And Rex the comments on Ivy League diversity were so acidicly ironic the fumes made my eyes water - good stuff!
© Free Blogger Templates Columnus by Ourblogtemplates.com 2008 | 3,710 | 14,282 | {"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-2016-18 | latest | en | 0.967568 |
https://nd.psychstat.org/lab/em_for_mediation_for_monents | 1,675,898,916,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500983.76/warc/CC-MAIN-20230208222635-20230209012635-00446.warc.gz | 428,911,068 | 7,221 | ### Site Tools
lab:em_for_mediation_for_monents
## EM for the estimate the covariance matrix
## function to calculate the parameters
par.est<-function(pM, pS){
sX2<-pS[1,1]
sM2<-pS[2,2]
sY2<-pS[3,3]
sXM<-pS[1,2]
sXY<-pS[1,3]
sMY<-pS[2,3]
mX <-pM[1]
mM <-pM[2]
mY <-pM[3]
pa<-sXM/sX2
pb<-(sMY*sX2-sXM*sXY)/(sX2*sM2-sXM^2)
pc<-(sXY*sM2-sXM*sMY)/(sX2*sM2-sXM^2)
ps1<-sX2
ps2<-sM2-sXM^2/sX2
ps3<-(sX2*sM2*sY2-sX2*sMY^2-sM2*sXY^2-sY2*sXM^2+2*sXM*sXY*sMY)/(sX2*sM2-sXM^2)
pm1<-mX
pm2<-mM - pa*mX
pm3<-mY - pb*mM - pc*mX
return(c(pm2,pm3,pa,pb,pc,ps2,ps3))
}
## the M-step
M_step<-function(sM, sS, N){
## sM: first moment vector
## sS: second moment
pM <- sM/N
pS <- sS/(N-1) - N/(N-1)*pM%*%t(pM)
return(list(pM=pM, pS=pS))
}
## the E-step
E_step<-function(dset, pM, pS){
X<-dset[,1]
M<-dset[,2]
Y<-dset[,3]
n<-dim(dset)[1]
sX2<-rep(0,n)
sM2<-rep(0,n)
sY2<-rep(0,n)
sXM<-rep(0,n)
sXY<-rep(0,n)
sMY<-rep(0,n)
mX <-rep(0,n)
mM <-rep(0,n)
mY <-rep(0,n)
for (i in 1:n){
## process missing data in X
if (!is.na(X[i])){
## X is available
if (!is.na(M[i])){
## M is available
if (!is.na(Y[i])){
## X, M, Y is available
mX[i]<-X[i]
mM[i]<-M[i]
mY[i]<-Y[i]
sX2[i]<-X[i]^2
sY2[i]<-Y[i]^2
sM2[i]<-M[i]^2
sXM[i]<-X[i]*M[i]
sXY[i]<-X[i]*Y[i]
sMY[i]<-M[i]*Y[i]
}else{
## X & M observed but Y is missing
mX[i]<-X[i]
mM[i]<-M[i]
mY[i]<-pM[3] + pS[3,1:2]%*%solve(pS[1:2,1:2])%*%(c(X[i]-pM[1], M[i]-pM[2]))
sX2[i]<-mX[i]*mX[i]
sM2[i]<-mM[i]*mM[i]
sY2[i]<-mY[i]*mY[i]+pS[3,3]-pS[3,1:2]%*%solve(pS[1:2,1:2])%*%(pS[1:2,3])
sXM[i]<-mX[i]*mM[i]
sXY[i]<-mX[i]*mY[i]
sMY[i]<-mM[i]*mY[i]
}
}else{
## M is missing
if (!is.na(Y[i])){
## X, Y is available but M is missing
mX[i]<-X[i]
mM[i]<-pM[2] + pS[2,c(1,3)]%*%solve(pS[c(1,3),c(1,3)])%*%(c(X[i]-pM[1],Y[i]-pM[3]))
mY[i]<-Y[i]
sX2[i]<-mX[i]*mX[i]
sM2[i]<-mM[i]*mM[i]+pS[2,2]-pS[2,c(1,3)]%*%solve(pS[c(1,3),c(1,3)])%*%(pS[c(1,3),2])
sY2[i]<-mY[i]*mY[i]
sXM[i]<-mX[i]*mM[i]
sXY[i]<-mX[i]*mY[i]
sMY[i]<-mM[i]*mY[i]
}else{
## X is observed but M and Y are missing
mX[i]<-X[i]
mM[i]<-pM[2] + pS[1,2]/pS[1,1]*(X[i]-pM[1])
mY[i]<-pM[3] + pS[1,3]/pS[1,1]*(X[i]-pM[1])
sX2[i]<-mX[i]*mX[i]
sM2[i]<-mM[i]*mM[i] + pS[2,2]-pS[1,2]^2/pS[1,1]
sY2[i]<-mY[i]*mY[i] + pS[3,3]-pS[1,3]^2/pS[1,1]
sXM[i]<-mX[i]*mM[i]
sXY[i]<-mX[i]*mY[i]
sMY[i]<-mM[i]*mY[i] + pS[2,3]-pS[1,2]*pS[1,3]/pS[1,1]
}
}
}else{
## X is missing
if (!is.na(M[i])){
## M is available
if (!is.na(Y[i])){
## X is missing, M & Y are available
mX[i]<-pM[1] + pS[1,2:3]%*%solve(pS[2:3,2:3])%*%(c(M[i]-pM[2], Y[i]-pM[3]))
mM[i]<-M[i]
mY[i]<-Y[i]
sX2[i]<-mX[i]*mX[i]+pS[1,1]-pS[1,2:3]%*%solve(pS[2:3,2:3])%*%pS[2:3,1]
sM2[i]<-mM[i]*mM[i]
sY2[i]<-mY[i]*mY[i]
sXM[i]<-mX[i]*mM[i]
sXY[i]<-mX[i]*mY[i]
sMY[i]<-mM[i]*mY[i]
}else{
## Y and X is missing but M is available
mX[i]<-pM[1]+pS[1,2]/pS[2,2]*(M[i]-pM[2])
mM[i]<-M[i]
mY[i]<-pM[3]+pS[2,3]/pS[2,2]*(M[i]-pM[2])
sX2[i]<-mX[i]*mX[i]+pS[1,1]-pS[1,2]^2/pS[2,2]
sM2[i]<-mM[i]*mM[i]
sY2[i]<-mY[i]*mY[i]+pS[3,3]-pS[2,3]^2/pS[2,2]
sXM[i]<-mX[i]*mM[i]
sXY[i]<-mX[i]*mY[i]+pS[1,3]-pS[1,2]*pS[2,3]/pS[2,2]
sMY[i]<-mM[i]*mY[i]
}
}else{
## X, M is missing
mX[i]<-pM[1]+pS[1,3]/pS[3,3]*(Y[i]-pM[3])
mM[i]<-pM[2]+pS[2,3]/pS[3,3]*(Y[i]-pM[3])
mY[i]<-Y[i]
sX2[i]<-mX[i]*mX[i]+pS[1,1]-pS[1,3]^2/pS[3,3]
sM2[i]<-mM[i]*mM[i]+pS[2,2]-pS[2,3]^2/pS[3,3]
sY2[i]<-mY[i]*mY[i]
sXM[i]<-mX[i]*mM[i]+pS[1,2]-pS[1,3]*pS[2,3]/pS[3,3]
sXY[i]<-mX[i]*mY[i]
sMY[i]<-mM[i]*mY[i]
}
}
}
sM<-c(sum(mX),sum(mM),sum(mY))
sS<-array(c( sum(sX2),sum(sXM),sum(sXY),sum(sXM),sum(sM2),sum(sMY),sum(sXY),sum(sMY),sum(sY2)),dim=c(3,3))
return(list(sM=sM, sS=sS))
}
## Matrice to store the results
R<-100
pairdel<-array(NA,dim=c(R,7))
em<-array(NA,dim=c(R,7))
em2<-array(NA,dim=c(R,7))
em3<-array(NA,dim=c(R,7))
true<-array(NA,dim=c(R,7))
listdel<-array(NA,dim=c(R,7))
ml<-array(NA,dim=c(R,7))
N<-100
for (j in 1:R){
## dset generation
X<-rnorm(N)
M<-.5+.5*X + sqrt(.1)*rnorm(N)
Y<-1+1*M + .1*X + sqrt(.3)*rnorm(N)
dset<-cbind(X,M,Y)
sampM<-c(sum(X),sum(M),sum(Y))
sampS<-array(c(sum(X^2),sum(X*M),sum(X*Y),sum(X*M),sum(M^2),sum(M*Y),sum(X*Y),sum(M*Y),sum(Y^2)),c(3,3))
## results from complete data analysis
para<-M_step(sampM, sampS, N)
true[j,]<-par.est(para$pM, para$pS)
## For the missing data analysis
for (i in 1:N){
# if (runif(1)<.1) X[i]<-NA
if (runif(1)<.1) M[i]<-NA
if (runif(1)<.1) Y[i]<-NA
}
dset<-cbind(X,M,Y)
e<-1
while (e>.0000001){
E.res<-E_step(dset,para$pM, para$pS)
M.res<-M_step(E.res$sM, E.res$sS, N)
e<-sum(abs(M.res$pM-para$pM))+sum(abs(M.res$pS-para$pS))
para<-M.res
}
em[j,]<-par.est(para$pM,para$pS)
temp1 <- prelim.norm(dset)
temp2 <- em.norm(temp1)
temp3 <- getparam.norm(temp1,temp2)
em3[j,]<-par.est(temp3$mu, temp3$sigma)
#test<-prelim.norm(dset)
#res<-em.norm(test)
#getparam.norm(test,res)
## ML method
## save the data
write.table(dset, "data.dat", na='.',row.names=F, col.names=F)
system('c:\\programs\\mplus\\mplus.exe mle.inp',show.output.on.console = F)
tempres<-scan('est.txt',quiet=T)
ml[j,]<-tempres[c(2,1,6,4,5,7,8)]
## the list wise delete method
isna<-is.na(dset)
sumisna<-apply(isna,1,sum)
listdata<-dset[sumisna==0,]
sampN[j]<-dim(listdata)[1]
temp<-cov(listdata,use='complete.obs')
par<-par.est(c(mean(listdata[,1]),mean(listdata[,2]),mean(listdata[,3])),temp)
listdel[j,]<-par
## pairwise delete
temp<-cov(dset,use='pairwise.complete.obs')
par<-par.est(c(mean(dset[,1],na.rm=T),mean(dset[,2],na.rm=T),mean(dset[,3],na.rm=T)),temp)
pairdel[j,]<-par
## EM for path model
temp<-cov(dset,use='pairwise.complete.obs')
par<-est(c(temp[1,1],temp[2,2],temp[3,3],temp[1,2],temp[1,3],temp[2,3],mean(dset[,1],na.rm=T),mean(dset[,2],na.rm=T),mean(dset[,3],na.rm=T)))
e<-1
while (e>.00001){
SS<-EMe(dset, par)
para<-est(SS)
e<-sum(abs(para-par))
par<-para
# print(par,digits=10)
}
em2[j,]<-para[c(8,9,1,2,3,5,6)]
}
apply(true,2,mean)
apply(pairdel,2,mean)
apply(em,2,mean)
apply(em2,2,mean)
apply(em3,2,mean)
apply(listdel,2,mean)
apply(ml,2,mean) | 3,078 | 5,889 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2023-06 | longest | en | 0.305637 |
https://blog.finxter.com/5-best-ways-to-split-a-tuple-into-groups-of-n-in-python/ | 1,721,936,866,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763861452.88/warc/CC-MAIN-20240725175545-20240725205545-00502.warc.gz | 113,102,885 | 18,099 | # 5 Best Ways to Split a Tuple into Groups of N in Python
π‘ Problem Formulation: Often while working with tuples in Python, developers face a scenario where a tuple needs to be divided into smaller tuples, each containing a specific number of elements (n). For instance, given a tuple like `(1, 2, 3, 4, 5, 6)`, the goal is to split it into groups of 2, resulting in `((1, 2), (3, 4), (5, 6))`.
## Method 1: Using a for loop and slicing
This method involves iterating over the length of the tuple, stepping by the group size `n`, and creating smaller tuples via slicing. The function defined can be adapted to any tuple size and group length.
Here’s an example:
```def split_tuple(tuple_to_split, n):
return tuple(tuple_to_split[i:i + n] for i in range(0, len(tuple_to_split), n))
example_tuple = (1, 2, 3, 4, 5, 6)
result = split_tuple(example_tuple, 2)
print(result)```
Output:
`((1, 2), (3, 4), (5, 6))`
The code defines a function `split_tuple` which takes a tuple and an integer `n`. It returns a new tuple, where each element is a tuple containing `n` values from the original tuple, using slicing to create each group.
## Method 2: Using itertools.islice()
The itertools.islice() function is perfect for creating an iterator that returns selected elements from the input tuple. When paired with tuple comprehension, it creates a neat solution for splitting the tuple into uniform groups of n items.
Here’s an example:
```from itertools import islice
def split_tuple_using_islice(tuple_to_split, n):
iterators = [iter(tuple_to_split)] * n
return tuple(tuple(islice(it, n)) for it in iterators)
example_tuple = (7, 8, 9, 10, 11, 12)
result = split_tuple_using_islice(example_tuple, 2)
print(result)```
Output:
`((7, 8), (9, 10), (11, 12))`
This approach takes the tuple to split and group size `n`, then creates a list of iterators of the same original tuple repeated `n` times. Using the `islice()` method, it slices through the tuple creating the groups of n.
## Method 3: Using List Comprehension
Although we start with a tuple, temporarily converting it to a list within a list comprehension is a quick way to implement the split. This leverages Python’s dynamic typing and the convenience of the list comprehension syntax.
Here’s an example:
```def split_tuple_with_list(tuple_to_split, n):
return tuple(tuple_to_split[i:i + n] for i in range(0, len(tuple_to_split), n))
example_tuple = ('a', 'b', 'c', 'd', 'e', 'f')
result = split_tuple_with_list(example_tuple, 3)
print(result)```
Output:
`(('a', 'b', 'c'), ('d', 'e', 'f'))`
This code snippet uses list comprehension to iterate through a range of indices, creating a new tuple from slices of the original tuple. These slices match the desired group size `n`.
## Method 4: Using the zip function with ‘*’ operator
Python’s built-in `zip` function can be applied creatively with the unpacking operator to transpose the tuple’s structure, which effectively groups the elements into the desired tuple size when the input tuple length is a multiple of `n`.
Here’s an example:
```def split_tuple_with_zip(tuple_to_split, n):
return tuple(zip(*[iter(tuple_to_split)]*n))
example_tuple = (10, 20, 30, 40, 50, 60)
result = split_tuple_with_zip(example_tuple, 2)
print(result)```
Output:
`((10, 20), (30, 40), (50, 60))`
In this snippet, an iterator is created from the tuple which is then repeated `n` times. The zip function then groups the elements into tuples based on their positions in these identical iterators.
## Bonus One-Liner Method 5: Using Generator Expression
A generator expression provides an elegant and efficient one-liner to split the tuple into groups of n. It’s especially useful when you only need to iterate over the groups once.
Here’s an example:
```example_tuple = (0, 9, 8, 7, 6, 5)
result = tuple(example_tuple[i:i + 3] for i in range(0, len(example_tuple), 3))
print(result)```
Output:
`((0, 9, 8), (7, 6, 5))`
This efficient one-liner uses a generator expression to produce the same result as the methods above, returning a new tuple consisting of smaller tuples, each containing 3 elements from the original tuple.
## Summary/Discussion
• Method 1: Using a for loop and slicing. Strength: Simple to understand. Weakness: Not the most Pythonic solution.
• Method 2: Using itertools.islice(). Strength: Utilizes efficient iterator protocols. Weakness: Might be less readable for those unfamiliar with itertools.
• Method 3: Using List Comprehension. Strength: Easy to comprehend, pythonic. Weakness: Involves implicit type conversion.
• Method 4: Using the zip function with ‘*’ operator. Strength: Elegant and concise. Weakness: Works only when tuple length is a multiple of n.
• Bonus Method 5: Using Generator Expression. Strength: Concise one-liner and memory-efficient. Weakness: Less intuitive for those unfamiliar with generator expressions. | 1,234 | 4,878 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2024-30 | latest | en | 0.74665 |
https://www.easyworksheet.com/states/TX/Grade8MathWorksheets.shtml | 1,553,546,227,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912204300.90/warc/CC-MAIN-20190325194225-20190325220225-00211.warc.gz | 735,395,569 | 13,121 | Texas TEKS Math 8
Create worksheets, tests, and quizzes for Texas TEKS Math 8.
User Name: Password: Worksheet Title: Practice Problems Test Quiz SOL Review Midterm Final Exam or fill in: To keep server load down, there is a maximum of 100 questions per worksheet. Create Answer Sheet (Pop-Up Window) Show how to solve it! (Pop-Up Window) Mix up the problems. (Good for tests) Multiple Choice (Good for Standardized Test practice) Move Instructions into Problems Interactive Online Test (students only! Limited to 20 questions at a time) Answer Blanks: Boxes Blanks Percent of problems with fractional coefficients 0 5 10 20 30 40 50 60 70 80 90 100 (Only where applicable) Start Numbering with: (Whole Numbers only) Save this EasyFramework (Teacher Plus+ Account Only!) as a HomeworkTestQuizOther Condense - Leave no room for student work Select the number of each type of objective:(Selecting Random will randomly generate all subtypes)Click on any title to see the free sample worksheet. (only the first few samples are free) (Random) (2.A) Number and operations. Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; a. Classifying Numbers (Natural, Whole, Integer, Irrational, Rational, Real) b. Illustrating the Density of Rational Numbers (Random) (2.B) Number and operations. Approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; (Random) (2.C) Number and operations. Convert between standard decimal notation and scientific notation; (Random) (2.D) Number and operations. Order a set of real numbers arising from mathematical and real-world contexts. (Random) (3.A) Proportionality. Generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation; (Random) (3.B) Proportionality. Compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; (Random) (3.C) Proportionality. Use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation. (Random) (4.A) Proportionality. Use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line; (Random) (4.B) Proportionality. Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; (Random) (4.C) Proportionality. Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems (Random) (5.A) Proportionality. Represent linear proportional situations with tables, graphs, and equations in the form of y = kx; (Random) (5.B) Proportionality. Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0; (Random) (5.C) Proportionality. Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; (Random) (5.D) Proportionality. Use a trend line that approximates the linear relationship between bivariate sets of data to make predictions; (Random) (5.E) Proportionality. Solve problems involving direct variation; (Random) (5.F) Proportionality. Distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0; (Random) (5.G) Proportionality. Identify functions using sets of ordered pairs, tables, mappings, and graphs; (Random) (5.H) Proportionality. Identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; (Random) (5.I) Proportionality. Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations. (Random) (6.A) Expressions, equations, and relationships. Describe the volume formula V = Bh of a cylinder in terms of its base area and its height; (Random) (6.B) Expressions, equations, and relationships. Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; (Random) (6.C) Expressions, equations, and relationships. Use models and diagrams to explain the Pythagorean theorem. (Random) (7.A) Expressions, equations, and relationships. Solve problems involving the volume of cylinders, cones, and spheres; (Random) (7.B) Expressions, equations, and relationships. Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders; (Random) (7.C) Expressions, equations, and relationships. Use the Pythagorean Theorem and its converse to solve problems; (Random) (7.D) Expressions, equations, and relationships. Determine the distance between two points on a coordinate plane using the Pythagorean Theorem. (Random) (8.A) Expressions, equations, and relationships. Write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; (Random) (8.B) Expressions, equations, and relationships. Write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants; (Random) (8.C) Expressions, equations, and relationships. Model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; (Random) (8.D) Expressions, equations, and relationships. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (Random) (9) Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. (Random) (10.A) Two-dimensional shapes. Generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; (Random) (10.B) Two-dimensional shapes. Differentiate between transformations that preserve congruence and those that do not; (Random) (10.C) Two-dimensional shapes. Explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; (Random) (10.D) Two-dimensional shapes. Model the effect on linear and area measurements of dilated two-dimensional shapes. (Random) (11.A) Measurement and data. Construct scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; (Random) (11.B) Measurement and data. Determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points; (Random) (11.C) Measurement and data. Simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected. (Random) (12.A) Personal financial literacy. Solve real-world problems comparing how interest rate and loan length affect the cost of credit; (Random) (12.B) Personal financial literacy. Calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator; (Random) (12.C) Personal financial literacy. Explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time; (Random) (12.D) Personal financial literacy. Calculate and compare simple interest and compound interest earnings; (Random) (12.E) Personal financial literacy. Identify and explain the advantages and disadvantages of different payment methods; (Random) (12.F) Personal financial literacy. Analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; (Random) (12.G) Personal financial literacy. Estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college. Permissions - Can you photocopy these worksheets? | 1,972 | 9,394 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2019-13 | longest | en | 0.834849 |
https://www.edplace.com/worksheet_info/11+/keystage2/year4/topic/1173/6560/2d-and-3d-shapes:-recognising-descriptions | 1,579,555,681,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250599789.45/warc/CC-MAIN-20200120195035-20200120224035-00482.warc.gz | 857,538,205 | 24,941 | # 2D and 3D Shapes: Recognising Descriptions
In this worksheet, students name the 2D and 3D shapes from the given clues.
Key stage: KS 2
Curriculum topic: Maths and Numerical Reasoning
Curriculum subtopic: 3D Shapes
Difficulty level:
### QUESTION 1 of 10
2-dimensional (2-D) shapes are flat and can only be drawn on paper.
3-dimensional (3-D) shapes are solid and can be picked up.
You should know the names of the following shapes.
Name the following shape:
2-d with six sides
Pentagon
Hexagon
Cube
Name the following shape:
3-d with six faces, which are not all the same
Cuboid
Hexagon
Cube
Name the following shape:
3-d with six identical faces
Pentagon
Hexagon
Cube
Name the following shape:
2-d with five sides
Pentagon
Hexagon
Cube
Name the following shape:
3-d and round
Circle
Pyramid
Sphere
Name the following shape:
2-d and round
Circle
Pyramid
Sphere
Name the following shape:
Any 2-d shape with straight sides
Rectangle
Polygon
Name the following shape:
A 2-d shape with 8 corners
Pentagon
Polygon
Octagon
Name the following shape:
A 3-d shape with 8 corners
Cuboid
Cone
Octagon
Name the following shape:
A 2-d shape which is half a circle
Hemicircle
Demicircle
Semicircle
• Question 1
Name the following shape:
2-d with six sides
Hexagon
• Question 2
Name the following shape:
3-d with six faces, which are not all the same
Cuboid
• Question 3
Name the following shape:
3-d with six identical faces
Cube
• Question 4
Name the following shape:
2-d with five sides
Pentagon
• Question 5
Name the following shape:
3-d and round
Sphere
• Question 6
Name the following shape:
2-d and round
Circle
• Question 7
Name the following shape:
Any 2-d shape with straight sides
Polygon
• Question 8
Name the following shape:
A 2-d shape with 8 corners
Octagon
• Question 9
Name the following shape:
A 3-d shape with 8 corners
Cuboid
• Question 10
Name the following shape:
A 2-d shape which is half a circle
Semicircle
---- OR ----
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Get started | 652 | 2,516 | {"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} | 3.625 | 4 | CC-MAIN-2020-05 | longest | en | 0.895993 |
http://mathhelpforum.com/calculus/202840-trig-limits-ugh-print.html | 1,526,849,431,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863684.0/warc/CC-MAIN-20180520190018-20180520210018-00548.warc.gz | 184,381,169 | 4,658 | Trig Limits Ugh
• Sep 2nd 2012, 09:54 AM
psilver1
Trig Limits Ugh
Been struggling with doing trig limits amd this problem is driving me insane. We are suppose to work the problem to sinx/x format. The problem is lim as t---0 tan^2(3t) / 2t. im sure its easy but not to me.
i started with doing lim t-0 sin^2 (3t)/ cos^2(3t)(2t) and im lost. am i even on thr right track
• Sep 2nd 2012, 10:03 AM
Deveno
Re: Trig Limits Ugh
$\displaystyle \frac{\tan^2(3t)}{2t} = \left(\frac{\sin(3t)}{3t}\right)^2\left(\frac{9t}{ 2\cos^2(3t)}\right)$
now perhaps it is a little easier?
• Sep 2nd 2012, 10:11 AM
psilver1
Re: Trig Limits Ugh
Could you explain how you came to those terms. I believe that's where I am struggling.
• Sep 2nd 2012, 12:41 PM
Deveno
Re: Trig Limits Ugh
square the left term in the parentheses, you get:
$\displaystyle \left(\frac{\sin(3t)}{3t}\right)^2 = \frac{\sin^2(3t)}{9t^2}$.
the 9's and one of the t's cancel with the term in parentheses on the right, leaving you with:
$\displaystyle \frac{\sin^2(3t)}{(2t)(\cos^2(3t))} = \frac{\tan(3t)}{2t}$
• Sep 2nd 2012, 02:21 PM
psilver1
Re: Trig Limits Ugh
Why wouldn't sin(3t)/3t be equal to 3
• Sep 2nd 2012, 02:56 PM
psilver1
Re: Trig Limits Ugh
Dang this problem has driven me up a wall. The answer is 0 according to the book. If I take tan^2(3t)/2t. Shouldn't I get sin^2(3t)/(2t)(cos^2(3t)). So in reality we have (sin3t)^2/(2t)(cos3t)^2. I'm sorry for being retarded. I just am looking for steps so I can see where I'm going off course.
• Sep 2nd 2012, 03:08 PM
Plato
Re: Trig Limits Ugh
Quote:
Originally Posted by psilver1
Why wouldn't sin(3t)/3t be equal to 3
It does not! $\displaystyle {\lim _{t \to 0}}\frac{{\sin (3t)}}{{3t}} = 1\;\& \;{\lim _{t \to 0}}\frac{{9t}}{{2\cos (3t)}} = 0$
• Sep 2nd 2012, 03:24 PM
psilver1
Re: Trig Limits Ugh
OK so (sin3t/3t)^2= (1)^2=1. I guess I am just confused with how you can put sin^2(3t) and just put it over 3t and then where the 9t/2t(cos^2(3t) came from. And how you just drop the t off the 2 on the bottom.
• Sep 2nd 2012, 05:33 PM
Soroban
Re: Trig Limits Ugh
Hello, psilver1!
Quote:
$\displaystyle \lim_{t\to0}\frac{\tan^2(3t)}{2t}$
Your first step is a good one: .$\displaystyle \frac{\sin^2(3t)}{2t\cos^2(3t)}$
We'd like to use the theorem: .$\displaystyle \lim_{\theta\to0}\frac{\sin\theta}{\theta} \:=\:1$
So we will "hammer" our problem into that form . . . legally.
We have: .$\displaystyle \frac{\sin^2(3t)}{2t}$
. . and we want: .$\displaystyle \frac{\sin^2(3t)}{(3t)^2} \:=\:\frac{\sin^2(3t)}{9t^2}$
How do we get it? .Multiply top and bottom by $\displaystyle \tfrac{9}{2}t$
. . $\displaystyle \frac{\sin^2(3t)}{2t}\cdot\frac{\frac{9}{2}t}{ \frac{9}{2}t} \;=\;\frac{\sin^2(3t)}{9t^2}\cdot\frac{9}{2}\:\!t$
The function becomes: .$\displaystyle \frac{\sin^2(3t)}{9t^2}\cdot\frac{1}{\cos^2(3t)} \cdot \frac{9}{2}\:\!t$
We have: .$\displaystyle \lim_{t\to0}\left\{ \left[\frac{\sin(3t)}{3t}\right]^2\!\!\cdot\frac{1}{\cos^2(3t)}\cdot\frac{9}{2}\: \!t \right\} \;=\; 1^2\cdot\frac{1}{1}\cdot 0 \;=\;0$
• Sep 2nd 2012, 05:40 PM
psilver1
Re: Trig Limits Ugh
Thank you so much. The 9/2 was where I was struggling. I need to brush up on my algebra. I knew I shouldn't have take 3 semesters off of math.
• Sep 2nd 2012, 08:18 PM
Prove It
Re: Trig Limits Ugh
Quote:
Originally Posted by psilver1
Been struggling with doing trig limits amd this problem is driving me insane. We are suppose to work the problem to sinx/x format. The problem is lim as t---0 tan^2(3t) / 2t. im sure its easy but not to me.
i started with doing lim t-0 sin^2 (3t)/ cos^2(3t)(2t) and im lost. am i even on thr right track
Have you ever heard of L'Hospital's Rule? It states that if you have an indeterminate limit \displaystyle \displaystyle \begin{align*} \frac{0}{0} \end{align*} or \displaystyle \displaystyle \begin{align*} \frac{\infty}{\infty} \end{align*}, then \displaystyle \displaystyle \begin{align*} \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} \end{align*}.
Here you have one of the \displaystyle \displaystyle \begin{align*} \frac{0}{0} \end{align*} form, so L'Hospital's Rule is appropriate.
\displaystyle \displaystyle \begin{align*} \lim_{t \to 0} \frac{\tan^2{3t}}{2t} &= \lim_{ t \to 0} \frac{\frac{d}{dt}\left( \tan^2{3t} \right) }{\frac{d}{dt} \left(2t\right)} \\ &= \lim_{ t \to 0} \frac{ 6\sec^2{3t}\tan{3t} }{ 2 } \\ &= \frac{6 \sec^2{0} \tan{0}}{2} \\ &= 0 \end{align*}
• Sep 2nd 2012, 08:28 PM
Amer
Re: Trig Limits Ugh
Quote:
Originally Posted by Prove It
Have you ever heard of L'Hospital's Rule? It states that if you have an indeterminate limit \displaystyle \displaystyle \begin{align*} \frac{0}{0} \end{align*} or \displaystyle \displaystyle \begin{align*} \frac{\infty}{\infty} \end{align*}, then \displaystyle \displaystyle \begin{align*} \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} \end{align*}.
Here you have one of the \displaystyle \displaystyle \begin{align*} \frac{0}{0} \end{align*} form, so L'Hospital's Rule is appropriate.
\displaystyle \displaystyle \begin{align*} \lim_{t \to 0} \frac{\tan^2{3t}}{2t} &= \lim_{ t \to 0} \frac{\frac{d}{dt}\left( \tan^2{3t} \right) }{\frac{d}{dt} \left(2t\right)} \\ &= \lim_{ t \to 0} \frac{ 6\sec^2{3t}\tan{3t} }{ 2 } \\ &= \frac{6 \sec^2{0} \tan{0}}{2} \\ &= 0 \end{align*}
It is clear he did not hear of it, he still stuck at the bases
• Sep 2nd 2012, 09:33 PM
Deveno
Re: Trig Limits Ugh
Quote:
Originally Posted by psilver1
Why wouldn't sin(3t)/3t be equal to 3
because:
$\displaystyle \lim_{x \to 0} \frac{\sin(x)}{x} = 1$, even if "x" is "3t" (it should be clear that as t goes to 0, so does 3 times t).
• Sep 2nd 2012, 09:42 PM
SworD
Re: Trig Limits Ugh
A quick intuitive way to evaluate this limit might be helpful. First, recognize that cos(x) at x = 0 is equal to 1. Therefore in this case, you can treat tan(x) as sin(x), since you are dividing by a quantity that approaches 1.
So, after separating the limit into simpler ones with which we are familiar, we are left with
$\displaystyle {\lim _{t \to 0}}\frac{{\sin (3t)}}{{2t}} \cdot {\lim _{t \to 0}}\sin (3t) = 1.5 \cdot 0 = 0$
Basically the numerator in the original limit "overpowers" the denominator in how fast it approaches zero, similar to how
$\displaystyle {\lim _{t \to 0}}\frac{{t^2}}{{t}} = 0$
• Sep 3rd 2012, 02:37 AM
Prove It
Re: Trig Limits Ugh
Quote:
Originally Posted by Amer
It is clear he did not hear of it, he still stuck at the bases
Then he can take it as something new and useful that he has learnt. | 2,530 | 6,540 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2018-22 | latest | en | 0.883232 |
https://www.studypool.com/discuss/492858/math-anweser-please-now?free | 1,508,344,770,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823016.53/warc/CC-MAIN-20171018161655-20171018181655-00339.warc.gz | 990,196,096 | 14,528 | Time remaining:
label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5
what 0.3/424.6
what0.4/428.41
whats 0.5/18.335
Oct 17th, 2017
what 0.3/424.6 = 0.0007065
what0.4/428.41 = 0.009337
whats 0.5/18.335 = 0.02727
Division problems like these are best done with a calculator. They can be completed using long division, but it is much more likely that you will make an error in doing so. The answers above were done using a calculator and rounded at the fourth significant figure. If you need more information about division, please let me know.
Apr 24th, 2015
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Oct 17th, 2017
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Oct 17th, 2017
Oct 18th, 2017
check_circle | 221 | 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} | 2.515625 | 3 | CC-MAIN-2017-43 | latest | en | 0.917411 |
https://root.cern.ch/doc/v624/vo003__LogicalOperations_8C_source.html | 1,713,816,231,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818337.62/warc/CC-MAIN-20240422175900-20240422205900-00430.warc.gz | 433,346,063 | 5,295 | ROOT Reference Guide
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vo003_LogicalOperations.C
Go to the documentation of this file.
1/// \file
2/// \ingroup tutorial_vecops
3/// \notebook -nodraw
4/// In this tutorial we learn how the RVec class can be used to
5/// express logical operations.
6///
7/// \macro_code
8/// \macro_output
9///
10/// \date May 2018
11/// \author Danilo Piparo
12
13using namespace ROOT::VecOps;
14
15void vo003_LogicalOperations()
16{
17
18 // Logical operations on RVec instances are made to be very easy to use.
19 RVec<double> v1{1., 2., 3.};
20 RVec<double> v2{3., 2., 1.};
21
22 // Let's start with operations which act element by element. In this case
23 // we expext a RVec which holds {1. > 3., 2. > 2., 3. > 1.}, i.e. {1, 0, 0}:
24 auto v1_gr_v2 = v1 > v2;
25 std::cout << v1 << " > " << v2 << " = " << v1_gr_v2 << std::endl;
26
27 // Other logical operations are supported, of course:
28 auto v1_noteq_v2 = v1 != v2;
29 std::cout << v1 << " != " << v2 << " = " << v1_noteq_v2 << std::endl;
30
31 // All returns true if all of the elements equate to true, return false otherwise.
32 // Any returns true if any of the elements equates to true, return false otherwise.
33 auto all_true = v1 > .5 * v2;
34 std::cout << std::boolalpha;
35 std::cout << "All( " << v1 << " > .5 * " << v2 << " ) = " << All(all_true) << std::endl;
36 std::cout << "Any( " << v1 << " > " << v2 << " ) = " << Any(v1_noteq_v2) << std::endl;
37
38 // Selections on the RVec contents can be applied with the "square brackets" operator,
39 // which is not only a way to access the content of the RVec.
40 // This operation can change the size of the RVec.
41 RVec<double> v{1., 2., 3., 4., 5.};
42 auto v_filtered = v[v > 3.];
43 std::cout << "v = " << v << ". v[ v > 3. ] = " << v_filtered << std::endl;
44
45 // This filtering operation can be particularely useful when cleaning collections of
46 // objects coming from HEP events. For example:
47 RVec<double> mu_pt{15., 12., 10.6, 2.3, 4., 3.};
48 RVec<double> mu_eta{1.2, -0.2, 4.2, -5.3, 0.4, -2.};
49
50 // Suppose the pts of the muons with a pt greater than 10 and eta smaller than 2.1 are needed:
51 auto good_mu_pt = mu_pt[mu_pt > 10 && abs(mu_eta) < 2.1];
52 std::cout << "mu_pt = " << mu_pt << " mu_pt[ mu_pt > 10 && abs(mu_eta) < 2.1] = " << good_mu_pt << std::endl;
53
54 // Advanced logical operations with masking can be performed with the Where helper.
55 auto masked_mu_pt = Where(abs(mu_eta) < 2., mu_pt, -999.);
56 std::cout << "mu_pt if abs(mu_eta) < 2 else -999 = " << masked_mu_pt << std::endl;
57}
A "std::vector"-like collection of values implementing handy operation to analyse them.
Definition RVec.hxx:296
auto All(const RVec< T > &v) -> decltype(v[0]==false)
Return true if all of the elements equate to true, return false otherwise.
Definition RVec.hxx:1013
RVec< T > Where(const RVec< int > &c, const RVec< T > &v1, const RVec< T > &v2)
Return the elements of v1 if the condition c is true and v2 if the condition c is false.
Definition RVec.hxx:1350
auto Any(const RVec< T > &v) -> decltype(v[0]==true)
Return true if any of the elements equates to true, return false otherwise.
Definition RVec.hxx:994 | 1,039 | 3,171 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-18 | latest | en | 0.491204 |
https://portfoliolanguageservices.com/2021/08/03/nfl-how-can-i-learn-to-interpret-a-confidence-interval/ | 1,657,157,981,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104683020.92/warc/CC-MAIN-20220707002618-20220707032618-00188.warc.gz | 506,729,625 | 12,637 | ### NFL: How can I learn to interpret a confidence interval?
The NFL is testing a new way of interpreting a confidence-interval in which the players’ accuracy in the play is tracked to a specific point on the ball.
The idea is to learn to see the confidence interval as a line that goes from zero to five.
The confidence-Interval Interpretation System, which will be used in two preseason games, is being tested at NFL training camps and preseason games in Arizona and Los Angeles.
The system uses a series of data points, called data points (PDs), to create a confidence intervals, or the percentage that a player’s accuracy in a play is within the range of the PDs.
The PDs are created using a formula that determines the percentage of the data points that are within the confidence intervals.
If a player misses a PD, the system will subtract one percent from the confidence-percentage.
If the player makes a PD in the confidence range, the confidence percentage will increase.
In the NFL, the PD is an average of the two PDs and a standard deviation.
The formula is a combination of the “standard deviation” (the range of PDs) and the “confidence interval.”
The formula can be interpreted as “confidence intervals increase.”
The goal is to increase the confidence that the players are actually performing well in the game.
The confidence intervals are calculated as a percentage, not a mean.
The system is being used at preseason games and training camps in Arizona.
The teams will test it on Tuesday and Wednesday.
The results will be released at the end of the season.
The PD is the percentage range of a player�s accuracy in one situation in which a player is not actually performing as expected.
The average PD is a .90, and the confidence ranges are .90 to 1.00.
For example, if a quarterback misses a 50-yard field goal in a 3-on-3 game, that means that the PD was .85.
If, however, a player missed a 50 yard field goal when the ball was snapped, that meant the PD had increased to .94.
The goal is not to just see a player perform better.
The goal of the system is to see a confidence range that is not below that player� s actual performance, and if a player makes the PD, then the PD will increase in that player’s confidence range.
The formula is different than other data points used to create confidence intervals in the NFL.
It is designed to give players a sense of how accurate they are, and that is what the PD system is meant to do.
The confidence interval is not a good indicator of how well a player performed.
It may be a reasonable way to measure whether a player was a good quarterback in a certain situation.
But it is not good enough to know whether the player was actually successful in a particular situation.
The expectation that players will play better in games, or play better at home, has not changed, but it has changed how we analyze the sport.
The expectation that every player is capable of being successful at every position in every game is not what is needed to measure how well players perform.
The data is not the same as it was a few years ago, but the trend is still there.
It just has been more complicated to see how much more effective players have been at each position in the sport over the last few years.
The players were able to get to the playoffs last year because they played well.
This year, players will have to play better to get the chance to play again.
The NFL is testing a new way of interpreting a confidence-interval in which the players’ accuracy in the play is… | 741 | 3,562 | {"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-2022-27 | latest | en | 0.965025 |
http://www.coderanch.com/t/427009/java/java/Simple-code-confusing | 1,467,119,887,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783396887.54/warc/CC-MAIN-20160624154956-00134-ip-10-164-35-72.ec2.internal.warc.gz | 457,697,796 | 10,767 | Win a copy of Mesos in Action this week in the Cloud/Virtualizaton forum!
# Simple code, but confusing
prasanna kanth
Greenhorn
Posts: 28
When the above code compile and run, it give 1,0 (I am confused how?)
when it pass the value its passing as 1 then the value should remain same when it returns zero.
and it should be like i = 1 + 0;
As per my idea it should give 1,1
Can any one explain clearly how it works here ?
Ranch Hand
Posts: 213
prasanna kanth wrote:When the above code compile and run, it give 0,1 (I am confused how?)
Are you sure it gives 0,1. Or does it give 1, 0.
Did you actually run the code?
Ranch Hand
Posts: 213
prasanna kanth wrote:
when it pass the value its passing as 1 then the value should remain same when it returns zero.
and it should be like i = 1 + 0;
In the code the incrementer is post increment......
prasanna kanth
Greenhorn
Posts: 28
Sorry, it actually returns 1,0
Ok if its a Post increment, what is the value be passed to the function 0 or 1
Ranch Hand
Posts: 213
The code will be evaluated as
which will be evaluated as
Can you say what will be the output of
prasanna kanth
Greenhorn
Posts: 28
If the initial value of i = 0, then it will be 1 at the end.
I am still not clear (sorry to bug u), when it pass the value as 1, that means i is not zero its incremented to 1 :!: ?
If yes, then when it returns zero, the statement should be like i = 1 + 0 right :roll:
How come the incremented i value become again 0?
Cheers!
Campbell Ritchie
Sheriff
Posts: 48947
60
This comes up often; lots of people get confused about what i++ is. And writing 0,1 when you mean 1,0 causes even more confusion!
This is a confusing bit of code, written to confuse, and difficult to read because you haven't indented it correctly.
And is that question from a book or website, in which case you ought to Quote Your Sources.
The value of f1(i) is 0. It always is, because there is return 0; in that method.
The value of i passed to f1 is 1, which you know because f1 prints 1,
The value of i before i++ is 0, and after i++ the value of i is 1. But there are two values there. There is the value of i, and the value of the subexpression, i++. They are different. The value of i++ is the old value of i, which is 0. So you are adding 0 and 0, getting 0, then re-assigning i to 0.
Ranch Hand
Posts: 213
prasanna kanth wrote:If the initial value of i = 0, then it will be 1 at the end.
No the value will be still 0 at the end.
There was a very good post about how the value of i becomes from 0 to 1, then back to 0 w.r.t memory.
It really explained well, will try to search and give you the link.
But the bottom line, i will be unchanged(here 0).
So in our case i = i++ + f1(i);
First value of i is used for the expression(ie 0), then it is incremented(i becomes 1) and passed to the method f1 which returns 0.
so the expression becomes 0 + 0 = 0 which is finally assigned back to i.
Ranch Hand
Posts: 213
Got the post ............ actually it was in the FAQ Post Increment Operator And Assignment
prasanna kanth
Greenhorn
Posts: 28
Big thanks to all, finally understand how it woks, it was cooking my mind for last two days... woow
Campbell Ritchie
Sheriff
Posts: 48947
60
You're welcome . It's nice when it works, isn't it. | 923 | 3,262 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2016-26 | longest | en | 0.889872 |
http://www.ck12.org/arithmetic/Proportions-to-Find-Part-a/enrichment/Find-the-Parts-Given-the-Percents-and-Whole-Example-3/r1/ | 1,490,279,493,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218187113.46/warc/CC-MAIN-20170322212947-00111-ip-10-233-31-227.ec2.internal.warc.gz | 458,674,923 | 25,491 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Proportions to Find Part a
## Cross - multiply to find a missing part of a proportion, a.
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Find the Parts Given the Percents and Whole - Example 3
### Explore More
Sign in to explore more, including practice questions and solutions for Proportions to Find Part a. | 155 | 586 | {"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-2017-13 | longest | en | 0.60139 |
https://edurev.in/course/quiz/attempt/-1_General-Aptitude-1/1a66f93a-a830-41ac-bb67-8118c632a186 | 1,670,261,583,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711042.33/warc/CC-MAIN-20221205164659-20221205194659-00001.warc.gz | 249,431,182 | 42,485 | General Aptitude - 1
General Aptitude - 1
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*Answer can only contain numeric values
General Aptitude - 1 - Question 1
The value of _____________. (Round off two decimal places).
Detailed Solution for General Aptitude - 1 - Question 1
General Aptitude - 1 - Question 2
How many pieces of 85 cm can be cut from a rod of 42.5 metre
Detailed Solution for General Aptitude - 1 - Question 2
General Aptitude - 1 - Question 3
Find the missing number
Detailed Solution for General Aptitude - 1 - Question 3
1st 23 + 5 = 28
2nd 45 + 5 = 50
3rd 35 + 5 = 40
*Answer can only contain numeric values
General Aptitude - 1 - Question 4
If a = 0.1039, then the value of is ___________ ( Round off to four decimal places)
Detailed Solution for General Aptitude - 1 - Question 4
General Aptitude - 1 - Question 5
Find the number of triangles in the figure.
Detailed Solution for General Aptitude - 1 - Question 5
As there are two triangles inside the large one. and each small triangle makes 4 triangles and the largest triangle makrs one. 4 x 2 + 1 = 9
General Aptitude - 1 - Question 6
a. b. c. d. e are five consecutive odd numbers, their average is
Detailed Solution for General Aptitude - 1 - Question 6
If 'a' is the odd no. then next consecutive odds are, a + 2, a + 4, a + 6, a + 8
[ If no observations are odd then the middle one is avg tor consecutive odd numbers.]
General Aptitude - 1 - Question 7
Introducing Asha to guests. Bhaskar said. "Her father is the only son of my father". How is Asha related to Bhaskar.
Detailed Solution for General Aptitude - 1 - Question 7
General Aptitude - 1 - Question 8
The area of the largest triangle that can be inscribed in a semi circle of radius r is
Detailed Solution for General Aptitude - 1 - Question 8
As ΔBAC is on hill diameter
General Aptitude - 1 - Question 9
A man had 16 dogs. All but 7 died. How many dogs was he left with
Detailed Solution for General Aptitude - 1 - Question 9
All but 7 died means except 7 dogs all others died i.e. 7 dogs are left
General Aptitude - 1 - Question 10
What angle is made by minute hand in 29 seconds?
Detailed Solution for General Aptitude - 1 - Question 10
In 3600 seconds it makes 360° (as if completes a circle)
∴ In 29 seconds it makes
General Aptitude - 1 - Question 11
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A can do the work if he is assisted by B and C on every third day.
Detailed Solution for General Aptitude - 1 - Question 11
General Aptitude - 1 - Question 12
Find the number of digits in 213
Detailed Solution for General Aptitude - 1 - Question 12
213 = ( 26)2 x 2 = (64)2 x 2 = (4096) x 2 = 8192 i.e. 4 digits
General Aptitude - 1 - Question 13
In the given figure AB is the diameter of the circle. Find the value o f ∠A C D
Detailed Solution for General Aptitude - 1 - Question 13
General Aptitude - 1 - Question 14
The minute hand of a clock is in North -East at 8 : 45. Then in which direction the hour hand will be at 1 : 30.
Detailed Solution for General Aptitude - 1 - Question 14
So. 1 : 30 and 8 : 45 difference = 4 h o u r : 45 mins =
and by that time clock's hour hand will move forward . in 12 horns, hour hand makes 360°.
General Aptitude - 1 - Question 15
Bombay express left delhi for bomb ay at 14: 30 hours, travelling at a speed of 60 km hr. and Rajdhani express left delhi for bombay at 16:30 hours on the same day at a speed of 80 km hr. How for from delhi the two trains will meet?
Detailed Solution for General Aptitude - 1 - Question 15
In two hours first train goes 120 km. (as speed = 60 km/hr)
Now relative speed = (80 - 60) km hour = 20 km hour.
Now 20 km is covered in 1 hour.
∴ 120 km is convered in
Which is the time for the 2nd train which travels at 80 km hour
∴ Total distance covered = 80 x 6 = 480 km.
General Aptitude - 1 - Question 16
A dishonest shop keeper sells sugar at cost price but cheats 10% on weight. What is his percentage profit loss
Detailed Solution for General Aptitude - 1 - Question 16
Let cost price of 100 g is 100 Rs.
∴ The cost price of 90 g is 90 Rs.
∴ he profits 10 Rs in each 90 Rs.
General Aptitude - 1 - Question 17
Statement
(i) All A are B
(ii) All A are C (Hi) Some C are D
Based on these statements find out which at the following conclusions are true.
(1) All c can be B
(2) All A are B as well as C.
Detailed Solution for General Aptitude - 1 - Question 17
This is the general diagram. But C can also be inside B. which is a possibility,
∴ both follows (c)
General Aptitude - 1 - Question 18
Find out in the given sentese if there is any error and mark the part having error as your answer, and if No error is there then mark 'd' as your answer.
(i) All the students of the academy will
(ii) Give a test
(iii) O f general aptitude in the afternoon
(iv) No error
Detailed Solution for General Aptitude - 1 - Question 18
’give a test' is wrong conect is ’take a test'.
*Answer can only contain numeric values
General Aptitude - 1 - Question 19
The reina inder o f the series l!+ 2 !+ 3 !+ 4 !+ + 100! when divided by 10 is____________.
Detailed Solution for General Aptitude - 1 - Question 19
l!+2!+3!+4! = 1 + 2 + 6+24 = 33
and each te rm > 5!. should have a 2 and 5 is the no (i.e. 5! = lx 2 x 3 x 4 x 5 )
Which is divisible by 10.
General Aptitude - 1 - Question 20
There are 8 identical bags of wheat except 1 bag all others have same weight but one bag is heavier what is the minimum number of weights requited to identify the bag with different weight by conventional balance.
Detailed Solution for General Aptitude - 1 - Question 20
Total 8 bags
take which one is heavier, next
again take heavier one
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17 docs|34 tests | 2,002 | 7,220 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-49 | latest | en | 0.810101 |
https://www.citehr.com/612226-gratuity-calculations-what-will-average-salary-gratuity.html | 1,582,270,468,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145443.63/warc/CC-MAIN-20200221045555-20200221075555-00232.warc.gz | 670,565,644 | 11,201 | Gratuity Calculations - What will be the Average Salary for Gratuity calculation in June 2019? - CiteHR
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Vaisu_21
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Cite.Co is a repository of information created by your industry peers and experienced seniors sharing their experience and insights.
I have worked for 24 years and my current basic salary is Rs 16000 p.m. It was Rs. 8500/- in 2009-10 than it was 9000/- in 2012-13, Rs. 10500/- in 2013-14 Rs. 12000/- in 2016-17 and currently it is Rs. 16000/- Now i am going retire. What will be the Average Salary for Gratuity calculation in June 2019.
There is no average salary for calculation of gratuity but gratuity is calculated on the last drawn salary. If your salary is Rs 16000 and have worked for 24 years, then your gratuity will be Rs 2,21,538, calculated at the rate of 15 days salary for every completed year of service.
For calculation of Gratuity not only the basic salary but the dearness allowance and such other allowances which are payable to an employee as per contract of employment should also be taken into account.The salary for the purpose of gratuity is the amount of salary which the employee gets while on work or on leave.
Suppose your salary is Rs 60000 per month. When you take say five days' leave with pay, you will get the same Rs 60000.Suppose you take 5 days' leave without pay,your pay will be reduced by Rs 10000,ie, 60000 divided by 30 multiplied by 5. That means 60000 is your monthly pay and it is for the convenience of the employer that they have made it as basic pay, HRA, washing allowance etc and for an employee whatever is payable is the gross salary. If that stand is taken your gratuity will be Rs 830769. That is 60000 divided by 26 (for gratuity calculation monthly salary is to be divided by 26 and not by 30) multiplied by 15 (to get 15 days salary)and then multiplied by 24 (your service)
However,most of the companies follow the first method and for them basic salary is the foundation and is always a weak foundation! I am sure having said what is basic salary under Provident Fund by the Supreme Court, the next battle is to define basic salary under Payment of Gratuity Act.It is to be noted that there is no much difference in the definition of wages under both these Acts.
Dear Sir,
Gratuity will be calculate on your last basic salary i.e. on Rs. 16000
Rs. 16000 /26 X 15 X 24
Thanks | 594 | 2,392 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-10 | latest | en | 0.966301 |
https://www.jiskha.com/display.cgi?id=1301361908 | 1,503,570,438,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886133449.19/warc/CC-MAIN-20170824101532-20170824121532-00509.warc.gz | 908,440,742 | 3,901 | # physics
posted by .
The four wires that lie at the corners of a square of side a= 5.60 cm are carrying equal currents i= 1.80 A into (+) or out of (-) the page, as shown in the picture.
Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.
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More Similar Questions | 656 | 2,635 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2017-34 | latest | en | 0.923002 |
https://codegolf.stackexchange.com/questions/187207/alphabet-completion-rate | 1,725,752,298,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650926.21/warc/CC-MAIN-20240907225010-20240908015010-00163.warc.gz | 164,665,276 | 82,986 | # Alphabet completion rate
## Introduction
How much of the English alphabet does a given string use? The previous sentence uses 77%. It has 20 unique letters (howmucftenglisapbdvr), and 20/26 ≃ 0.77.
## Challenge
For an input string, return the percentage of letters of the English alphabet present in the string.
• The answer can be in percentage or in decimal form.
• The input string can have upper and lower case, as well as punctuation. However you can assume they have no diacritics or accentuated characters.
## Test cases
Input
"Did you put your name in the Goblet of Fire, Harry?" he asked calmly.
Some valid outputs
77%, 76.9, 0.7692
Input:
The quick brown fox jumps over the lazy dog
All valid outputs:
100%, 100, 1
The expected output for "@#$%^&*?!" and "" is 0. • Suggested test cases: "@#$%^&*?!", ""
Commented Jun 21, 2019 at 10:35
• If 77% and 76.9 is accepted, is 77 accepted too? Commented Jun 21, 2019 at 10:43
• Percentages can have decimal parts too...
– Jo King
Commented Jun 21, 2019 at 11:54
• @Shaggy Last edit for OP was 16 hours ago, your answer was at 15 and your comment at 14. I mean, you're right but ??? Commented Jun 22, 2019 at 4:16
• If 20/26 may be rounded to 0.7692, 0.769 or 0.77, can I also round it to 0.8, 1 or 0? ;-) Commented Jun 22, 2019 at 22:42
# Python 3, 42 bytes
lambda s:len({*s.upper()}-{*s.lower()})/26
Try it online!
We filter all the non-alphabetic characters out of the string by taking the (set) difference of the uppercase and lowercase representations. Then, we take the length and divide by 26.
# Python 3, 46 bytes
lambda s:sum(map(str.isalpha,{*s.lower()}))/26
Try it online!
Count the unique alphabetic (lowercase) characters, and divide by 26. In Python 2 it would require 3 more characters; two for changing {*...} to set(...), and one for making 26 a float: 26., to avoid floor division.
# Python 3, 46 bytes
lambda s:sum(''<c<'{'for c in{*s.lower()})/26
Try it online!
Same length, essentially the same as the previous one, but without "built-in" string method.
• Why does the second one return 1.0 and not 1? (I didn't want to specifically disallow it so it wouldn't disadvantage specific languages, but I'm curious) Commented Jun 21, 2019 at 12:05
• @TeleportingGoat Division with a single slash always gives floats in Python 3, even if the operands are integers. For integer division, you'd use //, but then it would always be integer division, which is obviously not what we want here. It makes sense that they didn't make the data type of the output dependent on the specific values of the operands, which means always floats, even if it's a whole number.
– ArBo
Commented Jun 21, 2019 at 12:09
# MATL, 8 bytes
2Y2jkmYm
Try it at MATL Online
Explanation
2Y2 % Predefined literal for 'abcdefghijklmnopqrstuvwxyz'
j % Explicitly grab input as a string
k % Convert to lower-case
m % Check for membership of the alphabet characters in the string.
% Results in a 26-element array with a 1 where a given character in
% the alphabet string was present in the input and a 0 otherwise
Ym % Compute the mean of this array to yield the percentage as a decimal
% Implicitly display the result
# 05AB1E, 87 6 bytes
lASåÅA
-1 byte thanks to @LuisMendo.
6 bytes alternative provided by @Grimy:
láÙg₂/
Both programs output as decimal.
Explanation:
l # Convert the (implicit) input-string to lowercase
AS # Push the lowercase alphabet as character-list
å # Check for each if it's in the lowercase input-string
# (1 if truthy; 0 if falsey)
ÅA # Get the arithmetic mean of this list
# (and output the result implicitly)
l # Convert the (implicit) input-string to lowercase
á # Only leave the letters in this lowercase string
Ù # Uniquify it
g # Get the amount of the unique lowercase letters by taking the length
₂/ # Divide this by 26
# (and output the result implicitly)
• @LuisMendo alternatively, láêg₂/ is also a 6-byter. Commented Jun 21, 2019 at 10:44
• @LuisMendo Thanks (and you as well Grimy)! :) Commented Jun 21, 2019 at 10:49
# Octave / MATLAB, 33 bytes
@(s)mean(any(65:90==upper(s)',1))
Try it online!
### Explanation
@(s) % Anonymous function with input s: row vector of chars
65:90 % Row vector with ASCII codes of uppercase letters
upper(s) % Input converted to uppercase
' % Transform into column vector
== % Equality test, element-wise with broadcast. Gives a
% matrix containing true and false
any( ,1) % Row vector containing true for columns that have at
% least one entry with value true
mean( ) % Mean
# C# (Visual C# Interactive Compiler), 56 49 bytes
a=>a.ToUpper().Distinct().Count(x=>x>64&x<91)/26f
Try it online!
-6 bytes thanks to innat3
• you can save 6 bytes by comparing the decimal values of the characters 50 bytes (Character codes) Commented Jun 21, 2019 at 10:56
• @Innat3 49 bytes by changing the && to &. Commented Jun 21, 2019 at 11:09
• @KevinCruijssen ~2 mins off getting the -1 byte credit, already did that and was editing Commented Jun 21, 2019 at 11:10
• @ExpiredData Np, it was an obvious golf. Was mainly directing it to Innat :) Commented Jun 21, 2019 at 11:11
# K (oK), 19 15 bytes
Solution:
1%26%+/26>?97!_
Try it online!
Explanation:
Convert input to lowercase, modulo 97 ("a-z" is 97-122 in ASCII, modulo 97 gives 0-25), take unique, sum up results that are lower than 26, and convert to the percentage of 26.
1%26%+/26>?97!_ / the solution
_ / lowercase
97! / modulo (!) 97
? / distinct
26> / is 26 greater than this?
+/ / sum (+) over (/)
26% / 26 divided by ...
1% / 1 divided by ...
Notes:
• -1 bytes thanks to ngn, 1-%[;26] => 1-1%26%
• -3 bytes inspired by ngn #(!26)^ => +/26>?
• I'm looking forward to the explanation! I have no idea what that 97 is doing here Commented Jun 21, 2019 at 23:28
• Another 19 bytes alternative
– mkst
Commented Jun 22, 2019 at 9:58
• %[;26] -> 1%26%
– ngn
Commented Jun 22, 2019 at 10:23
• 1%26%#?(26>)#97!_
– ngn
Commented Jun 22, 2019 at 10:25
• – mkst
Commented Jun 23, 2019 at 4:44
# PowerShell, 55 52 bytes
($args|% *per|% t*y|sort|gu|?{$_-in65..90}).count/26
Try it online!
First attempt, still trying random ideas
EDIT: @Veskah pointed out ToUpper saves a byte due to the number range, also removed extra () and a space
Expansion:
($args|% ToUpper|% ToCharArray|sort|get-unique|where{$_-in 65..90}).count/26
Changes string to all loweruppercase, expands to an array, sorts the elements and selects the unique letters (gu needs sorted input), keep only characters of ascii value 97 to 122 (a to z) 65 to 90 (A to Z), count the total and divide by 26 for the decimal output
• Uppercase saves a byte Commented Jun 21, 2019 at 14:57
• oh, just noticed you have an extra space after -in. Commented Jun 21, 2019 at 19:04
• I didn't see this answer at first and solved it in a similar way, but with a different pipeline order: ($_|% *per|% *ay|?{$_-in65..90}|sort|gu).count/26 Later I came up with another way, but it turned out to be the same byte length as the first one ([regex]::Matches($_,'\w')|% v*|sort -u).count/26 Commented May 23 at 20:34 # APL (Dyalog Extended), 10 bytesSBCS Anonymous tacit prefix function. Returns decimal fraction. 26÷⍨∘≢⎕A∩⌈ Try it online! ⌈ uppercase ⎕A∩ intersection with the uppercase Alphabet ≢ tally length ∘ then 26÷⍨ divide by twenty-six • ⌹∘≤⍨⎕A∊⌈ – ngn Commented Jun 22, 2019 at 10:45 • @ngn That's very clever, but completely different. Go ahead and post that yourself. I'll be happy insert the explanation if you want me to. – Adám Commented Jun 22, 2019 at 23:32 • done&explained – ngn Commented Jun 23, 2019 at 12:11 # Perl 6, 27 24 bytes -3 bytes thanks to nwellnhof *.uc.comb(/<:L>/).Set/26 Try it online! • +1 Also, while this works just fine (and .lc would work too), from a "correctness" standpoint, .fc might be better (particularly if the challenge had non-English letters) Commented Jun 25, 2019 at 1:49 ## Bash and Gnu utils (81786860 42 bytes) bc -l<<<grep -io [a-z]|sort -fu|wc -l/26 -8 bytes thanks to @wastl -18 bytes thanks to Nahuel using some tricks I didn't know: • sort -f and grep -i ignore case • sort -u is a replacement for | uniq • 60 bytes: echo$(tr A-Z a-z|tr -cd a-z|fold -1|sort -u|wc -l)/26|bc -l Commented Jun 21, 2019 at 13:12
• Right. The variable is a reminder after another attempt. Thanks! Commented Jun 21, 2019 at 15:24
• 42 bytes Commented Jun 21, 2019 at 15:29
• Can't "grep -io [a-z]" be shortened to "grep -o [A-z]" ? Commented Jun 23, 2019 at 6:13
• @Gnudiff Assuming ASCII, that would also match all of [\^_]. Commented Jun 23, 2019 at 23:45
# R, 47 bytes
function(x)mean(65:90%in%utf8ToInt(toupper(x)))
Try it online!
Converts to upper case then to ASCII code-points, and checks for values 65:90 corresponding to A:Z.
• This fails when there are quotes in the input. Commented Jun 21, 2019 at 14:35
• @C.Braun Not in my tests... For instance, the first test case on TIO includes quotes and gives the correct result. Could you give an example? Commented Jun 21, 2019 at 17:34
• I do not quite understand what you have done in the header part on TIO, but running just the code above in an R interpreter does not work. You seem to be redefining scan to not split on quotation marks, like the default does? Commented Jun 24, 2019 at 18:37
• @C.Braun Got it, thanks! I've explicitly made it into a function (at a cost of 3 bytes) and I think it's OK now. Commented Jun 24, 2019 at 20:38
# Retina 0.8.2, 45 bytes
TLlpll_
+(.)(.*\1)
$2 . 100$*
^
13$* .{26} Try it online! Link includes test cases. Explanation: TLlpll_ Lowercase letters and delete punctuation. +(.)(.*\1)$2
Deduplicate.
.
100$* Multiply by 100. ^ 13$*
.{26}
Integer divide by 26 and convert to decimal.
• I think retina is the only language here using percentages for the output! Commented Jun 21, 2019 at 12:35
• Oh, nice trick with adding unary 13 before dividing! Why didn't I think of that.. >.> It would make my answer 44 bytes. I'll still leave my previous version, though. Commented Jun 21, 2019 at 13:11
• @TeleportingGoat Probably because Retina is also the only language from the ones posted thus far which doesn't have decimal division available. Only (unary) integer-division is possible. Commented Jun 21, 2019 at 13:19
# APL (Dyalog Extended), 8 bytes
⌹∘≤⍨⎕A∊⌈
Try it online!
⌈ uppercase
⎕A∊ boolean (0 or 1) vector of length 26 indicating which letters of the English Alphabet are in the string
⌹∘≤⍨ arithmetic mean, i.e. matrix division of the argument and an all-1 vector of the same length
# Java 8, 62 59 bytes
s->s.map(c->c&95).distinct().filter(c->c%91>64).count()/26.
-3 bytes thanks to @OlivierGrégoire.
Try it online.
Explanation:
s-> // Method with IntStream as parameter and double return-type
s.map(c->c&95) // Convert all letters to uppercase
.distinct() // Uniquify it
.filter(c->c%91>64) // Only leave letters (unicode value range [65,90])
.count() // Count the amount of unique letters left
/26. // Divide it by 26.0
• 59 bytes Commented Jun 23, 2019 at 11:28
• @OlivierGrégoire Thanks! I always forget about c&95 in combination with c%91>64 for some reason. I think you've already suggested that golf a few times before to me. Commented Jun 23, 2019 at 15:18
• Yes, I already suggested those, but that's OK, no worries ;-) Commented Jun 23, 2019 at 15:37
• Way longer, but more fun: s->{int r=0,b=0;for(var c:s)if((c&95)%91>64&&b<(b|=1<<c))r++;return r/26.;} (75 bytes) Commented Jun 24, 2019 at 8:15
# Charcoal, 11 bytes
Ｉ∕ＬΦβ№↧θι²⁶
Try it online! Link is to verbose version of code. Output is as a decimal (or 1 for pangrams). Explanation:
Ｌ Length of
β Lowercase alphabet
Φ Filtered on
№ Count of
ι Current letter in
↧ Lowercased
θ Input
∕ Divided by
²⁶ Literal 26
Ｉ Cast to string
Implicitly printed
## Batch, 197 bytes
@set/ps=
@set s=%s:"=%
@set n=13
@for %%c in (A B C D E F G H I J K L M N O P Q R S T U V W X Y Z)do @call set t="%%s:%%c=%%"&call:c
@cmd/cset/an/26
@exit/b
:c
@if not "%s%"==%t% set/an+=100
Takes input on STDIN and outputs a rounded percentage. Explanation:
@set/ps=
Input the string.
@set s=%s:"=%
Strip quotes, because they're a headache to deal with in Batch.
@set n=13
@for %%c in (A B C D E F G H I J K L M N O P Q R S T U V W X Y Z)do @call set t="%%s:%%c=%%"&call:c
Delete each letter in turn from the string. Invoke the subroutine to check whether anything changed, because of the way Batch parses variables.
@cmd/cset/an/26
Calculate the result as a percentage.
@exit/b
:c
Start of subroutine.
@if not "%s%"=="%t%" set/an+=100
If deleting a letter changed the string then increment the letter count.
# Pepe, 155 138 bytes
rEeEeeeeeEREeEeEEeEeREERrEEEEErEEEeReeReRrEeeEeeeeerEEEEREEeRERrErEErerREEEEEeREEeeRrEreerererEEEEeeerERrEeeeREEEERREeeeEEeEerRrEEEEeereEE
Try it online! Output is in decimal form.
Explanation:
rEeEeeeeeE REeEeEEeEe # Push 65 -> (r), 90 -> (R)
REE # Create loop labeled 90 // creates [65,66,...,89,90]
RrEEEEE # Increment (R flag: preserve the number) in (r)
rEEEe # ...then move the pointer to the last
Ree # Do this while (r) != 90
Re # Pop 90 -> (R)
RrEeeEeeeee rEEEE # Push 32 and go to first item -> (r)
REEe # Push input -> (R)
RE RrE # Push 0 on both stacks, (r) prepend 0
rEE # Create loop labeled 0 // makes input minus 32, so the
# lowercase can be accepted, since of rEEEEeee (below)
re # Pop 0 -> (r)
rREEEEEe REEee # Push item of (R) minus 32, then go to next item
RrE # Push 0 -> (R)
ree # Do while (R) != 0
rere # Pop 0 & 32 -> (r)
rEEEEeee # Remove items from (r) that don't occur in (R)
# Remove everything from (r) except the unique letters
rE # Push 0 -> (r)
RrEeee # Push reverse pointer pos -> (r)
REEEE # Move pointer to first position -> (R)
RREeeeEEeEe # Push 26 -> (R)
rRrEEEEee reEE # Divide it and output it
• Since Pepe is only a 4 command language really it's like 34.5 bytes if you encoded it as 2 bits per r e R E? Commented Jun 26, 2019 at 13:09
# K (oK), 19 bytes
1%26%26-#(!26)^97!_
Try it online!
# J, 30 bytes
26%~26-u:@(97+i.26)#@-.tolower
Try it online!
• 32! is too broad - it makes the rest of the expression treat some punctuation chars as letters, for instance try adding : in the example input
– ngn
Commented Jun 22, 2019 at 10:35
• @ngn I didn't test with punctuation at first. Thanks for reminding me.! Commented Jun 22, 2019 at 15:41
# Retina, 5746 35 bytes
.
$L [^a-z] D. . 100* ^ 13* _{26} -11 bytes taking inspiration from @Neil's trick of adding unary 13 before dividing. Another -11 bytes thanks to @Neil directly. Rounds (correctly) to a whole integer. Try it online. 57 46 40 bytes version which works with decimal output: .$L
[^a-z]
D.
.
1000*
C_{26}
-1\B
.
Same -11 bytes as well as an additional -6 bytes thanks to @Neil.
Outputs with one truncated decimal after the comma ( i.e. $$\0.1538\$$ ($$\\frac{4}{26}\$$) is output as 15.3 instead of 15.4). This is done by calculating $$\\lfloor{\frac{1000 × \text{unique_letters}}{26}\rfloor}\$$ and then inserting the decimal dot manually.
Try it online.
Explanation:
Convert all letters to lowercase:
.
$L Remove all non-letters: [^a-z] Uniquify all letters: D. Replace every unique letter with 1000 underscores: . 1000* Count the amount of times 26 adjacent underscores fit into it: C_{26} Insert a dot at the correct place: -1\B . • The .* could just be . for a 1 byte saving, but you can save another 10 bytes by using Deduplicate instead of doing it manually! – Neil Commented Jun 21, 2019 at 18:37 • @Neil Ah, didn't knew about the D-builtin, thanks! And not sure why I used .* instead of ... Thanks for -11 bytes in both versions! :) Commented Jun 21, 2019 at 19:25 • FYI I had a slightly different approach for the same byte count: Try it online! – Neil Commented Jun 21, 2019 at 21:00 • For the decimal version I found that -1\B matches the desired insertion position directly. – Neil Commented Jun 22, 2019 at 23:17 • @Neil Thanks again. Commented Jun 23, 2019 at 15:10 # Julia 1.0, 34 bytes s->sum('a':'z'.∈lowercase(s))/26 Uses the vectorized version of the ∈ operator, checking containment in the string for all characters in the range from a to z. Then sums over the resulting BitArray and divides by total number of possible letters. Try it online! • Welcome and great first answer! Commented Jul 3, 2019 at 21:43 # C, 96 bytes float f(char*s){int i=66,l[256]={};for(;*s;)l[1+*s++&~32]=1;for(;i<92;*l+=l[i++]);return*l/26.;} Try it online! # Perl 5-MList::Util=uniq -p, 24 bytes $_=uniq(lc=~/[a-z]/g)/26
Try it online!
# Stax, 9 bytes
░║üy$}╙+C Run and debug it • You can take a byte off the unpacked version by dropping u and using |b, but the savings disappear under packing. I might have an 8-byter, but the online interpreter is being weird and buggy. Commented Jul 2, 2019 at 19:58 • @Khuldraesethna'Barya: Nice find. I think the bug is probably an array mutation. I'm seeing some of that behavior now. Working on a minimal repro... Commented Jul 2, 2019 at 20:11 • Here's a repro of the problem I guess you're having with |b. It incorrectly mutates its operand rather than making a copy. I've created a github issue for the bug. github.com/tomtheisen/stax/issues/29 As a workaround, |b will work correctly the first time. After that, you may have to reload the page. If you found a different bug, if you can provide a reproduction, I'll probably be able to fix it. Commented Jul 2, 2019 at 20:20 • Stax 1.1.4, 8 bytes. Instructions: unpack, insert v at the start, insert |b after Va, run, remove the first v, remove |b, repack. Yep, that's the bug I found. Commented Jul 2, 2019 at 20:31 • @Khuldraesethna'Barya: I've released 1.1.5, and I believe this bug is fixed now. You can let me know if you still have trouble. Thanks. Commented Jul 9, 2019 at 0:27 # Jelly, 8 bytes ŒuØAe€Æm Try it online! ### Explanation Œu | Convert to upper case ØAe€ | Check whether each capital letter is present, returning a list of 26 0s and 1s Æm | Mean # JavaScript (Node.js), 45 bytes s=>~-s.match(/$|([a-z])(?!.*\1)/ig).length/26
Try it online!
# JavaScript (Node.js), 47 bytes
s=>(s.match(/([a-z])(?!.*\1)/ig)||[]).length/26
Try it online!
# Pyth, 9 bytes
cl@rw0G26
Try it online!
c 26 # Float division by 26 (alternative: replace 26 by lG)
l # Length of
@ # intersection of
r 0 # lowercase
w # input
G # and the lowercase alphabet
# Swift 5.9, 105100 89 bytes
let p={Float((65...90).filter((\$0+"").uppercased().map(\.asciiValue).contains).count)/26}
Using Float instead of Double saved a byte.
# Japt, 9 bytes
;CoU Ê/26
Try it
;CoU Ê/26 :Implicit input of string U
;C :Lowercase alphabet
oU :Remove the characters not included in U, case insensitive
Ê :Length
/26 :Divide by 26
# Python 2, 57 bytes
lambda i:len(set(o for o in i.lower()if o.isalpha()))/26.
Try it online!
A bit longer than the Python 3 answer from ArBo but posted as a different approach in Python 2 anyway.
# Ruby-n, 38 34 bytes
-4 bytes from @historcrat!
p (?A..?Z).count{|c|~/#{c}/i}/26.0
Try it online!
• @histocrat you are correct Commented Jun 21, 2019 at 21:50 | 6,151 | 19,482 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-38 | latest | en | 0.86863 |
https://www.gamedev.net/forums/topic/693363-trandforming-a-3d-point-to-the-2d-screen-given-the-view-direction/ | 1,542,668,085,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039746112.65/warc/CC-MAIN-20181119212731-20181119234731-00401.warc.gz | 827,146,042 | 34,868 | # Trandforming a 3D point to the 2D screen given the view direction
## Recommended Posts
I have a DXF file that I want to render onto the screen as an orthographic 2D image.
The view direction vector is given in the following format:
-0.720495631362985, -1.49503251161485, 0.495745735636187
I want to translate a point onto the screen, given the x, y and z coordinates in the form screen-x, screen-y. Google mostly delivers opengl solutions.
If the View direction is looking straight down (ie. the z-coordinate is removed), then the vector is as follows:
0,0,1
In which case ((int)x, (int)y)==(screen-x,screen-y)
I have asked this question before, but it would seem that that was before the board was upgraded.
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What actually is your question? (I don't mean to be snarky, but you said "I have asked this question before"... except, unless I'm missing something, you didn't ask a question)
Edited by masskonfuzion
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7 hours ago, dgcoventry said:
I want to translate a point onto the screen, given the x, y and z coordinates in the form screen-x, screen-y. Google mostly delivers opengl solutions.
How do I translate a point onto the screen?
I want to get the screen-x and screen-y, given that the viewing direction is x=-0.720495631362985,y= -1.49503251161485, z=0.495745735636187 and the view is orthographic.
If a line is from (0,0,0) to (100,100,100), how is it represented on the screen, given the viewing direction above? I hope this is clearer.
I've had this conversation before on here, but it was years ago and I can't remember how it was resolved.
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The typically way to do this would be to build a 3x3 rotation matrix matching the direction of the viewing vector you have been given, and then multiply each point by that matrix. You'll probably need to multiply that matrix by a scaling matrix to convert the output into window coordinates, but you get the general idea...
What API are you planning to use to draw the points on screen?
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Thanks.
I'll have a look at the link.
I want to render portions of the file as an SVG to be loaded into the browser, so I just need to know the 2D screen projection points in the event of the veiw being anything other than in plan. Hence OpenGL solutions are not really applicable.
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How can I derive the transformation matrix from the view direction?
It strikes me that the values given for the view vector have already been reduced to be plugged into a formula to calculate the screen coordinates. Or do I still need to find the cosines and sines and angles in 3d?
(Thanks for the assistance, by the way)
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The view vector defines the direction of the one axis of your camera system which passes through your center of the view. You typically don't want the camera to be tilted, so the viewing vector and the up vector is all you need to calculate the orientation matrix of the camera. Sines and cosines are not needed for this step; instead the cross product of vectors is what you need. Several threads in this forums discuss that topic; possible keyword for a search is "look-at matrix".
The fact that the projection is orthographic means that all projector line directions are identical to the view vector, so no opening angle is needed. However, also orthographic projection requires a camera position since 2 of its 3 dimensions are not irrelevant (also the 3rd is not irrelevant as soon as you use front-/backplane clipping). You further need to have a scaling, because there is a mapping of units in which the world is defined and units of the screen size. (swiftcoder already mentioned this above.) May be you want to use something like "the entire drawing should be seen" and "looking at the center of the bounding box of the entire drawing" for resolving such values.
Only if you have all this stuff, a view transform can be computed. The principles for this kind of math are not really different with respect to different graphic APIs.
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Thanks.
I have been searching Google using the terms "lookat" and "matrix", but I'm not terribly familiar with the nomenclature used. I've found something here, but again, I am unsure of how it applies to my proposed implementation.
As I explained above, I'm planning to generate a SVG file. Most views of the file will be in the plan view (just the x and y coordinates), but I want to make sure that the 3D capability is preserved if needed.
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A single view vector is not enough to describe the orientation of the camera, the camera can roll around the view direction. But as haegarr points out, you generally don't want your camera to be tilted, so you can probably get away with using (0, 0, 1) as your up direction.
In order to build your camera matrix you simply need 3 orthogonal vectors: right, up, view. These vectors are the columns of your matrix, in that order. To get your vectors you can use the cross product:
right = Cross(view, (0, 0, 1));
up = Cross(right, view);
The reason we recalculate the up vector is because (0, 0, 1) is only orthogonal if view.z == 0. Now if your camera looks in the same direction or in the exact opposite of (0, 0, 1) the cross product becomes 0, which means this will not work, so keep that in mind.
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I'm afraid my difficulties with matrices continues.
Supposing I have a point (100,100,50)
My view direction is defined by the vector (-0.720495631362985, -1.49503251161485, 0.495745735636187)
Up is in the direction (0,0,1)
The cross product of (-0.720495631362985, -1.49503251161485, 0.495745735636187) and (0,0,1) is (0,0.720495631362985,-1.49503251161485). Is this right?
If I cross this with (100,100,50), this gives (72.0495631362985,149.503251161485,-185.528032729634).
So my screenx=72 and screeny=150?
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× | 1,538 | 6,193 | {"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} | 2.78125 | 3 | CC-MAIN-2018-47 | latest | en | 0.943779 |
https://math.stackexchange.com/questions/1981157/regression-for-power-law | 1,558,716,740,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257699.34/warc/CC-MAIN-20190524164533-20190524190533-00400.warc.gz | 533,754,966 | 36,556 | # Regression for power law
I have some data (running time of an algorithm) and I think it follows a power law
$$y_\mathrm{reg} = k x^a$$
I want to determine $k$ and $a$. What I have done so far is to do a linear regression (least squares) through $\log(x), \log(y)$ and determine $k$ and $a$ from its coefficients.
My problem is that since the "absolute" error is minimized for the "log-log data", what is minimized when you look at the original data is the quotient
$$\frac{y}{y_\mathrm{reg}}$$
This leads to large absolute error for large values of $y$. Is there any way to make a "power-law regression" that minimizes the actual "absolute" error? Or at least does a better job at minimizing it?
Example:
The red curve is fit through the whole dataset. The green curve is fit through the last 21 points only.
Okay, since @JJacquelin asked for it I'm posting the data for the plot. The left column are the values of $n$ ($x$-axis), the right column are the values of $t$ ($y$-axis)
1.000000000000000000e+02,1.944999820000248248e-03
1.120000000000000000e+02,1.278203080000253058e-03
1.250000000000000000e+02,2.479853309999952970e-03
1.410000000000000000e+02,2.767649050000500332e-03
1.580000000000000000e+02,3.161272610000196315e-03
1.770000000000000000e+02,3.536506440000266715e-03
1.990000000000000000e+02,3.165302929999711402e-03
2.230000000000000000e+02,3.115432719999944224e-03
2.510000000000000000e+02,4.102446610000356694e-03
2.810000000000000000e+02,6.248937529999807478e-03
3.160000000000000000e+02,4.109296799998674206e-03
3.540000000000000000e+02,8.410178100001530418e-03
3.980000000000000000e+02,9.524117600000181830e-03
4.460000000000000000e+02,8.694799099998817837e-03
5.010000000000000000e+02,1.267794469999898935e-02
5.620000000000000000e+02,1.376997950000031709e-02
6.300000000000000000e+02,1.553864030000227069e-02
7.070000000000000000e+02,1.608576049999897034e-02
7.940000000000000000e+02,2.055535920000011244e-02
8.910000000000000000e+02,2.381920090000448978e-02
1.000000000000000000e+03,2.922614199999884477e-02
1.122000000000000000e+03,1.785056299999610019e-02
1.258000000000000000e+03,3.823622889999569313e-02
1.412000000000000000e+03,3.297452850000013452e-02
1.584000000000000000e+03,4.841355780000071440e-02
1.778000000000000000e+03,4.927822640000271981e-02
1.995000000000000000e+03,6.248602919999939054e-02
2.238000000000000000e+03,7.927740400003813193e-02
2.511000000000000000e+03,9.425949999996419137e-02
2.818000000000000000e+03,1.212073290000148518e-01
3.162000000000000000e+03,1.363937510000141629e-01
3.548000000000000000e+03,1.598689289999697394e-01
3.981000000000000000e+03,2.055201890000262210e-01
4.466000000000000000e+03,2.308686839999722906e-01
5.011000000000000000e+03,2.683506760000113900e-01
5.623000000000000000e+03,3.307920660000149837e-01
6.309000000000000000e+03,3.641307770000139499e-01
7.079000000000000000e+03,5.151283440000042901e-01
7.943000000000000000e+03,5.910637860000065302e-01
8.912000000000000000e+03,5.568920769999863296e-01
1.000000000000000000e+04,6.339683309999486482e-01
1.258900000000000000e+04,1.250584726999989016e+00
1.584800000000000000e+04,1.820368430999963039e+00
1.995200000000000000e+04,2.750779816999994409e+00
2.511800000000000000e+04,4.136365994000016144e+00
3.162200000000000000e+04,5.498797844000023360e+00
3.981000000000000000e+04,7.895301083999981984e+00
5.011800000000000000e+04,9.843239714999981516e+00
6.309500000000000000e+04,1.641506008199996813e+01
7.943200000000000000e+04,2.786652209900000798e+01
1.000000000000000000e+05,3.607965075100003105e+01
1.258920000000000000e+05,5.501840400599996883e+01
1.584890000000000000e+05,8.544515980200003469e+01
1.995260000000000000e+05,1.273598972439999670e+02
2.511880000000000000e+05,1.870695913819999987e+02
3.162270000000000000e+05,3.076423412130000088e+02
3.981070000000000000e+05,4.243025571930002116e+02
5.011870000000000000e+05,6.972544795499998145e+02
6.309570000000000000e+05,1.137165088436000133e+03
7.943280000000000000e+05,1.615926472178005497e+03
1.000000000000000000e+06,2.734825116088002687e+03
1.584893000000000000e+06,6.900561992643000849e+03
(sorry for the messy scientific notation)
• Since tou have the estimates of $k$ and $a$, did you try a nonlinear regression ? – Claude Leibovici Oct 23 '16 at 15:37
• @ ox539 : I think that I have the solution : I tested it successfully with data obtained from a scan of your graph. But the scan cannot give accurate data because the points on the graph are too large circles. Please, post your data. Then I will give the method of solving with numerical result. Preferably, the data should be two separated .txt files ($n$ and $y=t/s$). – JJacquelin Oct 28 '16 at 8:47
• @JJacquelin I posted the data. Is the .csv format OK? – 0x539 Oct 28 '16 at 21:03
• I think this question should be on stats.stackexchange.com – Rodrigo de Azevedo Oct 29 '16 at 7:20
• @ 0x539 : Ok for the data. See my new answer. – JJacquelin Oct 29 '16 at 14:34
We have $n$ ordered pairs $(x_k,y_k)$. Let
$$\tilde{x}_k := \log (x_k) \qquad \qquad \qquad \tilde{y}_k := \log (y_k)$$
and build $n$-dimensional vectors $\tilde{\mathrm x}$ and $\tilde{\mathrm y}$. We are looking for the line
$$\tilde{y} = c_0 + c_1 \tilde{x}$$
that "best" fits the $n$ ordered pairs $(\tilde{x}_k,\tilde{y}_k)$. Hence, we have the following linear system
$$\tilde{\mathrm y} = \begin{bmatrix} | & |\\ 1_n & \tilde{\mathrm x}\\ | & |\end{bmatrix} \begin{bmatrix} c_0\\ c_1\end{bmatrix} =: \mathrm M (\tilde{\mathrm x}) \, \mathrm c$$
where coefficients $c_0$ and $c_1$ can be estimated by solving the unconstrained optimization problem
$$\begin{array}{ll} \text{minimize} & \| \mathrm M (\tilde{\mathrm x}) \, \mathrm c - \tilde{\mathrm y} \|\end{array}$$
Unfortunately, this leads to poor results, as the logarithm amplifies small errors and attenuates large errors. Hence, we introduce the weight matrix
$$\mathrm W := \mbox{diag} (w_1, w_2, \dots, w_n)$$
and solve the following weighted unconstrained optimization problem instead
$$\boxed{\begin{array}{ll} \text{minimize} & \| \mathrm W \left( \mathrm M (\tilde{\mathrm x}) \, \mathrm c - \tilde{\mathrm y} \right) \|\end{array}}$$
Interesting results can be obtained when the weights grow exponentially, say, $w_k = 1.25^k$. Minimizing the $1$-norm, the $2$-norm and the $\infty$-norm, we have
and, in logarithmic scale,
MATLAB + CVX code
clear all; close all; clc;
n = size(data,1);
% extract columns
x = data(:,1);
y = data(:,2);
% take logarithms
x_log = log(x);
y_log = log(y);
% build M matrix
M = [ ones(n,1), x_log ];
% weight matrix
W = diag(1.25.^[1:1:n]);
C = [];
% minimize 1-norm
cvx_begin
variable c(2)
minimize( norm(W*(M*c-y_log),1) )
cvx_end
C = [C, c];
% minimize 2-norm
cvx_begin
variable c(2)
minimize( norm(W*(M*c-y_log),2) )
cvx_end
C = [C, c];
% minimize infinity-norm
cvx_begin
variable c(2)
minimize( norm(W*(M*c-y_log),Inf) )
cvx_end
C = [C, c];
% compute the three lines
Y_log = M * C;
% take exponentials (entrywise)
Y_est = exp(Y_log);
% linear plot
figure;
plot(x,y,'r.-',x,Y_est(:,1),'m.-',x,Y_est(:,2),'b.-',x,Y_est(:,3),'c.-');
legend('raw data','1-norm','2-norm','Inf-norm',4);
xlabel('x');
ylabel('y');
% log plot
figure;
loglog(x,y,'r.-',x,Y_est(:,1),'m.-',x,Y_est(:,2),'b.-',x,Y_est(:,3),'c.-');
legend('raw data','1-norm','2-norm','Inf-norm',4);
xlabel('x');
ylabel('y');
where data.txt contains the raw data posted in the question. The three coefficient vectors are
>> C
C =
-18.3048 -18.9205 -19.5212
1.8978 1.9425 1.9844
The difficulty comes from the oversimplified model with the chosen function $t=kn^a$. The corresponding curve drawn on log-log system of axes is not a straight line. Moreover, the curve is too far from a straight line to achieve a good fitting on so many decades of variation of $n$ and $t$.
Even if you take the last 21 points, it's too much because the corresponding straight line (green) doesn't fit the last points. The fitting can be accurate only on a smaller range where the curvature of the curve remains negligible.
For example, with the 10 last points the result of linear regression is shown on the next graph :
One see on the left figure that the fitting is much improved. But if we consider the whole set of points (on the right figure) the fitting is worse for the first points.
The conclusion is evident : it is impossible to achieve a good fit for all the points with a model of the form $t=kn^a$ with only two adjustable parameters $k$ and $a$.
All depends on what you want do with the model. If it's for practical computation (for example interpolation) you can divide the whole range in a series of segments (for example each one corresponding to one decade) and use for each section the different values of $k,n$ obtained from linear regression.
In other cases, a more sophisticated model is required with more adjustable parameters and non-linear regression. It's a hard task if both the absolute and relative deviations have to be minimized on a large range (several decades) of data.
The best is if the choice of functions in the model is oriented by physical consideration when the data comes from real experiment. In the present case, without further information, a polynomial function was chosen with four parameters. This model leads to the result below :
All the points where taken in the linear regression for the coefficients of the polynomial function.
• Can't weighting be used? It seems to work. – Rodrigo de Azevedo Oct 30 '16 at 4:20
• Of course, you can try weighting. But I think that any method applied with the simple model $t=kn^a$ will give a good fitting only for a small range, not on the whole range. This is confirmed by your answer and results : The fit is good for about the last 10 points. The fit is very poor for the majority of the points, except the last ones. The discrepancy is especially big for a lot of the first points. If your goal is only to have a model convenient for the last points, there is no need for a complicated method : just use the last points and forget all the others. – JJacquelin Oct 30 '16 at 6:25
• @JJacquelin I used the $t = kn^a$ model because the time complexity of algorithms usually looks like $O(n^a)$. – 0x539 Oct 30 '16 at 8:10
• @0x539 : I well understand that on the practical viewpoint. But don't be surprised if the fitting isn't good on the whole the range of the variables : $O(n^a)$ doesn't mean that this empirical law is exact. More terms might be influant, requiring a model with more adjustable parameters. – JJacquelin Oct 30 '16 at 10:50 | 3,617 | 10,563 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-22 | latest | en | 0.68035 |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-5-section-5-1-verifying-trigonometric-identities-exercise-set-page-658/12 | 1,680,324,045,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949701.0/warc/CC-MAIN-20230401032604-20230401062604-00438.warc.gz | 868,731,630 | 12,391 | ## Precalculus (6th Edition) Blitzer
To verify the given identity, $\tan \theta +\cot \theta =\sec \theta \csc \theta$ Recall Trigonometric Identities, \begin{align} & {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1 \\ & \tan \theta =\frac{\sin \theta }{\cos \theta } \\ & \cot \theta =\frac{\cos \theta }{\sin \theta } \\ \end{align} Use the above identities and solve the left side of the given expression, \begin{align} & \tan \theta +\cot \theta =\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta } \\ & =\frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta \cos \theta } \\ & =\frac{1}{\sin \theta \cos \theta } \\ & =\frac{1}{\sin \theta }\left( \frac{1}{\cos \theta } \right) \end{align} Recall Reciprocal Identities, \begin{align} & \csc \theta =\frac{1}{\sin \theta } \\ & \sec \theta =\frac{1}{\cos \theta } \\ \end{align} Therefore, $\tan \theta +\cot \theta =\sec \theta \csc \theta$ Hence, it is proved that the given identity holds true. | 341 | 972 | {"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": 3, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2023-14 | latest | en | 0.471295 |
https://assignmenthelp.xyz/vehicle-netwrok-in-matlab/ | 1,537,809,938,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267160620.68/warc/CC-MAIN-20180924165426-20180924185826-00122.warc.gz | 459,701,902 | 13,764 | Select Page
# The Birth of Vehicle Netwrok in MATLAB
Each such combination is known as an instantiation of the parent collection. Their used waned due to the limited computational power available at the moment, and some theoretical issues which weren't solved for a number of decades (that I will detail at the conclusion of this post). The best thing about this sort of software is the fact that it is relatively user friendly. One of the simplest strategies to design a structure is to produce layers of elements. Still, most probably you should exchange the aged starter for the new one. Matlab online assistance and tutorials are available here. It's also wise to have a rough comprehension of how a fundamental neural network operates and the way that it can process data.
Learn with the experts our tutors can assist with the whole vital subjects that your son or daughter needs for passing their exams. Not mentioning, utilize the prior questions to ensure you landed what you picked to have. Beyond understanding the algorithms, there's also a practical question of the way to generate the input data in the very first location. You are going to be notified whenever the author creates a post. Each link is connected with weight. The web has brought an entirely new degree of assistance. Our essay help online provides the ideal essay assignment assistance and essay writing help.
The first weights are going to be between 0 and 1, but note that the last weights don't will need to be. The body comprises range of muscles. It's an involuntary muscle that has striped and smooth tissues. The cardiac muscle calls for a distinctive electrical system for sending the right signals, at the suitable time, to operate properly. Even straightforward animal brains are capable of functions that are now not possible for computers. It's about machines and a new means to address problems.
## The One Thing to Do for Vehicle Netwrok in MATLAB
Vehicle network is just one of the fields that can be regarded as highly specialized because it addresses the problem certain statements. These networks have to be capable of an endless number of responses. Learning vector quantization (LVQ) networks utilize a way of classifying patterns that aren't linearly separable. You may design a neural network to inform your whether or not there's a tumor in the image, but it isn't a trivial job for a neural network to let you know where it's located. Radial basis networks offer an alternative, quick process for designing nonlinear feedforward networks.
If you do choose to let your network determine whether a given image comprises a tumor, you would require a big number of images without tumors also. Basic varieties of neural networks are easy to implement directly. Of course, they play a significant role in data mining processes. These artificial neural networks attempt to replicate only the most fundamental elements of this complicated, versatile, and effective organism. By the end, you will understand how to construct your very own flexible, learning network, very similar to Mind.
The implementation makes it rather simple to add extra panels to an application. This approach lends itself to physical implementation on a huge scale in a little package. The central nervous system coordinates the performance of all portions of the body and is the biggest portion of the nervous system. I'm a newbie in regards to this technology thing and I'll appreciate it very much if you were able to help me with my.
Is today the day you begin your own small business. In the easiest case, these goods are simply summed, fed through a transfer function to create an outcome, and then output. The item was initially released in 2003. You may now browse and order all holt and mcdougal goods in the same region.
## The Honest to Goodness Truth on Vehicle Netwrok in MATLAB
You'll find here a run of short Matlab Programs that you're encouraged to download and try. This book gives a detailed introduction to communication systems. In case you have any questions, french essay writing service please don't hesitate to get in touch with us.
The activation usually uses one of these functions. There are various varieties of activation function but among the simplest would be step function. Lastly, the processing element is prepared to output the consequence of its transfer function. At this time any input training vector could be presented to the network and it'll respond with the right output vector. There are not any feedback loops. This block does not have any input ports. It has no output ports.
You will discover a compact libraries of functions that you may download and use freely. In addition, there are many programming libraries that contain neural network functionality and that may be utilized in custom implementations. Next region of the program needs to be executed just only once in the start. The students that are solving problems that are associated with the vehicles network always has the choice to require expert guidance. Help your kids with homework and you won't be disappointed. Do you need assistance with this assignment. | 984 | 5,155 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2018-39 | longest | en | 0.954702 |
https://winter.group.shef.ac.uk/chemdex/chemistry/mlxzq_grid?element=Ar | 1,726,076,933,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651390.33/warc/CC-MAIN-20240911152031-20240911182031-00619.warc.gz | 591,475,476 | 4,793 | # MLXZQ± Grid
## MLXZq± grid for argon (Ar) for Q = -6: [ArXxLlZz]6-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = -5: [ArXxLlZz]5-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = -4: [ArXxLlZz]4-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = -3: [ArXxLlZz]3-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = -2: [ArXxLlZz]2-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = -1: [ArXxLlZz]-
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = 0: [ArXxLlZz]
The number of compounds found is 1.
The intensity of the colour of each table cell relates to the percentage of compounds found with the [MLXZ] classification associated with that cell. A separate table for each value of q± is plotted. Select any entry in the tables where there is shading to see a list of compounds of argon with that [MLXZ] classification.
EN➝ 8
X+2Z = 0 [Ar]
100%
X+2Z = 1
X+2Z = 2 [ArZ]
0
X+2Z = 3
X+2Z = 4 [ArZ2]
0
X+2Z = 5
X+2Z = 6 [ArZ3]
0
X+2Z = 7
X+2Z = 8 [ArZ4]
0
X+2Z = 9
X+2Z = 10 [ArZ5]
0
X+2Z = 11
X+2Z = 12 [ArZ6]
0
## MLXZq± grid for argon (Ar) for Q = 1: [ArXxLlZz]+
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = 2: [ArXxLlZz]2+
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = 3: [ArXxLlZz]3+
The number of compounds found is 0.
## MLXZq± grid for argon (Ar) for Q = 4: [ArXxLlZz]4+
The number of compounds found is 0. | 665 | 1,547 | {"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-2024-38 | latest | en | 0.871756 |
http://slidegur.com/doc/1648792/quadratic-formula---pha-math-central | 1,569,110,334,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574710.66/warc/CC-MAIN-20190921231814-20190922013814-00375.warc.gz | 181,685,206 | 10,600 | Quadratic Formula - PHA Math Central
```Do Now:
WRITE THE EQUATION
FORMULA FROM
MEMORY!!!!
Take out HW-hand in
Imaginary Numbers!
We will
Investigate how to find
the equation of a
Formula WORKSHEET –
odds only!!!
Intro:
equation is:
y = ax2 + bx + c
The coefficients are: a , b, c
The
variables are: y, x
The
ROOTS (or
solutions) of a
polynomial are
its x-intercepts
The
x-intercepts
occur where y =
0.
Roots
Example: Find the
roots: y = x2 + x - 6
Solution: Factoring:
y = (x + 3)(x - 2)
0 = (x + 3)(x - 2)
The roots are:
x = -3; x = 2
Roots
After centuries of
work,
mathematicians
realized that as long
as you know the
coefficients, you can
find the roots of the
doesn’t factor!
y ax 2 bx c, a 0
b b 2 4ac
x
2a
Watch this:
eature=related
(another time…)
http://vihart.com/doodling/
Extra Credit if you create a video/song/anything
creative!! You have 2 weeks!
Solve: y = 5x 8x 3
a 5, b 8, c 3
2
8 64 60
x
10
2
b b 4ac
8
4
x
x
2a
10
2
(8) (8) 4(5)(3)
8 2
x
x
2(5)
10
8 2
x
10
8 2 10
x
1
10
10
82 6 3
x
10 10 5
Roots
2
y 5 35 8 35 3
y 5 9 25 24 5 3
45
24 3
y
2
25
5
y 5(1) 8(1) 3
9
24
15
y
y 583
5
5
5
y0
y0
Plug in your
If you’re right,
you’ll get y = 0.
2
Solve : y 2x 7x 4
DO NOW ** WRITE THE
EQUATION FOR THE
MEMORY then solve the
Class Work:
AS PROMISED….
Imaginary numbers!!
WE will:
Check out the world of
IMAGINARY NUMBERS!!!
WORKSHEET – 1-10!!!
7
49
32
Solve : y 2x 7x 4 x
4
a 2, b 7, c 4
7 81
x
2
b b 4ac
4
x
7 9 2 1
2a
x
x
4
4 2
2
(7) (7) 4(2)(4)
16
x
x
4
2(2)
4
2
Remember: All the terms must be on one
side BEFORE you use the quadratic
formula.
•Example: Solve 3m2 - 8 = 10m
•Solution: 3m2 - 10m - 8 = 0
•a = 3, b = -10, c = -8
Free Fallin’
The acceleration of
gravity (g) for objects in
free fall at the earth's
surface is 9.8 m/s2.
Galileo found that all
things fall at the same
rate.
Free Fall
The rate of falling
increases by 9.8 m/s
every second.
Height = ½ gt2
For example:
½ (9.8 )12 = 4.9 m
½(9.8)22 = 19.6 m
½ (9.8)32 = 44.1 m
½ (9.8)42 = 78.4 m
Free Fall
A ball thrown horizontally
will fall at the same rate as
a ball dropped directly.
Free Fall
A ball thrown into the air
will slow down, stop, and
then begin to fall with the
acceleration due to gravity.
When it passes the
thrower, it will be traveling
at the same rate at which it
was thrown.
Free Fall
An object thrown upward at an angle to the ground follows a curved
path called a parabola.
Air Resistance
• In air…
– A stone falls faster than a
feather
• Air resistance affects
stone less
• In a vacuum
– A stone and a feather will fall
at the same speed.
Air Resistance
• Free Fall
– A person in free fall reaches a
terminal velocity of around 54
m/s
– With a parachute, terminal
velocity is only 6.3 m/s
• Allows a safe
landing
The initial velocity is the coefficient for the middle
term, and the initial height is the constant term.
The coefficient on the leading term comes from the
force of gravity. This coefficient is negative, since
gravity pulls downward, and the value will either be
"4.9" (if your units are "meters") or "16" (if your
units are "feet"). In general, the format is:
s(t) = –gt2 + v0t + h0
...where "g" here is the "4.9" or the "16" derived
from the value of the force of gravity (technically,
it's half of the force of gravity, but you probably
don't need to know that right now), "v0" ("veenaught", or "vee-sub-zero") is the initial velocity,
and "h0" ("aitch-naught", or "aitch-sub-zero") is the
initial height.
An object is launched at 19.6 meters per second
(m/s) from a 58.8-meter tall platform. The equation
for the object's height s at time t seconds after
launch is s (t) = –4.9t2 + 19.6t + 58.8, where s is in
meters. When does the object strike the ground?
What do we know vs. What do we need to know? (3
min)
I'll set s equal to zero, and solve:
0 = –4.9t2 + 19.6t + 58.8
0 = t2 – 4t – 12
0 = (t – 6)(t + 2)
Then t = 6 or t = –2. The second solution is from two
seconds before launch, which doesn't make sense in this
context. (It makes sense on the graph, because the line
crosses the x-axis at –2, but negative time won't work in
this word problem.) So "t = –2" is an extraneous solution,
and I'll ignore it.
The object strikes the ground six seconds after launch.
An object in launched directly upward at 64 feet per
second (ft/s) from a platform 80 feet high. What
will be the object's maximum height? When will it
attain this height?
Think Pair Share (3 min)
What do I know?
What do I need to find out??
The initial height is 80 feet above ground and the
initial speed is 64 ft/s. Since my units are "feet",
then the number for gravity will be 16, and my
equation is:
s(t) = –16t2 + 64t + 80
Yes?
They want me to find the maximum height. For a
negative quadratic like this, the maximum will be at
the vertex of the upside-down parabola. So they
really want me to find the vertex. From our past
experience with graphing, I know how to find the
vertex;
in this case, the vertex is at (2, 144):
x = –b/2a = –(64)/2(–16) = –64/–32 = 2
Y = s(2) = –16(2)2 + 64(2) + 80 = –16(4) + 128 + 80
= 208 – 64 = 144
But what does this vertex tell me? According to my
equation, I'm plugging in time values and extracting
height values, so the input "2" must be the time and
the output "144" must be the height.
It takes two seconds to reach the maximum height of
144 feet.
2 4 84
x
6
2 88
x
6
2
2 4 • 22
b b 4ac
x
x
6
2a
2
(2) (2) 4(3)(7) x 2 2 22
x
6
1 22
2(3)
x
3
Solve:
3x2 = 7 - 2x
Solution: 3x2 + 2x - 7 =
0
a = 3, b = 2, c = -7
``` | 2,506 | 5,745 | {"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-2019-39 | latest | en | 0.539074 |
https://www.physicsforums.com/threads/how-to-calculate-attractive-force-between-mag-electromag.820782/ | 1,726,094,978,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651405.61/warc/CC-MAIN-20240911215612-20240912005612-00768.warc.gz | 866,663,184 | 16,757 | # How to calculate attractive force between mag & electromag?
In summary, the attractive force between a magnet and an electromagnet can be calculated using the formula F = (μ0 * m1 * m2)/ (2 * π * r^2), where F is measured in Newtons or pound-force and is inversely proportional to the square of the distance between them. This force is always positive and is affected by the magnetic dipole moment of the electromagnet, with a stronger electromagnet resulting in a stronger attractive force.
I am aware of the complexity of magnetic fields, all i need is a ballpark functional equation of distance between an electromagnet and a permanent magnet. Can anyone point me in the right direction?
## 1. How do you calculate the attractive force between a magnet and an electromagnet?
The attractive force between a magnet and an electromagnet can be calculated using the following formula: F = (μ0 * m1 * m2)/ (2 * π * r^2), where F is the attractive force in Newtons, μ0 is the permeability of free space (4π * 10^-7), m1 and m2 are the magnetic dipole moments of the magnet and electromagnet respectively, and r is the distance between them.
## 2. What units are used to measure the attractive force between a magnet and an electromagnet?
The attractive force between a magnet and an electromagnet is typically measured in Newtons (N) or pound-force (lbf).
## 3. How does the distance between a magnet and an electromagnet affect the attractive force?
The attractive force between a magnet and an electromagnet is inversely proportional to the square of the distance between them. This means that as the distance between them increases, the attractive force decreases.
## 4. Can the attractive force between a magnet and an electromagnet be negative?
No, the attractive force between a magnet and an electromagnet is always positive. It represents the force pulling the two objects together, regardless of their polarity.
## 5. How does changing the magnetic dipole moment of the electromagnet affect the attractive force?
The magnetic dipole moment of the electromagnet directly affects the attractive force between the magnet and electromagnet. As the magnetic dipole moment increases, the attractive force also increases. This means that a stronger electromagnet will have a stronger attractive force on the magnet.
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1K | 583 | 2,522 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2024-38 | latest | en | 0.927659 |
https://forum.azimuthproject.org/plugin/ViewComment/19193 | 1,576,408,824,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00337.warc.gz | 360,783,653 | 2,267 | Matthew wrote:
> For one, we get a category, which I am going to call \$$\mathbf{Mult}\$$
> - The objects are the morphisms of \$$\mathbf{N}\$$
> - The identity is the identity functor \$$\mathbf{1}_{\bullet}\$$, corresponding to the scaling \$$1 \times \cdot\$$
> - Morphisms in this category are functors \$$F : \mathbf{N} \to \mathbf{N}\$$
> - Morphism composition is functor composition \$$\bullet\$$
In a category, each morphism goes from one particular object to one particular object. You're not specifying how this works for \$$\mathbf{Mult}\$$.
But I can guess: morphisms in \$$\mathbf{Mult}\$$ are not really functors \$$F : \mathbf{N} \to \mathbf{N}\$$; rather, each functor \$$F : \mathbf{N} \to \mathbf{N}\$$ gives infinitely many morphisms in \$$\mathbf{Mult}\$$, one for each object of \$$\mathbf{Mult}\$$. Objects of \$$\mathbf{Mult}\$$ can be identified with natural numbers, and if a functor \$$F : \mathbf{N} \to \mathbf{N}\$$ maps the object \$$n\$$ to the object \$$n'\$$, we decree that there's a morphism
$(F,n) : n \to n'$
in \$$\mathbf{Mult}\$$. We compose these in the obvious way:
$(F',n') \circ (F,n) = (F' \circ F, n) .$
This is an example of a sort of well-known construction. | 391 | 1,214 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2019-51 | longest | en | 0.747863 |
https://www.physicsforums.com/threads/geomertical-optics-derivation-of-graph-of-u-v-against-u.767204/ | 1,532,307,065,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676594675.66/warc/CC-MAIN-20180722233159-20180723013159-00000.warc.gz | 954,278,589 | 15,653 | # Homework Help: Geomertical optics- derivation of graph of (u+v) against u
1. Aug 23, 2014
### somecelxis
1. The problem statement, all variables and given/known data
may i know how to derive the the sha[pe of graph and get the point of min (2f , 4f) ? i really have no idea how to get the shape of the graph and the min point. The book give it without any explaination.
2. Relevant equations
3. The attempt at a solution
#### Attached Files:
• ###### DSC_0074.jpg
File size:
21.5 KB
Views:
134
2. Aug 23, 2014
### Simon Bridge
Do you have an equation that related u,v, and f?
Put v=d-u, and solve for d.
3. Aug 23, 2014
### somecelxis
what equation is that? v=d-u i have only 1/u +1/v =1/f in my book
4. Aug 23, 2014
### Simon Bridge
1/u + 1/v = 1/f is a good place to start - that's the lensmakers formula.
can you rearrange that equation to make v the subject?
5. Aug 23, 2014
### somecelxis
v= uf /(u-f) what shall i do next?
6. Aug 23, 2014
### Simon Bridge
OK - so if that is v, then v+u = ? | 327 | 1,021 | {"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-2018-30 | latest | en | 0.862606 |
https://subscription.packtpub.com/book/data/9781783987603/1 | 1,701,504,932,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100381.14/warc/CC-MAIN-20231202073445-20231202103445-00578.warc.gz | 633,265,114 | 28,532 | #### Overview of this book
Learning Bayesian Models with R
Credits
www.PacktPub.com
Preface
Free Chapter
Introducing the Probability Theory
The R Environment
Introducing Bayesian Inference
Machine Learning Using Bayesian Inference
Bayesian Regression Models
Bayesian Classification Models
Bayesian Models for Unsupervised Learning
Bayesian Neural Networks
Bayesian Modeling at Big Data Scale
Index
## Chapter 1. Introducing the Probability Theory
Bayesian inference is a method of learning about the relationship between variables from data, in the presence of uncertainty, in real-world problems. It is one of the frameworks of probability theory. Any reader interested in Bayesian inference should have a good knowledge of probability theory to understand and use Bayesian inference. This chapter covers an overview of probability theory, which will be sufficient to understand the rest of the chapters in this book.
It was Pierre-Simon Laplace who first proposed a formal definition of probability with mathematical rigor. This definition is called the Classical Definition and it states the following:
The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible. --Pierre-Simon Laplace, A Philosophical Essay on Probabilities
What this definition means is that, if a random experiment can result in mutually exclusive and equally likely outcomes, the probability of the event is given by:
Here, is the number of occurrences of the event .
To illustrate this concept, let us take a simple example of a rolling dice. If the dice is a fair dice, then all the faces will have an equal chance of showing up when the dice is rolled. Then, the probability of each face showing up is 1/6. However, when one rolls the dice 100 times, all the faces will not come in equal proportions of 1/6 due to random fluctuations. The estimate of probability of each face is the number of times the face shows up divided by the number of rolls. As the denominator is very large, this ratio will be close to 1/6.
In the long run, this classical definition treats the probability of an uncertain event as the relative frequency of its occurrence. This is also called a frequentist approach to probability. Although this approach is suitable for a large class of problems, there are cases where this type of approach cannot be used. As an example, consider the following question: Is Pataliputra the name of an ancient city or a king? In such cases, we have a degree of belief in various plausible answers, but it is not based on counts in the outcome of an experiment (in the Sanskrit language Putra means son, therefore some people may believe that Pataliputra is the name of an ancient king in India, but it is a city).
Another example is, What is the chance of the Democratic Party winning the election in 2016 in America? Some people may believe it is 1/2 and some people may believe it is 2/3. In this case, probability is defined as the degree of belief of a person in the outcome of an uncertain event. This is called the subjective definition of probability.
One of the limitations of the classical or frequentist definition of probability is that it cannot address subjective probabilities. As we will see later in this book, Bayesian inference is a natural framework for treating both frequentist and subjective interpretations of probability. | 770 | 3,826 | {"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} | 3.625 | 4 | CC-MAIN-2023-50 | latest | en | 0.920803 |
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# 4.01: Fundamentos de E
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# X g(x) 0 \$325 5 \$400 10 \$475 Write the equation of the line in point-slope, slope-intercept, and standard forms.
### Another question on Mathematics
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Choose the equation that represents the graph below: (1 point) graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 will award ! | 283 | 1,001 | {"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-2024-30 | latest | en | 0.869581 |
http://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/chapter-7-section-7-2-trigonometric-integrals-7-2-exercises-page-484/22 | 1,524,541,641,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946453.89/warc/CC-MAIN-20180424022317-20180424042317-00147.warc.gz | 423,877,403 | 13,290 | ## Calculus: Early Transcendentals 8th Edition
$$\int\tan^2\theta\sec^4\theta d\theta=\frac{\tan^3\theta}{3}+\frac{\tan^5\theta}{5}+C$$
$$A=\int\tan^2\theta\sec^4\theta d\theta$$ In encounter with an integral with $\tan x$ and $\sec x$, 3 basic formulas need to be remembered: $$(\tan x)'=\sec^2 x$$ $$(\sec x)'=\sec x\tan x$$ $$\sec^2 x=1+\tan^2 x$$ We would use them for transformations as follows $$A=\int(\tan^2\theta\sec^2\theta)sec^2\theta d\theta$$ $$A=\int[\tan^2\theta(1+\tan^2\theta)]sec^2\theta d\theta$$ *To do the Substitution here, we would let $u=\tan\theta$ Let $u=\tan\theta$. Then $du=\sec^2\theta d\theta$. Which means, $$A=\int u^2(1+u^2)du$$ $$A=\int(u^2+u^4)du$$ $$A=\frac{u^3}{3}+\frac{u^5}{5}+C$$ $$A=\frac{\tan^3\theta}{3}+\frac{\tan^5\theta}{5}+C$$ | 326 | 775 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2018-17 | latest | en | 0.507569 |
https://avia_en_ru.academic.ru/5650/control_discrete | 1,708,493,299,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473370.18/warc/CC-MAIN-20240221034447-20240221064447-00814.warc.gz | 131,295,161 | 11,515 | # control discrete
control discrete
дискретный сигнал управления
Авиасловарь. . 2004.
### Смотреть что такое "control discrete" в других словарях:
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# In each production lot for a certain toy, 25 percent of the
Author Message
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Joined: 07 Jul 2003
Posts: 56
In each production lot for a certain toy, 25 percent of the [#permalink]
### Show Tags
09 Feb 2004, 12:43
This topic is locked. If you want to discuss this question please re-post it in the respective forum.
In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?
(A) 15 (B) 25 (C) 30
(D) 35 (E) 40
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Joined: 03 Jul 2003
Posts: 652
### Show Tags
09 Feb 2004, 12:58
Assume Total = 100
N(R) = N(R&A) + N(R&B) = 25
N(Bl) = N(Bl&A) + N(Bl&B) = 75
N(A) = N(R&A) + N(Bl&A) =50
N(B) = N(R&B) + N(Bl&B) 50
N(R&A) = 10
Solving these eqn, gives N(Bl&B) = 35.
Where,
N(X) = Number of X
R = red,
Bl =Blue
A = type A
B = type B
09 Feb 2004, 12:58
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Let a ≠ 0, b and c be real numbers. Show that, if there is areal valued f such that f(f(x)) = ax^2 + bx + c for every real x, then (b - 1)^2 ≤ 4(ac + 1) I don't know how to this, but I was told that several guys with a good knowledge in calculus had a lot of trouble and a smart 14- year-old boy gave a correct proof using high school algebra. Can someone help?
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Not the answer you are looking for? Search for more explanations. | 353 | 1,303 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2017-22 | longest | en | 0.521127 |
https://math.stackexchange.com/questions/2082634/whats-the-name-of-a-number-that-cannot-be-represented-with-a-finite-number-of-d | 1,566,357,647,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00556.warc.gz | 557,310,760 | 30,556 | # What's the name of a number that cannot be represented with a finite number of digits in a specific base?
I'm writing some code, and I'm trying to succintly explain that $0.1$ has infinitely many repeating decimals in base 2 ($0.0\overline{0011}_2$).
How can I succintly explain this to a programmer, in a source code comment, without using $\LaTeX$ or too advanced UTF-8 symbols? Does it have a name?
• non-terminating. – symplectomorphic Jan 3 '17 at 22:56
• This only answers your second question; however, the following link may be of use. It's called a repeating decimal. (Who knew! :)) Even though you're using base 2, I suppose the decimal is for "decimal point". – Fine Man Jan 3 '17 at 22:56
I would say "$0.1$ is non-terminating in base $2$". "A repeating decimal" would also be an appropriate phrase to use in place of "non-terminating".
If you're trying to demonstrate that it's non-terminating, I can't suggest anything better than just saying "$0.1$ is '$0.000110011\ldots$' in base $2$". I'd recommend not trying to explain any further in comments; if they don't understand what "non-terminating" means, they can look it up.
In your example, you would say that $0.1_{10}$ is not a binary fraction, meaning that it cannot be expressed as a fraction with a denominator that is a power of $2$.
For example, $0.75_{10}$ can be expressed as $\frac{3}{2^2}$, so it is a binary fraction. | 386 | 1,401 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2019-35 | latest | en | 0.959055 |
https://www.techylib.com/el/view/coralmonkey/thermodynamics_unit_mounds_park_academy | 1,529,552,000,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864019.29/warc/CC-MAIN-20180621020632-20180621040632-00153.warc.gz | 926,918,305 | 16,880 | # Thermodynamics Unit - Mounds Park Academy
Μηχανική
27 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)
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Thermodynamics Unit
Heat Transfers
Heat in Phase Changes
Thermochemical Equations
Heat Transfers: pp. 293
298
Heat in Phase Change: pp. 307
-
221
Thermochemical Equations
: pp. 303
306
Assignment 1:
Heat Problems
1.
How much heat does 32.0 g of water absorb when it is heated from 25.0
o
C to
80.0
o
C?
q =
32.0g x 4.18
j
x 55.0
o
C =
7360 j
g
o
C
2.
How much heat is absorbed when 88.0 g of wate
r is heated from 5
o
C to 37
o
C?
q =
88.0g x 4.18
j
x 32
o
C =
10,000 j
*this is
rounded to
g
o
C
one digit
because of
t
he 5
o
C
3.
When 435 J of heat is added to 3.4 g of olive oil at 21
o
C
, the
temperature
increases to
85.
o
C. What is the specific heat of olive oil?
435 j = 3.4g x C x 64
o
C =
2.00
j
g
o
C
Would olive oil or water have a larger temperature change given the same amount
of energy?
The olive
oil would have a greater temperature change because it has
a smaller specific heat. (Takes less energy to raise the temp 1
o
C)
4.
1500 joules of heat are added to 50.0g of water. How much would the
temperature change? Would the temperature increase or
decrease?
1500 j = 50.0g x 4.18
j
x
t =
7.2
o
C
g
o
C
5.
How many joules are required to heat 100.0g of copper from 10.0
o
C to 100.0
o
C?
q = 100.0g x 0.385
j
x 90.0
o
C =
347 j
g
o
C
The same quantity of heat is added to 100.0g of aluminum at 10.0
o
C. W
hich gets
hotter, the copper or the aluminum? Explain.
The Cu gets hotter because it have a lower specific heat than Al.
6.
A 15.0g sample of metal at 100.0
o
C is added to 100.0g of water at 21.0
o
C. The
temperature of the water increases to 22.2
o
C. What
is the specific heat of the
metal?
q H
2
O absorbed = 100.0g x 4.18
j
x 1.2
o
C = 502 j from metal
g
o
C
502 j released by metal = 15.0g metal x C of metal x 77.8
o
C
C = 0.430
j
g
o
C
7.
A 10.0g sample o
f copper that was 100.0
o
C was added to a sample of water at
25.0
o
C. The temperature of the water increased to 35.0
o
C. What was the mass of
the water sample?
q metal = 10.0g x 0.385
j
x 65.0
o
C = 250. joules
g
o
C
250. j abs
orbed from metal = m x 4.18
j
x 10.0
o
C
g
o
C
m = 5.98g H
2
O
8.
One gram of anthracite coal when burned evolves about 7300 calories. What
weight of coal is required to heat 4.0 liters of water from room temperature
(20.0
o
C) to
the boiling point (100.0
o
C)?
q to heat H
2
O = 4000g x 1.00
cal
x 80.0
o
C = 320000 cal
g
o
C
32000 cal needed, 1 gram generates 7300 cal, so
32000 cal
=
44g of anthracite
7300 cal
Assignment 2:
Heat in Phase Chan
ges
1.
What energy is required to change 1 gram of water at 100
o
C to steam at 100
o
C?
540 cal
are required (called the heat of vaporization)
2.
How much energy is required to change 100 moles of water at 0
o
C to ice at 0
o
C?
100 moles x
18.0
15
g
= 1801.5
g of water
1 mole
1801.5g x 80.0 cal/g = 144,120
cal =
100,000 to 1 sig fig
3.
How much heat does it take to vaporize 1.0 moles of water at 100
o
C?
1.0 mole H
2
O x
18.015g
= 18.07g H
2
O
1 mole H
2
O
18.015g H
2
O x 540 cal/g = 9728 cal =
9700cal to 2 sig fig
4.
How much heat is liberated when 18.0g of water vapor turns into rain?
1.0 mole H
2
O x
18.015g
= 18.07g H
2
O
1 mole H
2
O
18.015g H
2
O x 540 cal/g = 9728 cal
=
9700cal to 2 sig fig
5.
How much heat is removed from your hand when 18g of snow melts on your
glove?
18g x 80.0 cal/g = 1440 cal =
1400 cal to 1 sig fig
6.
How much heat is liberated when 450.0g of steam at 100
o
C is changed to water
at
20
o
C?
450.0g 540 cal/g = 243000cal
total = 280,000cal
450.0g x 1
cal
x 80.0
o
C = 36000cal
to 2 sig fig
g
o
C
7.
Calculate the amount of heat required to convert 20.0g of ice at 0.0
o
C to steam at
100
o
C.
20.0g x
80.0 cal/g = 1600 cal
total =
14400
cal
20.0g x
1
cal
x 100.0
o
C = 2000 cal
to 3 sig fig
g
o
C
20.0g x 540 cal/g = 10800cal
8.
Calculate the amount of heat required to convert 15.0g of ice at
-
8.0
o
C to
steam at
105.0
o
C. (Specific heats: ice = 0.500cal/g
o
C; water = 1.00cal/g
o
C; steam =
0.480cal/g
o
C)
15.0g x 0.500
cal
x 8.0
o
C = 60. cal
g
o
C
15.0g x 80.0 cal/g = 1200 cal
total = 11000 cal
15.0g x 1
cal
x 100.0
o
C = 1500 cal
to 2 sig fig
g
o
C
15.0g x 540 cal/g = 8100 cal
15.0g x 0.480
cal
x 5
.0
o
C = 36 cal
g
o
C
9.
Calculate the heat evolved when 65.0g of liquid at 0.0
o
C forms ice at 0.0
o
C.
65
.0g x 80.0 cal/g = 5200 cal or
5.20 x 10
3
cal to 2 sig fig
10.
Calculate the amount of heat required to liquefy 20.0g of alcohol at its freezing
point. (Heat of fusion for alcohol is 24.9cal/g)
20.0g x 24.9 cal/g =
498 cal
Assignment
3:
Thermochemical Equations Given Heat of
Reaction.
1.
Define
a. endothermic
a reaction in which energy is absorbed
b. exothermic
a reaction in which energy is released
c. enthalpy
heat (energy) changes in a reaction
2.
For the reaction:
C
8
H
18
(l) +
25/2 O
2
(g)
8 CO
2
(g) + 9 H
2
O (g) + 1300 kJ
a.
Is the reaction exothermic or endothermic?
exothermic
b.
How much energy is released when 456.0g of C
8
H
18
burns?
456,0g C
8
H
18
x
1 mole C
8
H
18
x
1300kJ
=
5190kJ
114.22g C
8
H
18
1 mole C
8
H
18
c.
H =
-
1300kJ
d.
How does the energy of the reactants compare to the energy of the products?
Draw a sketch of the graph of energy vs. time.
3.
For the reaction:
2 CO
2
(g)
2 CO (g) + O
2
(g)
H = +43.9 kJ
a.
Write the ther
mochemical equation (put the heat in the equation).
43.9kJ + 2 CO
2
(g)
㈠2O (朩† ⁏
2
(g)
b.
Is the reaction exothermic or endothermic?
endothermic
c.
How much energy is required to decompose 5.0L of CO
2
gas?
5.0L CO
2
x
1 mole CO
2
x
43.
9kJ
=
46kJ
22.4L CO
2
2 mole CO
2
d.
How does the energy of the products compare to the energy of the reactants?
The energy of the products is higher than the energy of the reactants.
e.
How much energy is needed to form 64.0g of O
2
gas?
64g O
2
x
1 mole O
2
x
43.9kJ
=
88kJ
32.00g O
2
1 mole O
2
f.
How many grams of CO
2
gas can be decomposed when 29 kJ of energy is
available?
29kJ x
2 mole CO
2
x
44.04g CO
2
=
58g CO
2
43.9kJ
1
mole CO
2
g.
What is the energy released per mole of carbon monoxide?
1 mol CO x
43.9kJ
=
21.95kJ
2 mole CO
4.
When water is formed from hydrogen gas and oxygen gas, 1.61 kJ/ g H
2
O of
energy is released.
a.
What the heat released per mole o
f water?
1.61kJ
x
18.01g H
2
O
=
29.0kj/mole
H
2
O
g H
2
O 1 mole H
2
O
b.
Is the reaction exothermic or endothermic?
exothermic
c.
Write the thermochemical equation (reaction including the heat)
2 H
2
(g) + O
2
(g)
㈠2
2
O (g) + 58.0k
J
(
2 moles H
2
O x 29.0kJ/ mole
)
d. In the formation of 150.0g of water, how much energy would be evolved?
150.0g H
2
O x
1 mole H
2
O
x
58.0kJ
=
241.5kJ
18.01g H
2
O
2 mole H
2
O
Assignment 4:
Thermoche
mical Reactions and Calculating
the Heat of Reaction
(
H or Change in 䕮瑨alpy)
.
1.
A 2.5 g sample of Mg is placed in 150.0 mL of HCl. The temperature of the
water increased from 15.0
o
C to 45.0
o
C.
Calculate the total heat released in the reaction.
q = 150.0g x 4.18
j
x 30.0
o
C = 18810j
g
o
C
Calculate the number of moles of Mg.
2.5g Mg x
1 mole Mg
= .10 mole Mg
24.3g Mg
Calculate the
H (
heat per mole of Mg
)
.
18810j
=
x joules
x =
-
188100j or
-
190kJ
0.10 mol Mg 1 mol Mg
Is the reaction exothermic or endothermic?
exothermic
Write the
thermochemical equation (
equation including the heat released
)
.
Mg (s) + 2 HCl (aq)
M权l
2
(aq) + H
2
(g) + 190kJ
2.
If 21 g of propane is burned under 150.0 g of water, the temperature of the water
increases from 21.0
o
C to 21.6
o
C.
What is the heat released by this process?
q = 150.0g x 4.18
j
x 0.6
o
C = 376.2j
g
o
C
How many moles of propa
ne burned?
21g C
3
H
8
x
1 mole C
3
H
8
= 0.476 moles
44.094g C
3
H
8
What is the heat per mole (Molar Heat of Combustion or
H) for propane?
376.2 joules
=
x joules
=
-
790j
0.476 mole C
3
H
8
1 mole C
3
H
8
Write the react
ion for the combustion of propane showing the heat.
(thermochemical equation)
C
3
H
8
(g) + 5 O
2
(g)
㌠3O
2
(g) + 4 H
2
O (g) + 790j
Assignment 5:
Calculating
H
wi瑨 Hea琠o映Forma瑩on Chart
.
Calculate the
H for each of the following reactions:
CaO (s) + CO
2
(g)
CaCO
3
(s)
2 C
2
H
2
(g) + 5 O
2
(g)
4 CO
2
(g) + 2 H
2
O (g)
2 NH
3
(g)
N
2
(g) + 3 H
2
(g)
2 HNO
3
(l)
N
2
O
5
(g) + H
2
O (g)
SO
3
(g) + H
2
O (g)
H
2
SO
4
(l)
2 Na (s) + 2 HCl (g)
2 NaCl (s) + H
2
O (l)
HNO
3
(l) + NaOH (s)
NaNO
3
(s) H
2
O (l)
Na
2
SO
4
(s) + 10 H
2
O (l)
Na
2
SO
4
* 10 H
2
O (s)
TiCl
4
(l) + 2 H
2
O (l)
TiO
2
(s) + 4 HCl (g)
NH
4
Cl (s)
NH
3
(g) + HCl (g)
Assignment 6:
Calculating
H
with Hess’ Law
.
Assignment 7:
Thermochemical Equations.
2 H
2
O
2
(aq)
㈠2
2
O (l) + O
2
(g) + 108 kJ
Is the reaction exothermic or endothermic?
exothermic
What is the
H
got the reaction?
-
108 kJ
Whi
ch has more energy, the products or the reactants?
R
eactants have more energy
How much energy is released when 56.0g of H
2
O
2
decomposes?
56.0g x
1mol H
2
O
2=
x
108kJ
=
8
8.
9 kJ released
34.02g H
2
O
2
2
mol H
2
O
2
N
2
H
4
(g)
+ O
2
(g)
N
2
+ H
2
O (l)
H
-
㘲㜮㘠kJ
Write the thermochemical equation.
N
2
H
4
(g) + O
2
(g)
N
2
+ H
2
O (l) + 627.6 kJ
Is the reaction exothermic or endothermic?
exothermic
Will it feel hot or cold?
hot
Which has more energy, the reactant or products? Show graph
with energy.
Reactants
How much energy is released when 82.0g of N
2
O
4
is reacted?
82.0g N
2
O
4
x
1 mole N
2
H
4
x
627.6 kJ
=
1700 kJ
(2 sig fig)
30.03g N
2
H
4
1 mole N
2
H
4
CaCO
3
(s)
C慏 (s) † † O
2
(g)
H
=4
㈮㔠kc慬
Write the thermochemical equation.
42.5 kcal + CaCO
3
(s)
C慏 (s)††⁃O
2
(g)
Is the reaction exothermic or endothermic?
endothermic
Which has more energy, the reactants or the products?
Products have more energy
How much energy is
(absorbed or released) when 501.0g of CaCO
3
decomposes?
501.0g CaCO
3
x
1 mol CaCO
3
x
42.5 kcal
=
213 kcal absorbed
100.09g CacO
3
1 mol CaCO
3
Would this reaction tend to be spontaneous (happen)? Why?
No, it is endotherm
ic and so
not favorable in terms of energy change.
Assignment 8:
Thermochemical Equations.
Solid sulfur combines with oxygen gas to form sulfur dioxide gas. The
H
re慣ti潮 is
-
㈹㜠2J
Write the thermochemical equation for the reaction.
S (s)
+ O
2
(g)
2
+ 297 kJ
Which has more energy, the reactants or the products?
Reactants
Is the reaction exothermic or endothermic?
Exothermic
Would it feel hot or cold?
Hot
How much sulfur dioxide will be formed when 400.0 kJ of energy is
released?
400.0kJ x
1 mol SO
2
x
64.064g SO
2
=
86.3g SO
2
297 kJ 1 mol SO
2
How much energy is released when 82.0g of sulfur reacts?
82.0g S x
1 mol S
x
297 kJ
=
759 kJ
released
32.07g S 1mol S
Ethyne gas (C
2
H
2
) reacts with oxygen gas in a combustion reaction and produces
2512 kJ of energy per mole of ethyne.
Write the thermochemical equation.
C
2
H
2
(g) + 2 ½ O
2
(g)
㈠2O
2
(g) + H
2
O (g) + 2512 kJ
What
is the
H
for the reaction?
-
2512 kJ
Is the reaction exothermic or endothermic? Show graph with energy.
exothermic
Would this reaction tend to be spontaneous (happen) in terms of energy change?
Yes
, it is exothermic as so is favorable in terms of ene
rgy change. Systems tend
toward lower energy.
How much energy is released when 25.0g of ethyne reacts?
25.0g C
2
H
2
x
1 mol C
2
H
2
x
2512 kJ
=
2410 kJ released
26.04g C
2
H
2
1 mol C
2
H
2
How much ethyne was burned if 4001 kJ of ener
gy was released?
4001 kJ x
1 mol C
2
H
2
x
26.04g C
2
H
2
=
41.48g C
2
H
2
2512 kJ
1 mol C
2
H
2
Assignment 9:
Thermochemical Equations
.
Methane (CH
4
) undergoes combustion.
1.
Use the heat of formation chart to calculate the
H
for the reaction.
CH
4
(g) + 2 O
2
(g)
CO
2
(g) + 2 H
2
O (g)
1(
-
17.889kcal) + 2(0kcal) 1(
-
94.0518kcal) + 2(
-
57.7979kcal)
=
-
17.889kcal
=
-
209.6476kcal
-
209.6476kcal
(
-
17.889kcal) =
-
192kcal
2.
Write the thermochemical equation.
CH
4
(g) + 2 O
2
(g)
2
(g) + 2 H
2
O (g) + 192kcal
3.
Is the reaction exothermic or endothermic?
exothermic
4.
Which has more energy, reactants or products? Draw a graph to show the energy
relation
ships on the reaction.
Reactants have more energy!
5.
How many grams of methane are needed to produce 4000.0 kcal of energy?
4000.0kcal x
1 mol CH
4
x
16.05g
=
334kcal
192kcal 1 mol CH
4
6.
How much heat is relea
sed per gram of methane?
192kcal
=
12.0kcal/g
16.05g CH
4
7.
Would you expect this reaction to be spontaneous at room temperature? What is
the driving force?
The change in enthalpy is very favorable (a large negative number)
bec
ause the reaction is very exothermic. The change in entropy is
probably not significant as it goes from all gases to all gases. So, Gibbs
Free Energy is probably negative and the reaction is spontaneous.
Calculate the enthalpy change
(
H
)潲 the re慣ti潮 in which s潬id 慬uminum re慣ts
with s潬id ir潮(III) 潸ode t漠or潤uce s潬id ir潮 慮d s潬id 慬uminum 潸ode.
Gi癥n:
㈠2l (s)† †
㌯㈠2
2
(g)
2
O
3
(s)
H
-
ㄶ〱1kJ
㈠2e
s)† †㌯㈠2
2
(g)
2
O
3
(s)
H =
-
㠲ㄠkJ
flip:
Fe
2
O
3
(s)
2 Fe +
3/2 O
2
(g)
H = +821 kJ
Al (s) + Fe
2
O
3
(s)
Fe (s) + Al
2
O
3
(s)
H =
-
786 kJ
1.
Write the thermochemical equation.
Al (s) + Fe
2
O
3
(s)
Fe
s) † † l
2
O
3
(s) + 786 kJ
2.
Is the reaction exothermic or endothe
rmic?
exothermic
3.
Would the reaction get hot or cold?
Hot
4.
Which has more energy, reactants or products? Draw a graph to show the energy
relationships on the reaction.
The
Reactants
have more energy.
5.
How many grams of iron(III) oxide are neede
d to produce 4000.0 kJ of energy?
4000.0 kJ x
1 mol Fe
2
O
3
x
159.689g Fe
2
O
3
=
813
g
786 kJ
1 mol Fe
2
O
3
6.
How much heat is released per gram of aluminum?
786 kJ
=
29.1 kJ/g Al
26.98g Al
7.
Would you expect th
is reaction to be spontaneous at room temperature? What is
the driving force?
The change in enthalpy is very favorable (a large negative number) because the
reaction is very exothermic. The change in entropy is probably not signi
ficant as
it goes from al
l solids to all solids
. So, Gibbs Free Energy is probably negative
and the reaction is spontaneous.
Calculate the heat of reaction for the following:
2 C (graphite) + H
2
(g)
C
2
H
2
(g)
given:
x4:
4
C (graphite) +
4
O
2
(g)
4
2
(g)
H
-
㌹㌮㔠k䨠
H
-
ㄵ㜴⸰
2
H
2
(g) +
1
O
2
(g)
2
H
2
O (l)
H =
-
㈸㔮㠠kJ
H
-
㔷ㄮ5
㈠2
2
H
2
(g) + 5 O
2
(g)
㐠4O
2
(g) + 2 H
2
O (l)
H =
-
㈵㤸⸸2kJ
flip:
㐠4O
2
(g) + 2 H
2
O (l)
㈠C
2
H
2
(g) + 5
O
2
(g)
H =㈵㤸⸸2kJ
4
C (杲慰hite) †
H
2
(g)
C
2
H
2
(g)
H
=㐵㌮4
C (杲慰hite) †
H
2
(g)
C
2
H
2
(g)
H
=㈲㘮2
Evaluate this reaction in terms of
H
,
S, and
G.
The
H is positive, so not favorable.
The
S is pr
obably positive, but only marginally as it goes from one solid and one
gas to only one gas. This is favorable as it is an increase in entropy.
So
G is negative at higher temperatures.
Do you think this reaction would be spontaneous?
The change in e
nthalpy is
unfavorable (a positive
number) because
the reaction is
endothermic
. The change
in entropy is probably positive as it ends with only
gases
. S
o, Gibbs Free Energy is
negative
at higher temperatures. | 6,283 | 15,477 | {"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} | 4.15625 | 4 | CC-MAIN-2018-26 | latest | en | 0.894603 |
https://www.convertunits.com/from/pace+%5BRoman%5D/to/meter | 1,600,962,988,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400219221.53/warc/CC-MAIN-20200924132241-20200924162241-00519.warc.gz | 776,975,402 | 8,545 | ## ››Convert pace [Roman] to metre
pace [Roman] meter
Did you mean to convert pace [great] pace [Roman] to meter
How many pace [Roman] in 1 meter? The answer is 0.67567567567568.
We assume you are converting between pace [Roman] and metre.
You can view more details on each measurement unit:
pace [Roman] or meter
The SI base unit for length is the metre.
1 metre is equal to 0.67567567567568 pace [Roman], or 1 meter.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between pace [Roman] and metres.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of pace [Roman] to meter
1 pace [Roman] to meter = 1.48 meter
5 pace [Roman] to meter = 7.4 meter
10 pace [Roman] to meter = 14.8 meter
15 pace [Roman] to meter = 22.2 meter
20 pace [Roman] to meter = 29.6 meter
25 pace [Roman] to meter = 37 meter
30 pace [Roman] to meter = 44.4 meter
40 pace [Roman] to meter = 59.2 meter
50 pace [Roman] to meter = 74 meter
## ››Want other units?
You can do the reverse unit conversion from meter to pace [Roman], or enter any two units below:
## Enter two units to convert
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## ››Definition: Meter
The metre, symbol: m, is the basic unit of distance (or of "length", in the parlance of the physical sciences) in the International System of Units. The internationally-accepted spelling of the unit in English is "metre", although the American English spelling meter is a common variant. However, both American and non-American forms of English agree that the spelling "meter" should be used as a suffix in the names of measuring devices such as chronometers and micrometers.
## ››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! | 557 | 2,168 | {"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-2020-40 | latest | en | 0.818846 |
https://tech-story.net/download-udemy-probability-and-statistics-complete-course-2023-2023-3/ | 1,721,889,535,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518579.47/warc/CC-MAIN-20240725053529-20240725083529-00648.warc.gz | 488,113,227 | 9,588 | ## Description
Probability and Statistics: Complete Course 2023, the probability and statistics training course has been published by Udemy Academy. This course is designed to take you from a beginner to an expert in probability and statistics. This software is designed to be practical and suitable for anyone who wants to use statistics in data science, business analytics or any other field to make better informed decisions. The videos are full of practical examples and explanations so you’ll never get confused, and all the techniques mentioned are implemented in Microsoft Excel so you can use them right away.
No prior knowledge is required except for the 2 optional videos at the end of the continuous distribution chapter, where knowledge of calculus is required. The key concepts taught in this course are: Descriptive statistics: means, measures of spread, correlation and many more. Data cleanup: identify and delete redundant data. Data Visualization: All standard techniques for data visualization built into Excel. Probability: independent events, conditional probability and Bayesian statistics. Discrete distribution: binomial, Poisson, expectation and variance and approximation. Continuous distribution: normal distribution, central limit theorem and continuous random variables
### What you will learn
• Descriptive Statistics
• Data visualization
• Probability theory
• Bayesian statistics
• Discrete distribution (binomial, Poisson and Moore)
• Continuous distribution (normal etc.)
• Hypothesis tests
• regression
• Type I and II errors
• Test Chi– Squared
### Who is this course suitable for?
• Data scientists
• People who study statistics
• Anyone looking to increase their decision-making power with a thorough understanding of statistics.
### Probability and Statistics: Complete Course 2023
• Publisher: Udemy
• teacher : Woody Lewenstein
• English language
• Education level: all levels
• Number of courses: 103
• Training duration: 16 hours and 19 minutes
### Course prerequisites
• No pre-requisites for most of the course. One small optional section requires knowledge and calculus, but other than that this is suitable for beginners.
### Installation guide
After Extract, view with your favorite Player.
Subtitle: None
Quality: 720p
### Size
13.58 GB
4.5/5 – (1481 points) | 458 | 2,324 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-30 | latest | en | 0.877999 |
https://artofproblemsolving.com/wiki/index.php?title=Tree_(graph_theory)&diff=next&oldid=136432 | 1,632,019,115,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056656.6/warc/CC-MAIN-20210919005057-20210919035057-00417.warc.gz | 156,569,835 | 9,528 | # Difference between revisions of "Tree (graph theory)"
A tree is an undirected graph which is both connected and acyclic. Equivalently, a tree is a graph $G=(V,E)$ such that for any two vertices $u, v \in V$ with $u \neq v$, there is exactly one path connecting $u$ and $v$ in $G$. Every tree on $|V|=n$ vertices has exactly $n-1$ edges. | 100 | 339 | {"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": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-39 | latest | en | 0.962797 |
https://nrich.maths.org/public/leg.php?code=-333&cl=4&cldcmpid=1363 | 1,508,744,709,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00871.warc.gz | 767,988,588 | 9,664 | # Search by Topic
#### Resources tagged with Investigations similar to Earth Shapes:
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### Geometry and Gravity 1
##### Stage: 3, 4 and 5
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.
### The Invertible Trefoil
##### Stage: 4 Challenge Level:
When is a knot invertible ?
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##### Stage: 5 Challenge Level:
Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.
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##### Stage: 5 Challenge Level:
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
### Few and Far Between?
##### Stage: 4 and 5 Challenge Level:
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
### Reaction Rates!
##### Stage: 5
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
### Take Ten Sticks
##### Stage: 3 and 4 Challenge Level:
Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
### Bent Out of Shape
##### Stage: 4 and 5 Challenge Level:
An introduction to bond angle geometry.
### Odd Stones
##### Stage: 4 Challenge Level:
On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.
### Stirling Work
##### Stage: 5 Challenge Level:
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
### Carbon Footprints
##### Stage: 4 Challenge Level:
Is it really greener to go on the bus, or to buy local?
### The Power of Dimensional Analysis
##### Stage: 4 and 5
An introduction to a useful tool to check the validity of an equation.
### Big and Small Numbers in Physics
##### Stage: 4 Challenge Level:
Work out the numerical values for these physical quantities.
### CSI: Chemical Scene Investigation
##### Stage: 5 Challenge Level:
There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...
### Diamonds Aren't Forever
##### Stage: 5 Challenge Level:
Ever wondered what it would be like to vaporise a diamond? Find out inside...
### Clear as Crystal
##### Stage: 5 Challenge Level:
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
### Mach Attack
##### Stage: 5 Challenge Level:
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
### Modelling Assumptions in Mechanics
##### Stage: 5
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
### Smoke and Daggers
##### Stage: 5 Challenge Level:
We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .
### What Salt?
##### Stage: 5 Challenge Level:
Can you deduce why common salt isn't NaCl_2?
### Perfect Eclipse
##### Stage: 4 Challenge Level:
Use trigonometry to determine whether solar eclipses on earth can be perfect.
### Robot Camera
##### Stage: 4 Challenge Level:
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
### Big and Small Numbers in Chemistry
##### Stage: 4 Challenge Level:
Get some practice using big and small numbers in chemistry.
### A Rational Search
##### Stage: 4 and 5 Challenge Level:
Investigate constructible images which contain rational areas.
### Designing Table Mats
##### Stage: 3 and 4 Challenge Level:
Formulate and investigate a simple mathematical model for the design of a table mat.
### Witch's Hat
##### Stage: 3 and 4 Challenge Level:
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
### Alternative Record Book
##### Stage: 4 and 5 Challenge Level:
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
### Track Design
##### Stage: 4 Challenge Level:
Where should runners start the 200m race so that they have all run the same distance by the finish?
##### Stage: 5
Read about the mathematics behind the measuring devices used in quantitative chemistry
### Big and Small Numbers in the Living World
##### Stage: 3 and 4 Challenge Level:
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
### Big and Small Numbers in the Physical World
##### Stage: 4 Challenge Level:
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
### Genetic Intrigue
##### Stage: 5
Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .
### Escape from Planet Earth
##### Stage: 5 Challenge Level:
How fast would you have to throw a ball upwards so that it would never land?
### Spokes
##### Stage: 5 Challenge Level:
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
### Sextet
##### Stage: 5 Challenge Level:
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
### Problem Solving: Opening up Problems
##### Stage: 1, 2, 3 and 4
All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .
### A Different Differential Equation
##### Stage: 5 Challenge Level:
Explore the properties of this different sort of differential equation.
### Chance of That
##### Stage: 4 and 5 Challenge Level:
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
### Peeling the Apple or the Cone That Lost Its Head
##### Stage: 4 Challenge Level:
How much peel does an apple have?
### Twizzles Venture Forth
##### Stage: 4 Challenge Level:
Where we follow twizzles to places that no number has been before.
### Eight Ratios
##### Stage: 4 Challenge Level:
Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.
### Snookered
##### Stage: 4 and 5 Challenge Level:
In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?
### Two Regular Polygons
##### Stage: 4 Challenge Level:
Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?
### Spiroflowers
##### Stage: 5 Challenge Level:
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
### There's Always One Isn't There
##### Stage: 4 Challenge Level:
Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
##### Stage: 4 and 5 Challenge Level:
Some of our more advanced investigations
### Trig-trig
##### Stage: 4 and 5 Challenge Level:
Explore the properties of combinations of trig functions in this open investigation.
### Taking Trigonometry Series-ly
##### Stage: 5 Challenge Level:
Look at the advanced way of viewing sin and cos through their power series.
### Scale Invariance
##### Stage: 5 Challenge Level:
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1. | 1,805 | 8,217 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2017-43 | longest | en | 0.860348 |
http://docplayer.net/20232089-Lesson-objectives-procedure.html | 1,571,680,355,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987781397.63/warc/CC-MAIN-20191021171509-20191021195009-00443.warc.gz | 57,956,590 | 32,864 | # Lesson Objectives. Procedure
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5 LOAN SHOP (15 min.) 23. I need 4 volunteers for this activity. Each of you will be a loan officer from one of the financial institutions on the Loan Calculations Worksheet. I will come to you one by one and ask you for the terms of the loan. Then I will decide which loan to go with. Everyone else needs to be paying attention because you need to get the monthly payment down on your sheets as well. 24. On the sheets all the terms are filled in except the monthly payment. To find the monthly payment, you divide the Total Cost of the Loan box by the number of months that you have to pay the loan back. You may want to ask students to raise their hands and guess how to do this. It can help to use a transparency of this sheet so you are able to write in the monthly payments. 25. Choose your first loan officer. Walk up to her or him, shake hands. Introduce yourself and ask about each of the terms, saving the monthly payment for last. 26. Is this is a fixed rate loan or a variable rate loan? All the loan rates are fixed. What could happen if it was a variable rate? The rate could change and I might have higher payments. 27. After the students tell you what the monthly payment will be ask the class, Can I afford this payment? 28. Point out that the longer the term of the loan the more you pay in interest, so even though the payments are smaller, you are really paying more. 29. Also notice that the interest rate goes up the longer the term of the loan is. This is because the financial institution knows that the longer you own the car, the more risk exists that it will break down and you will stop paying on the loan. They manage that risk by charging you more. 30. If my credit report contained information about late payments on other bills, would my interest rate go up or down? Up! 31. I chose Syracuse Cooperative Federal Credit Union as my loan provider because they had the best loan terms that I could afford. Generally, you want to get the loan with the shortest term and the lowest interest rate you can find that you can afford to make the payments on. 32. A student may point out that it costs more than the \$250 I budgeted per month to spend on the car payment. Discuss how I might cut back on other expenses to make that slightly higher payment and how much money that will save me in the long term. Mortgages and other long term loans are the same, paying just a little bit more up front can save you lots of money in the long term. 101
6 CHECK AND REGISTER (3 min.) 33. Have students fill out a check for their first payment on the loan and fill out a check register to keep track of the expenses. Do this together as a class. Note to instructor We have calculated this at 57 minutes of teaching time. This is the minimum, it can take much longer. Feel free to adjust the time according to students needs. 102
9 Name Date Directions Calculate the monthly payments for each loan and then decide which loan would be best for me based on what I can afford per month. Loan Company Length of Loan APR Monthly Payment Total Cost of Loan HSBC Bank 2 years (24 months) 5% \$ \$6, Syracuse Cooperative Federal Credit Union Chase Bank 3 years (36 months) 4 years (48 months) 6% \$ \$6, % \$ \$7, M & T Bank 5 years (60 months) 10% \$ \$8, How do you get a loan? 1. Look at all the options and get your Truth in Lending Statement (form requiring banks and credit unions by law to give you all the terms of any loan). 2. Make sure you can easily afford the one you choose (no more then 20% of your income for a car or 30% for a house). 3. Fill out the application. 4. The credit union or bank will check out your past history of payments, number of loans and credit cards you have, how much money you owe, and any past judgments against you. 5. They will judge you on the 3 C s of Credit. 6. They let you know by mail if you are confirmed. If you are you get a check, buy the car, and start making payments. (If you are denied the loan they are legally required to tell you why they denied you (Truth in Lending). 105
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13 Reliability (1=worst 5=best) Price Gas Mileage (city/highway) Safety (1= worst 5=best) Space 5 \$ 5,575 26/30 4 Seats 5 people Here are some reviews from owners. Owner 1 Pros ENGINE AND TRANSMISSION LONGEVITY Cons Looks, power, handling... Multiple electrical gremlins... Oversensitive Toyota alarm that goes off too easy... Gas mileage is not as good as they say, not safe, interior is too small (5'11") Overall Review: This car will mechanically last forever, but accessory wise is the pits!!! And handling does not even qualify for second rate. Also I had a 2005 Corolla as a rental for 6 weeks and 1,700 miles... Toyota s handling is still not as good as its competition (VW). I also have a friend who owns a 2003 Camry... After these three Toyotas... Would never buy one!!! Owner 2 Pros Very dependable, good gas mileage, paint still looks good, almost everything still works. It actually does great off-road, doesn't die out on me when I get the engine wet. It accelerates well. Cons I had to replace the motor mounts at about 90K. The starter went out shortly after that. Some of the interior gadgetry seems a little cheap. The seat belt recoil springs quit working about 3 years ago. Overall Review: A lot of things about this 9 year-old car still seem new. The doors and windows work perfectly. The engine, with 140,000 miles, sounds and performs like it is still new. Hardly any oil consumption, no leaks. I will probably get another one of these if this one ever wears out. 109
14 Reliability (1= worst 5= best) Price Gas Mileage (city/highway) Safety (1= worst 5=best) Space 5 \$6,500 29/36 4 Seats 5 people Here are some reviews from owners. Owner 1 Pros: Very reliable, car is 11 years old and drives like new. I bought it in 98 with 30,000 miles it has 176,000 miles now and it still drives the same. Only minor maintenance was required (tires, brakes, oil changes). It is not a luxury car of course, but it's very comfortable, yet spartan. Gas mileage is great, air conditioning works well, sound system is decent. In short, everything in this car works the way it is supposed too. Trouble-free. Cons Well it is not a sports car and it can be slow sometimes, but I don t really care. I am not a fast driver. Overall Review Overall it is nothing special, but it is a great reliable transportation. If you are a car fanatic who demands extreme performance and handling well, why are you even reading this? The Civic is obviously not the car for you. But if you need an extremely reliable and comfortable car for daily driving, it can't get any better than this. Owner 2 Pros 179,000 miles and only 750 dollars in repairs...minus the givens such as tire, brakes, and normal wear...great, reliable, economical car. Cons As it ages, most problems seem to be electrical...windows, locks, nothing that keeps it from on the road, just little annoying stuff. Overall Review: Wish the new civic was more like the Why change a good thing? 110
16 Name Date Directions Calculate the monthly payments for each loan and then decide which loan would be best for me based on what I can afford per month. Loan Company Length of Loan APR Monthly Payment Total Cost of Loan HSBC Bank 2 years (24 months) 5% \$6, Syracuse Cooperative Federal Credit Union Chase Bank 3 years (36 months) 4 years (48 months) 6% \$6, % \$7, M & T Bank 5 years (60 months) 10% \$8, How do you get a loan? 1. Look at all the options and get your Truth in Lending Statement (form requiring banks and credit unions by law to give you all the terms of any loan). 2. Make sure you can easily afford the one you choose (no more then 20% of your income for a car or 30% for a house). 3. Fill out the application. 4. The credit union or bank will check out your past history of payments, number of loans and credit cards you have, how much money you owe, and any past judgments against you etc. 5. They will judge you on the 3 C s of Credit. 6. They let you know by mail if you are confirmed. If you are you get a check, buy the car, and start making payments. (If you are denied the loan they are legally required to tell you why they denied you (Truth in Lending). 112
17 Name Date Directions Make this check out to the financial institution for the amount of the monthly car payment. Then record the payment in the check register below to make sure you always know how much money you have in your checking account. 101 Date PAY TO THE ORDER OF \$ DOLLARS Syracuse Cooperative Federal Credit Union For Eastside Office 723 Westcott Street Syracuse, NY Southside Office 401 South Avenue Syracuse, NY Signature /11 Paycheck /14 Groceries
18 114
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### LESSON TITLE: Taming the Tongue. THEME: God wants us to watch what we say. SCRIPTURE: James 3:1-12 CHILDREN S DEVOTIONS FOR THE WEEK OF:
Devotion NT349 CHILDREN S DEVOTIONS FOR THE WEEK OF: LESSON TITLE: Taming the Tongue THEME: God wants us to watch what we say. SCRIPTURE: James 3:1-12 Dear Parents Welcome to Bible Time for Kids! Bible | 8,039 | 34,608 | {"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} | 3.5 | 4 | CC-MAIN-2019-43 | latest | en | 0.965209 |
https://www.physicsforums.com/threads/using-fourier-transform-to-find-moving-average.693210/ | 1,511,552,448,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934808742.58/warc/CC-MAIN-20171124180349-20171124200349-00055.warc.gz | 823,762,269 | 15,877 | # Using fourier transform to find moving average
1. May 22, 2013
### brianhurren
can you use fourier transform to find a moving average on a data set?
so, you do a fourier transform on your one dimensional data set.
next remove high order harmonics from FT result.
do reverse fourier transform on new FT result.
And, vola! smoothed out data set.
2. May 27, 2013
### Simon Bridge
Some of the high order terms are needed to smooth out the wobbles introduced by the low order terms.
Remove enough high order terms and you get a sine wave no matter what the data was ... so how do you, systematically, decide which terms to remove?
3. May 28, 2013
### brianhurren
thats what I would like to know. I heard that FFT is used to analise climate change data, but I cant see how FFt would applie to a random set of data that has no periodic signal, except maybe as a means to calculate a rolling average. exactly as you point out, how do you decide which harmonics to leave out. which window would you use (Hanning, square etc).
4. May 28, 2013
### Simon Bridge
Impossible to tell without specifics.
Do you have an example?
I think it is unlikely that the fft is used in the manner you imagine... i.e. it is probably not being applied to random data with no discernable signal.
5. May 31, 2013
### olivermsun
Yes, absolutely. The conventional moving average is just a convolution of your original signal with a rectangular window of some length. This is equivalent to pointwise multiplying the Fourier transforms of the signal and a rectangular and inverting (See Convolution, and especially the section on Fast convolution algorithms).
Right. And there's no reason you have to limit yourself to a rectangular window filter.
6. May 31, 2013
### olivermsun
It's a good question. Mainly you are looking for signals which stand out above the "noise" and which you don't already know about or which have a frequency which is the same as some known, plausible mechanism which affects climate.
How "broad" a peak appears in Fourier space also tells you how far from perfectly periodic a signal might be. Just to give you an example, we expect the seasons in some region to vary on a yearly cycle, but if you were to look at a spectrum of the temperature record, you'd find a peak around 1 cycle/year which is pretty sharp but not a perfect spike. This is because the actual temperature variations can arrive slightly earlier or later each year. | 567 | 2,450 | {"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 | longest | en | 0.953305 |
https://forum.civiljungle.com/how-to-calculate-a-45-degree-chamfer/ | 1,708,620,078,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473824.13/warc/CC-MAIN-20240222161802-20240222191802-00817.warc.gz | 264,127,620 | 64,589 | Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this user should be reported.
# How to Calculate a 45 Degree Chamfer?
For example, if a chamfer has an angle of 45 degrees and leg lengths of 0.010″, then one way of dimensioning will be to use the convention 0.010″ (0.25 mm) x 45°. Alternatively, you can use the convention 0.010″ (0.25 mm) x 0.010″ (0.25 mm), which will only state the leg length values.
## How to Calculate a 45 Degree Chamfer?
Calculating a 45 degree chamfer can be a daunting task for those who are not familiar with the process. However, with the right tools and a bit of practice, it can be relatively easy to achieve. A chamfer is a beveled edge that is used to transition the corner of an object. This type of transition is often used in the fabrication of furniture, cabinets, and other items that require an angled edge. In this article, we’ll discuss the process of calculating a 45 degree chamfer and the necessary tools required to do so.
To calculate a 45 degree chamfer, the most important tool you will need is a protractor. A protractor is used to measure angles and is typically made up of two arms with a center point. It is important to ensure that the arms of the protractor are perpendicular to the object on which you are measuring the angle. Once the protractor is in place, you can then use it to measure the desired angle.
When measuring the angle for a 45 degree chamfer, it is important to ensure that the angle is at exactly 45 degrees. To do this, place the protractor on the corner of the object and make sure the arms of the prot | 385 | 1,642 | {"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} | 3.625 | 4 | CC-MAIN-2024-10 | longest | en | 0.912727 |
https://www.howmany.wiki/u/How-many--gallon-%5BUK%5D--make--1.5--cc | 1,547,912,046,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583668324.55/warc/CC-MAIN-20190119135934-20190119161934-00121.warc.gz | 834,999,511 | 11,061 | # How many gallons [UK] make 1.5 cc?
There is 0.00032995387244863 gallon [UK] in 1.5 cubic centimeters
### Cubic Centimeters to Gallons [UK] Converter
Enter values here: Results here:
Detailed result here
Here you can find how many gallons [UK] are there in any quantity of cubic centimeter. You just need to type the cubic centimeters value in the box at left (input) and you will get the answer in gallons [UK] in the box at right (output).
## How to convert 1.5 cubic centimeters to gallons [UK]
To calculate a value in cubic centimeters to the corresponding value in gallons [UK], just multiply the quantity in cubic centimeters by 0.00021996924829909 (the conversion factor).
Here is the formula:
Value in gallons [UK] = value in cubic centimeters × 0.00021996924829909
Supose you want to convert 1.5 cc into gallons [UK]. In this case you will have:
Value in gallons [UK] = 1.5 × 0.00021996924829909 = 0.00032995387244863
## Values Near 0.9 cubic centimeter in gallons [UK]
Note: Values are rounded to 4 significant figures. Fractions are rounded to the nearest 8th fraction.
cubic centimeters to gallons [UK]
0.9cubic centimeter = 0.000198gallon [UK]
1cubic centimeter = 0.00022gallon [UK]
1.1cubic centimeters = 0.000242gallon [UK]
1.2cubic centimeters = 0.000264gallon [UK]
1.3cubic centimeters = 0.000286gallon [UK]
1.4cubic centimeters = 0.000308gallon [UK]
1.5cubic centimeters = 0.00033gallon [UK]
1.6cubic centimeters = 0.000352gallon [UK]
1.7cubic centimeters = 0.0003739gallon [UK]
1.8cubic centimeters = 0.0003959gallon [UK]
1.9cubic centimeters = 0.0004179gallon [UK]
2cubic centimeters = 0.0004399gallon [UK]
2.1cubic centimeters = 0.0004619gallon [UK]
Using this converter you can get answers to questions like:
• How many gallons [UK] are in 1.5 cc?
• 1.5 cc are equal to how many gallons [UK]?
• How much are 1.5 cc in gallons [UK]?
• How to convert cubic centimeters to gallons [UK]?
• What is the cubic centimeters to gallons [UK] conversion factor?
• How to transform cubic centimeters in gallons [UK]?
• What is the formula to convert from cubic centimeters to gallons [UK]? among others. | 659 | 2,131 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2019-04 | longest | en | 0.68284 |
https://www.includehelp.com/golang/binary-literals.aspx | 1,718,288,374,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861451.34/warc/CC-MAIN-20240613123217-20240613153217-00475.warc.gz | 748,164,838 | 37,818 | # Binary Literals in Golang
Golang | Binary: In this tutorial, we are going to learn about the binary literals, how to use binary values in Go Language?
Submitted by IncludeHelp, on April 07, 2021
## Binary numbers
Binary is a number system with base 2, it has 2 values (0 and 1).
In Go programming language, a binary literal can be written with a prefix 0b or 0B (Zero and alphabet B either in lowercase or uppercase). The value which is prefixed with 0b or 0B is considered as a binary value and it can be used in the program statements like a binary value can be assigned to a variable or constant, can be used within an expression, can be assigned in an array, etc.
Examples:
```0b00
0b11
0B10
0b11100
0b1111
0b11110000
```
## Assigning a binary value to a variable & constant
In the below example, we are creating a variable and a constant, and assigning binary values to them.
Example of assigning binary values to a variable & a constant
```// Golang program to demonstrate the example of
// assigning binary values to
// a variable & a constant
package main
import (
"fmt"
)
func main() {
// variable
var a int = 0b1110011
// constant
const b int = 0b1111
// printing the values
fmt.Println("a = ", a)
fmt.Println("b = ", b)
// printing values in the binary format
fmt.Printf("a = %b\n", a)
fmt.Printf("b = %b\n", b)
}
```
Output:
```a = 115
b = 15
a = 1110011
b = 1111
```
## Using a binary value in an expression
A binary value can also be used within an expression. In the below program, we are declaring two variables, assigning them with binary values, and finding their sum with a binary value "0b11" which is equivalent to 2.
Example of using binary values in an expression
```// Golang program to demonstrate the example of
// Example of using binary values
// in an expression
package main
import (
"fmt"
)
func main() {
// variables
a := 0b10011
b := 0b11111
// calculating the sum of a, b and 0b11
c := a + b + 0b11
// printing the values
fmt.Println("a = ", a)
fmt.Println("b = ", b)
fmt.Println("c = ", c)
// printing values in the binary format
fmt.Printf("a = %b\n", a)
fmt.Printf("b = %b\n", b)
fmt.Printf("c = %b\n", c)
}
```
Output:
```a = 19
b = 31
c = 53
a = 10011
b = 11111
c = 110101
``` | 648 | 2,250 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-26 | latest | en | 0.729632 |
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