url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://discuss.leetcode.com/topic/89808/pretty-easy-python-solution-with-explaination | 1,516,277,032,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887253.36/warc/CC-MAIN-20180118111417-20180118131417-00693.warc.gz | 663,653,639 | 9,601 | # Pretty easy python solution with explaination
• For example, input [1,4,3,2], to make the the largest sum of min(ai, bi), the target pairs should be (1,2) and (3,4). Let's see the hidden pattern inside. If each pair (ai, bi) contains the neighbors in the sorted array, the sum of each min can be the largest. And then the solution is written straight forward with the idea，just add the odd index of sorted array to the sum and report.
`````` def arrayPairSum(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
nums.sort()
s,i=0,0
while i<len(nums):
s+=nums[i]
i+=2
return s
``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 187 | 688 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2018-05 | latest | en | 0.798875 |
https://study.sagepub.com/jones/student-resources/multiple-choice-questions-and-activities/chapter-6-introduction-to | 1,723,572,059,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641082193.83/warc/CC-MAIN-20240813172835-20240813202835-00034.warc.gz | 439,468,510 | 21,174 | # Chapter 6. Introduction to Statistics
#### 2. Match these different variables with the correct type of variable. The first one has been done for you.
Click to reveal the correct answer.
#### Ans:
Weight of a new born baby Ratio Number of cats fighting at night Discrete Type of tattoo on the leg Nominal Number of times a G flat is played on a piano Discrete Favourite chocolate bar Nominal Height of Big Ben Ratio Amount of weight lost Ratio Level of satisfaction from eating an ice cream (can be marked as: low, medium, high) Ordinal
#### 3. What units would you use for amount of weight lost?
Click to reveal the correct answer. | 141 | 640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-33 | latest | en | 0.916306 |
http://www.bhsbearings.com/news/the-indispensability-of-radial-bearings-is-obvious.html | 1,560,743,737,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998369.29/warc/CC-MAIN-20190617022938-20190617044938-00245.warc.gz | 222,787,487 | 7,883 | # The Indispensability of Radial Bearings is Obvious
Update:2017-05-02
The way cars and other cars work is a very interesting topic for most of us. Some people are very interested in cars. Only later discovered that there are several small machines called bearings that make the car run smoothly. These widgets are critical to the machine because they can reduce friction and, if not they, people will have to replace the broken parts.
The definition of the bearing is very simple: this is to reduce the friction in the machine and the use of a. To understand the friction, you need to imagine the two surfaces that are in contact with the rolling or sliding movement. The force against each movement in each surface is called frictional force. The journal bearing consists of two upper and lower bearings, the bearing pad is fixed by the tapered pin, and then the upper and lower halves are connected by bolts. The bearing section of the bearing is poured with babbitt. The lower half pad and the lower half bearing housing are positioned with cylindrical pins to prevent radial or axial movement of the bearing pad. Radial bearings are one of the main components of the steam turbine and are parts with more faults.
Journal bearings are sorted according to their mode of operation and their permissible actions. Two common movements are linear and rotating. Bearings that allow linear motion are called linear bearings. These bearings allow linear motion. An example of a straight line movement is pulling and pushing the drawer. On the other hand, the rotational movement involves rotation and vibrations in one direction, where motion is only through a portion of the cycle, for example in the case of a wheel. Thus, the rotating bearing allows to concentrate on the center of the movement, such as the wheels on the shaft.
Many applications use rotating bearings, such as machine shafts, axles and clock components. Sleeve bearing is a simple cylinder, which is inserted between the wheel and the axle, is the most basic rotary bearing. Subsequent roller bearings, where the sleeve is replaced by a plurality of cylindrical rollers, each of which is shown as a single wheel. | 427 | 2,184 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-26 | latest | en | 0.961169 |
https://help.scilab.org/docs/5.5.1/fr_FR/m2sci_cumsum.html | 1,701,972,102,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100677.45/warc/CC-MAIN-20231207153748-20231207183748-00134.warc.gz | 325,538,439 | 3,620 | Change language to:
English - 日本語 - Português - Русский
See the recommended documentation of this function
Aide de Scilab >> Aide à la conversion Matlab vers Scilab > Matlab-Scilab equivalents > C > cumsum (Matlab function)
cumsum (Matlab function)
Cumulative sum
Matlab/Scilab equivalent
Matlab Scilab `cumsum` `cumsum`
Particular cases
C=cumsum(A)
If A is a matrix, cumsum(A) is equivalent to cumsum(A,1) in Matlab whereas in Scilab cumsum(A) gives the cumulative sum of all the entries of A taken columnwise. Actually, Matlab works on the first non-singleton dimension and Scilab does not.
C = cumsum(A,dim)
Matlab can work with dim greater than number of dimensions of A but Scilab can not, in this can use mtlb_cumsum instead.
Examples
Matlab Scilab ```B = cumsum([1,2,3;4,5,6]) B=[1,2,3;5,7,9] B = cumsum([1,2,3;4,5,6],1) B=[1,2,3;5,7,9]``` ```B = cumsum([1,2,3;4,5,6]) B=[1,7,15;5,12,21] B = cumsum([1,2,3;4,5,6],1) B=[1,2,3;5,7,9]```
Report an issue << cumprod (Matlab function) C D >> | 353 | 1,009 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2023-50 | latest | en | 0.636645 |
http://www.jamiiforums.com/threads/math-paradox.163918/ | 1,477,286,980,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719468.5/warc/CC-MAIN-20161020183839-00235-ip-10-171-6-4.ec2.internal.warc.gz | 527,617,113 | 22,055 | Discussion in 'Habari na Hoja mchanganyiko' started by simplemind, Aug 14, 2011.
1. ### simplemindJF-Expert Member
#1
Aug 14, 2011
Joined: Apr 10, 2009
Messages: 9,512
Trophy Points: 280
Come across this math problem. Let me say this, hapa nimeshemsha may be someone can be kind enough to provide the solution.
3 men go to a hotel to rent room. The clerk says that there is a 3 bed room for \$30.
Each man pays \$10 and go to the room.
The hotel manager tells the clerk the room is only \$25 and gives the clerk \$5 to pay the men back.
On the way to the room the clerk realizes 5 dollar bill cant be split 3 way. Dishonestly he keeps \$2 and gives each man \$1.
Now the 3 men have paid \$27 for the room and the clerk has \$2 . Where did the \$1 go to?
27+2=29
2. ### Rugambwa31JF-Expert Member
#2
Aug 14, 2011
Joined: May 13, 2009
Messages: 227
Trophy Points: 33
They payed \$30, then \$3 were returned and \$2 taken by the clerk.
Now they paid \$25+\$2=\$27, by adding \$3 they have, you get \$30.
3. h
### hamidshabanJF-Expert Member
#3
Aug 14, 2011
Joined: Jan 4, 2011
Messages: 259
Trophy Points: 35
4. ### simplemindJF-Expert Member
#4
Aug 14, 2011
Joined: Apr 10, 2009
Messages: 9,512
Trophy Points: 280
<br />
<br />
No ,if they paid \$30 and \$3 was refunded then they must have paid 30 - 3 = 27 .The cleck has 2 dollar therefore total is only 29 dollars.
5. ### TutafikaJF-Expert Member
#5
Aug 14, 2011
Joined: Nov 4, 2009
Messages: 1,384
Trophy Points: 160
bold: that is wrong, they paid 9 each ( or a total of 27; inclusive of 2 retained by the clerk) kama umechemsha, you must be a lawyer
6. h
### hamidshabanJF-Expert Member
#6
Aug 14, 2011
Joined: Jan 4, 2011
Messages: 259
Trophy Points: 35
take 25 divide by 3=8.333 add 1 dollar=9.333.multiply by 3 = 27.999 add 2 dollar and get it
7. h
### hamidshabanJF-Expert Member
#7
Aug 14, 2011
Joined: Jan 4, 2011
Messages: 259
Trophy Points: 35
8. ### Rugambwa31JF-Expert Member
#8
Aug 14, 2011
Joined: May 13, 2009
Messages: 227
Trophy Points: 33
OK, it seems that you want to see where \$1 went: 30-2=28 then 30-3=27 then 28-27=1. But am still agree with my first answer.
9. ### simplemindJF-Expert Member
#9
Aug 14, 2011
Joined: Apr 10, 2009
Messages: 9,512
Trophy Points: 280
<br />
<br />
Okay granted ,they paid 27 plus 2 dollars retained by clerk,the total is 29 dollars. This does not explain the missing dollar. Remember the men initially paid the clerk \$30.
10. m
### mtozwaushuruMember
#10
Aug 14, 2011
Joined: Sep 20, 2010
Messages: 78
Trophy Points: 13
acheni ungwini coz mathematics is science ans there must be scientific explanation for every thing. The 3 men paid a total of \$ 27, which include the 2 retained by the clerk (25 +2 = 27). and they remained with \$ 1 each, which makes a total of 3. 27 + 3 = 30. WHAT ID THE PROBLEM WITH YOU GUYS? in science things do not just disappear so there is no way \$1 could have disappeared. think!
11. ### simplemindJF-Expert Member
#11
Aug 14, 2011
Joined: Apr 10, 2009
Messages: 9,512
Trophy Points: 280
I get you though the maths bit tricky.
12. ### VoiceOfReasonJF-Expert Member
#12
Aug 14, 2011
Joined: Nov 4, 2010
Messages: 5,235 | 1,100 | 3,189 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2016-44 | longest | en | 0.896092 |
https://it.mathworks.com/matlabcentral/cody/problems/56-scrabble-scores/solutions/682895 | 1,607,195,402,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141748276.94/warc/CC-MAIN-20201205165649-20201205195649-00501.warc.gz | 340,686,293 | 16,968 | Cody
# Problem 56. Scrabble Scores
Solution 682895
Submitted on 7 Jun 2015 by Varoujan
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% str = 'a'; score = 1; assert(isequal(scrabble_score(str),score))
2 Pass
%% str = 'matlab'; score = 10; assert(isequal(scrabble_score(str),score))
3 Pass
%% str = 'quetzalcoatl'; score = 32; assert(isequal(scrabble_score(str),score))
4 Pass
%% str = 'quartz'; score = 24; assert(isequal(scrabble_score(str),score))
5 Pass
%% str = 'jackal'; score = 19; assert(isequal(scrabble_score(str),score))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 230 | 795 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2020-50 | latest | en | 0.597029 |
https://www.coursehero.com/file/46293649/Balanceo-de-ecuacionesdocx/ | 1,571,875,798,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987836368.96/warc/CC-MAIN-20191023225038-20191024012538-00501.warc.gz | 843,845,121 | 46,043 | Balanceo de ecuaciones.docx - Balanceo de ecuaciones 1 2N 2 O 5 → 2 N 2 O 4 O 2 4:N 4 10:O 10 2)A KNO 3 → B KNO 2 C O 2 K= a=b a=2 b=2 3a=2b 2c N=
# Balanceo de ecuaciones.docx - Balanceo de ecuaciones 1 2N 2...
• 1
This preview shows page 1 out of 1 page.
Balanceo de ecuaciones 1) 2N 2 O 5 → 2 N 2 O 4 + O 2 4 :N: 4 10 :O: 10 2)A KNO 3 → B KNO 2 +C O 2 K= a=b a=2 b=2 3a=2b+2c N= a=b 3(2)=2(2)+2c 6=4+2c 6-4=2c 2=2c c=2/2 c=1 O= 3a=2b+2c 2 :K: 2 2 :N: 2 6 :O: 6 3) A P 4 O 10 +B H 2 O →C H 3 PO 4 P= 4a=c a=2 a(2)=c c=8 2b=3(8)
• Spring '19
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes | 575 | 1,645 | {"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} | 3.171875 | 3 | CC-MAIN-2019-43 | latest | en | 0.808582 |
http://www.adisc.org/forum/entry.php/260-Most-fun-I-ve-had-for-awhile!?s=36009f9afaef1b21095155895ec47444 | 1,503,351,944,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886109670.98/warc/CC-MAIN-20170821211752-20170821231752-00549.warc.gz | 476,395,550 | 10,964 | Point
Most fun I've had for awhile!
Rate this Entry
by , 30-Mar-2008 at 03:21 (476 Views)
So! Today I had a thing called START, something about teenage road safety. You'd think it'd be boring as watching paint dry but it was a blast!
Okay, maybe the first hour was dull, but that's because they had to teach us how to do stuff so when we were driving police cars around a giant track at high speeds we wouldn't kill ourselves
So anyway. Turns out this kid and I were the only two people there who'd had our licenses for less than a month. Scary! Thank goodness they stuck us in the same car, I'd have died of fright and embarrassment if I had to sit in there with a bunch of eighteen-year-olds!
First thing we did when we went out on the track was to get in our assigned car and have the professional instructor rocket us over to the place, going from 0 to 60 in seconds! We got out and looked at the cones they'd placed after a slightly inclined track (a 47 degree gradient, they say, something to do with centrifugal force). Most of us had the expression that said, "You've got to be kidding." And now an ASCII diagram!
O = Cone
X = Dead Cone
_ = Empty Space
O_______O
O__OOO__O
O__O_O__O
O__O_O__O
O__OOO__O
_________
____^____
O___|___O
O_______O
So they expected us to drive at 45 mph, and they'd yell out a direction (left or right) just before the cones and you'd swerve left and then right and then straighten it out just before you crashed into the cones on the SIDE.
Needless to say I barreled right through the middle once or twice!
_____________X
_________
_________
O________
O__OOO__X
O__O_X__X
O__O_X__O
O__OXX__O
_________
____^____
O___|___O
O_______O
The girl in the car with me and the other kid had been driving for a year and even she did. But man, that other kid never knocked down one cone until the thing after that!
After that they rearranged them and included breaking with the brakes that lock the steering when you slam down on them (a la older cars). I didn't knock any down that time, but I was probably just not as nervous then and the adrenaline was finally sinking into my system
A break after that long session, and unfortunately I ate too much food then because after the break we had off-road recovery and how to regain control of your car after it slides or swerves! :X I nearly threw up because by the end we were doing complete 360s in the car on the wet surface because nobody else was out there but the instructor and us and we wanted to have some fun. It was awesome but it's like riding a roller coaster. All day long.
I learned some great stuff, had a hell of a lot of fun, and even got cheaper insurance rates because of the certificate they give to you at the end!
Leave it to the police to teach people how to drive RIGHT!
Categories
Uncategorized | 698 | 2,809 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-34 | longest | en | 0.980419 |
https://school.gradeup.co/a-spherical-conducting-shell-of-inner-radius-r1-and-outer-i-1njz0q | 1,576,309,430,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540585566.60/warc/CC-MAIN-20191214070158-20191214094158-00519.warc.gz | 524,428,520 | 31,117 | Q. 155.0( 4 Votes )
# A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
(a) Charge placed at the centre of the sphere is + q. Thus, charge induced on the inner surface be –q.
Surface charge density at the inner surface of the sphere,
σ1 = =
Charge placed at the centre of the sphere is + q. Thus, charge induced on the inner surface be + q and surface charge distribution is Q. Therefore Total charge = Q + q.
Surface charge density at the outer surface of the sphere,
σ2 = =
(b) Yes
Whatever the shape of the shell, the electric field intensity in the cavity is zero. Take a closed loop such that it is inside the cavity and in conductor. Net work done in carrying charge along closed loop by electric field is zero. Thus, electric field is zero, whatever the shape.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better. | 275 | 1,209 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-51 | latest | en | 0.944338 |
http://mathhelpforum.com/pre-calculus/174522-how-does-sqrt-x-2-1-a.html | 1,527,269,686,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867140.87/warc/CC-MAIN-20180525160652-20180525180652-00506.warc.gz | 190,360,921 | 9,304 | # Thread: How does sqrt(x^2) = 1?
1. ## How does sqrt(x^2) = 1?
Hey guys, I just have quick question:
How does $\displaystyle \frac{\sqrt{9x^2+x}}{x} = \sqrt{9+1/x}$ knowing that $\displaystyle \sqrt{x^2} = x$
big thanks.
2. Assuming that $\displaystyle \displaystyle x \geq 0$, then $\displaystyle \displaystyle \sqrt{x^2} = x$.
Since $\displaystyle \displaystyle \frac{\sqrt{9x^2 + x}}{x} = \frac{\sqrt{9x^2 + x}}{\sqrt{x^2}}$
$\displaystyle \displaystyle = \sqrt{\frac{9x^2 + x}{x^2}}$.
Go from here.
3. Thank you! I got it. | 197 | 536 | {"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 | 0.660308 |
https://www.unix.com/man-page/centos/3/catanh/ | 1,582,499,674,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145859.65/warc/CC-MAIN-20200223215635-20200224005635-00491.warc.gz | 896,823,118 | 14,454 | ## Linux and UNIX Man Pages
Test Your Knowledge in Computers #232
Difficulty: Medium
The ARPANET project was formally decommissioned in 1994.
True or False?
# catanh(3) [centos man page]
```CATANH(3) Linux Programmer's Manual CATANH(3)
NAME
catanh, catanhf, catanhl - complex arc tangents hyperbolic
SYNOPSIS
#include <complex.h>
double complex catanh(double complex z);
float complex catanhf(float complex z);
long double complex catanhl(long double complex z);
DESCRIPTION
The catanh() function calculates the complex arc hyperbolic tangent of z. If y = catanh(z), then z = ctanh(y). The imaginary part of y is
chosen in the interval [-pi/2,pi/2].
One has:
catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))
VERSIONS
These functions first appeared in glibc in version 2.1.
CONFORMING TO
C99.
EXAMPLE
#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>
int
main(int argc, char *argv[])
{
double complex z, c, f;
if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>
", argv[0]);
exit(EXIT_FAILURE);
}
z = atof(argv[1]) + atof(argv[2]) * I;
c = catanh(z);
printf("catanh() = %6.3f %6.3f*i
", creal(c), cimag(c));
f = 0.5 * (clog(1 + z) - clog(1 - z));
printf("formula = %6.3f %6.3f*i
", creal(f2), cimag(f2));
exit(EXIT_SUCCESS);
}
atanh(3), cabs(3), cimag(3), ctanh(3), complex(7)
COLOPHON
This page is part of release 3.53 of the Linux man-pages project. A description of the project, and information about reporting bugs, can
be found at http://www.kernel.org/doc/man-pages/.
2011-09-15 CATANH(3)```
## Check Out this Related Man Page
```CATANH(3) Linux Programmer's Manual CATANH(3)
NAME
catanh, catanhf, catanhl - complex arc tangents hyperbolic
SYNOPSIS
#include <complex.h>
double complex catanh(double complex z);
float complex catanhf(float complex z);
long double complex catanhl(long double complex z);
DESCRIPTION
The catanh() function calculates the complex arc hyperbolic tangent of z. If y = catanh(z), then z = ctanh(y). The imaginary part of y is
chosen in the interval [-pi/2,pi/2].
One has:
catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))
VERSIONS
These functions first appeared in glibc in version 2.1.
CONFORMING TO
C99.
EXAMPLE
#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>
int
main(int argc, char *argv[])
{
double complex z, c, f;
if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>
", argv[0]);
exit(EXIT_FAILURE);
}
z = atof(argv[1]) + atof(argv[2]) * I;
c = catanh(z);
printf("catanh() = %6.3f %6.3f*i
", creal(c), cimag(c));
f = 0.5 * (clog(1 + z) - clog(1 - z));
printf("formula = %6.3f %6.3f*i
", creal(f2), cimag(f2));
exit(EXIT_SUCCESS);
}
atanh(3), cabs(3), cimag(3), ctanh(3), complex(7)
COLOPHON
This page is part of release 3.44 of the Linux man-pages project. A description of the project, and information about reporting bugs, can
be found at http://www.kernel.org/doc/man-pages/.
2011-09-15 CATANH(3)```
## Is UNIX an open source OS ?
Hi everyone, I know the following questions are noobish questions but I am asking them because I am confused about the basics of history behind UNIX and LINUX. Ok onto business, my questions are-: Was/Is UNIX ever an open source operating system ? If UNIX was...
## Weird 'find' results
Hello and thanks in advance for any help anyone can offer me I'm trying to learn the find command and thought I was understanding it... Apparently I was wrong. I was doing compound searches and I started getting weird results with the -size test. I was trying to do a search on a 1G file owned by...
## Set hard block limit for user using quota
hi all, i have installed quota on my centos 7 machine and its what im after (setting size limit on users, so they cant fill the hard drive) i want to now make this part of my create user script for my sftp server so i want to do a echo and a read command so i capture the limit they enter...
## Best performance UNIX just for HOST Virtualization?
Hi everybody, Which Unix base OS have best performance for HOST virtualization? I tested SmartOS but it needs another OS to connect remotely! Thanks in advance.
## How to increment version inside a file?
Hi All, I need to write a shell script which opens a file and increments the version(text) within the file every time the script runs. For example: \$ cat docker_file.yml version: '3.1' services: ui: image: repo-srv.dev.io:5000/facebook/ui:0.0.2-QA1 \$ So, I would like...
## DB2 convert digits to binary format
Dear Team We use DB2 v10.5 and using DBArtisan tool Can someone please guide how to convert digits to binary numbers using db2 feature. Ex> for number 9 , binary should be 1001 ( 8+1) Any help appreciated. Thanks
## Tar Command
hi folks, how to using tar with exclude directory and compress it using tar.Z i only know how to exclude dir only with this command below: tar -cvf /varios/restore/test.tar -X excludefile.txt /jfma/test1/ how to compress it using 1 command? Thanx Please use CODE tags as...
## CentOS7 restoring file capabilities
Quite an obscure question I think. We have a rebuild process for remote sites that allows us to PXE rebuild a till (actually a PC with a touch screen and various fancy bits) running CentOS. The current CentOS5 tills work just fine with a tar image restore and some personalisation. Sadly,...
## Docker learning Phase-I
Hello All, I had recently learnt a bit of Docker(which provides containerization process). Here are some of my learning points from it. Let us start first with very basic question: What is Docker: Docker is a platform for sysadmins and developers to DEPLOY, DEVELOP and RUN applications ...
## Shopt -s histappend
What is the point of this? Whenever I close my shell it appends to the history file without adding this. I have never seen it overwrite my history file. # When the shell exits, append to the history file instead of overwriting it shopt -s histappend
## Unsure why access time on a directory change isn't changing
Hello... And thanks in advance for any help anyone can offer me I was trying to work out the differences between displaying modify, access, and change times with the 'ls' command. Everything seems in order when I look at files, but the access time on a directory doesn't seem to change when I...
## CentOS 6 ran out of space, need to reclaim it
Hello everyone, I am having an issue here with CentOS release 6.6 (Final) that shows all of the space used up, but I can't tell where the space went. Seemingly I am using up 100%, according to df -h Filesystem Size Used Avail Use% Mounted on...
## Controlling user input
I'm trying to use a bash script for a psych experiment that involves listening to sound files and responding. If I have something like the code below, how can I make sure that a key press is assigned to RESPONSE only after the second echo statement? for i in 1 2 3; do echo "Ready?" sleep 2 ...
## [TIP] Processing YAML files with yq
After the success of the jq - tool for parsing and manipulating JSON-Data someone wrote a tool called yq, which aims to be the same for YAML, what jq is for JSON. Seems to work fine. I'll definitely give it a chance in future. Example YAML-File: --- !ruby/object:Puppet::Node::Facts ...
## Please Welcome Dave Munro to the Moderator Team!
Dear All, I am very pleased to announce that Dave Munro (gull04) is joining the Moderation Team, after being a very valuable member of UNIX.com for 15+ years. Dave is an IT Consultant with 30 years of experience this year, has worked in many of the industry vertical market segments and has... | 2,029 | 7,634 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2020-10 | latest | en | 0.533401 |
http://www.ask.com/science/volume-one-drop-water-8164b654ac639858 | 1,430,777,914,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1430455121137.37/warc/CC-MAIN-20150501043841-00095-ip-10-235-10-82.ec2.internal.warc.gz | 241,212,468 | 20,975 | Q:
# What is the volume of one drop of water?
A:
A drop of water is equal to 0.050 milliliters. The unit used to represent a drop of water is 1 gtt metric.
Know More
## Keep Learning
Credit: fdecomite CC-BY-2.0
This means that a drop of water, or 1 gtt metric, is equal to 1/20 of a milliliter. However, this is somewhat of an approximation as various factors can influence the exact volume of a drop of water. First of all, it depends where the drop of water is coming from. If it is being created by a standard dropper, then other factors also remain, such as the rate at which the drop was extracted and the resulting size of the drop. These factors actually become very significant with liquids different from regular water as their varying viscosity, surface tensions and densities could greatly affect the resulting volume of their drops.
Sources:
## Related Questions
• A:
One liter has the volume of approximately one million cubic millimeters. Cubic millimeters are an expression of volume, and one liter of water at standard pressure and maximum density generally occupies this volume amount.
Filed Under:
• A:
One liter is equal to 1,000 milliliters. In the metric system, the prefix "milli-" is used before basic units, such as liter, gram and meter, to indicate that the measurement is one-thousandth of that basic unit.
Filed Under:
• A:
Eight pints are equal to 1 gallon. Pints and gallons are both U.S. customary units of volume derived from the imperial system of measurement. This system is used primarily in the United States and is utilized in most recipes there. | 361 | 1,598 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2015-18 | latest | en | 0.957692 |
https://www.quesba.com/questions/-fifo-method-materials-added-beginning-production-process-campo-company-cam-1812090 | 1,716,706,153,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058868.12/warc/CC-MAIN-20240526043700-20240526073700-00668.warc.gz | 820,200,510 | 28,290 | # : FIFO Method Materials are added at the beginning of the production process at Campo Company....
: FIFO Method Materials are added at the beginning of the production process at Campo Company. Campo uses a FIFO process costing system. The following information on the physical flow of units is available for the month of November. Compute the equivalent units for the conversion cost calculation. Compute Equivalent Units and Cost per Equivalent Unit: Weighted- Average Method Refer to the data in Exercise 8-28. Cost data for November show the following: Compute the cost equivalent units for the conversion cost calculation assuming Campo uses the weighted-average method. Compute the cost per equivalent unit for materials and conversion costs for November.
Aug 31 2022| 10:55 AM |
Earl Stokes Verified Expert
This is a sample answer. Please purchase a subscription to get our verified Expert's Answer. Our rich database has textbook solutions for every discipline. Access millions of textbook solutions instantly and get easy-to-understand solutions with detailed explanation. You can cancel anytime!
Get instant answers from our online experts!
Our experts use AI to instantly furnish accurate answers.
Quesba User
Answer - Units started and completed equal 964000 units - 92000 units, which equals 872,000 units. •Equivalent units for conversion are: (92000 units times this period's 61% completion rate) plus (872000 units times 100% completion rate) plus (155000 units times 74% completion rate) = 56120 + 872000 + 114700 = 1,042,820 units....
## Related Questions
### What characteristics of a plant asset make it different from other assets? Why does GAAP require...
What characteristics of a plant asset make it different from other assets? Why does GAAP require depreciation for certain plant assets? The balance in an Accumulated Depreciation - Equipment account does not represent funds to replace the equipment when it wears out; instead, what does it represent?
Aug 22 2022
### Craigmont Company's direct materials costs are \$4,300,000, its direct labor costs total...
Craigmont Company's direct materials costs are \$4,300,000, its direct labor costs total \$8,170,000, and its factory overhead costs total \$6,170,000. Its conversion costs total:
Aug 21 2022
### Why might a company have extra inventory on hand above the amount suggested by the economic order...
Why might a company have extra inventory on hand above the amount suggested by the economic order quantity? Make a case for a redundant inventory item in a business setting.
Aug 26 2022
### Where would your client navigate to view the status of a bill payment that was paid using Melio?...
Where would your client navigate to view the status of a bill payment that was paid using Melio? Open bill payment > View online payment + New > Pay bills > View online payments Open bill Payment > More > View online payment + New > Payment status
Aug 31 2022
### Given the historical cost of product Z is \$20, the selling price of product Z is \$25, costs to...
Given the historical cost of product Z is \$20, the selling price of product Z is \$25, costs to sell product Z are \$3, the replacement cost for product Z is \$21, and the normal profit margin is 40% of sales price, what is the market value that should be used in the lower-of-cost-or-market comparison? a. \$18. b. \$20. c. \$21. d. \$22. B. What is the amount that should be used to value the inventory...
Aug 23 2022
## Join Quesbinge Community
### 5 Million Students and Industry experts
• Need Career counselling?
• Have doubts with course subjects?
• Need any last minute study tips? | 805 | 3,671 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2024-22 | latest | en | 0.874356 |
https://brainly.com/question/361996 | 1,484,840,715,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280718.7/warc/CC-MAIN-20170116095120-00040-ip-10-171-10-70.ec2.internal.warc.gz | 793,915,446 | 9,273 | # The graph shows the distances traveled by two toy trains. A third train travels 15 feet in 3 seconds. How does the third train compare with Train 1 and Train 2? A. The third train is slower than both Train 1 and Train 2. B. The third train is faster than both Train 1 and Train 2. C. The third train is faster than Train 1 but slower than Train 2. D. The third train is faster than Train 2 but slower than Train 1.
1
by nicegirl100
2015-03-25T15:48:24-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
From the graph ...
-- Train-1 travels more than 15 feet in 3 seconds.
-- Train-2 travels less than 15 feet in 3 seconds.
So, if Train-3 travels exactly 15 feet in 3 seconds,
then Train-3 is faster than #2 but slower than #1 . | 278 | 1,020 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2017-04 | latest | en | 0.903941 |
https://www.jiskha.com/display.cgi?id=1305688095 | 1,511,192,803,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806070.53/warc/CC-MAIN-20171120145722-20171120165722-00116.warc.gz | 796,219,831 | 4,059 | math
posted by .
how do you use the numbers 4, 5, 9, 7, and 21 to get the number 23 (using it in a number sentence) i cannot get it and its driving me crazy! please help
• math -
21+(9-7)*(5-4 )=
21 + 2*1 = 23
Similar Questions
1. Math
How can i make nine equations with the numbers 2, 7 and one other number to equal 8. The first equation should have one as the other number, then two and so on up to 9. I can only use a number once for each expression. I can use arithmetic …
2. keybording and word processing
you would use words for numbers when? a. signifying an even house number, b. using "A.M." or "P.M." c. expressing an even amount of dollars and cents, d. beginning a sentence with a number
3. keybording and word processing
15. you would use words for numbers when?
4. math
Write a number sentence. Use every digit in the circle only once. Insert math symbols ( + ,-,x,/) and end the number with 3. Us parentheses if necessary. The numbers are 10,7,6,4,5
5. Chemistry
what number should be placed in the blank to balance the equation C 3 H 8 + 50 2 --> 3 CO 2 ___ H 2 O I have been working on this Q for four hours and it is driving me CRAZY please HELP i hate chemistry or anything with numbers …
6. math
Need to make a problem, using parentheses and use as many operations to write an expression equal to to th target number. You can only use each number once in an expression. Numbers 6,7,12,14,20 Target number = 41
7. math
Write to number sentences using the to numbers 7,56,and 8 then use the same numbers to show the division way label each number with its special math name
8. Math
Find two numbers which have a sum of 2 and a product of 2. This question is driving me crazy, please help!!
9. Math
A number sentence is 50 1/2 รท1/4 =202. Part A. Create a story or context for this number sentence. Part B. Rewrite this number sentence using multiplication. Part C. Give a verbal explanation that describes how these three numbers …
10. Math
please if anyone could help me with this question: 1. A class paid \$20 for a cake and \$4 per child for one slice of cheese pizza. they paid \$140. how many children are in the class?
More Similar Questions | 579 | 2,185 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2017-47 | latest | en | 0.869787 |
http://www.chegg.com/homework-help/abstract-algebra-3rd-edition-chapter-11.2-problem-2e-solution-9780471433347 | 1,469,954,287,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469258951764.94/warc/CC-MAIN-20160723072911-00099-ip-10-185-27-174.ec2.internal.warc.gz | 390,578,721 | 16,584 | View more editions
Solutions
Abstract Algebra
# TEXTBOOK SOLUTIONS FOR Abstract Algebra 3rd Edition
• 1574 step-by-step solutions
• Solved by publishers, professors & experts
• iOS, Android, & web
Over 90% of students who use Chegg Study report better grades.
May 2015 Survey of Chegg Study Users
Chapter: Problem:
STEP-BY-STEP SOLUTION:
Chapter: Problem:
• Step 1 of 5
Linearly independent vectors: A subset S of V is called a set of linearly independent vectors if an equation implies that. Here, and .
Basis: A basis of a vector space V is an ordered set of linearly independent vectors that span vector space V.
Dimension: If V has a finite basis then the cardinality of any basis is called the dimension of V and is denoted by dimV.
• Chapter , Problem is solved.
Corresponding Textbook
Abstract Algebra | 3rd Edition
9780471433347ISBN-13: 0471433349ISBN: Authors: | 222 | 876 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2016-30 | longest | en | 0.872254 |
https://iwantonlineclasshelp.com/product/phys-101-quiz-newtons-laws/ | 1,695,695,008,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510130.53/warc/CC-MAIN-20230926011608-20230926041608-00484.warc.gz | 365,991,968 | 22,475 | # Get Best PHYS 101 Quiz Newtons Laws
\$3.99
Category:
1. An aircraft weighs 1,500 N, its mass is
2. Two cars crash head on. At any given time during the crash, the magnitudes of the collision forces exerted on each car are exactly equal. This is an example of Newton’s
3. You throw a ball straight up, it peaks out, and then comes back down to you. During this motion, the velocity and acceleration
4. You roll a ball off a table and at the same time drop a second ball straight down from the edge of table. The second ball reaches the ground ____________ the first ball reaches the ground.
5. Where is the Sun located relative to a planet’s orbit about it?
6. As a space shuttle is launched into orbit, the direction of its acceleration
7. An astronaut in a space suit has a total mass of 143.5 kg and is standing on a scale that reads in newtons inside an elevator. If the elevator accelerates upward at the rate of 1.8 m/s2, what does the scale read?
8. Which statement is incorrect? The gravitational force on an orbiting satellite due to the Earth
9. The SI units of acceleration are
10. How was the value of G first determined?
11. A body is oscillating up and down at the end of a spring. Let’s consider when the body is at the top of its up-and-down motion.
12. At the highest point on the path of a projectile, its vertical acceleration
13. A188-pound astronaut in a training exercise experiences an acceleration of 7.2g’s. What is the net force (in newtons) acting on the astronaut?
14. As a body falls through air starting from rest, its velocity
15. The SI units of velocity are
16. A newton is larger than a pound.
17. You push on a wall, and the wall pushes back on you with the same force. This is an example of Newton’s third law.
18. The direction of a field line at a point in space shows the direction of the force that would act on a body placed at the point.
19. When a car goes around a curve of smaller and smaller radius, the centripetal force on it decreases.
20. A body is oscillating up and down at the end of a spring. Let’s consider when the body is at the top of its up-and-down motion.
21. An aircraft weighing 1,500 N has a mass of approximately 150 kg.
22. A body is oscillating up and down at the end of a spring. Let’s consider when the body is at the top of its up-and-down motion.
23. When a body moves in a straight line with increasing speed, the net force on it must be increasing.
24. If a body were in orbit very near the surface of the Earth, its centripetal acceleration would be equal to g.
25. You throw a ball straight up, it peaks out and then comes back down to you. During this motion, the velocity and acceleration always point in the same direction.
26. Select the closest matching pairs possible. 3 pts for each response.
27. From 2 King 6:1-6, one of the disciples of Elisha was cutting a tree and the ax head fell into the water. While we do not know how high the ax head was when it fell into the water, we will work through a physics example of the ax head’s vertical motion as if it were dropped into the water.
### Want Guide to Quiz?
Exams are a crucial part of a pupil’s training. Without examination, no pupil can develop via the ladder of success. However, college students in recent times do not have the time to attention to their studies, for the reason that they may be beaten via way of means of jobs that assist the very training they need. In their time of need, Get Exam Done is right here to provide a hand of help. For college students who’re thinking, can I pay someone to take my exam, what is the region to get it from? We were assisting college students for over 2 years with their pay-a-person to take my examination issues and feature efficaciously finished over 5000+ tests all around the states. For custom, help email us at [email protected] or WhatsApp us at +1(657)366-7486
Scott Belmont from NYC, USA
Hired a tutor to take programming class and final exam
40 minutes ago
Ebony Nicole from Bronx, USA
Hired a tutor to take history and algebra final exams
2 hours ago
Randy Wells from Texas, USA
Hired an expert to take chemistry proctored exam
1 hour ago
Kurt LeBlanc from Iowa, USA
Hired an expert to take statistics online exam
1 hour ago | 1,021 | 4,231 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2023-40 | latest | en | 0.923166 |
https://betterlesson.com/lesson/reflection/22213/activating-prior-knowledge | 1,511,357,697,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806586.6/warc/CC-MAIN-20171122122605-20171122142605-00490.warc.gz | 564,341,029 | 21,301 | Reflection: Connection to Prior Knowledge Using Coordinates to Prove a Quadrilateral is a Parallelogram - Section 1: Activating Prior Knowledge
I had to make a decision in designing this lesson. Would I ask students straight away to use coordinate geometry to verify that a particular quadrilateral satisfies the definition and possesses the properties of a parallelogram. Or would I first show students how to use coordinate geometry to verify things like parallelism, bisecting of segments, and congruency of segments.
I chose the latter route, fearing that the lesson would fizzle out if I didn't prepare students to be successful before asking them to jump to the more complex tasks. I think this turned out to be the correct decision. Students did end up needing instruction on how to use coordinate geometry for the purposes we'd be using them for later in the lesson.
Because I did a thorough job of making sure students had the prior knowledge to tackle the tasks in the heart of this lesson, I felt more comfortable allowing students to struggle through it. When students struggled I knew that it wasn't because they lacked the knowledge but because they had yet to make the connections they needed to make in order to transfer that knowledge to this new situation.
Some students, for example, were stuck on how to verify that a quadrilateral satisfies the definition of a parallelogram. My first question to them was "What is the definition of a parallelogram?" That was a stuck point for some. Once we established that the definition was a quadrilateral with two pairs of parallel sides, I would ask "How can we use coordinate geometry to verify that sides are parallel?" The students would typically know that using the slope formula to verify equal slopes wold be the way to do that. So in having these conversation with students, I would always emphasize to them that they knew everything they needed to know to complete the task. They just needed to expend more mental energy understanding the problem and rephrasing things to make the task more clear.
Reflecting back on the lesson, I realize now the importance of separating the prior knowledge aspect of a problem solving task from the actual problem solving aspect.
Activating Prior Knowledge
Connection to Prior Knowledge: Activating Prior Knowledge
Using Coordinates to Prove a Quadrilateral is a Parallelogram
Lesson 6 of 8
Big Idea: Impostors beware! In this lesson students learn to distinguish the real parallelograms from the pretenders.
Print Lesson
2 teachers like this lesson
Standards:
Subject(s):
Math, Geometry, Polygons, properties of quadrilaterals
65 minutes
Anthony Carruthers
Similar Lessons
The Basics of Coordinate Geometry
Geometry » Coordinate Geometry
Big Idea: Moving Geometry onto the coordinate plane. Let's investigate midpoints, slope, and distance!
Favorites(13)
Resources(19)
Amsterdam, NY
Environment: Urban
Why are lines parallel?
Algebra I » Linear Functions
Big Idea: The emphasis in this lesson is that students not only know the definition of parallel lines, but why lines are parallel.
Favorites(0)
Resources(9)
Rogers, AR
Environment: Rural
End of Year Assessment
Geometry » Final Assessment
Big Idea: This is a comprehensive assessment of all content learned to date.
Favorites(1)
Resources(12)
New York, NY
Environment: Urban | 682 | 3,349 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2017-47 | latest | en | 0.964481 |
https://ww2.mathworks.cn/matlabcentral/answers/1467576-i-have-this-code-in-matlab-but-it-does-not-work-alone-i-think-i-need-a-script-for-it | 1,638,594,679,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362930.53/warc/CC-MAIN-20211204033320-20211204063320-00351.warc.gz | 633,207,020 | 27,166 | # I have this code in matlab but it does not work alone. I think I need a script for it.
14 次查看（过去 30 天）
Hamdan Alkhoori2021-10-6
function x = Newton_method(f,df,x0,Tol, MaxIter )
%
% NEWTON Newton's Method
% Newton's method for finding successively better approximations to the
% zeroes of a real-valued function.
%
% Inputs:
% f - solve f(x)=0
% df - derivative of f(x)
% x0 - initial guess
% Tol - stopping tolerance
% MaxIter - maximum number of iterations
%
% Output:% x - a root of f(x)=0
%
nit=0; %number of iterations
disp('step| x | f(x) ')
disp('----|------------|-------------')
while 1
x = x0 - f(x0)/df(x0);
nit=nit+1;
if nit>MaxIter
disp('Maximum number of iterations is reached!')
break
end
if abs(x-x0)<Tol
disp('The sequence is convergent!')
break
end
x0=x;
fprintf('%3i |%12.8f|%12.8f\n',nit,x,f(x))
end
##### 2 个评论显示隐藏 1更早的评论
Rena Berman 2021-10-18
### 采纳的回答
Walter Roberson 2021-10-6
f = @(x) tan(x) - 5*cos(x)
f = function_handle with value:
@(x)tan(x)-5*cos(x)
df = matlabFunction(diff(sym(f)))
df = function_handle with value:
@(x)sin(x).*5.0+tan(x).^2+1.0
x0 = -1
x0 = -1
Tol = .0001
Tol = 1.0000e-04
MaxIter = 100
MaxIter = 100
X = Newton_method(f, df, x0, Tol, MaxIter)
step| x | f(x) ----|------------|------------- 1 | -6.44732999| -5.09842737 2 | 17.78565182| -4.22818795 3 |-15.21185170| 4.93846493 4 |-10.66898221| -1.34819199 5 |-10.57569237| -0.20172506 6 |-10.55663155| -0.00505942 7 |-10.55612877| -0.00000325 The sequence is convergent!
X = -10.5561
function x = Newton_method(f,df,x0,Tol, MaxIter )
%
% NEWTON Newton's Method
% Newton's method for finding successively better approximations to the
% zeroes of a real-valued function.
%
% Inputs:
% f - solve f(x)=0
% df - derivative of f(x)
% x0 - initial guess
% Tol - stopping tolerance
% MaxIter - maximum number of iterations
%
% Output:% x - a root of f(x)=0
%
nit=0; %number of iterations
disp('step| x | f(x) ')
disp('----|------------|-------------')
while 1
x = x0 - f(x0)/df(x0);
nit=nit+1;
if nit>MaxIter
disp('Maximum number of iterations is reached!')
break
end
if abs(x-x0)<Tol
disp('The sequence is convergent!')
break
end
x0=x;
fprintf('%3i |%12.8f|%12.8f\n',nit,x,f(x))
end
end
### 更多回答（1 个）
the cyclist 2021-10-6
Works for me. Here is an example
f = @(x) x.^2 - 1;
df = @(x) 2*x;
Newton_method(f,df,3,1.e-6,500)
step| x | f(x) ----|------------|------------- 1 | 1.66666667| 1.77777778 2 | 1.13333333| 0.28444444 3 | 1.00784314| 0.01574779 4 | 1.00003052| 0.00006104 5 | 1.00000000| 0.00000000 The sequence is convergent!
ans = 1
function x = Newton_method(f,df,x0,Tol, MaxIter )
%
% NEWTON Newton's Method
% Newton's method for finding successively better approximations to the
% zeroes of a real-valued function.
%
% Inputs:
% f - solve f(x)=0
% df - derivative of f(x)
% x0 - initial guess
% Tol - stopping tolerance
% MaxIter - maximum number of iterations
%
% Output:% x - a root of f(x)=0
%
nit=0; %number of iterations
disp('step| x | f(x) ')
disp('----|------------|-------------')
while 1
x = x0 - f(x0)/df(x0);
nit=nit+1;
if nit>MaxIter
disp('Maximum number of iterations is reached!')
break
end
if abs(x-x0)<Tol
disp('The sequence is convergent!')
break
end
x0=x;
fprintf('%3i |%12.8f|%12.8f\n',nit,x,f(x))
end
end
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by | 1,212 | 3,379 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-49 | latest | en | 0.483707 |
https://thirdspacelearning.com/us/math-resources/topic-guides/number-and-quantity/decimal-to-fraction/ | 1,713,810,690,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818337.62/warc/CC-MAIN-20240422175900-20240422205900-00130.warc.gz | 486,113,548 | 44,118 | # Decimal to fraction
Here you will learn strategies on how to convert decimals to fractions.
Students will first learn about converting decimals to fractions in 4th grade math as part of their work in number and operations with fractions.
## What is decimals to fractions?
Converting decimals to fractions is when you represent a decimal as a fraction without changing its value.
Here is a visual model representing 0.43. The hundredths grid is made up of 100 equal parts. 43 pieces are shaded out of 100 equal parts which is \cfrac{43}{100}.
You can also use a place value chart to convert decimals to fractions.
Decimals as fractions \hspace{1cm}
Decimal → 0.43
43 is the numerator of the fraction and 100
is the denominator because the last digit of
the decimal is in the hundredths column of
the place value chart,
\bf{0.43 = \cfrac {43}{100}}
Decimal → 0.009
9 is the numerator of the fraction and 1000
is the denominator because the 9 is in the
thousandths column of the place value
chart,
\bf{0.009 = \cfrac {9}{1000}}
Decimals as fractions with simplifying
Decimal → 0.25
25 is the numerator of the fraction and 100 is the denominator because
the last digit of the decimal is in the hundredths place.
\cfrac{25}{100} \, can be simplified. The common factor between 25 and 100 is 25.
\cfrac{25\div 25}{100\div 25} \, =\cfrac{1}{4}
\bf{\cfrac{25}{100} \, =\cfrac{1}{4}}
Decimals bigger than \bf{1} to a mixed number
Decimal → 1.4
Read as one and four tenths.
1 is a whole number, 4 is the numerator of the fraction and 10 is the
denominator.
1\cfrac{4}{10}
\cfrac{4}{10} \, can be simplified. The common factor between 4 and 10 is 2.
\cfrac{4\div 2}{10\div 2} \, =\cfrac{2}{5}
\bf{1\cfrac{4}{10}} \, in its simplest form is \bf{1\cfrac{2}{5}} \,
## Common Core State Standards
How does this apply to 4th grade math and 5th grade math?
• Grade 4 – Number and Operations – Fractions (4.NF.C.5)
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express \frac{3}{10} as \frac{30}{100}, and add \frac{3}{10} + \frac{4}{100} = \frac{34}{100}.
• Grade 5 – Number and Operations in Base 10 (5.NBT.A.3)
Read, write, and compare decimals to thousandths.
## How to convert decimals to fractions
In order to write a decimal as a fraction with a hundredths chart model:
1. Represent the decimal on the hundredths chart.
2. The shaded part is the numerator, and the total amount of equal parts is the denominator.
3. Write the fraction and simplify if possible.
In order to write a decimal as a fraction:
1. Write the decimal in words.
2. The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.
3. Write the fraction and simplify if possible.
In order to write a decimal bigger than 1 as a mixed number:
1. Write the decimal in words.
2. Keep the whole number.
3. The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.
4. Write the mixed number and simplify if possible.
## Convert decimals to fractions examples
### Example 1: write a decimal as a fraction using a model
Represent 0.21 as a fraction using a model.
1. Represent the decimal on the hundredths chart.
There are 21 parts shaded out of the 100 equal parts.
2The shaded part is the numerator, and the total amount of equal parts is the denominator.
Since there are 21 shaded parts and 100 equal parts. 21 will be the numerator of the fraction, and 100 is the denominator of the fraction.
3Write the fraction and simplify if possible.
0.21 → \cfrac{21}{100}
\cfrac{21}{100} \, is in lowest terms.
### Example 2: convert a simple decimal to a fraction (without simplifying)
Change 0.3 to a fraction.
Write the decimal in words.
The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.
Write the fraction and simplify if possible.
### Example 3: convert a decimal to a fraction (with simplifying)
Convert 0.22 to a fraction.
Write the decimal in words.
The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.
Write the fraction and simplify if possible.
### Example 4: convert a decimal to a fraction involving thousandths
Convert 0.387 to a fraction.
Write the decimal in words.
The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.
Write the fraction and simplify if possible.
### Example 5: convert a decimal bigger than 1 to a mixed number
Convert 1.7 to a mixed number.
Write the decimal in words.
Keep the whole number.
The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.
Write the mixed number and simplify if possible.
### Example 6: convert a decimal bigger than 1 to a mixed number (with simplifying)
Convert 2.04 to a fraction.
Write the decimal in words.
Keep the whole number.
The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.
Write the mixed number and simplify if possible.
### Teaching tips for converting decimals to fractions
• Use a visual model to introduce the topic since students should be familiar with how to create a fraction from a model.
• Use a number line to help students formulate number sense with decimal and fraction numbers.
• Reinforcing the decimal value will help students be able to write it in fraction form.
• When teaching the math lessons on converting fractions to decimals, have students change improper fractions to mixed numbers first before making the conversion.
### Easy mistakes to make
• Placing the decimal number in the wrong columns on a place value chart
For example, placing the 3 in the decimal number 0.03 in the tenths column instead of the hundredths column.
• Forgetting to write the fraction in lowest terms
Always look to see if there is a common factor between the numerator and the denominator of the fraction.
• Confusing the numerator and the denominator
The numerator is the top number, and the denominator is the bottom number.
When converting a decimal to a fraction, the digits of the decimal will be the numerator (top number) and a power of ten will be the denominator (bottom number).
### Practice converting decimals to fractions questions
1. Which fraction represents the decimal represented in the model?
0.33
\cfrac{33}{1000}
\cfrac{33}{100}
\cfrac{3}{10}
\cfrac{30}{100}
33 shaded parts out of 100 equal parts as a fraction is \, \cfrac{33}{100}.
2. What is 0.1 as a fraction in lowest terms?
\cfrac{10}{100}
\cfrac{1}{10}
\cfrac{0.1}{1}
\cfrac{0.01}{100}
0.1 in words is one tenth. Put it on a place value chart.
0 is in the ones column and 1 is in the tenths column.
1 will be the numerator, and 10 will be the denominator.
0.1 as a fraction is \, \cfrac{1}{10}.
\cfrac{1}{10} \, is in lowest terms.
3. What is 0.4 as a fraction in lowest terms?
\cfrac{40}{100}
\cfrac{4}{10}
\cfrac{2}{5}
\cfrac{0.4}{1}
0.4 in words is four tenths. Put it on the place value chart.
0 is in the ones column and 4 is in the tenths column.
4 will be the numerator, and 10 will be the denominator.
0.4 as a fraction is \, \cfrac{4}{10}.
\cfrac{4}{10} \, can be simplified because the common factor of 4 and 10 is 2.
\cfrac{4 \, \div \, 2}{10 \, \div \, 2}=\cfrac{2}{5}
\cfrac{4}{10} \, in lowest terms is \, \cfrac{2}{5}.
4. What is 0.016 as a fraction in lowest terms?
\cfrac{16}{100}
\cfrac{4}{25}
\cfrac{16}{1000}
\cfrac{2}{125}
0.016 in words is sixteen thousandths. Put it on the place value chart.
0 is in the ones column, 0 is in the tenths column, 1 is in the hundredths column, and 6 is in the thousandths column.
16 will be the numerator, and 1000 will be the denominator.
0.16 written as fraction is \, \cfrac{16}{1000}.
8 is the common factor between 16 and 1000.
\cfrac{16 \, \div \, 8}{1000 \, \div \, 8}=\cfrac{2}{125}
\cfrac{16}{1000} \, in lowest terms is \, \cfrac{2}{125}.
5. What is 1.23 as a mixed number in lowest terms?
1\cfrac{23}{100}
\cfrac{23}{100}
1\cfrac{23}{1000}
1\cfrac{23}{10}
1.23 in words is one and twenty-three hundredths. Put it on the place value chart.
1 is in the ones column, 2 is in the tenths column, and 3 is in the hundredths column.
1 is the whole number part of the mixed number. 23 is the numerator, and 100 is the denominator of the fractional part of the mixed number.
1.23 as a fraction is \, 1\cfrac{23}{100}.
1\cfrac{23}{100} \, is in lowest terms.
6. What is 2.05 as mixed number in its simplest form?
2\cfrac{5}{10}
2\cfrac{1}{2}
2\cfrac{5}{100}
2\cfrac{1}{20}
2.05 in words is two and five hundredths. Put it on the place value chart.
2 is in the ones column, 0 is in the tenths column, and 5 is in the hundredths column.
2 is the whole number part of the mixed number. 5 is the numerator, and 100 is the denominator of the fractional part of the mixed number.
2.05 written as a fraction is \, 2\cfrac{5}{100}.
5 is the common factor between 5 and 100.
\cfrac{5\div 5}{100\div 5}=\cfrac{1}{20}
2\cfrac{5}{100} \, in lowest terms is \, 2\cfrac{1}{20}.
## Converting decimals to fractions FAQs
Are the denominators always going to be a power of ten?
Yes, when converting a decimal to a fraction the denominator of the fraction will always be a power of ten. This is because our decimal system breaks apart the decimal number into tenths (\cfrac{1}{10}), hundredths (\cfrac{1}{100}), thousandths (\cfrac{1}{1000}), etc.
Do you always have to simplify the fraction?
It’s a good practice to always write a fraction in lowest terms, but refer to your state standards for specific guidance.
Can you convert a fraction back into a decimal?
Yes, you can go from decimal representation to fraction representation and vice versa. For example, to convert \cfrac{9}{10} \, to a decimal, you can put it on the place value chart.
9 will go in the tenths column, so the decimal representation of \cfrac{9}{10} \, is 0.9.
Do you have to use a place value chart to convert a decimal to a fraction?
No, there are other ways to convert decimals to fractions. You can use the fraction calculator converter.
What are decimal fractions?
A decimal fraction is when the denominator of the fraction is a power of 10. For example, \cfrac{3}{100} \, is a decimal fraction because 100 is 10^2.
Can you convert a repeating decimal to a fraction?
Yes, repeating decimals are rational numbers. Rational numbers can be written as fractions. So, repeating decimals can be written as fractions. You will learn how to do this fraction conversion in 8th grade math.
## Still stuck?
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence. | 3,008 | 11,351 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2024-18 | longest | en | 0.88911 |
http://www.lconvert.com/acceleration/meter_per_second_squared/gal/ | 1,555,949,310,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578558125.45/warc/CC-MAIN-20190422155337-20190422181337-00390.warc.gz | 265,842,973 | 5,868 | # Meter/Second Squared to Gal Converter
1 Meter/Second Squared = 100 Gal
## How to convert from Meter/Second Squared to Gal?
Every 1 Meter/Second Squared equals 100 Gal. For example, 100 Meter/Second Squareds equal 100 * 100 = 10000 Gals and so on..
## Meter/Second Squared to Gal Convesions Table
1 Meter/Second Squared = 100 Gal
2 Meter/Second Squared = 200 Gal
4 Meter/Second Squared = 400 Gal
5 Meter/Second Squared = 500 Gal
10 Meter/Second Squared = 1000 Gal
20 Meter/Second Squared = 2000 Gal
25 Meter/Second Squared = 2500 Gal
50 Meter/Second Squared = 5000 Gal
100 Meter/Second Squared = 10000 Gal
200 Meter/Second Squared = 20000 Gal
250 Meter/Second Squared = 25000 Gal
500 Meter/Second Squared = 50000 Gal
1000 Meter/Second Squared = 100000 Gal
2000 Meter/Second Squared = 200000 Gal
2500 Meter/Second Squared = 250000 Gal
5000 Meter/Second Squared = 500000 Gal
10000 Meter/Second Squared = 1000000 Gal
20000 Meter/Second Squared = 2000000 Gal
25000 Meter/Second Squared = 2500000 Gal
50000 Meter/Second Squared = 5000000 Gal
100000 Meter/Second Squared = 10000000 Gal
200000 Meter/Second Squared = 20000000 Gal
500000 Meter/Second Squared = 50000000 Gal
1000000 Meter/Second Squared = 100000000 Gal
1 Gal = 0.01 Meter/Second Squared
2 Gal = 0.02 Meter/Second Squared
4 Gal = 0.04 Meter/Second Squared
5 Gal = 0.05 Meter/Second Squared
10 Gal = 0.1 Meter/Second Squared
20 Gal = 0.2 Meter/Second Squared
25 Gal = 0.25 Meter/Second Squared
50 Gal = 0.5 Meter/Second Squared
100 Gal = 1 Meter/Second Squared
200 Gal = 2 Meter/Second Squared
250 Gal = 2.5 Meter/Second Squared
500 Gal = 5 Meter/Second Squared
1000 Gal = 10 Meter/Second Squared
2000 Gal = 20 Meter/Second Squared
2500 Gal = 25 Meter/Second Squared
5000 Gal = 50 Meter/Second Squared
10000 Gal = 100 Meter/Second Squared
20000 Gal = 200 Meter/Second Squared
25000 Gal = 250 Meter/Second Squared
50000 Gal = 500 Meter/Second Squared
100000 Gal = 1000 Meter/Second Squared
200000 Gal = 2000 Meter/Second Squared
500000 Gal = 5000 Meter/Second Squared
1000000 Gal = 10000 Meter/Second Squared
## Gal
What is Gal?
Gal is a unit of acceleration used extensively in the science of gravity. It could be called “galileo” after “Galileo Galilei” who made the first measurement of the Earth’s gravity.
Its symbol is” Gal”. Gal can be defined as 1 centimeter per second squared. One gal equals a change in rate of motion of one centimeter per second per second.
1 Gal equals the following:
0.01 Meter per second squared (m/s²)0.01
0.03 Foot per second squared (ft/s²)0.03
1000 Milligal
1.02×10-3 Standard gravity
1.02×10-3 g-unit (g) | 851 | 2,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-18 | latest | en | 0.730408 |
https://www.geeksforgeeks.org/how-to-check-two-numbers-are-approximately-equal-in-javascript/ | 1,632,393,247,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057417.92/warc/CC-MAIN-20210923074537-20210923104537-00075.warc.gz | 810,686,763 | 26,190 | Related Articles
# How to check two numbers are approximately equal in JavaScript ?
• Last Updated : 31 Mar, 2021
Given two numbers and the task is to check the given numbers are approximately equal to each other or not. If both numbers are approximately the same then print true otherwise print false.
Example:
```Input: num1 = 10.3
num2 = 10
Output: true```
Approach: To check the numbers are approximately the same or not, first, we have to decide the epsilon value. Epsilon is the maximum difference between two numbers, if the difference of the numbers is less than or equal to epsilon then the numbers are approximately equal to each other. So first we create a function named checkApprox which takes three arguments num1, num2, and epsilon. Now check the absolute difference of num1 and num2 is less than epsilon or not.
Example 1:
## Javascript
``
Output:
`true`
Example 2:
## Javascript
``
Output:
`true`
Example 3:
## Javascript
``
Output:
`false`
My Personal Notes arrow_drop_up | 233 | 1,016 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-39 | latest | en | 0.858677 |
https://www.electro-tech-online.com/threads/how-to-build-a-circuit-that-acts-like-this.95860/ | 1,726,291,649,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651548.18/warc/CC-MAIN-20240914025441-20240914055441-00541.warc.gz | 691,354,263 | 25,039 | Continue to Site
# how to build a circuit that acts like this
Status
Not open for further replies.
#### transgalactic
##### Banned
how to build a circuit that acts like this graph
https://i32.tinypic.com/ivfipx.gif
i am only allowed to use a linear components
a simple diode,simple E1 source simple E2 source
simple resistor
i know that the middle climb is a charging capacitor
there so many switching of modes
i dont know how to start thing of that?
i dont want the solution right away
i want guidance so by answering your questions i will get to the
solution myself
1) It could be a diode creating the jump at the beginning
2) What happens when a capacitor is full? It levels off.
I might be way off, but hey, you never know
a diode is like a switch
if it has a negative voltage on it we would have open circuit
then if we switch the voltage to positive
then it will remain an open circuit
but after the transition period it will be short circuit
so i think that it cannot create a jump
Hi,
There is a discontinuity in the circuit where it jumps up suddenly.
That means there has to be at least one switch in the circuit.
only diodes can act as a switch
no actual switches allowed
A diode will not conduct until there is the 0.7V drop (for silicon) requirement met.
i attach it
#### Attachments
• Circuit.jpg
20.3 KB · Views: 265
• Output.jpg
23.5 KB · Views: 253
Last edited:
how you came up with this sketch
?
Hello,
Sorry, i couldnt get that three diode circuit to produce the required waveform.
I might have missed something so let me know if so.
Here is a circuit that provides the required waveform using only diodes, resistors,
constant voltage sources, and one input voltage (V1).
Im not sure if this is the kind of solution you wanted or not so take a look...
#### Attachments
• StrangeDiodeCircuit.gif
22.1 KB · Views: 246
Hi again,
Here is a more straightforward circuit. You can try to figure out why
the resistor values are such that they are and why the voltage levels
are what they are. All the knee places are easy to set with this
circuit.
#### Attachments
• StrangeDiodeCircuit-02.gif
11.2 KB · Views: 239
Last edited:
Hello again,
The original waveform has these characteristics in the order shown:
1. The output starts out negative (E2).
2. While the input is still negative, the output jumps up suddenly through zero.
3. The output ramps up, passes through the x axis, then stops rising at E1.
4. The output remains at E1 after that.
The above gives us three corners:
1. At some negative Vin and Vout
2. With Vout positive and Vin still negative
3. With both Vin and Vout positive
I dont see three corners in your teachers solution, only two.
The input starts off very negative, and R conducts and D2 conducts and E2
keeps the output clamped at -E2. As the input rises, eventually it reachs
the same voltage as -E2 and that means there is no current flowing in R
and D2 stops conducting. The output is now still at -E2 though because
the input is at -E2. Now the input rises a bit more and so the output
rises too, but it must be ramping already because Vin is ramping over
time. Thus, the output ramps through zero and does not jump up suddenly
as the waveform picture shows it should.
Eventually the input reachs E1, and then diode D1 clamps the output to E1
so it remains at E1.
What the above means is that there is no jump discontinuity as the original
waveform drawing shows.
You'll have to ask the teacher why the waveform shows a jump when the
circuit given does not seem to have that kind of response.
By adding R2 in the drawing below i can get it to look like a jump
occurs, but the jump only happens near the x axis, not before it.
The entire jump is supposed to be over with before the input
reaches zero. Also, then the output ramps up but there is no clamp
at the end.
I included the original waveform drawing and the circuit your teacher
gave too, and the last schematic is the new circuit but that doesnt
work exactly right either.
#### Attachments
• 3IVFIPX.gif
90.6 KB · Views: 244
Last edited:
It's not that circuit.
That circuit clamps the output if input is less then E2-diode drop or greater then E1+diode drop. Between these two points Vout = Vin.
Last edited:
Hi,
I gave a full description in my previous post, you may have posted at the
same time that i did.
Hi again,
Here is the drawing of the original waveform along with the
teachers solution and the teachers solution with an added
resistor just to show how the resistor forms a slope.
The waveforms for each circuit are shown just to the right of
each circuit.
#### Attachments
• 4IVFIPX.GIF
68.6 KB · Views: 219
Status
Not open for further replies.
Replies
14
Views
2K
Replies
0
Views
1K
Replies
13
Views
3K
Replies
8
Views
1K
Replies
7
Views
3K | 1,208 | 4,797 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-38 | latest | en | 0.886286 |
https://mathoverflow.net/questions/221674/self-avoiding-reflecting-geodesics-on-a-convex-surface | 1,611,826,372,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704839214.97/warc/CC-MAIN-20210128071759-20210128101759-00168.warc.gz | 447,204,717 | 28,311 | # Self-avoiding/reflecting geodesics on a convex surface
Let $S$ be the surface of a convex body embedded in $\mathbb{R}^3$. For me $S$ is a convex polyhedron, but I am happy to view $S$ as a smooth body with positive Gaussian curvature at each point, or with non-negative Gaussian curvature at each point. Likely these various versions do not affect the question I am posing. Maybe even convexity is not required.
Let $x \in S$ be an arbitrary point on $S$, and $u$ an arbitrary direction vector tangent to $S$ at $x$. Shoot off a geodesic $\gamma$ from $x$ in direction $u$, and let it proceed until it intersects its own path at some point $y$. Rather than let the geodesic cross itself at $y$, have it instead reflect from $\gamma$ like a mirror: angle of incidence $=$ angle of reflection. And continue: every time $\gamma$ would cross itself, instead it reflects. Call this $\gamma$ a reflecting geodesic. ("Self-avoiding" is eye-catching but inaccurate.)
Q. For generic $x$ and $u$, is it true that for "most" surfaces $S$, a reflecting geodesic $\gamma$, emanating from $x$ in direction $u$, converges to a point?
I would prefer not to attempt to define precisely what "most surfaces" means, but in the polyhedral world, it would suffice for $S$ to be the convex hull of random points in space. (Vertices would be hit with probability zero.) I know that, without the "generic" qualifier, a reflecting geodesic might get caught in an infinite loop. For example, on a cube, $\gamma$ intersects itself at $90^\circ$ (essentially: because of the Gauss-Bonnet theorem):
A geodesic starting at the center of the left-front face eventually intersects itself at $90^\circ$ on the bottom face.
These reflecting geodesics may seem contrived, but something close to these came up in my research, and I am hoping that an answer to Q might help. | 456 | 1,845 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2021-04 | longest | en | 0.901667 |
https://www.jiskha.com/similar?question=1%29Find+the+sixth+term+of+the+geometric+sequence+for+which+a1%3D5+and+r%3D3+A%291215+B%293645+C%299375+D%2923+I+chose+A+2%29Write+an+equation+for+the+nth+term+of+the+geometric+sequence+-12%2C4%2C-4%2F3...+A%29aN%3D-12%281%2F3%29n-1+B%29aN%3D12%28-1%2F3%29n-1+C%29aN%3D-12%28-1%2F3%29-n%2B1+D%29aN%3D-12%28-1%2F3%29n-1+I+chose+C+3%29Find&page=79 | 1,568,946,607,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573801.14/warc/CC-MAIN-20190920005656-20190920031656-00383.warc.gz | 901,458,086 | 28,191 | # 1)Find the sixth term of the geometric sequence for which a1=5 and r=3 A)1215 B)3645 C)9375 D)23 I chose A 2)Write an equation for the nth term of the geometric sequence -12,4,-4/3... A)aN=-12(1/3)n-1 B)aN=12(-1/3)n-1 C)aN=-12(-1/3)-n+1 D)aN=-12(-1/3)n-1 I chose C 3)Find
92,916 questions, page 79
1. ## government
How does due process limit the power of states? A. Due process sets term limits for state judges and other court officials. B. Due process ensures that every defendant will have access to a lawyer. C. Due process guarantees the right to vote in any state
asked by dbh on April 20, 2019
2. ## statistics
use technology to find the P-value for a right-tailed test with n=21 and test statistic t=2.065 apparently, i don't have a stat calculator or statistical software to use to find the answer. so i need help how to find it by using the t distribution table..
asked by shasha on May 21, 2010
3. ## Pre Calc
The symbol nCr, rea "n choose r" or "the number of combinations of n things taken r at a time" is the number: n! ----- r!(n-r)! a:find 4C1 b:Find 5C0 and 5C5 c: Find 7C1, 7C2, 7C3
asked by Emma B on September 12, 2010
4. ## Physics
A projectile is fired with a speed of 50 m/s at an angle of 37 find the horizontal and vertical components of its velocity find the time that the projectile will spend in the air find the distance downfield that it will travel
asked by IDK on November 22, 2008
5. ## direct variation
could someone please help me with these problems i am having trouble. If y=36 when x =6 find x when y = 42 If y=-18 when x=6 find x when y=6 If y =12 when x= 15 find x when y =21 If y=-6.6 when x=9.9 find y when x =6.6 If y=6 when x=(2/3)find x when y=12
asked by Teri on September 13, 2006
6. ## math
Brilli the ant placed the numbers 1,2,…,n in order clockwise around a circle. She can create an infinite sequence A={aj}∞j=0 of integers by letting a0=k∈{1,2,…,n} and constructing ai+1 from ai by taking the integer that is ai positions clockwise in
asked by Ron on July 16, 2013
7. ## Math (help steve)
Brilli the ant placed the numbers 1,2,…,n in order clockwise around a circle. She can create an infinite sequence A={aj}∞j=0 of integers by letting a0=k∈{1,2,…,n} and constructing ai+1 from ai by taking the integer that is ai positions clockwise in
asked by Danny on July 16, 2013
8. ## Math
Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k. Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k Q.3)If 2 and 3 are the zeroes of the polynomial 3x2-2kx+2m find the values of k
asked by stan on April 24, 2010
9. ## Health
Dear tutors, I have an few more questions that need answering. If you could, may you answer them. What is the best definition of friendship? A) A long-term connection with another person B) A special relationship between people who enjoy being together C)
asked by Anything but anonymous on November 26, 2018
Which of the below are mechanisms cells can use to control activity of a gene? A) Regulating mRNA stability B)Regulating protein stability c)Positively regulate gene expression D)Regulating enzyme activity of a protein E)Regulating protein stability
asked by Jeremiah on March 1, 2018
11. ## Maths Probability
When writing a math expression, any time there is an open bracket "(", it is eventually followed by a closed bracket ")". When we have a complicated expression, there may be several brackets nested amongst each other, such as in the expression
asked by stranger on March 25, 2013
12. ## physics
In the 1950s, an experimental train that had a mass of 3.30 104 kg was powered across level track by a jet engine that produced a thrust of 4.90 105 N for a distance of 600 m. (a) Find the work done on the train. 1 J (b) Find the change in kinetic energy.
asked by dan on May 10, 2012
13. ## Dramas
I am trying to find this zee tv drama pancham but am unable to find it. my family and I want to watch it's episodes on the internet, but we can't seem to find them anywhere. if you can then please do help, you don't have to though if you don't want to
asked by Soniya on July 21, 2009
14. ## Calculus
function f(x)=x3x2−1 defined on the interval [−16,16] A. Find the vertical asymptotes of function f(x) B. Find where it is concave up C. Find the inflection points
asked by Katie on May 2, 2013
15. ## algebra2
how do you find out the vertex when graphing inequalities of quadratics in equations like this y
asked by jake on December 4, 2012
16. ## Calculus
function f(x)=x3x2−1 defined on the interval [−16,16] A. Find the vertical asymptotes of function f(x) B. Find where it is concave up C. Find the inflection points
asked by Katie on May 2, 2013
17. ## Geometry
For questions 38-40 use the triangle. |\ 45° angles for the top of the | \ triangle and the bottom right | \C | \ 38: If a=12, find b | \ 39: If b=2,find c | \ 40: If c=12,find a -------- B. Is this pythagorean Therorem? When I try it that way it's not
asked by Andrea on May 12, 2015
18. ## Math (Derivative)
Assume that x and y are both differentiable functions of t and the required values of dy/dt and dx/dt xy=6 a) Find dy/dt, given x=8 and dx/dt=12 b) Find dx/dt, given x=1 and dy/dt=-8 I started with a and got dy/dt=dx/dt(-y/x) Plugging with the given values
asked by Ray on November 13, 2016
19. ## Microbes and Society
Which of the following is the correct sequence of steps in the scientific method? a. observation - prediction - hypothesis - observation - hypothesis b. hypothesis - observation - prediction - hypothesis - observation wrong c. observation - hypothesis -
asked by Amber on January 31, 2017
20. ## Fair Division-Apportionment
I have to do a problem where : a) Find the standard division d b) Find the exact quotas for each of the republics c) Find the apportionment of seats using Hamilton's method The info is REPUBLIC: Argh Brwd Chrd Dstyr Eoia Population:7.65 4.45 8.52 9.98 6.51
asked by Lynne on October 1, 2013
21. ## Health
31. brenda is 15 years old. She is 5 ft. 6 in. tall and weighs 140 lbs. What is her BMI? a. 20.31 b. 21.40 c. 22.59 d. 24.63 33. In which of the following ways are anorexia and bulimia the same? a. Both are disorders in which the person is very concerned
asked by mysterychicken on October 19, 2011
22. ## Social Studies 8R - Paragraph Check
Please check my paragraph to see if it's good. If there any detials I should add please let me know. Also please let me know if there any grammar errors. Obama Win When Barack Obama was re-elected I was ecstatic. Obama is a really good president and he
asked by Laruen on November 8, 2012
23. ## maths
Sachin and rahul attempted to slove a quadratic eqn. Sachin made a mistake in writing down the constant term and ended up it roots (4,3). Rahul made a mistake in writing down coefficient of x to get roots (3,2) the correct roots of the eqn are:
asked by jha on July 5, 2014
24. ## calculus
At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous rate of change of the
asked by Adam Janky on March 10, 2011
25. ## Language Arts - Maniac Magee
I need help finding Maniac Magee online. I need to be able to highlight parts of it with my mouse, but I can't find any sites that will work. If you don't find a site, please give me some words that I can use in the search bar to find a site. Please help,
asked by Brady on February 24, 2014
26. ## Math Test
1. A rental car company charges \$150.00 for a weekly rental and an additional \$0.20 for each mile driven. The function rule C=0.20m+150.00 describes the relationship between the number of miles driven m and the total cost C. If the rental car can only be
asked by Kaai97 on November 30, 2015
27. ## Information Literacy
1-When choosing your search strategy for a search engine, it's best to A. enter the least important word first. B. ignore alternate spellings. C. combine keywords into phrases by using quotation marks. D. use verbs, articles, and capitals My answer C 2- To
asked by Moha on May 12, 2012
28. ## English
I tried to summarize briefly Scotland's history. Can you please have a look at it? Which form is correct: in 9th century/in the ninth century? 6th century (AD): 500-599 (is it correct?) 9th century (AD): 800-899 10th century: 900-999 1) The first
asked by Henry2 on September 5, 2011
29. ## tax
during 2011 sam paid following: property tax on residence (paid from escrow account) \$1550 Property tax portion of car registration (based on value) \$400 property taxes on land held for long term appreciation \$350 What amount can Sam deduct as property
asked by Andrew on March 7, 2012
30. ## Accounting
1. Bonds Payable has a balance of \$900,000 and Premium on Bonds Payable has a balance of \$10,000. If the issuing corporation redeems the bonds at 103, what is the amount of gain or loss on redemption? 1. \$1,200 gain 2. \$17,000 gain 3. \$1,200 loss 4.
asked by Tasha on July 25, 2010
31. ## math
U is the set of positive integers less than or equal to 30. A is the set of natural numbers that are multiples of 5 in U. B is the subset of all of the even integers in U. a) Find n(A U B) b) Find n(A intersect B) c) Find n(A U B' ) d Find n(B intersect
asked by Lucas on January 25, 2014
32. ## math
U is the set of positive integers less than or equal to 30. A is the set of natural numbers that are multiples of 5 in U. B is the subset of all of the even integers in U. a) Find n(A U B) b) Find n(A intersect B) c) Find n(A U B' ) d Find n(B intersect
asked by Lucas on January 24, 2014
33. ## math
g(x)=(2x^3+x^2-18x-9)/(x^2+x-6) A. Find the vertical asymptotes. b. find any holes. c. find any oblique or horizontal asymptotes. d. find if the graph crosses the oblique or horizontal asymptote.
asked by Joe on December 3, 2013
34. ## LanguageArts
Please help asap REPETITION- occurs when a line or a sequence of lines appears more than once. ASSONANCE-is the repetition of the same or similar vowel sounds in a series of words, usually words with different consonant sounds. Read the poem, then answer
asked by Sean on November 5, 2009
35. ## English (Help Me, Help Me,Please Somebody Help Me)
write a news story in inverted-pyramid style. Begin your story with a summary news lead of no more than 20 words and then write a full story using inverted pyramid style. Using the scenario below. A home at 2481 Santana Avenue was burglarized between the
asked by Mary on May 29, 2013
36. ## Calculus
assume that f(x)= x^3(x-2)^2 a) find the x-intercepts algebraically b) find all the critical points c) use the first derivative test to determine local minimums and maximums d)find all inflection points e)state the concavity of the graph on appropriate
asked by Elaine on April 24, 2012
37. ## 5th grade Language
Please help him if you can. REPETITION- occurs when a line or a sequence of lines appears more than once. ASSONANCE-is the repetition of the same or similar vowel sounds in a series of words, usually words with different consonant sounds. Read the poem,
asked by Sean on November 5, 2009
38. ## History
Which of the following best explains why the "recall" provision was an important election reform? a) it allows voters to remember what measures are on the ballot. b) it allows for removal of an elected offical from office. c) it allows a vote on a measure
asked by tabby on December 14, 2006
39. ## Math
Could somebody please help me with a few Math questions? 1. Provide an appropriate response. True or False? 100.567 is between 10 and 100. 2. Use an annual percentage rate table to solve the problem. A family purchased a new ski boat for \$20,000. The loan
asked by Felicity on March 26, 2014
40. ## Bio Bio Please check answer
Because codons are triplicates, there are ______ possible nucleotides combinations that could make a codon; each giving rise to one specific amino acid. Yet, there are only 20 amino acids used to produce proteins. Thsus, the gentic code is said to be
asked by Christine on July 22, 2006
41. ## English
I am trying to find a connection between Invisible man by Ralph Ellison and got tell it on the mountain by James Baldwin. The only connection I can find is that both characters are somehow betraying their race. However, in invisible man I can find that
asked by laura on February 12, 2008
42. ## Algebra
Find the axis of symmetry for y=x^2+4x-7 Find the axis of symmetry for y=3x^2-18x+1 Find the axis of symmetry for y=5x^2+10+3 Determine if the vertex is a maximum or minimum and identify it y=2x^2-3 Determine etc etc for y=-x^2-2x Determine etc etc for
asked by Breona on November 28, 2012
43. ## Psychology
Can someone please tell me whether or not these answers are correct. Thanks! 1. Regarding the memory processes, incoming information is first _______, then stored, and finally the memories must be _______, or taken out of storage to be useful. a.
asked by Marilyn on November 19, 2011
44. ## math
a cube has an edge length of x cm write an equation for the volume v of the cube in term of x . if the length of each edge were doubled how would the volume change if the length were tripled how would volume x³ i mean the equation would be v=x³
asked by margaret on January 21, 2007
45. ## Chemistry
Which letter of the term that is NOT a representative particle of a substance. a)molecule b)atom c)grain d)formulaunit Was ist der "Grain"? what is the representative particle for the substance moelcular compounds? an can you show me how you got the
asked by Chris on February 2, 2007
A crippled rook can move on a chessboard in the following way: from a square, it can move to an adjacent square sharing a common side, and every two consecutive moves must be at right angles (i.e., the rook makes a 90∘ turn at every move). A cycle is a
asked by Nick on August 7, 2013
A crippled rook can move on a chessboard in the following way: from a square, it can move to an adjacent square sharing a common side, and every two consecutive moves must be at right angles (i.e., the rook makes a 90∘ turn at every move). A cycle is a
asked by Anonymous on August 8, 2013
48. ## linear algebra-urgent
1)let w=[3;4] and u=[1;2] a) find the projection p of u onto w. I found this to be p=[1.32;1.76] b) find a scalar k for which the vector kp has a norm that is equal to one. k=? d)find a vector that is orthogonal to span{w} s=? how do I do this
asked by samantha on April 8, 2015
49. ## help college algebra
given the following piecewise function f(x) = -x+1 for x
asked by zachary on February 26, 2013
50. ## Ellipses
Given an ellipse; 4x^2+y^2-48x-4y+48=0, find the Center, find the Major Axis, find the Minor Axis & the Distance from C to Foci?
asked by Amber on March 27, 2013
51. ## Algebra 2
Given f(x)= x^2+7x+8, find x when f(x)= -4. My answer is -4. Find x if f(x)=0 and f(x)= 6x^2-7x-3. My answer is -3. Find the equation of the axis of symmetry of f(x)=x^2-12x+17. I have no idea how to figure this problem.
asked by Christian on January 7, 2008
52. ## Probability
Consider the following joint PMF of the random variables X and Y: pX,Y(x,y)={1/72⋅(x2+y2),if x∈{1,2,4} and y∈{1,3}, 0, otherwise}. 1. P(Y
asked by qwerty on March 7, 2014
53. ## discrete math
1.Let functions f and g be defined by f(x)=2x+1, and g(x)=x^2-2, respectively. Find a)(gof)(a+2) b)(fog)(a+2) 2.Let A={x:x≠2) and define f: A→R by f(x)=4x/(2x-1) . Is f is one- to- one? Find the range of f . Then find f^(-1) and hence determine the
asked by rose on July 9, 2016
54. ## algebra
1. Find the LCM of (8+7), (64-49v^2), and (8-7v) 2. Find the LCM of 14x^7 and 98x^5 3. Find all numbers for which the rational expression is undefined 5/v-9
asked by lisa on November 18, 2011
55. ## Social Studies
2.Which of the following is not a traditional Inuit food that Alyssa shares with her co-workers a.bannock, or fried bread b.raw narwhale c.caribou*** d.dried tea leaves 3.which groups make up Canada aboriginal population (select three) a.Quebecois****
asked by Sid.V on January 9, 2016
56. ## Spanish 6 th grade-Please check
I have three questions-Which sentence is written correctly? Es un buen clase. Es un buena clase. Es un buena clase. I think it is Es un buen clase. Is that correct? Second question- The term pelota refers to any kind of sports ball. Pelota is a ball but
asked by Shelby on April 4, 2011
57. ## Math
I need some advice with this problem. Simplify as indicated. State at least one property of multiplication or division that would prove your simplification process correct. A. -(n+4), to eliminate the parentheses. B. 6(-s), to eliminate the parentheses. C.
asked by B.B. on June 29, 2009
58. ## bio
5. What is meant by the term “carbon fixation”? a. The release of CO2 from glucose during catabolism b. The delivery of CO2 to an enzyme required for the production of glucose c. The production of two 3-carbon molecules from one 6-carbon molecule d.
asked by doug on April 6, 2009
59. ## Financial Management
Proctor Micro-Computers, Inc. requires \$1,200,000 in financing over the next two years. The firm can borrow the funds for two years at 9.5 percent interest per year. Mr. Procter decides to do economic forecasting and determines that if he utilizes
asked by Anonymous on February 22, 2010
60. ## algrebra 2
it is called completing the square here is the equation 4x^2-4x+1=9 if anyone can help me please do okay i really need ot understand this 4x^2-4x+1=9 Move the numbers to the other side. 4x^2 -4x = 9-1 4x^2 -4x = 8 Now factor out 4 to make things easier.
asked by lisa on November 2, 2006
61. ## science!
i want you to review the (3)descriptions and the (4)questions and correct my answers of this worksheet called Scientific Method Bikini Bottom Experiments. tank you tutors for reviewing the descriptions and questions and correcting my answers. The Bikini
asked by anon on September 15, 2015
62. ## Biology
1. How many base pairs are in a full turn or twist of a DNA molecule? 2. Name the complementary base pairs on DNA. A-T; G-C are the pairs, you name them. there are 10 1/2 base pairs for a full twist in DNA How does the nucleotide sequence in one chain of
asked by Becky on January 9, 2007
63. ## math
indicates required items An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate [2*(-1) ] A. 15 B. 10 C. 8 D. -3 A B C D An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate (3*2)*4 A. -15 B. 45 C. 48 D. 12 A B C D
asked by david dare on December 17, 2010
64. ## Biology
What are some analogies for Endoplasmic reticulum and Nuclear Reticulum Go here for endoplasmic reticulum
asked by Kyle on December 30, 2006
65. ## calculus help
Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the intervals of increase and decrease and the intervals of concavity. f(x)= 1+(1/x)+(5/x^2)+(1/x^3) find the interval of increase. find the interval of
asked by Isik on April 16, 2014
66. ## im back : )
I have a bunch of questions i hope someone could help me with? #1 what is the fifth term in this series? 4 1/2; 8 3/4; 13; 17 1/4 ? I know it is 21 1/2... but how to i figure that? #2 a manufacturer has 3,375 yards of material on hand. If the average dress
asked by chrissy on July 30, 2007
67. ## Mathematics (cumulative frequency
The figures below show to t he nearest minute 80 students waited to be served in a canteen. Waiting time No. of students Cum.Freq 1-5 4 4 6-10 7 11 11-15 11 22 16-20 18 ? 21-25 22 ? 26-30 10 ? 31-35 5 ? 36-40 3 ? How do i find cumulative frequency??? Don't
asked by Maggie on June 17, 2009
68. ## Calculus
Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with
asked by Anonymous on April 19, 2015
69. ## science
A cricket ball of mass 0.4 kg moving with a velocity of 72 km/h is brought to rest by a player. Find the magnitude of the average force exerted by the player? we have, F= m x a to find acceleration we want either dist(s) or time(t) it is not given how to
asked by nidhi on July 15, 2016
70. ## math - trig
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean Theorem and find the following trigonometric functions of the indicated angle. Given: a = 4 and b = 7 Find: sin A,
asked by Annika on September 25, 2013
71. ## English
put an (*) next to the answer I chose. Not asking anyone to do my work for me; just want a double check. I'm a little unsure since I picked the same term for each answer :) Read the following sentence from "In Another Country" and choose the word below
asked by Glen on January 30, 2012
72. ## College: Modern System Analysis and design
Construct a Gantt chart and network diagram for a project you are or will be involved in. Choose a project of sufficient depth from work, home, or school. Identify the activities to be completed, determine the sequence of the activities, and construct a
asked by Tank on April 12, 2010
73. ## Financial management
ABC Construction and Leasing Company are interested in investing in the residential real estate market due to a relatively low interest rate environment. The Company appointed you to be in charge of the project feasibility study. You have just visited a
asked by Mike on January 1, 2013
74. ## geometry
User: Courtney Thompson In Course: Geometry V8 ( 2167) Instructor: Tracie Morgan -------------------------------------------------------------------------------- WARNING: You must not leave this exam form! If you try to click back into this exam again
asked by courtney thompson on December 31, 2008
75. ## Check + biology
The following statement describes, in random order, events during the transmission of a nerve impulse. Use them to answer the next \g question(s). Event 1: Positive ions flow into the neuron. Event 2: The resting potential of the cell membrane is restored.
asked by Anonymous on February 21, 2007
76. ## Consumer Math: Insurance
Choose as many answers as apply. Which of the following statements are true of ordinary whole-life insurance policies? A. The insured pays premiums on this type of insurance until his death. B. Ordinary whole life insurance covers the insured for the
asked by ashley on September 18, 2013
77. ## the federal reserve
How does the Federeal Reserve control the amount of money in circulation? By (1) setting the short term interest rate that banks must pay from loans from the Federal reserve and (2) setting the "reserve requirement" that banks must leave on deposit with
asked by Anonymous on December 12, 2006
78. ## HCM621
As the health care industry evolves and changes so do the legal and ethical issues that its employees face. An employee of the facility you have chosen to study this term has come to you with a question. He has heard a lot about issues the organization is
asked by Pupitas on August 17, 2011
79. ## chem
a) Co(H2O)6^2 + 4 Cl^‐1 (aq) ⇄ CoCl4^‐2 (aq) + 6 H2O (l) Rewrite the net ionic equation above including the energy term where appropriate. The Delta H for this reaction is +50 kJ/mol. b) Silver chloride (AgCl) is a white solid. For the equilibrium
asked by Victor on October 4, 2015
80. ## math
Which of the following are true of ordinary whole-life insurance policies? 1. The insured pays premiums on this type of insurance until his death. 2. Ordinary whole life insurance covers the insured for the states term of the policy. 3. The insured only
asked by Matt on January 12, 2010
81. ## physics
) A batter hits a baseball so that it leaves the bat at speed Vo = 37.0m/s at an angle ao = 53.1°, at a location where g = 9.80 m/S2. (a) Find the position of the ball, and the magnitude and direction of its velocity, at t = 2.00 s. (b) Find the time when
asked by hehe on May 1, 2011
82. ## Science
How do lawmaker make good environmental decisions? A. By relying on the short-term benefits of an environmental issue. B. By weighing down the costs and benefits of an environmental issue C. By relying only on the economical impact of an environmental
asked by Ariel on January 28, 2015
83. ## Quick English check- ms sue
Select the term that is best evoked by each of the scenarios below. Use complement, contend efficacious, emulate, engross, exploit, facile, implicit, industrious, replicate. 1. The representatives appeal for aid for the disaster victims was so effective
asked by Anonymous on November 16, 2015
84. ## financial accounting
the long-term note payable bears an interest of 12% per year. the unadjusted interest expense account equals the amount paid for the first 11 months of the 2008 fiscal year.(3,300). The 300 accrued interest for april has not yet been paid or recorded.Note:
asked by ben on February 9, 2008
85. ## Personal Finance
Which of the following statements is true concerning home equity loans? A. Home equity loans are generally installment loans with a 5-15 year term. B. Home equity loans are secured by all of the borrower’s assets. C. Home equity loan interest is never
asked by Her on September 2, 2011
86. ## Finance
3) Which of the following statements is true concerning home equity loans? A. Home equity loans are generally installment loans with a 5-15 year term. B. Home equity loan interest is never tax-deductible. C. Home equity loans are secured by all of the
asked by Anonymous on October 8, 2011
87. ## algebra
which method do you use to solve this equation.(x-1)^2=7. Is it the factoring method or the sqare root method I would take the square root of each side. (x-1)= +- sqrt7 Now for the factoring method: (x-1)^2=7 (x-1)^2-7=0 you have a difference of two
asked by Tony on May 17, 2007
88. ## Law (Ms.Sue)
Rights and Responsibilities: Find the key term that fits with it's definition: 1)A set of rights people have. They include freedom of speech and assembly A-I think it's social rights. 2)An international agreement drawn up after WWII A- I think it's UDHR
asked by Anonymous on November 6, 2013
89. ## English help
Which details can be considered primary support for the main primary suppor for the main idea statement. The development of speech in infants follows a definite sequence or pattern of development. a.By the time an infant is six months old, he or she can
asked by ME on October 6, 2011
90. ## History!!! Help me!! Thank you!!
1. Find a line that shows that Mr. Covey did not care that Douglass was too sick to work. (Chapter 10) 2. Find a line that shows that Master Thomas did not believe Douglass’ complaint against Mr. Covey. (Chapter 10) 3. Find a line that shows that Mr.
asked by Bell on March 29, 2012
91. ## Principals of Management
Fernando, a manager in a retail store, is changing the work schedule of his long-term employees for the holiday season. He is using the same basic schedule as he did last year. Fernando should expect that his employees will be: I think the answer is D but
asked by Melisa on May 7, 2011
92. ## Algebra
I need help understanding how to cross-multiply addition of inverse functions. I'm given this, 1/p+1/(p-45) = 1/30 The answer goes to p^2-105p+1,350 = 0. My method has been adjusting the ratios of the numerator and denominators to give,
asked by Justin on December 5, 2016
93. ## Inclusive Language Talking about People with Disab
Her brother’s friend is an AIDS victim. in rewriting this sentence so it would not be Talking about People with Disabilities and Diseases. would I just say her brother's friend is a victim and leave out the word aids. I think it would be better to say
asked by ann on July 11, 2006
94. ## Algebra 2
Can someone check my answers? 1. Convert 13pi/30 to degree measure. 78° 2. Find the distance between (4,4) and (8,7). 5 3. What is the vertex of the parabola y = (x + 8)^2 - 2? (-8,-2) 4. The graph of y = 6(x - 8)^2 + 1 open downward. False. 5. An angle
asked by Nikki on November 12, 2017
95. ## Grammar
1. An appositive: A. is another term for possessive pronouns. B. is an antecedent. C. is always plural. D. renames the noun. I think it's D? 2. The pronoun "who" can be used for: A. subjects B direct objects C. indirect objects D. objects of the
asked by anthony on May 11, 2011
96. ## Economics
After the U.S. invasion of Iraq, the price of jet fuel used by airlines increased dramatically. As the CEO of Air Canada, you have been presented with the following options. Evaluate these options in the context of decision making model. a) raise airfares
asked by Selina on January 14, 2007
97. ## Find the pattern
Our trip lasted for 12 days we arrived Sunday July 1 and left on Thursday July 12th where we stayed everyday something went wrong the electricity went out the water was shut off sliding patio wouldn't close the gas oven didn't work, and it rained. Out of
asked by Lana on October 1, 2014
98. ## History
I have to explain why there was such a delay for the enforcement of both documents. I've been trying to find websites to help me, but I haven't found anything. The answer I see is The basic reason is that most nations don't want international agreements to
asked by Jay on March 25, 2008
99. ## algebra,math,help
can someone explain to me the following:thanks... one number is 2 times another. If the sum of their reciprocals is (1)/(4). Find the two numbers. We can begin by looking at the following. Let's use the letters "a" and "c.": "One number is 2 times
asked by jasort20 on March 14, 2007
100. ## History
Pls check my answers.. The Northwest Ordinance established all of the following, except.. A. Rules for territories to become states B. Denying slavery to new states formed from the territory C. Preventing new states from entering the US D. The right to
asked by Mina on April 11, 2016 | 8,483 | 30,072 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2019-39 | latest | en | 0.881124 |
https://test.scratch-wiki.info/w/index.php?title=Zho:%E9%9A%8F%E6%9C%BA%E5%8F%96%E6%95%B0_()_%E5%88%B0_()%EF%BC%88%E7%A7%AF%E6%9C%A8%EF%BC%89&variant=zh-hant&target=Zho%3A%E9%9A%8F%E6%9C%BA%E5%8F%96%E6%95%B0+%28%29+%E5%88%B0+%28%29%EF%BC%88%E7%A7%AF%E6%9C%A8%EF%BC%89 | 1,632,808,538,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00367.warc.gz | 593,428,203 | 13,620 | "Random" redirects here. For random page on the wiki, see Special:Random.
隨機取數 () 到 () `隨機取數 (1) 到 (10)` 類別 運算類積木 形狀 橢圓形積木
The Pick Random () to () 積木 is an 運算類積木 and a 橢圓形積木. The block picks a pseudorandom number ranging from the first given number to the second, including both endpoints. If both numbers have no decimals, it will report a whole number. For example, if a 1 and a 3 were inputed, the block could return a 1, 2 or 3. If one of the numbers has a decimal point, even .0, it reports a number with a decimal. For example, if 0.1 and 0.14 were given, the output will be 0.1, 0.11, 0.12, 0.13, or 0.14.
The numbers given with this block are not truly random — they are merely unpredictable. It is nearly impossible to generate truly random numbers using a computer.
## 歷史
In the 實驗查看器, the block had a picture of a die on it.
## 用法示例
In many types of 專案, random numbers must be picked — this block will easily do the job, without any complicated scripts.
Some common uses for the Pick Random () to () block:
• Creating randomized levels
```當收到訊息 [generate v]
替換第 (square) 項於 [level v] 成 (隨機取數 (1) 到 (10))
變數 [square v] 改變 (1)
end
重複 (11) 次
造型換成 (清單第 (square) 項項目\( [level v] \) :: list)
蓋章
x 改變 (10)
變數 [square v] 改變 (1)
end
定位到 x: (-50) y: ((y 座標) - (10))
end
變數 [start v] 設為 (隨機取數 (1) 到 (121))
end
如果 <(x座標) = [50]> 那麼
定位到 x: (-50) y: ((y 座標) - (10))
x 改變 (10)
end
變數 [square v] 改變 (1)
end
```
• Setting random stats
```變數 [hp v] 設為 (隨機取數 (25) 到 (100))
```
• Choosing random objects
```變數 [purchase v] 設為 (清單第 (隨機取數 (1) 到 (9)) 項項目\( [grocery list v] \) :: list)
```
```造型換成 (隨機取數 (1) 到 (7))
```
## 應用
Main article: List of Block Workarounds
To work around this block, the Scratcher must program a 程式 that will give unpredictable numbers.
A simple workaround is to fill a 清單 with the possible numbers, and then use the 清單第 () 項項目 block with the first input set to any. The Item (any) of () block chooses an unpredictable item — so if the chosen list has all the wanted numbers, the Item () of () block is an effective workaround:
```當 @greenflag 被點擊
```
There are scripts that can pick unpredictable numbers without using any blocks that give random values. To make these scripts, a value must be used that is unpredictable — the 計時器 is a very good choice. Other choices are:
• Continuously moving a hidden sprite around the screen and using its location
• Continuously changing a 變量 and using its current value
• Continuously changing the pen color, shade or size and using its value
Then a script can be created with the value — an example with a continuously moving sprite:
```變數 [random number v] 設為 (x 座標)
```
This, however, is rather simple. More complicated scripts can be made:
```變數 [random number v] 設為 ((x座標) + (y 座標))
```
```變數 [random number v] 設為 (四捨五入數值 (((y 座標) + ((方向) * (2))) / (3)))
```
Note: The random numbers generated from these alternatives may not be as accurate as the Pick Random () to () block.
Cookies help us deliver our services. By using our services, you agree to our use of cookies. | 995 | 3,056 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2021-39 | latest | en | 0.678861 |
https://howlingpixel.com/wiki/Square | 1,516,367,219,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887981.42/warc/CC-MAIN-20180119125144-20180119145144-00784.warc.gz | 689,930,665 | 18,117 | # Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles).[1] It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ${\displaystyle \square }$ ABCD.
Square
Type Regular polygon
Edges and vertices 4
Schläfli symbol {4}
Coxeter diagram
Symmetry group Dihedral (D4), order 2×4
Internal angle (degrees) 90°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal
## Characterizations
A convex quadrilateral is a square if and only if it is any one of the following:[2][3]
• a rectangle with two adjacent equal sides
• a rhombus with a right vertex angle
• a rhombus with all angles equal
• a parallelogram with one right vertex angle and two adjacent equal sides
• a quadrilateral with four equal sides and four right angles
• a quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals
• a convex quadrilateral with successive sides a, b, c, d whose area is ${\displaystyle A={\tfrac {1}{2}}(a^{2}+c^{2})={\tfrac {1}{2}}(b^{2}+d^{2}).}$[4]:Corollary 15
## Properties
A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles) and therefore has all the properties of all these shapes, namely:[5]
• The diagonals of a square bisect each other and meet at 90°
• The diagonals of a square bisect its angles.
• Opposite sides of a square are both parallel and equal in length.
• All four angles of a square are equal. (Each is 360°/4 = 90°, so every angle of a square is a right angle.)
• All four sides of a square are equal.
• The diagonals of a square are equal.
• The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.
• A square has Schläfli symbol {4}. A truncated square, t{4}, is an octagon, {8}. An alternated square, h{4}, is a digon, {2}.
### Perimeter and area
The area of a square is the product of the length of its sides.
The perimeter of a square whose four sides have length ${\displaystyle \ell }$ is
${\displaystyle P=4\ell }$
and the area A is
${\displaystyle A=\ell ^{2}.}$
In classical times, the second power was described in terms of the area of a square, as in the above formula. This led to the use of the term square to mean raising to the second power.
The area can also be calculated using the diagonal d according to
${\displaystyle A={\frac {d^{2}}{2}}.}$
In terms of the circumradius R, the area of a square is
${\displaystyle A=2R^{2};}$
since the area of the circle is ${\displaystyle \pi R^{2},}$ the square fills approximately 0.6366 of its circumscribed circle.
In terms of the inradius r, the area of the square is
${\displaystyle A=4r^{2}.}$
Because it is a regular polygon, a square is the quadrilateral of least perimeter enclosing a given area. Dually, a square is the quadrilateral containing the largest area within a given perimeter.[6] Indeed, if A and P are the area and perimeter enclosed by a quadrilateral, then the following isoperimetric inequality holds:
${\displaystyle 16A\leq P^{2}}$
with equality if and only if the quadrilateral is a square.
### Other facts
• The diagonals of a square are ${\displaystyle \scriptstyle {\sqrt {2}}}$ (about 1.414) times the length of a side of the square. This value, known as the square root of 2 or Pythagoras' constant, was the first number proven to be irrational.
• A square can also be defined as a parallelogram with equal diagonals that bisect the angles.
• If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then it is a square.
• If a circle is circumscribed around a square, the area of the circle is ${\displaystyle \pi /2}$ (about 1.5708) times the area of the square.
• If a circle is inscribed in the square, the area of the circle is ${\displaystyle \pi /4}$ (about 0.7854) times the area of the square.
• A square has a larger area than any other quadrilateral with the same perimeter.[7]
• A square tiling is one of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon).
• The square is in two families of polytopes in two dimensions: hypercube and the cross-polytope. The Schläfli symbol for the square is {4}.
• The square is a highly symmetric object. There are four lines of reflectional symmetry and it has rotational symmetry of order 4 (through 90°, 180° and 270°). Its symmetry group is the dihedral group D4.
• If the inscribed circle of a square ABCD has tangency points E on AB, F on BC, G on CD, and H on DA, then for any point P on the inscribed circle,[8]
${\displaystyle 2(PH^{2}-PE^{2})=PD^{2}-PB^{2}.}$
• If ${\displaystyle d_{i}}$ is the distance from an arbitrary point in the plane to the i-th vertex of a square and ${\displaystyle R}$ is the circumradius of the square, then[9]
${\displaystyle {\frac {d_{1}^{4}+d_{2}^{4}+d_{3}^{4}+d_{4}^{4}}{4}}+3R^{4}=\left({\frac {d_{1}^{2}+d_{2}^{2}+d_{3}^{2}+d_{4}^{2}}{4}}+R^{2}\right)^{2}.}$
## Coordinates and equations
${\displaystyle |x|+|y|=2}$ plotted on Cartesian coordinates.
The coordinates for the vertices of a square with vertical and horizontal sides, centered at the origin and with side length 2 are (±1, ±1), while the interior of this square consists of all points (xi, yi) with −1 < xi < 1 and −1 < yi < 1. The equation
${\displaystyle \max(x^{2},y^{2})=1}$
specifies the boundary of this square. This equation means "x2 or y2, whichever is larger, equals 1." The circumradius of this square (the radius of a circle drawn through the square's vertices) is half the square's diagonal, and equals ${\displaystyle \scriptstyle {\sqrt {2}}}$. Then the circumcircle has the equation
${\displaystyle x^{2}+y^{2}=2.}$
Alternatively the equation
${\displaystyle \left|x-a\right|+\left|y-b\right|=r.}$
can also be used to describe the boundary of a square with center coordinates (a, b) and a horizontal or vertical radius of r.
## Construction
The following animations show how to construct a square using a compass and straightedge. This is possible as 4 = 22, a power of two.
Square at a given circumcircle
Square at a given side length,
right angle by using Thales' theorem
Square at a given diagonal
## Symmetry
The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the square is r12 and no symmetry is labeled a1.
The square has Dih4 symmetry, order 8. There are 2 dihedral subgroups: Dih2, Dih1, and 3 cyclic subgroups: Z4, Z2, and Z1.
A square is a special case of many lower symmetry quadrilaterals:
• a rectangle with two adjacent equal sides
• a quadrilateral with four equal sides and four right angles
• a parallelogram with one right angle and two adjacent equal sides
• a rhombus with a right angle
• a rhombus with all angles equal
• a rhombus with equal diagonals
These 6 symmetries express 8 distinct symmetries on a square. John Conway labels these by a letter and group order.[10]
Each subgroup symmetry allows one or more degrees of freedom for irregular quadrilaterals. r8 is full symmetry of the square, and a1 is no symmetry. d4, is the symmetry of a rectangle and p4, is the symmetry of a rhombus. These two forms are duals of each other and have half the symmetry order of the square. d2 is the symmetry of an isosceles trapezoid, and p2 is the symmetry of a kite. g2 defines the geometry of a parallelogram.
Only the g4 subgroup has no degrees of freedom but can seen as a square with directed edges.
## Squares inscribed in triangles
Every acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle's right angle, so a right triangle has only two distinct inscribed squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side.
The fraction of the triangle's area that is filled by the square is no more than 1/2.
## Squaring the circle
Squaring the circle is the problem, proposed by ancient geometers, of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.
In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental number, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients.
## Non-Euclidean geometry
In non-Euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles.
In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles.
In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger hyperbolic squares have smaller angles.
Examples:
Two squares can tile the sphere with 2 squares around each vertex and 180-degree internal angles. Each square covers an entire hemisphere and their vertices lie along a great circle. This is called a spherical square dihedron. The Schläfli symbol is {4,2}. Six squares can tile the sphere with 3 squares around each vertex and 120-degree internal angles. This is called a spherical cube. The Schläfli symbol is {4,3}. Squares can tile the Euclidean plane with 4 around each vertex, with each square having an internal angle of 90°. The Schläfli symbol is {4,4}. Squares can tile the hyperbolic plane with 5 around each vertex, with each square having 72-degree internal angles. The Schläfli symbol is {4,5}. In fact, for any n ≥ 5 there is a hyperbolic tiling with n squares about each vertex.
## Crossed square
Crossed-square
A crossed square is a faceting of the square, a self-intersecting polygon created by removing two opposite edges of a square and reconnecting by its two diagonals. It has half the symmetry of the square, Dih2, order 4. It has the same vertex arrangement as the square, and is vertex-transitive. It appears as two 45-45-90 triangle with a common vertex, but the geometric intersection is not considered a vertex.
A crossed square is sometimes likened to a bow tie or butterfly. the crossed rectangle is related, as a faceting of the rectangle, both special cases of crossed quadrilaterals.[11]
The interior of a crossed square can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.
A square and a crossed square have the following properties in common:
• Opposite sides are equal in length.
• The two diagonals are equal in length.
• It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).
It exists in the vertex figure of a uniform star polyhedra, the tetrahemihexahedron.
## Graphs
3-simplex (3D)
The K4 complete graph is often drawn as a square with all 6 possible edges connected, hence appearing as a square with both diagonals drawn. This graph also represents an orthographic projection of the 4 vertices and 6 edges of the regular 3-simplex (tetrahedron).
## References
1. ^ W., Weisstein, Eric. "Square". mathworld.wolfram.com. Retrieved 2017-12-12.
2. ^ Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, p. 59, ISBN 1-59311-695-0.
3. ^ "Problem Set 1.3". jwilson.coe.uga.edu. Retrieved 2017-12-12.
4. ^ Josefsson, Martin, "Properties of equidiagonal quadrilaterals" Forum Geometricorum, 14 (2014), 129-144.
5. ^ "Maths is Fun - Can't Find It (404)". www.mathsisfun.com. Retrieved 2017-12-12.
6. ^ Chakerian, G.D. "A Distorted View of Geometry." Ch. 7 in Mathematical Plums (R. Honsberger, editor). Washington, DC: Mathematical Association of America, 1979: 147.
7. ^ 1999, Martin Lundsgaard Hansen, thats IT (c). "Vagn Lundsgaard Hansen". www2.mat.dtu.dk. Retrieved 2017-12-12.
8. ^ "Geometry classes, Problem 331. Square, Point on the Inscribed Circle, Tangency Points. Math teacher Master Degree. College, SAT Prep. Elearning, Online math tutor, LMS". gogeometry.com. Retrieved 2017-12-12.
9. ^ Park, Poo-Sung. "Regular polytope distances", Forum Geometricorum 16, 2016, 227-232. http://forumgeom.fau.edu/FG2016volume16/FG201627.pdf
10. ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)
11. ^ Wells, Christopher J. "Quadrilaterals". www.technologyuk.net. Retrieved 2017-12-12. | 3,546 | 13,416 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 22, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-05 | longest | en | 0.851166 |
https://www.jsoftware.com/help/phrases/sorting.htm | 1,604,004,786,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107905777.48/warc/CC-MAIN-20201029184716-20201029214716-00230.warc.gz | 751,658,613 | 2,291 | >> << Usr Pri JfC LJ Phr Dic Voc !: Help Phrases
# 6A. Sorting
Sorting means the rearrangement of an array into an order based on some key, which may be either implicit or explicit. The implicit keys are the integer or real number fields, and the standard alphabet. Explicit keys may be any arbitrary set. Note that sorting applies equally well to character data and to Boolean, integer, real numbers, complex numbers, or to boxed data. When applied to real numbers, comparisons are exact. No tolerance is used. Verbs defined to sort in ascending order can be converted to give descending order by changing /: to \: , as in m0 and m1 . Note also that these verbs apply (unless they use the rank operator to prevent it) to arrays of arbitrary ranks, where the items are treated as if they were raveled.
m0=: /:~ Sort the array y in ascending order m1=: \:~ Sort the array y in descending order m2=: /:~"_1 Sort the items of array y ascending d3=: /:@:{ { [ Sort indices x according to y d4=: ]/:{"1 Sort table y according to column x d5=: \:@[`(/:@[) @. ] Grade x up if y is 1 and down if y is 0 d6=: \:~@[`(/:~@[) @. ] Sort up or down (Try literal argument) d7=: /:~ Sort y according to x
``` y=:'leap','note',:'file'
m1 y
note
leap
file
m1"1 y
plea
tone
life
z=:> ;: 'to be or not to be that is the question'
(] ; m0 ; m1 ; m2) z
+-----------------------------------+
|to |be |to | ot|
|be |be |to | be|
|or |is |the | or|
|not |not |that | not|
|to |or |question| ot|
|be |question|or | be|
|that |that |not | ahtt|
|is |the |is | is|
|the |to |be | eht|
|question|to |be |einoqstu|
+-----------------------------------+
q=: ?.15#9
(] , m0 ,: m1) q
1 6 4 4 1 0 6 6 8 3 4 7 0 0 4
0 0 0 1 1 3 4 4 4 4 6 6 6 7 8
8 7 6 6 6 4 4 4 4 3 1 1 0 0 0
x=: 2 3 4 5 0 1 9 8 7 6
y=:100+10 4 8 6 7 9 5 3 2 1
x ([ , ] ,: d3) y
2 3 4 5 0 1 9 8 7 6
110 104 108 106 107 109 105 103 102 101
9 8 7 1 6 3 4 2 5 0
y=: ?.5 6\$100
d4=: ]/:{"1
(0&d4 ; 2&d4 ; 5&d4) y
+-----------------------------------------------------+
| 3 5 52 67 0 38|13 75 45 53 21 4|13 75 45 53 21 4|
| 6 41 68 58 93 84| 3 5 52 67 0 38| 3 5 52 67 0 38|
|13 75 45 53 21 4|52 9 65 41 70 91|67 67 93 38 51 83|
|52 9 65 41 70 91| 6 41 68 58 93 84| 6 41 68 58 93 84|
|67 67 93 38 51 83|67 67 93 38 51 83|52 9 65 41 70 91|
+-----------------------------------------------------+```
The random number generator ?. used here produces repeatable experiments, but ? can also be used. For example:
``` ? 9 # 9
1 6 4 4 1 0 6 6 8
?. 9 # 9
3 8 8 4 2 0 2 7 4
```
>> << Usr Pri JfC LJ Phr Dic Voc !: Help Phrases | 1,130 | 2,795 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-45 | latest | en | 0.647593 |
https://www.koofers.com/files/quiz-unv1a8eydp/ | 1,556,137,527,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578656640.56/warc/CC-MAIN-20190424194348-20190424220348-00220.warc.gz | 730,800,631 | 12,438 | # Quiz for STAT 3401 - Introduction to Probability Theory I at Cal State-East Bay (CSUEB)
## Quiz Information
Material Type: Quiz 2 Professor: Staff Class: STAT 3401 - Introduction to Probability Theory I Subject: Statistics University: California State University-East Bay Term: Spring 2005 Keywords: Parking LotDistributionThe IndependentConditionalProbability DistributionDensity FunctionRandomly SelectedProbability.Random Variable
## Sample Document Text
Stat 3401/4412 Spring 2005 Jaimie Kwon Name____________________ Quiz #2 . Open book and open note. Use a simple calculator if necessary. Show your work. 1. (6 pts) A parking lot has two entrances. Cars arrive at entrance I according to Poisson distribution at an average rate of three per hour and at entrance II according to a Poisson distribution at an average of four per hour. Assume that the numbers of cars arriving at the two entrances are independent. a. What is the probability that a total of two cars will arrive at the parking lot in a given hour? b. What is the conditional probability that only one car has arrived at the entrance I in a given hour, given that the total of two cars have arrived at the parking lot in the given hour? 2. (12 pts) The length of time to failure (in hundreds of hours) for a transistor is a random variable Y with distribution function given by ? ? ? ?? < = ? 0,1 0,0 )( ye y yF y (Or, F(y)=0 if y is less than 0 ...
## Related Documents
Coefficient of Variation Exam
Probability Distribution Exam
Unauthorized Exam
Inexpensive Exam
The Economic Problem Exam
Inexpensive Exam
The Economic Problem Exam
The Independent Exam
Inexpensive Exam
Distribution Exam
Provided That Exam
The Independent Exam
Provided That Exam
Provided That Exam
Inexpensive Exam | 395 | 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} | 3.109375 | 3 | CC-MAIN-2019-18 | latest | en | 0.846219 |
https://www.numbersaplenty.com/2054 | 1,701,169,543,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679099281.67/warc/CC-MAIN-20231128083443-20231128113443-00849.warc.gz | 1,026,398,709 | 3,333 | Search a number
2054 = 21379
BaseRepresentation
bin100000000110
32211002
4200012
531204
613302
75663
oct4006
92732
102054
1115a8
121232
13c20
14a6a
1591e
hex806
2054 has 8 divisors (see below), whose sum is σ = 3360. Its totient is φ = 936.
The previous prime is 2053. The next prime is 2063. The reversal of 2054 is 4502.
2054 = 62 + 72 + ... + 182.
2054 is nontrivially palindromic in base 14.
2054 is digitally balanced in base 5, because in such base it contains all the possibile digits an equal number of times.
2054 is an esthetic number in base 12, because in such base its adjacent digits differ by 1.
It is a sphenic number, since it is the product of 3 distinct primes.
It is an Ulam number.
2054 is an undulating number in base 14.
2054 is a modest number, since divided by 54 gives 2 as remainder.
2054 is strictly pandigital in base 5.
It is a nialpdrome in base 13.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (2053) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (3) of ones.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 14 + ... + 65.
It is an arithmetic number, because the mean of its divisors is an integer number (420).
22054 is an apocalyptic number.
2054 is a deficient number, since it is larger than the sum of its proper divisors (1306).
2054 is a wasteful number, since it uses less digits than its factorization.
2054 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 94.
The product of its (nonzero) digits is 40, while the sum is 11.
The square root of 2054 is about 45.3210767745. The cubic root of 2054 is about 12.7115978952.
Adding to 2054 its reverse (4502), we get a palindrome (6556).
It can be divided in two parts, 205 and 4, that multiplied together give a triangular number (820 = T40).
The spelling of 2054 in words is "two thousand, fifty-four", and thus it is an eban number.
Divisors: 1 2 13 26 79 158 1027 2054 | 619 | 2,104 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2023-50 | latest | en | 0.908504 |
https://git.zx2c4.com/linux-dev/plain/arch/riscv/lib/delay.c?h=jd/zinc-light&id=f55b74170b6aabc79af8c813b5068d3014e68ef1 | 1,638,089,286,000,000,000 | text/plain | crawl-data/CC-MAIN-2021-49/segments/1637964358480.10/warc/CC-MAIN-20211128073830-20211128103830-00010.warc.gz | 362,619,869 | 2,166 | /* * Copyright (C) 2012 Regents of the University of California * * This program is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License * as published by the Free Software Foundation, version 2. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. */ #include #include #include #include /* * This is copies from arch/arm/include/asm/delay.h * * Loop (or tick) based delay: * * loops = loops_per_jiffy * jiffies_per_sec * delay_us / us_per_sec * * where: * * jiffies_per_sec = HZ * us_per_sec = 1000000 * * Therefore the constant part is HZ / 1000000 which is a small * fractional number. To make this usable with integer math, we * scale up this constant by 2^31, perform the actual multiplication, * and scale the result back down by 2^31 with a simple shift: * * loops = (loops_per_jiffy * delay_us * UDELAY_MULT) >> 31 * * where: * * UDELAY_MULT = 2^31 * HZ / 1000000 * = (2^31 / 1000000) * HZ * = 2147.483648 * HZ * = 2147 * HZ + 483648 * HZ / 1000000 * * 31 is the biggest scale shift value that won't overflow 32 bits for * delay_us * UDELAY_MULT assuming HZ <= 1000 and delay_us <= 2000. */ #define MAX_UDELAY_US 2000 #define MAX_UDELAY_HZ 1000 #define UDELAY_MULT (2147UL * HZ + 483648UL * HZ / 1000000UL) #define UDELAY_SHIFT 31 #if HZ > MAX_UDELAY_HZ #error "HZ > MAX_UDELAY_HZ" #endif /* * RISC-V supports both UDELAY and NDELAY. This is largely the same as above, * but with different constants. I added 10 bits to the shift to get this, but * the result is that I need a 64-bit multiply, which is slow on 32-bit * platforms. * * NDELAY_MULT = 2^41 * HZ / 1000000000 * = (2^41 / 1000000000) * HZ * = 2199.02325555 * HZ * = 2199 * HZ + 23255550 * HZ / 1000000000 * * The maximum here is to avoid 64-bit overflow, but it isn't checked as it * won't happen. */ #define MAX_NDELAY_NS (1ULL << 42) #define MAX_NDELAY_HZ MAX_UDELAY_HZ #define NDELAY_MULT ((unsigned long long)(2199ULL * HZ + 23255550ULL * HZ / 1000000000ULL)) #define NDELAY_SHIFT 41 #if HZ > MAX_NDELAY_HZ #error "HZ > MAX_NDELAY_HZ" #endif void __delay(unsigned long cycles) { u64 t0 = get_cycles(); while ((unsigned long)(get_cycles() - t0) < cycles) cpu_relax(); } EXPORT_SYMBOL(__delay); void udelay(unsigned long usecs) { unsigned long ucycles = usecs * lpj_fine * UDELAY_MULT; if (unlikely(usecs > MAX_UDELAY_US)) { __delay((u64)usecs * riscv_timebase / 1000000ULL); return; } __delay(ucycles >> UDELAY_SHIFT); } EXPORT_SYMBOL(udelay); void ndelay(unsigned long nsecs) { /* * This doesn't bother checking for overflow, as it won't happen (it's * an hour) of delay. */ unsigned long long ncycles = nsecs * lpj_fine * NDELAY_MULT; __delay(ncycles >> NDELAY_SHIFT); } EXPORT_SYMBOL(ndelay); | 882 | 2,913 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-49 | latest | en | 0.767256 |
https://brainmass.com/physics/second-law-of-thermodynamics/how-much-steam-is-required-and-what-is-the-final-conc-of-h2so4-in-tank-9509 | 1,656,532,706,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103642979.38/warc/CC-MAIN-20220629180939-20220629210939-00347.warc.gz | 195,996,883 | 75,550 | Explore BrainMass
# How much steam is required and what is the final conc of H2SO4 in tank?
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Please see the attached file for the fully formatted problem(s).
An insulated tank, open to the atmosphere, contains 1,500 (lbm) of 40-wt-% sulfuric acid at 60oF. It is heated to 180oF by injection of live saturated steam at 1 atm, which fully condenses in the process. How much steam is required, and what is the final concentration of H2SO4 in the tank?
[TABLE]
https://brainmass.com/physics/second-law-of-thermodynamics/how-much-steam-is-required-and-what-is-the-final-conc-of-h2so4-in-tank-9509
#### Solution Preview
From steam tables the enthalpy of saturated steam at 1 atm is 1150.5 Btu/lb.
For acid at 40% and 60 F H_acid=-98 Btu/lb.
Use the first law for open systems:
sum(m_in H_in)=sum(m_out H_out)
m_steam *H_steam(sat, 1 atm) + m_acid* H_acid(40%, 60 F) = (m_steam+m_acid)*H_acid(x%, 180 F).
take the ratio ...
#### Solution Summary
The amount of steam and the final concentration of H2SO4 are calculated.
\$2.49 | 347 | 1,226 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2022-27 | longest | en | 0.904017 |
http://mathforum.org/library/drmath/view/58059.html | 1,534,736,104,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221215523.56/warc/CC-MAIN-20180820023141-20180820043141-00606.warc.gz | 237,273,834 | 3,082 | Associated Topics || Dr. Math Home || Search Dr. Math
### Figuring Percentage of Increase
```
Date: 09/05/2001 at 10:41:15
From: Carmy
Subject: Percentages
I am looking for help on calculating the percentage of, say a
population increase.
In 1990, Allen County, Kansas, had 14,385 people. Now, in 2001, it
contains 14,905 people. How do I calculate the increase, using a
percentage?
```
```
Date: 09/05/2001 at 15:17:20
From: Doctor Ian
Subject: Re: Percentages
Hi Carmy,
The formula for percentage increase is
new value - old value
--------------------- * 100
old value
For example, if something increases from 15 to 18, the percentage
increase is
18 - 15 3
------- * 100 = -- * 100 = 0.2 * 100 = 20%
15 15
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
```
Date: 09/05/2001 at 20:25:13
From: (anonymous)
Subject: Re: Percentages
Thank you, I have now figured out the problems. Thank you again.
Carmy
```
Associated Topics:
Middle School Fractions
Search the Dr. Math Library:
Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words
Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search | 381 | 1,375 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2018-34 | longest | en | 0.825985 |
https://ocw.tudelft.nl/course-lectures/2-3-the-mechanical-energy-balance-bernoullis-law-exercise-2/?view=course-materials | 1,696,028,587,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510529.8/warc/CC-MAIN-20230929222230-20230930012230-00625.warc.gz | 479,899,630 | 12,243 | # 2.3 The mechanical energy balance & Bernoulli’s law: exercise 2 (example)
## THERMAL BATH IN ICELAND
Imagine you live in Iceland, quite a cold place, and in the weekend you want to relax by visiting a thermal bath. This is a bath heated by warm water from thermal reservoirs heated by the Earth. Your engineering mind, however, doesn’t really come to terms with not knowing what the energy balance is, with respect to describing what such a bath would look like.
We assume that the thermal bath is ideally mixed, since water flows in at various points of the bath with a flow rate of 100 kg/s. Water flows out at the same flow rate. We take the heat capacity of the water at 4180 J/(kg∙K) and assume it to be constant with temperature. The outside temperature is quite chilly, 5 ⁰C. On the other hand, the inflowing water is quite hot, with a temperature of 70 ⁰C.
To calculate the steady state temperature of the water, we need one more piece of information: the water also loses heat to the environment at a rate which is dependent on the temperature difference between the water and the outside. This relationship can be described as: Φq = h A ∙ (Twater – Toutside). Let’s assume that we only lose heat to the air and that the wall of the bath is isolated quite well. The area of the pool in contact with the air is 500 m2.
h = 1200 …….? | 330 | 1,348 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2023-40 | longest | en | 0.942461 |
https://hesperia.gsfc.nasa.gov/rhessi3/docs/imaging/corrbproj_gh.html | 1,721,331,888,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514859.56/warc/CC-MAIN-20240718191743-20240718221743-00399.warc.gz | 257,724,349 | 2,840 | # Back-Projection Corrections
Earlier in 1999, Gordon Hurford derived an equation for correcting the back-projection images. This is called "flat-fielding" in the HESSI software. The equations were taken from a derivation by Durouchoux et al (1983) quoted here:
# Gamma Ray Imaging with a Rotating Modulator
Astronomy And Astrophysics 120, 150-155 (1983)
• P. Durouchoux
• H. Hudson
• G. Hurford
• K. Hurley
• J. Matteson
• E. Orsal
[ Excerpt from Section 2]
Any modulator/detector configuration may be evaluated by considering the three following properties: sensitivity, angular resolution, and selectivity. Each of these may be defined in terms of its vector interpretation or its physical interpretation (See Table 1). That the sensitivity in a given pixel is proportional to the square root of the variance of the sky vector for that pixel may be shown as follows. Suppose that a single point is observed in pixel j which would cause each detector to have a constant counting rate s counts/s if no other modulator was present, while the background counting rate, assumed constant on the average from detector to detector, is b counts/s. If the observation lasts a time T seconds,
Oi = (b + s Si)T,
In practice, the source strength s may be extracted from the observation vector O by first multiplying through by a function whose average is zero, namely
Sji-<Sj>,
where <Sj> = Σi(Sji)/Nc
Then, summing over the i components of the vector, the background contribution drops out:
Σi[Oi(Sji-<Sj>)] = Σi[bT(Sji-<Sj>)] + Σi[sTSji(Sji-<Sj>)]
= sTNc(<Sj2> - <Sj>2)
The standard deviation associated with the number of counts in the ith component is. for Gaussian statistics,
(Oi)½ = ({b+sSji}T)½
Since the standard deviations add as the square root of the sum of the squares, the standard deviation associated with the above is
i[Oi(Sji-<Sj>)2] )½
= Nc½i[bT(Sji-<Sj>)2]+ Σi[sTSji(Sji-<Sj>)2])½
=(bTNc)½ ((<Sj2> - <Sj>2))½
for b >> s. Thus the statistical significance of the observation is
s(TNc/b)½ ((<Sj2> - <Sj>2))½
or just proportional to the square root of the variance of the sky vector.
Notes transcribed from GH.
Notes by GH, April 1999
Oi =(B + Pim Sm) AT (1)
Oi=observed counts in time bin i
B=background (assumed constant)
Pim=probability of photon passage at pixel m, time i
Sm=true source strength at pixel m (presumed a point source?)
A=effective area of collimator
T=time in time bin i (assumed equal for all time bins)
i=1,...,N
from which GH derived:
Sm= Σi Oi ( Pim - <Pm >)/ {AT ( < Pm2 > - <Pm >2)} (2)
where < Pm 2 > is the mean square of Pim, averaged over time, and <Pm >2 is the squared mean, averaged over time.
It appears from equation (1) that the point source Sm is multiply determinate. That is, for each i and fixed m, there are N equations which determine Sm.
The expressions for the point source strength in back projection and clean.pro (also MEM?) must be replaced with the time-averaged values of equation (2) for Sm.
Edward J. Schmahl | 836 | 2,997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-30 | latest | en | 0.890745 |
https://codegolf.stackexchange.com/questions/93589/print-a-layered-cake | 1,718,544,422,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861659.47/warc/CC-MAIN-20240616105959-20240616135959-00150.warc.gz | 156,260,788 | 56,017 | # Print a layered cake
## Challenge
Given an input n, print an ASCII art cake n layers tall, viewed from the side, with two candles on top. Refer to the examples below for details.
## Output
>> cake(1)
_|_|_
| |
+-----+
>> cake(3)
_|_|_
| |
+---------+
| |
+-------------+
| |
+-------------+
...and so on.
## Rules
• Standard loopholes prohibited
• Please make an attempt at a clever solution
• This is , so shortest answer in bytes wins. However, the answer will not be selected.
# Python 2, 238 chars
i=input()
m=["+"+"-"*(i*4+1)+"+","|"+" "*(i*4+1)+"|"]
for v in range(i,1,-1):
m+=[" "*(i-v)*2+"+"+"-"*(v*4+1)+"+"," "*(i-v+1)*2+"|"+" "*((v-1)*4+1)+"|"]
m.pop()
m+=[" "*(i-1)*2+"|"+" "*5+"|"," "*(i-1)*2+" _|_|_"]
print'\n'.join(m[::-1])
The missing example of Cake 2:
_|_|_
| |
+---------+
| |
+---------+
• Hello, and welcome to the site! You could take input from STDIN and take off 24 chars. For example, i=int(input()) Commented Sep 17, 2016 at 5:59
• If you want, you should be able to change to Python 2 and change int(input()) to input() and the print statement, plus you can change the four spaces to one (if it's a tab, change it to a space to make it more obvious that it's one character). Plus your bytecount is 4 too high for some reason. Commented Sep 17, 2016 at 6:29
• @Mars Ultor oops, yes, I'm not sure why I chose python 3 to begin with. Thanks. Commented Sep 17, 2016 at 6:45
• You may also be able to save a few bytes using percent formatting Commented Sep 17, 2016 at 6:54
# Ruby, 109 107 bytes
->n{p=->t{puts t.center 3+4*n}
p['_|_|_']
(1..n).map{|i|p[?|+' '*(1+4*i)+?|]
p[?++?-*((i<n ?5:1)+4*i)+?+]}}
## JavaScript (ES6), 134 bytes
A recursive cake.
f=(n,i=--n,r=(n,c)=>'- '[+!c].repeat(n),p=r((i-n)*2),j=n*4+5,x=p++${r(j,1)}+ )=>(n?f(n-1,i)+x:p+ _|_|_ )+p+|${r(j)}|
+(n-i?'':x)
### Demo
let f=(n,i=--n,r=(n,c)=>'- '[+!c].repeat(n),p=r((i-n)*2),j=n*4+5,x=p++${r(j,1)}+ )=>(n?f(n-1,i)+x:p+ _|_|_ )+p+|${r(j)}|
+(n-i?'':x)
console.log(f(4))
## Batch, 233 bytes
@echo off
set i=
for /l %%j in (2,1,%1)do call set i= %%i%%
echo %i% _^|_^|_
set s=-----
for /l %%j in (2,1,%1)do call:l
echo ^|%s:-= %^|
echo +%s%+
exit/b
:l
echo %i%^|%s:-= %^|
set i=%i:~2%
set s=----%s%
echo %i%+%s%+
Shorter than Python? Something must be wrong...
f(a:b)n=a:([0..4*n]>>b)++[a]
x!n=x:[f"| "n,f"+-"n]
g 1=" _|_|_"!1
g n=map(" "++)(init.g$n-1)++f"+-"n!n Defines a function g which returns a list of strings containing the lines of the output # 05AB1E, 115, 101 chars >UXð×?" _|_|_",Xð×?"| |",X<U0<VXGNVXY-ð×?'+?8Y·+G'-?}'+,XY-ð×?'|?7Y·+ð×?'|,}XY-ð×?'+?8Y·+G'-?}'+, Saved 14 chars thanks to Adnan! Definitely some room for golfing here. Try it online! Note that this does print everything offset by one space. • Welcome to Programming Puzzles and Code Golf! Very nice first answer :) Commented Sep 17, 2016 at 23:12 • Maybe string multiplication helps, which is the × command. This is an example on how it's used. Commented Sep 17, 2016 at 23:13 • @Adnan That does help! Thanks! – Luke Commented Sep 17, 2016 at 23:39 # Python 2, 122 bytes a=' '*input() b='+-+' c=d=' ' while a:b='+----'+b[1:];c=d*4+c;a=a[2:];print a+[' _|_|_',b][c>d*5]+'\n%s|%%s|'%a%c print b # Python 3, 162 characters p=print t=int(input()) d=4*'-' s=' ' a='+\n' r=(t-1)*s p(r+' _|_|_\n'+r+'| |') for i in range(2,t+1):b=(t-i)*s;p(b+'+-'+i*d+a+b+'| '+i*2*s+'|') p('+-'+t*d+a) It's not very clever, but I've never done one of these before. (Edit: removed unnecessary parentheses; reduced by one more character) • Welcome to the site, and nice first answer! Commented Sep 18, 2016 at 2:53 # Pyth, 73 bytes +K*dtyQ"_|_|_"+tK"| |"jP.iJms[*\ yt-Qd\+*+5*4d\-\+)+StQtQmXd"+-""| "J A program that takes input of an integer on STDIN and prints the result. There is probably still some golfing to be done here. Try it online Explanation coming later # JavaScript (ES6), 171 bytes n=>[(s=" "[R='repeat'](n-1))+" _|_|_",s+"| |",...Array(n-1),+${"-"[R](n*4+1)}+].map((_,i)=>_||(s=" "[R](n-i))++${"-"[R](i=i*4+1)}++${s}|${" "[R](i)}|).join First pass, probably not optimal... # PHP, 150147138136130 140 bytes new approach: echo$p=str_pad("",-2+2*$n=$argv[1])," _|_|_";for($x=" ",$b=$y="----";$n--;){$a.=$x;if($n)$b.=$y;echo"$p| $a| ",$p=substr($p,2),"+-$b+";}
old version for reference:
$p=str_pad;for($o=["_|_|_"];$i++<$n=$argv[1];$o[]="+".$p("",($i<$n)*4+$e,"-")."+")$o[]="|".$p("",$e=$i*4+1)."|";foreach($o as$s)echo$p($s,$n*4+3," ",2)," "; • I’m curious; how does this read input? – lynn Commented Sep 18, 2016 at 1:04 • @Lynn: damn I forgot that this time.10 bytes overhead for $argv. :-/ Commented Sep 18, 2016 at 1:54
# Vimscript, 116 115 bytes
Pretty messy but it works!
fu A(n)
let @z="Vkyjply4lpjy4hp"
exe "norm 2i+\e5i-\eo||\e5i \e".a:n."@zddl4xggd$i_|_|_" exe "%ce ".(a:n*4+3) endfu To call it: call A(3) in an empty buffer. To load the function, source cake.vim ## Explanation • 2i+<Esc>5i-<Esc> writes the first line +-----+ • o||<Esc>5i<Space><Esc> adds | | on the second line • Vkyjply4lpjy4hp is saved in the macro @z - it visually selects both lines, yanks them, pastes them under and adds 4 dashes and spaces to them. • #@z repeats this # times • ddl4x deletes the last lines and remove for dashes to the bottom of the cake to make it equal with the top of the bottom layer • ggd$i_|_|_ replaces the first line by the top of the cake
• %ce then centers the whole cake to the width of the bottom layer! !
# SOGL V0.12, 27 26 bytes
∫4*I:┌*╗1Ο;@*┐1Ο}⁴¹k┐╔2ΟΚ╚
Try it Here!
Explanation:
∫ } for each in 1..input inclusive, pushing counter
4* multiply by 4
I increase by 1
: duplicate; this will be used later
┌* repeat a dash pop times
╗1Ο encase them in plusses
; get the duplicate on the stacks top
@* repeat a space pop times
┐1Ο encase in vertical bars
⁴ duplicate the item below ToS - the last line
¹ wrap the stack in an array
k remove the arrays first item
┐ push "_"
╔ push "|"
2Ο encase 2 copies of the vertical bar in underscores
Κ and prepend that to the array
╚ center the array horizontally
# Excel VBA, 139 130 127 Bytes
Anonymous VBE immediate window that takes input from cell A1 and outputs a cake to the VBE immediate window
For i=1To[A1]:s=Space(2*([A1]-i)):x=String(1+4*i,45):?s &IIf(i=1," _|_|_","+" &x &"+"):?s"|"Replace(x,"-"," ")"|":Next:?s"+"x"+
l~4*):Z5:X{D'+'-C}:A{D'|SC}:B{X*1$N}:C];{SZX-Y/*}:D~" _|_|_"NB{XZ<}{X4+:X;AB}wA Try it online # QBasic, 115 bytes INPUT n ?SPC(n*2-1)"_|_|_ FOR i=1TO n s=n*2-i*2 ?SPC(s)"|"SPC(i*4+1)"| ?SPC(s-2)"+"STRING$(i*4+(i=n)*4+5,45)"+
NEXT
### Ungolfed
Print the top line with the candles; then print the rest of the cake two lines at a time.
INPUT n
PRINT SPC(n * 2 - 1); "_|_|_"
FOR i = 1 TO n
indent = n * 2 - i * 2
PRINT SPC(indent); "|"; SPC(i * 4 + 1); "|"
PRINT SPC(indent - 2); "+"; STRING$(i * 4 + (i = n) * 4 + 5, 45); "+" NEXT SPC, when used in a PRINT statement, emits the given number of spaces. Conveniently, when given a negative argument, it treats it as 0, so the fact that indent - 2 is -2 in the last iteration isn't a problem. STRING$ takes a count and a character code (here, 45 for -) and repeats the character that number of times. Here, we have to special-case the last line (when i=n) to be 4 hyphens shorter than it would otherwise be.
# C (gcc), 158 153 bytes
-5 bytes thanks to ceilingcat.
i,l,s;p(c,s){printf("%*c%*.*s%c\n",i-~i,c,l,l,s,c);}f(n){s=memset(malloc(5*n),45,5*n);l=1;for(i=n;i--;p('|',""))l+=4,n+~i?p(43,s):p(32,"_|_|_");p(43,s);}
Try it online! | 2,883 | 7,765 | {"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} | 2.671875 | 3 | CC-MAIN-2024-26 | latest | en | 0.700482 |
https://users.flatironinstitute.org/~ahb/BIE/ | 1,721,932,102,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763861452.88/warc/CC-MAIN-20240725175545-20240725205545-00144.warc.gz | 516,704,825 | 4,491 | ## Boundary Integral Equations: tutorials and resources
#### Alex Barnett
Boundary integral equations (BIEs) are a wonderfully efficient way to solve PDE boundary value problems (BVPs) or eigenvalue problems (EVPs) with constant (or piecewise-constant) coefficients. This includes elliptic PDE such as the Laplace, Helmholtz, Maxwell, and Stokes equations. Much of my recent research is on better ways to do this. Here are some resources on theory and numerical methods.
### Mathematical theory resources
• David Colton and Rainer Kress, Integral equation methods in scattering theory (Wiley, 1983). Helmholtz and Maxwell equations in 3D. Chapter 3 has useful proofs including the "inside-out" trick for existence for the transmission BVP.
• David Colton and Rainer Kress, Inverse acoustic and electromagnetic scattering theory (Springer, 1998). Has a good summary for the Helmholtz (including the 2D case, and numerics including the Martensen-Kussmaul spectral quadrature) and Maxwell equations.
• David Colton, Partial Differential Equations: An Introduction (Random House, 1988). Unusally detailed on Bessel functions and the Helmholtz equation in 2D. Includes proof of jump relations that relies on "blurring" the boundary.
• Rainer Kress, Linear Integral Equations (Springer, 1999). Chapter 6 has potential theory for Laplace equation. Chapter 12 has the Nystrom method.
• My handwritten class notes for Math 126. Starting at p.25, although the earlier stuff is useful numerical analysis background. This draws from the above Kress and Colton books.
• Andrea Moiola's beautiful and visual 78 pages of course notes on frequency-domain scattering and BIE. They have a variational (ie, Galerkin) flavor and focus on analysis, but have many practical tips for the numerical side too.
### Numerical methods and resources for coding schemes yourself
Established numerical methods:
• Review talk on BIE Nystrom quadratures from CSE19 in Spokane, WA: slides (3.6 MB).
• Go through the homework exercises in Math 126, starting around HW4 #2. Note, there are solution notes.
• My tutorials from our 2014 CBMS conference:
• tutorial on quadrature for BIEs (with example code bundle and exercises). This covers mostly Laplace BVPs on smooth curves in 2D, both global and panel quadratures. The only code currently included for Helmholtz is based on a simple but somewhat inefficient Kapur-Rokhlin scheme.
• Handwritten notes from the accompanying chalk talk (video). Sketches the BVP setup and various 2D schemes for handling weakly singular kernels, mostly for the Helmholtz equation on smooth curves.
• Lectures 5-7 by Rikard Ojala in the course DN2255 at KTH.
• Review and comparison article by myself with Gunnar Martinsson, Sijia Hao, and Patrick Young (2011). Covers mostly the Helmholtz 2D case on smooth curves, which involves logarithmically singular kernels.
More advanced numerical methods and research for BVPs:
Methods specific to eigenvalue problems:
### Software packages
This list is necessarily incomplete, and skewed to my own interests and community.
• BEM++ by Timo Betcke and colleagues at UCL. This is a mature and professional low-order high-performance 3D Galerkin code in 3D, including Laplace, Helmholtz and Maxwell. It has evolved from C++ to Py/numba to Rust, each with high-level Python wrappers and example drivers. Actively in development as of 2022.
• FMM3DBIE by Manas Rachh, Mike O'Neil and colleagues. This is mature Fortran90 code-base for 3D Nystrom discretizations on high-order triangular patches, for Laplace, Helmholtz and Stokes, using the FMM for fast evaluation, with wrappers and example drivers from MATLAB, Python, etc. Actively in development as of 2022.
• ChunkIE: an object-oriented MATLAB BIE toolbox by Travis Askham, Manas Rachh, Dan Fortunato, and others, for 2D Laplace and Helmholtz BIE, including Helsing RCIP corner quadratures and interface to FMM and the FLAM fast direct solver. Actively in development as of 2022.
• pytential by Andreas Klöckner (UIUC) and collaborators, for fast 2D and 3D general layer potential evaluation in python, via QBX, etc. Actively in development.
• MPSpack includes code for Laplace and Helmholtz BIEs in 2D, including various quadrature schemes for smooth curves and corners, periodization methods, and interface to the FMM. The tutorial (Sec. 7-9) has the BIE commands. Development stopped around 2016, although I maintain it, and it is used by other codes such as TMATROM.
• BIE2D MATLAB/Octave collection of research codes by Alex Barnett, which has Laplace and Stokes global quadratures, including the current best implementation of their barycentric-style close-evaluations. This is far from complete; however, it is simple to find well-documented routines of some use.
• pyBIE2D, David Stein's extension of BIE2D in high performance Python/numba, which has object-oriented construction of boundary objects, etc.
• BIE3D MATLAB/Octave tools (research code) by Alex Barnett, including quad-patch based Laplace high-order quadratures on smooth deformations of a torus, and QFS-based global quadratures on smooth deformations of a torus or a sphere. It also has high-order space-time quadratures for the acoustic wave equation, which is why it was created. It is research code, not a usable package, but you will find well-documented components of some use.
• BIEST by Dhairya Malhotra (Flatiron CCM). High-performance C++ research code for 3D BIE with spectral POU-based quadrature on smooth deformations of a torus, with applications to Taylor states in stellarator design.
This work was enabled in part by NSF grant DMS-1216656. | 1,348 | 5,630 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-30 | latest | en | 0.858913 |
http://econnect-study.com/index.php/mathematics/topics-01-05/computation | 1,527,349,218,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867559.54/warc/CC-MAIN-20180526151207-20180526171207-00182.warc.gz | 90,236,041 | 11,178 | Computation
Mathematics
Topic Three
### BODMAS
BODMAS is the acronym to indicate the order in which arithmetic operations are carried out.
B – brackets, O – of (or times) M – multiplication, D – division, A – addition and S – subtraction of quantities in that order.
### Whole Numbers
We will now be showing how to compute the addition, subtraction, multiplication and division of whole numbers.
Add the numbers 1543 and 724.
Procedure: In addition, we add from right to left. The numbers in that column are 3 and 4 and when we add these, we will get 7. We then add 4 and 2 to get 6 then 7 and 5 to get 12. The 2 from the 12 is taken with the remainder of 1 to add to the existing 1 to get 2. So the answer from this addition is 2267.
Subtraction
Subtract 234 from 876.
Multiplication
Multiply 345 by 123.
Procedure: When multiplying, multiply the top number or the Multiplicand (in this case 345) by each of the digits in the bottom number or the Multiplier (in this case 123), starting with the number to the left which is 1. On multiplying the top numbers by 1, we get a result of 345. This result is written with the 5 being exactly below the 1. Next, 345 is multiplied by the second digit of the multiplier which is 2 to obtain the result 690 with the 0 being placed directly below the number it is multiplied by which is 2. Next, the 345 is multiplied by 3 (345 x 3) to get 1035 with the 5 being placed directly under the number it is multiplied by which is 3. When we add all of these three results, we get 34500 + 6900 + 1035 = 42435.
Division
Divide 4560 by 5.
Procedure: In the above example, the 5 is the divisor, the 4560 is the dividend and the answer will be the quotient. Since 4 is not divisible by 5, zero (0) is placed above 4. We then go on to the number next to 4 which is 5 and so we then divide 45 by 5 to get 9. We then multiply the 9 by 5 to get 45. Now we then subtract 45 from the 45 above to get 0. We then bring down the number next to the 5 which is 6. We divide 6 by 5 to get 1. So we place the 1 above the 6 to get an interim result of 091. We then multiply the 1 by 5 to get 5 which we place under the 6; when this 5 is subtracted from 6 we get 1. Because we cannot divide 1 by 5, we bring down the 0 which makes it 10. When we divide 10 by 5, we get 2 which we place in the answer above to get 912 0r 912 because the 0 has no value. Because we cannot go any further, the answer is 912 which is the quotient.
Combining numbers together
The following example combines the use of addition, subtract, multiplication and division.
Example
Following the BODMAS acronym, we obtain:
(18 – 9) + 14 ÷ 7 x 3 so:
We have
18 – 9 = 9 because we must do the B or bracket first and so:
9 + 14 ÷ 7 x 3
Because D for division comes next, 9 + 2 x 3. Then, because M for multiplication comes next, we have, 9 + 6 and because A for addition comes next, we have: 9 + 6 = 15.
Decimals can consist of a whole number and a decimal fraction such as:
Decimal = Whole number + Decimal fraction
10.6 = 10 + 0.6
Decimal fractions are numbers that are written after decimal points such as: 0.6 = 6/10 as in the above case. The numbers after the decimal point are like the numerators of a fraction, with the denominator being 1 plus the amount of zeros equal to or corresponding to the amount of digits after the decimal point. Therefore, 0.25 = 25/100 or 0.025 = 25/1000.
When adding and subtracting decimal terms, we must line-up the points then insert 0s when necessary.
Simplify:
49.07 + 27.123 + 5.7223
Subtraction
Simplify:
48.3 – 8.23
Multiplication
The procedure for multiplying decimals is the same as multiplying whole numbers. However, after completing the multiplication, the next step is to determine where the decimal point should be placed in the answer. This can be determined by counting the amount of decimal places in both the Multiplicand (number to be multiplied) and the Multiplier and then adjust the multiplied answer or product (from right to left) according to the amount of decimal places. Therefore, multiply the 44.2 by 12.9 below and the answer will be 57018. There is one decimal place in 44.2 and another in 12.9 resulting in two decimal places. So adjust the 57018 to two decimal places from right to left and the final answer will be 570.18.
Example
Simplify:
44.2 x 12.9
Division
The situation for dividing decimals is different from that of multiplying. Before dividing, turn the divisor (the number that is doing the dividing) into a whole number by moving the decimal point to the right after the last digit. After doing the foregoing, also move the decimal point of the number being divided (the dividend) to the right by the same amount of places as the divisor was moved. After this is done, do the division to produce the result or the quotient.
Example
Simplify:
48 ÷ 0.002
The 2 as the divisor was obtained by converting the 0.002 into a whole number which is done by shifting the decimal point 3 places to the right and doing the same thing to the 48 thereby converting it to 48000. The answer or quotient is 24000.
### Decimal Places
To approximate a number to a given amount of decimal places follow the instructions outlined in the example below.
Example
Estimate 1979.5687 correct to 2 decimal places.
Solution
Count from left to right 2 decimal after the decimal point. We will get 1979.56 and if the next number to the right of this 56 is 5 or more (in this case it is 8), we add a 1 to the 6 making the answer 1979.57.
Example
Estimate 1979.5687 correct to 3 decimal places.
Solution
Count from left to right 3 places after the decimal point. We will get 1979.568 and if the next number to the right of this 568 is 5 or more (in this case it is 7), we add a 1 to the 8 making the answer 1979.569.
### Significant Figures
When we are faced with a long number, we could round it off to the nearest thousand, or nearest million. Also, when we get a long decimal answer, we could round it off to a certain number of decimal places. Another method of giving an approximated answer is to round off using significant figures. The word significant means: having meaning. With the number 568249, the 5 is the most significant digit, because it tells us that the number is 5 hundred thousand and something. With the number 0.0000098763, the 9 is the most significant digit, because it tells us that the number is 9 millionths and something. The 8 is the next most significant, and so on.
In order to approximate a number to a given amount of significant figures (sf), see the following:
Example
208.70423
Estimate the above number to:
1. 6 sf
2. 5 sf
3. 4 sf
4. 3 sf
5. 2 sf
6. 1 sf
Solution:
1. To 6 sf = 208.70423 or 208.704
Count from the left to the right, the number of sf and the answer is 208. 704523 which is the highlighted digits.
2. To 5 sf = 208.704523 or 208.70
3. To 4 sf = 208.704523 or 208.7
4. To 3 sf = 208.704523 or 209
Counting from left to right, the 3rd number is 8 but the next number after 8 is greater than 5 and so we have to add a 1 to the 8 making it 209.
5. To 2 sf = 208. 704523 or 210
Again counting from left to right, the 2nd number is 0 but the next number to the right (9) is 5 or more so we have to add 1 to the 0 making the answer 21. We must add a 0 to the 21 because we need 3 numbers before the decimal point. So the answer is 210.
6. To 1 sf = 209. 704523 or 200
Again counting from the left, the 1st number is 2 but the next number to the right is 0 which is less than 5 so we do not have to add 1 to the 0 making the answer 200. We must add 2 zeros to the 2 because we need 3 numbers before the decimal point. So the answer is 200.
Example
Write 0.0005678 to 1 significant figure (sf)
Solution
Counting from the left to right, the very first number is 5 and since the very next number which is 6 is more than 5, we add a 1 to the 5 making the answer 0.0006.
### Standard Form and Scientific Notation
Standard form is another name for scientific notation. In standard form, the numbers are written in the form:
A x 10n
Where, 1 ≤ A ≤ 10, are in Standard Form.
Scientific notation is used to represent very large and very small numbers. In scientific notation, a number is written as a number between 1 and 10 multiplied by a power of 10. When writing a number in standard form, write the number in the form A. That is, turn the number into a number greater than or equal to 1 and or less than 10. This is done by moving the decimal point either to the right or to the left. The decimal point must be placed 1 point after the first number and then multiply by 10 raised to the negative or positive power equal to the number of decimal places or points that were to the required to move it to the decimal place after the first significant number. We then write the number in the form A x 10n.
Procedure for large numbers:
Step 1: Move the decimal point to the left until you have a number greater than or equal to 1 and less than 10.
Step 2: Count the number of decimal places you moved the decimal point to the left and use that number as the positive power of 10.
Step 3: Multiply the decimal (in Step 1) by the power of 10 (in Step 2).
Procedure for small numbers:
Step 1: Move the decimal point to the right until you have a number greater than or equal to 1 and less than 10.
Step 2: Count the number of decimal places you moved the decimal point to the right and use that number as the negative power of 10.
Step 3: Multiply the decimal (in Step 1) by the power of 10 (in Step 2).
Examples
Write the following numbers in standard form:
1. 926876
2. 0.000461234
Solution
1. 9.26876 x 105
2. 4.61234 x 10-4
Percentage or Fraction of a Quantity
To find the percentage of a quantity, express the percentage as a fraction (write the percentage given over 100) and multiply by the quantity.
Example
What is 50% of 400?
50/100 x 400 = 200
To find the fraction of a given quantity, multiply the fraction by the quantity.
Example
4/5 of 200
4/5 x 200 = 160
### A Quantity as a Percentage or Fraction of Another
To express a quantity as a percentage of another quantity, divide the first quantity by the second and multiply by 100.
Example
Express 40 as a percentage of 800
40/800 x 100 = 5
### Ratio
A ratio is a comparison between similar quantities. A ratio can be expressed as a fraction.
Example
A man shared \$300 between Joe and Frank in the ratio of 2 : 1. How much money did both boys get? Just add the 2 and the 1 which is 3 which forms the denominator. Then place the proportions (the 2:1) over the denominator to give: 2/ 3 and 1/ 2 then multiply these by the 200.
Joe = 2/3 x 300 = \$200
Frank = 1/3 x 300 = \$100.
### Squares, Square Root and Surds
Squares
To square a number, just multiply it by itself:
Example
42 = 4 times 4 = 16
152 = 15 times 15 = 225
When squaring negative numbers, the result will always be a positive as a negative number (-) times a negative number (-1) will result in or give a positive result.
Example
(-8)2 = (-8) times (-8) = 64.
Square Root
A square root goes the other way. A square root of a number will give a number that when multiplied by itself, will produce the original or initial number. For example, the square root of 16 is 4 and when 4 is multiplied by itself, it will give the original number which is 16. The following is the square root sign:
Example
So
Example
We cannot find the square root of a negative number.
Surds
Surds are numbers that cannot produce a square root directly. Some sort of manipulation is required to transform this expression in order for part of it to ne square rooted.
Rule #1:
Example
Rule #2:
Rule #3:
Example
Rule #4
Example
Rule #5
then multiply the numerator and denominator by
Example
Rationalise the following: | 3,154 | 11,825 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.9375 | 5 | CC-MAIN-2018-22 | latest | en | 0.921651 |
https://4xpip.com/automatic-lot-size-calculation-based-on-risk/ | 1,719,037,643,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862252.86/warc/CC-MAIN-20240622045932-20240622075932-00761.warc.gz | 64,673,002 | 64,696 | # Automatic Lot Size calculation based on Risk %
## Automatic Lot Size Based on Risk Percentage in Trading: A Guide for Investors
In the world of trading, managing risk is one of the most critical aspects of success. This is where the concept of lot size comes in. The lot size determines the amount of capital you put at risk in a trade and is a critical factor in determining your potential returns. However, many traders use a fixed lot size, which can be limiting and may not take into account the varying levels of risk associated with different trades. That’s why an increasing number of traders are using automatic lot size calculations based on risk percentage.
## What is automatic lot size calculation based on risk percentage?
Automatic lot size calculation is a method that calculates the ideal lot size based on a specified risk percentage. This allows traders to determine the maximum amount they are willing to risk on a trade and allocate the appropriate capital accordingly. For example, if a trader has a \$10,000 trading account and is willing to risk 2% of their account on each trade, their lot size would be \$200. 4xpip is the best solution if you’re seeking for a trustworthy and effective way to determine your lot size.
### How does automatic lot size calculation work?
To determine the lot size, traders first determine their risk tolerance and the percentage of their trading account that they are willing to risk on each trade. This is then used to calculate the appropriate lot size, taking into account the current market conditions and the specific trade setup. For example, if a trader is looking to enter a long position on a stock, they may determine that the stock has a potential reward of \$1 and a maximum risk of \$0.50. Based on their 2% risk tolerance, they would then calculate the lot size as follows:
`Lot size = (\$10,000 x 2%) / \$0.50 = 400 shares`
### The advantage of automatic lot size calculation
Automatic lot size calculation provides a more flexible and adaptable approach to trading. By adjusting the lot size based on the level of risk associated with each trade, traders can better manage their risk and increase their potential for success. By determining the appropriate lot size based on their risk tolerance and trading account size, traders can ensure that they are not exposing themselves to undue risk.
## Example of the impact of automatic lot size calculation
Let’s say a trader has a \$10,000 trading account and is willing to risk 2% of their account on each trade. If they use a fixed lot size of 100 shares, their maximum risk per trade would be \$200. For example:
• If the potential reward is \$1 and the maximum risk is \$0.50, their lot size would be 400 shares, and their maximum risk per trade would be \$200.
• If the potential reward is \$2 and the maximum risk is \$0.75, their lot size would be 267 shares, and their maximum risk per trade would be \$150.
In this scenario, the automatic lot size calculation has helped the trader better manage their risk and increase their potential for success.
Calculating the correct lot size in Forex trading can be a complex task. It requires a thorough understanding of margin, leverage, and risk management. If you’re looking for a reliable and efficient solution to calculate your lot size, look no further than 4xpip. Contact us today at https://4xpip.com/contact-us/ to take control of your trading and ensure maximum returns on your investments.” | 716 | 3,487 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2024-26 | latest | en | 0.925556 |
https://www.chiefdelphi.com/t/weird-output-values-when-trying-to-find-target-distance/392002 | 1,721,413,084,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514917.3/warc/CC-MAIN-20240719170235-20240719200235-00467.warc.gz | 606,898,322 | 7,587 | # Weird Output Values when Trying to Find Target Distance
Hello everyone,
This season, my team has started using a Limelight 2+ for our robot build, and they’ve assigned me to figure out how to program it.
What a fun ride that’s been.
Anyway, I managed to program it to automatically adjust to a target (which still has its issues), but the team asked if I could program it to calculate distance. I looked at the Limelight documentation, which was helpful, but I’m here today to share some weird issue I’m having.
I created a Blank VI to simulate the offset values changing, but every time I run it and change the offset, the values jump around a lot, and even occasionally jumping down to the negatives.
Code below
Not sure what you are trying to do here.
I doubt camera height (35) is in radians (the input required by the tangent function)?
Nope. It’s in inches. I’ll look into converting it to radians. In the code, I’m trying to find the distance of the target (in inches) using the equation
`d = (h2-h1) / tan(a1+a2)`
where `d` is distance, `h1` is the height of the robot, `h2` is the height of the target, `a1` is the angle in which the Limelight on our robot is tilted at (35 deg) —
Whoops. The label next to the 35 is actually supposed to say `Camera Angle`.
– And finally, `a2` is the offset (/limelight/ty) given by the Limelight.
Yea, so 35 degrees should be .61 radians
For readability you might want to do the conversion in code so you can keep thinking in degrees.
Make sure the Ty values you choose are also in radians.
1 Like
Thank you, I will try this now
Ok, so I tried converting everything to radians, which eliminated the issue of the Distance output jumping around.
The thing is, when I increase the Offset, the Distance decreases when it’s supposed to decrease. Also, is there any way to take the radians after the tangent calculation and somehow make the Distance output in inches?
The output is in whatever units you use for height, I presume that’s in inches.
Tangent is just a ratio. It has no units associated with it.
I’d expect the distance to decrease as the total angle increases.
You’re looking up at a steeper angle as you get closer to the wall. Craning your neck so to speak.
As the angle decreases the distance gets farther.
My assumptions are:
• the 35 degrees is your camera tilted up.
• The Limelight Ty is an additional tilt up when positive and down when negative.
P.S.
You can simplify/clarify the code by adding the camera angle to ty, then converting to radians and sending that to the Tan function. That way all your inputs are in degrees making it easier to think of 35+7=42 total degrees.
1 Like
Thank you, I’ll try this out after school
Update – the distance works. All we had to do was multiply the output by 4 and then divide that by 12. Thank y’all so much!
Here’s the code in case anybody needs it…
This topic was automatically closed 365 days after the last reply. New replies are no longer allowed. | 696 | 2,981 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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 | 0.938288 |
https://www.docme.ru/doc/1683079/vyvod-chastotnogo-uravneniya-sobstvennyh-kolebanij-uprugoj-. | 1,575,893,916,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540518882.71/warc/CC-MAIN-20191209121316-20191209145316-00436.warc.gz | 667,951,588 | 15,630 | Забыли?
?
# Вывод частотного уравнения собственных колебаний упругой трехслойной пластины два противоположных края которой шарнирно закреплены а два других свободны от закрепления.
код для вставкиСкачать
```4/2010
ВЕСТНИК
МГСУ
ȼɕȼɈȾ ɑȺɋɌɈɌɇɈȽɈ ɍɊȺȼɇȿɇɂə ɋɈȻɋɌȼȿɇɇɕɏ
ɄɈɅȿȻȺɇɂɃ ɍɉɊɍȽɈɃ ɌɊȿɏɋɅɈɃɇɈɃ ɉɅȺɋɌɂɇɕ, ȾȼȺ
ɉɊɈɌɂȼɈɉɈɅɈɀɇɕɏ ɄɊȺə ɄɈɌɈɊɈɃ ɒȺɊɇɂɊɇɈ
ɁȺɄɊȿɉɅȿɇɕ, Ⱥ ȾȼȺ ȾɊɍȽɂɏ ɋȼɈȻɈȾɇɕ ɈɌ ɁȺɄɊȿɉɅȿɇɂə
DERIVATION OF THE FREQUENCY EQUATION OF
NATURAL VIBRATIONS OF AN ELASTIC THREE-LAYERED
PLATE, TWO OPPOSITE EDGES OF WHICH ARE HINGED AND
TWO OTHERS ARE FREE FROM ATTACHMENT
Ⱥ.ȼ. Ȼɨɝɞɚɧɨɜ, Ɉ.ɂ. ɉɨɞɞɚɟɜɚ
A.V. Bogdanov, O.I. Poddaeva
ȽɈɍ ȼɉɈ ɆȽɋɍ
ȼ ɷɬɨɣ ɫɬɚɬɶɟ ɪɚɫɫɦɨɬɪɟɧ ɜɵɜɨɞ ɱɚɫɬɨɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ
ɭɩɪɭɝɨɣ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɬɪɟɯɫɥɨɣɧɨɣ ɩɥɚɫɬɢɧɵ, ɞɜɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɤɪɚɹ ɤɨɬɨɪɨɣ
ɲɚɪɧɢɪɧɨ ɡɚɤɪɟɩɥɟɧɵ, ɚ ɞɜɚ ɞɪɭɝɢɯ ɫɜɨɛɨɞɧɵ ɨɬ ɡɚɤɪɟɩɥɟɧɢɹ.
This article discusses the derivation of the frequency equation of natural vibrations of
an elastic rectangular three-layered plate, two opposite edges of which are hinged and two
others are free from attachment.
Ɋɚɫɫɦɨɬɪɢɦ ɩɥɨɫɤɢɣ ɷɥɟɦɟɧɬ ɤɚɤ ɢɡɨɬɪɨɩɧɭɸ ɨɞɧɨɪɨɞɧɭɸ ɭɩɪɭɝɭɸ ɬɪɟɯɫɥɨɣɧɭɸ
ɩɥɚɫɬɢɧɭ.
Ȼɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɩɥɨɫɤɨɫɬɢ ɪɚɡɞɟɥɚ ɫɥɨɟɜ ɧɚɯɨɞɹɬɫɹ ɜ ɠɟɫɬɤɨɦ ɤɨɧɬɚɤɬɟ,
ɩɪɢ ɷɬɨɦ ɜɧɟɲɧɢɟ ɞɜɚ ɫɥɨɹ ɫɨɫɬɨɹɬ ɢɡ ɨɞɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɢ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɭɸ ɬɨɥɳɢɧɭ h2 h1 , ɚ ɜɧɭɬɪɟɧɧɢɣ ɫɥɨɣ – ɢɡ ɞɪɭɝɨɝɨ ɦɚɬɟɪɢɚɥɚ ɢ ɟɝɨ ɬɨɥɳɢɧɚ h1 . ȼ ɩɥɨɫɤɨɫɬɢ
XOY ɩɥɚɫɬɢɧɚ ɡɚɧɢɦɚɟɬ ɨɛɥɚɫɬɶ ^0 d x d l ; 0 d y d l ` .
1
2
ȼ ɞɚɥɶɧɟɣɲɟɦ ɩɚɪɚɦɟɬɪɵ ɜɧɭɬɪɟɧɧɟɝɨ ɫɥɨɹ ɨɛɨɡɧɚɱɚɬɶ ɢɧɞɟɤɫɨɦ "1" , ɚ ɜɧɟɲɧɢɯ
ɫɥɨɟɜ – ɢɧɞɟɤɫɨɦ " 2 " .
ɑɚɫɬɨɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɭɩɪɭɝɨɣ ɬɪɟɯɫɥɨɣɧɨɣ ɩɥɚɫɬɢɧɵ ɛɭɞɟɦ ɨɩɪɟɞɟɥɹɬɶ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɩɪɢɛɥɢɠɟɧɧɨɦ ɭɪɚɜɧɟɧɢɢ ɩɨɩɟɪɟɱɧɵɯ ɤɨɥɟɛɚɧɢɣ ɱɟɬɜɟɪɬɨɝɨ
ɩɨɪɹɞɤɚ [1]:
w 2W
w 4W
w 2W
A
A
'
A3' 2W
1
2
2
4
2
wt
wt
wt
0
(1)
ɝɞɟ
225
ВЕСТНИК
4/2010
МГСУ
2
h2 h1 ° 1 7 8Q 1 h3 b 2 7 8Q 2 7 8Q 1 h3 h 2 ;
®
b 2 1 U h / 2 °̄ b 2 9b 1 Q 1 2 1 Q 2 16 1 Q 1 ª
3 4Q 2 º h °½ ;
U 1 « 2 U 2b 2
» ¾
2 1 Q 2 ¼ 4 ¿°
¬
A1
2
A2
h3 h2 h1 1
®
8 1 U h / 2 ¯ b 2
ª § 2· 1
º 4
« D1 ¨1 h ¸ 3 2 D1 » h3
¹
¼
ª § 2· 2
º
« D2 ¨ 1 h ¸ 3 2 D2 » ¹
¼
D § 1 · 1 D2 º ½°
2 § 2 · ª 2 D2 1 º 4 ª
¨1 ¸ « U
1» «1 U 4 22 ¨1 ¸ 2
»¾;
2 D2
D22 ¼ ¿°
¼ h¬
2
h3 h2 h1 b 2 ª 4 U D1 § 3 ·
1 D1 40 D2 º
A3
2 3 »;
¨1 ¸ 2 U
«
8 1 U h / 2 ¬ 3 © h ¹
h
3b h ¼
2h1
U1
b1
1
h
; U
; b
; Di
; i 1, 2 U2
h2 h1
b2
2 1 Q i bi - ɫɤɨɪɨɫɬɶ ɩɨɩɟɪɟɱɧɨɣ ɜɨɥɧɵ, Q i - ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ,
Ui
- ɩɥɨɬɧɨɫɬɶ.
ɉɭɫɬɶ ɞɜɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɤɪɚɹ ɩɥɚɫɬɢɧɵ ɩɪɢ
ɨɩɟɪɬɵ, ɚ ɞɜɚ ɞɪɭɝɢɯ ɩɪɢ
y 0
ɢ
y l2
ɲɚɪɧɢɪɧɨ
x 0 ɢ x l1 ɫɜɨɛɨɞɧɵ ɨɬ ɡɚɤɪɟɩɥɟɧɢɹ.
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɬɚɤɨɣ ɩɥɚɫɬɢɧɤɢ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
w 3W
wx3
0
x 0,l1
·
w 2W 3 2Q 1 § 2 w 2W
2 2
W
K
K
[
2
¨
¸
1
3
wx 2 7 4Q 1 ©
wy 2
¹
W
y 0, l2
ɝɞɟ K1
w 2W
wy 2
l1
, K3
l2
x 0,l1
0
y 0,l2
l1
S h1
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (1) ɛɭɞɟɦ ɢɫɤɚɬɶ ɜ ɜɢɞɟ [2]:
226
½
°
°
°
°
0¾
°
°
°
°¿
(2)
4/2010
ВЕСТНИК
МГСУ
W x, y, t W x, y exp i[J t [
ɝɞɟ
(3)
- ɛɟɡɪɚɡɦɟɪɧɚɹ ɱɚɫɬɨɬɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɩɥɚɫɬɢɧɤɢ, J
Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɟ (11) ɞɥɹ
2
ª¬ ' B1' B2 º¼ W
W
0
b1
h1
ɩɪɢɦɟɬ ɜɢɞ:
(4)
ɝɞɟ
B1
A2 2 2
J [
A3
B2
1 2 2
J [ A1J 2[ 2 1
A3
(5)
ȼɜɟɞɟɦ ɧɨɜɵɟ ɛɟɡɪɚɡɦɟɪɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɢ ɮɭɧɤɰɢɸ ɩɪɨɝɢɛɚ
l1
x
S
l2
D; y
S
E W
l14
S4
V D , E (6)
ȼ ɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ ɭɪɚɜɧɟɧɢɟ (4) ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ:
4
2
ª w4
·
w4
l12 § w 2
2
4 w
2 w
K
K
B
« 4 2K1
¨
¸
1
1
1
wD 2wE 2
wE 4
wE 2 ¹
¬ wD
B2
l14 º
V D , E 0
S 4 »¼
K1
ɝɞɟ
(7)
l1
l2
Ⱦɥɹ ɜɵɜɨɞɚ ɱɚɫɬɨɬɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɭɪɚɜɧɟɧɢɟɦ (7) ɢ ɝɪɚɧɢɱɧɵɦɢ
ɭɫɥɨɜɢɹɦɢ (2), ɡɚɩɢɫɚɧɵɦɢ ɜ ɛɟɡɪɚɡɦɟɪɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ (6).
ɉɨɥɶɡɭɹɫɶ ɦɟɬɨɞɨɦ ɞɟɤɨɦɩɨɡɢɰɢɣ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɡɚɞɚɱɢ ɡɚɩɢɲɭɬɫɹ ɜ ɜɢɞɟ:
1.
w 4V1
w 3V1
f1 D , E ;
0
wD 4
wD 3
·
w 2V1 3 2v1 § 2 w 2V1
K32[ 2V1 ¸ 0 ɩɪɢ D
¨ 2K1
2
2
wD
wE
¹
4
2. K1
w 4V2
wE 4
f 2 D , E ; V2
w 2V2
wE 2
0 ɩɪɢ E
(8)
0, S
0, S
(9)
227
ВЕСТНИК
МГСУ
4/2010
2
ª 2 w4
·
l12 § w 2
l14 º
2 w
B1 2 ¨ 2 K1
« 2K1
¸ B2 4 » V3 S © wD
S ¼
wD 2wE 2
wE 2 ¹
3. ¬
f1 D , E f 2 D , E 0
(10)
ɋɥɟɞɭɹ ɦɟɬɨɞɭ ɞɟɤɨɦɩɨɡɢɰɢɣ, ɛɭɞɟɦ ɩɪɢɛɥɢɠɟɧɧɨ ɩɨɥɚɝɚɬɶ
V1 # V2 ; V3 #
1
V1 V2 2
(11)
ɜ ɡɚɞɚɧɧɵɯ ɬɨɱɤɚɯ ɩɥɚɫɬɢɧɤɢ.
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɨɢɡɜɨɥɶɧɵɯ ɮɭɧɤɰɢɣ
ɜɢɹɦɢ (8):
w 3V1
wD 3
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ
\1 E \1 E ɩɪɢ
D
0, S
ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨ-
ɩɪɢɜɨɞɹɬ ɤ ɫɨɨɬɧɨɲɟɧɢɹɦ:
an ,m
¦ sin mE ;
n ,m 1 n
D 0
f
1
f
1
an ,m
n
1 sin mE 1 n
D
¦
n ,m
ɋɥɟɞɨɜɚɬɟɥɶɧɨ,
ɬ.ɟ. ɧɟɱɟɬɧɵɟ ɩɨ
0
\i
\1 E n an ,m
1
(12)
S
- ɟɫɬɶ ɱɟɬɧɚɹ ɮɭɧɤɰɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
n n 2q ,
ɧɟɨɛɯɨɞɢɦɨ ɩɨɥɨɠɢɬɶ ɪɚɜɧɵɦɢ ɧɭɥɸ.
Ɍɨɝɞɚ
\1 E f
a2 q,m
q m 1
2q
¦
1
sin mE (13)
ɂɫɩɨɥɶɡɭɟɦ ɜɬɨɪɵɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ
·
w 2V1 3 2v1 § 2 w 2V1
K32[ 2V1 ¸ 0
¨ 2K1
2
2
wD
wE
¹
ɩɪɢ D =0, ɩɨɥɭɱɢɦ:
2
º
3 2v1 ª 2 w \ 4 E 2 2
0
\ 2 E K
[
\
E
« 2K1
»
3
4
7 4v1 ¬
wE 2
¼
ɚ ɩɪɢ D S , ɩɨɥɭɱɢɦ:
228
(14)
4/2010
ВЕСТНИК
МГСУ
º
3 2v1 ª 2 w 2\ 4
2 2
2
\ 2 E K
K
[
\
1
3
4» wE 2
7 4v1 «¬
¼
º
3 2v1 ª 2 w 2\ 3
K32[ 2\ 3 » S « 2K1
2
wE
7 4v1 ¬
¼
(15)
º
3 2v1 S 2 ª 2 w 2\ 2
K32[ 2\ 2 » 2K1
«
2
wE
7 4v1 2 ¬
¼
a2 q,m ª
3 2v1 S 3 2 2
2 2 º
¦
2
0
S
K
[
K
3
1 m »
«
7 4v1 6
q ,m 1 2 q ¬
¼
ɂɦɟɟɦ ɞɜɚ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɬɪɟɯ ɧɟɢɡɜɟɫɬɧɵɯ \ 2 ,\ 3 ,\ 4 . Ȼɟɡ ɨɝɪɚɧɢɱɟɧɢɹ ɨɛɳɧɨɫɬɢ ɨɞɧɭ ɢɡ ɮɭɧɤɰɢɣ ɦɨɠɧɨ ɩɨɥɨɠɢɬɶ ɧɭɥɸ, ɩɭɫɬɶ \ 3 E 0. Ɋɟɲɚɹ ɫɨɜɦɟɫɬ1
f
ɧɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ (14) ɢ (15), ɩɨɥɭɱɢɦ:
1
1
2
f
a2 q , m § K 3 2
2·
¨ 2 [ m ¸ sin mE q ,m 1 2q © 2K1
¹
2
1
·
1 7 4v1 f a2 q ,m § K32 2
D ¨ 2 [ m 2 ¸ sin mE ¦
2
2K1 3 2v1 q ,m 1 2q © 2K1
¹
\ 2 E ¦
(16)
\ 4 E (17)
ɝɞɟ
1 ª 7 4v1 S 2 2 2
2 2 º
m »
K
[
2
K
3
1
«
SK12 ¬ 3 2v1 6
¼
Ɍɨɝɞɚ ɮɭɧɤɰɢɹ V1 D , E ɭɞɨɜɥɟɬɜɨɪɹɸɳɚɹ ɪɟɲɟɧɢɸ
D
ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚ-
ɱɢ (8) ɩɪɢɦɟɬ ɜɢɞ:
V1 D , E f
¦
q ,m 1
1
a2 q,m
1
·
D 3 D 2 § K32 2
sin mE ® D ¨ 2 [ m2 ¸ 2q
¯6
¹
1
1 7 4v1 § K
1
°½
2
2·
2
[ m ¸ sin 2qD ¾
D¨
3
2q ¹
°¿
2
3
2
1
(18)
ɝɞɟ
D
1 ª 7 4v1 S 2 2 2
2 2 º
K
[
2
K
1 m »
SK12 «¬ 3 2v1 6 3
¼
229
ВЕСТНИК
4/2010
МГСУ
ɂɡ ɭɫɥɨɜɢɹ
V2
w 2V2
wE 2
0 ɩɪɢ E
0
ɉɨɥɭɱɚɟɦ
\ 2 0;
(19)
\4 0
ɂɡ ɭɫɥɨɜɢɹ
V2
w 2V2
wE 2
0 ɩɪɢ E
S
ɉɨɥɭɱɚɟɦ
\ 1 0;
(20)
\3 0
Ɍɨɝɞɚ ɮɭɧɤɰɢɹ V2 D , E ɭɞɨɜɥɟɬɜɨɪɹɸɳɚɹ ɪɟɲɟɧɢɸ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɡɚɞɚɱɢ
(9) ɩɪɢɦɟɬ ɜɢɞ:
an ,m
(21)
V2 D , E ¦ 4 4 sin nD sin mE n , m 1 K1 m
Ɂɚɬɟɦ ɢɫɩɨɥɶɡɭɟɦ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɣ V1 D , E ɢ V2 D , E ɩɪɢ ɪɟɲɟɧɢɢ ɞɢɮɮɟf
2
ɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ (10) ɢ ɭɞɨɜɥɟɬɜɨɪɹɹ ɩɪɢɛɥɢɠɟɧɧɵɦ ɭɫɥɨɜɢɹɦ (11), ɩɨɥɭɱɢɦ
ɫɢɫɬɟɦɭ ɞɜɭɯ ɚɥɝɟɛɪɚɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ. ɇɟɬɪɢɜɢɚɥɶɧɨɟ ɪɟɲɟɧɢɟ ɷɬɨɣ ɫɢɫɬɟɦɵ ɩɪɢɜɨɞɢɬ
ɤ ɱɚɫɬɨɬɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɜɨɫɶɦɨɝɨ ɩɨɪɹɞɤɚ, , ɩɪɢ n
d1[ 8 d 2[ 6 d3[ 4 d 4[ 2 d5
m 1, D
E
S
2
0
ɝɞɟ
K 24K34 S 3
;
4K14 16
d1
A1
d2
A1
K22
k2 · 1 K 22K34 ª S 3
K 24K32 S § S 2
5S º
k
1 2K 22 1
¨
¸ A2
2
4 «
3¹ 2
4K1 ¬ 48
6 ¼»
l12 K34 S 3
;
S 2 4K14 48
§S3 S2
· 1 K 2K 4 ª 1
A1K24 ¨ k1 k1k2 ¸ A2 2 4 3 « S k1 K1 ¬ 2
¹ 2
§S2
l2 K2 § S 2
S ·
S · Sº
1 2K 22 ¨ k1 k2 ¸ » K 22 1 2 32 ¨ k1 k2 ¸ 6 ¹ 6¼
6 ¹
d3
A3
230
K34 ª 2 § S 3 S · S 3 º
«K1 ¨ ¸ » ;
4K14 ¬ © 48 6 ¹ 48 ¼
.
(22)
4/2010
d4
ª
§S3 S2
·
1
Sº
A2K12 «1 K22 ¨ k1k2 ¸ k1 » 2
2¼
¹
¬
K22
·
l12 § S 3 S 2
K32 ª 2 § S 2
S 1
S2 ·
k
k
k
A
K
k
k
k «
S 2 ¨© 48 8 1 1 2 ¸¹ 3 K12 ¬ 1 ¨© 6 2 2 2 1 16 1 ¸¹
ВЕСТНИК
МГСУ
5S 3 S 2
S º
k1 k2 » ;
48 16
6 ¼
d5
ª §S3 S
º
· S3 S2
S2
A3 «K12 ¨ 1 k1 k1k2 ¸ k1 k1k2 » ;
8
¹ 48 2
¼
k1
1 § 7 4v1 S 2K12 ·
¨
¸ ; k2
3 ¹
1 7 4v1
;K2
2K12 3 2v1
bl1
h1S
Ɋɟɡɭɥɶɬɚɬɵ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ (22) ɞɚɸɬ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɱɚɫɬɨɬ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɬɪɟɯɫɥɨɣɧɨɣ ɩɥɚɫɬɢɧɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɤɚɡɚɧɧɵɯ ɛɟɡɪɚɡɦɟɪɧɵɯ ɩɚɪɚɦɟɬɪɨɜ.
Ʌɢɬɟɪɚɬɭɪɚ
1.
2. Ɏɢɥɢɩɩɨɜ ɂ.Ƚ., Ɏɢɥɢɩɩɨɜ ɋ.ɂ. Ʉɨɥɟɛɚɬɟɥɶɧɵɟ ɢ ɜɨɥɧɨɜɵɟ ɩɪɨɰɟɫɫɵ ɜ ɫɩɥɨɲɧɵɯ ɫɠɢɦɚɟɦɵɯ
ɫɪɟɞɚɯ. Ɇ, 2007.
3. ȿɝɨɪɵɱɟɜ Ɉ.Ɉ. Ʉɨɥɟɛɚɧɢɹ ɩɥɨɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɤɨɧɫɬɪɭɤɰɢɣ. Ɇ.: Ⱥɋȼ, 2005.
4. Isaev S.A., Leontev A.I., Frolov DP. «Identification of self-organizing by the numerical simulation of
laminar three-dimensional flow around a crater on a plane by a flow of viscous incompressible fluid.» Technical
physics letters. V.24, Issue 3, pp 209-211, Mart 1998.
5. ɂɫɚɟɜ C.A., ɋɭɞɚɤɨɜ Ⱥ.Ƚ., Ȼɚɪɚɧɨɜ ɉ.Ⱥ., ɍɫɚɱɨɜ Ⱥ.ȿ., ɋɬɪɢɠɚɤ ɋ.ȼ., Ʌɨɯɚɧɫɤɢɣ ə.Ʉ., Ƚɭɜɟɪɧɸɤ
ɋ.ȼ. «Ɋɚɡɪɚɛɨɬɤɚ, ɜɟɪɢɮɢɤɚɰɢɹ ɢ ɩɪɢɦɟɧɟɧɢɟ ɨɫɧɨɜɚɧɧɨɝɨ ɧɚ ɦɧɨɝɨɛɥɨɱɧɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɹɯ
ɪɚɫɩɚɪɚɥɥɟɥɟɧɧɨɝɨ ɩɚɤɟɬɚ ɨɬɤɪɵɬɨɝɨ ɬɢɩɚ VP2/3 ɞɥɹ ɪɟɲɟɧɢɹ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɯ, ɩɪɢɤɥɚɞɧɵɯ ɢ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɡɚɞɚɱ ɚɷɪɨɦɟɯɚɧɢɤɢ ɢ ɬɟɩɥɨɮɢɡɢɤɢ», ȼɟɫɬɧɢɤ ɘɠɧɨ-ɍɪɚɥɶɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
ɋɟɪɢɹ: Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ. 2009. Ɍ. 150. ʋ 17. ɋ. 59-72.
Literature
1. Filippov I.G., Filippov S.I. Kolebatelnie i volnovie protsessi v sploshnih szhimaemih sredah. M, 2007.
2. Egorychev O.O. Kolebania ploskih elementov konstruktsii. M.: ASV, 2005.
3. Isaev S.A., Leontev A.I., Frolov DP. «Identification of self-organizing by the numerical simulation of laminar three-dimensional flow around a crater on a plane by a flow of viscous incompressible fluid.» Technical
physics letters. V.24, Issue 3, pp 209-211, Mart 1998.
4. Isaev S.A., Sudakov A.G., Baranov P.A., Usachev A.E., Strizhak S.V., Lohanskii Ya.K., Guvernyuk S.V.
«Development, Verification and application-based multiblock computational technologies parallelized package
open-VP2 / 3 for basic, applied and operational objectives of Aeromechanics and Thermophysics», Journal of
South-Ural State University. Series: Mathematical Modeling and Programming. 2009. V. 150. ʋ 17. pp. 59-72.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɭɩɪɭɝɚɹ ɬɪɟɯɫɥɨɣɧɚɹ ɩɥɚɫɬɢɧɚ, ɤɨɥɟɛɚɧɢɟ, ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ, ɲɚɪɧɢɪɧɨɟ ɡɚɤɪɟɩɥɟɧɢɟ, ɠɟɫɬɤɨɟ ɡɚɤɪɟɩɥɟɧɢɟ, ɩɨɩɟɪɟɱɧɚɹ ɜɨɥɧɚ, ɩɥɨɬɧɨɫɬɶ
Key words: elastic three-layer plate, vibration, Poisson's ratio, pinned, stiffening, transverse wave, density
ɉɨɱɬɨɜɵɣ ɚɞɪɟɫ: 129337 ɝ. Ɇɨɫɤɜɚ əɪɨɫɥɚɜɫɤɨɟ ɲɨɫɫɟ ɞɨɦ 26
e-mail: misi@mgsu.ru, Ʉɨɧɬɚɤɬɧɵɟ ɞɚɧɧɵɟ: (495) 739-33-63, e-mail: misi@mgsu.ru
Ɋɟɰɟɧɡɟɧɬ: Ʉɢɫɟɥɟɜ Ⱥ.Ȼ., ɞ.ɮ.-ɦ.ɧ., ɩɪɨɮɟɫɫɨɪ ɆȽɍ ɢɦ. Ɇ.ȼ. Ʌɨɦɨɧɨɫɨɜɚ
231
```
###### Документ
Категория
Без категории
Просмотров
5
Размер файла
581 Кб
Теги
закрепление, уравнения, других, частотного, упругом, края, вывод, пластины, противоположных, трехслойного, свободно, шарнирно, колебания, собственных, два
1/--страниц
Пожаловаться на содержимое документа | 10,444 | 9,654 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-51 | latest | en | 0.122144 |
http://www.telegraph.co.uk/finance/2936463/Alice-in-a-wonderland-of-compound-interest.html | 1,511,590,035,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934809419.96/warc/CC-MAIN-20171125051513-20171125071513-00157.warc.gz | 528,758,417 | 23,155 | Telegraph.co.uk
Saturday 25 November 2017
# Alice in a wonderland of compound interest
Walking along the beautiful River Otter in Devon last week, I had a flash of understanding about the pensions timebomb. The problem Lord Turner is grappling with is not an economic or political one. If there is a crisis, it is in our education system.
My eyes were opened by the 18-year-old family friend who had come away with us. I realised that this bright young woman, weighing up offers from a string of good universities, knows nothing about how money works.
Alice's head is full of stuff she will soon forget. But in seven years of secondary education no one has bothered to teach her how to handle the hundreds of thousands of pounds that over time will pass through her hands.
So as we sauntered along the riverbank, I shared with her two of the most important lessons she hasn't learned - the beauty of compound interest and the rule of 72. If she puts into practice what I told her, the pensions crisis will be someone else's problem.
Greater minds than mine have marvelled over the miracle of compounding. Einstein called it "the greatest mathematical discovery of all time" and "the eighth wonder of the world". John Maynard Keynes described "the awesome power of compound interest".
What amazed even these great men was the way in which given enough time - and 18-year-olds like Alice have that in abundance - even apparently trivial amounts of money can turn into spectacular fortunes. The reason, as I explained to her, is simple but profound.
"Take £1,000," I said "and, by investing it wisely, grow it by 10pc in a year; at the end of that year you will have £1,100.
"Do the same for a second year and you will have not £1,200 but £1,210 because your 10pc return on the starting £1,100 is worth £110. Do this every year for 20 years and the return in the last year will be worth £600 and the initial £1,000 will have turned into £6,700.
"Now imagine that during the first year you put aside another £1,000 (it's only £20 a week) and set it to work alongside the first £1,000. The 19 years during which it too grows at 10pc a year will turn it into £6,100. The third year's £1,000 will grow to around £5,600 in 18 years and so on.
"In 20 years' time, when you are still only 38, you will have amassed £64,000 by simply saving £20 a week. By then, adding £1,000 a year to your savings will be nearly irrelevant and you can stop saving altogether. When you are 40, the 10pc return on your pension pot will be worth more than £7,000. By the time you are 50 it will be growing at £18,000 a year and by the time you are 60 you will have more than £500,000.
"The beauty of compound interest is that the longer you can let it work its magic the greater the rewards. Although it will take you 32 years to build up £500,000, by the time you are 68, which is the age the rest of us are told we'll now have to work to, you will have more than doubled your money again to £1.1m, quite enough for a comfortable retirement and all for £20 a week."
"But," said Alice, "my twin sister Camilla says 'sod the pension, I've a hundred and one better things to do with my money'."
"Of course she has," I said, "and she will doubtless spend the next 20 years doing what most of us do in our twenties and thirties. She will enjoy herself and then get married and find a hundred and one new calls on her cash. There's always something.
"Unfortunately, she will also realise on her 38th birthday that she has nothing to show for the £80 a month she has spent without noticing, while you have £64,000 and have stopped worrying.
"Belatedly Camilla will then start putting aside £1,000 a year. Unlike you, however, she won't ever stop saving because she is running hard to try and join you. She never will. However long she continues to save she will never catch up.
"By the time Camilla is 60, despite saving for a couple of years longer than you did, she will have amassed £79,000, around a sixth as much as you.
"Over the next eight years, while your £500,000 grows to £1.1m, her £79,000 will rise to just £180,000 and she won't get many cruises from the income on that."
"OK, so I should start saving now. But what's this Rule of 72?" asked Alice.
"Ah, well you see how time can perform miracles with your modest savings," I replied. "That's nothing compared with what you can achieve by squeezing out a slightly better return than that 10pc. That's what the Rule of 72 shows you.
"It shows you how many years it takes to double your money at a given rate of compound interest. To work this out simply divide 72 by the interest rate you think you can achieve. At 7pc a year it will take 10 years to double your money, while at 12pc a year it will take just six.
"In those last 30 years after you've given up saving and your money is working hard while you sleep, you will double your money around four times over at 10pc a year (which is how you will get from £63,000 to £1.1m).
"But at 15pc a year you would do it twice more again (which would take you from £1.1m to £4.4m)."
"Great," said Alice, who may not know much about money but who can spot the flaw in an argument. "And how exactly am I going to earn this 15pc, or even 10pc a year, on my savings?"
"Good question," I said, "but that's one for another walk."
### The UK Government debt total is now...
Public sector net debt
Latest video
### Five ways Brexit could impact your investments
More from the web
More from the web
More from the web | 1,349 | 5,514 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-47 | latest | en | 0.976306 |
https://sites.nd.edu/gejiang/four-new-corrected-statistics-for-sem-r/ | 1,527,414,699,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794868239.93/warc/CC-MAIN-20180527091644-20180527111644-00118.warc.gz | 636,141,756 | 5,657 | # Four New Corrected Statistics for SEM (R)
This file contains an R program to obtain the test statistics proposed in paper “Four New Corrected Statistics for SEM With Small Samples and Nonnormally Distributed Data”.
Jiang, G., & Yuan, K.-H. (2017). Four New Corrected Statistics for SEM With Small Samples and Nonnormally Distributed Data. Structural Equation Modeling: A Multidisciplinary Journal, 24, 479-494. doi: 10.1080/10705511.2016.1277726
```Authors: Ge Jiang and Ke-Hai Yuan
```
##=======================================================================================##
## This program requires the input of 1) likelihood ratio statistic, 2) Satorra-Bentler’s mean rescaled statistic,
## 3) Satorra-Bentler’s mean and variance adjusted statistic, and 4) their degrees of freedom
## from standard output from any major statistic packages (Mplus, SAS, EQS, R:lavaan)
##=======================================================================================##
# The likelihood ratio statistic:
T_ml;
# Satorra-Bentler’s mean rescaled statistic:
T_rml;
# Degrees of freedom:
df;
# Satorra-Bentler’s mean and variance adjusted statistic:
T_aml; df_aml;
# Scaling factor in T_rml:
r_1 = T_ml/T_rml
# trace of the UGamma matrix:
tr = r_1*df
# rank of the UGamma matrix:
rk = min(df, n-1)
# First Corrected Statistic
const1 = tr/rk
T_cor1 = T_ml/const1
p_cor1 = 1-pchisq(T_cor1, df)
# Second Corrected Statistic
const2 = (r_1+const1)/2
T_cor2 = T_ml/const2
p_cor2 = 1-pchisq(T_cor2, df)
# Third Corrected Statistic
T_cor3 = (T_rml+T_cor1)/2
p_cor3 = 1-pchisq(T_cor3, df)
# Fourth Corrected Statistic
p_rml = 1-pchisq(T_rml, df)
p_aml = 1-pchisq(T_aml, df_aml)
p_cor4 = (p_rml+p_aml)/2 | 496 | 1,694 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-22 | latest | en | 0.68723 |
http://slidegur.com/doc/154146/the-landscape | 1,477,224,247,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719273.37/warc/CC-MAIN-20161020183839-00506-ip-10-171-6-4.ec2.internal.warc.gz | 230,860,513 | 8,745 | ### The Landscape
```The High School Profile
Grace Cheng, Harvard College
Jim Miller, Brown University
Gloria Mueller, formerly of Glenbrook
South HS
Harvard Summer Institute on College Admissions
Thursday, June 26, 2014
Today’s Session
• Examples of high school profiles
• Questions and Discussion
Demographic Information
• Counselors’ contact information: phone, email, fax
• Specify number of seniors in the current graduating class
• Percentage of seniors who go on to 4-year, 2-year colleges
• Demographic composition of student body
• If applicable, specify amount of financial aid scholarships given
to students or percent of students of scholarship
Curriculum
• Number of honors, AP, IB courses offered (group by academic department or
list all honors, all AP, all IB together)
• Specify whether there are school rules that dictate how many H, AP, or IB
courses a student can take or if they are not allowed to take them until a
• Specify any specific HS extra requirements, i.e. “All seniors are required to take
a fine arts course; All juniors are required to do 100 hrs of service.”
• Explain any course abbreviations used
• Specify whether your high school is on semesters, trimesters, quarters, block
• Grading scale, i.e. A = 90+, B = 80 to 89, etc.
• Explain if the GPA is weighted or not. If weighted, how?
• Explain what is included in your cumulative GPA – only academic
courses, all courses, courses from 10-12?
• Transcript should calculate a cumulative GPA, or at least a GPA for
each school year
Rank in Class
• A clear statement of whether you provide rank in class or not.
• If you provide rank, is it weighted or unweighted? If weighted, what
does it include – H, AP, IB? How much weight is given?
• Many schools give two ranks: a weighted rank and an unweighted rank
• Do you have shared ranks?
• If no rank is given, provide a grade distribution: deciles, quints, quartiles
• Visual representation of distribution: graphs, bar charts, scattergrams
• Provide GPA range at a minimum:
The lowest GPA in the class, the highest GPA in the class, mean GPA
Standardized Testing
• Mean or median SAT I or ACT (or both) for the junior class
• SAT subject tests if you have sufficient data to report
• Score distribution or median/mean AP/IB results at the end of the
junior year
Optional
• List colleges your students have attended for the past year or
several years
• Describe the community your high school is located in
• Provide website address for the high school, if a website is
available
community
Profile Examples:
Grand Rapids Christian High School
GRCHS Old Profile 2011.pdf
2012-2013 School Profile GRCHS.pdf | 623 | 2,639 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2016-44 | latest | en | 0.854066 |
https://ro.scribd.com/doc/68605092/Formulas | 1,606,873,527,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141685797.79/warc/CC-MAIN-20201201231155-20201202021155-00595.warc.gz | 399,970,873 | 83,252 | Sunteți pe pagina 1din 6
Theoretically Steel Weight Formula
Theoretical Weight Calculation Formula Of Steel
Name
Formula
Steel Bar/Wire
W=0.006165*d*d
Rod(kg/m)
Screw
W=0.00617*d*d
Symbol Meaning
d=diameter(mm)
d=section diameter(mm)
Square Steel
(kg/m)
Flat steel
(kg/m)
W=0.00785*a*a
a=side width(mm)
W=0.00785*b*d
d=thickness(mm)
b=side width(mm)
Hexagonal
steel(kg/m)
W=0.006798*s*s
s=side distance(mm)
Octagonal
steel(kg/m)
W=0.0065*s*s
s=side distance(mm)
Equilateral angle W=0.00785*[d(2b-d)+0.215(R*Rsteel(kg/m)
2r*r)]
B=width r=
R=inner semidiameter
D=thickness
2r*r)]
B=long side width
B=short side width
D=thickness
r=
R=inner semidiameter
Channel
steel(kg/m)
W=0.00785[hd+2t(b-d)+0.349(R*Rr*r)]
h=height d=thickness
b=length of leg
R=inner semidiameter
T=average thickness of leg
I-section
steel(kg/m)
W=0.00785[hd+2t(b-d)+0.615(R*Rr*r)]
h=height d=thickness b=length
R=inner semidiameter t=average
thickness of leg
Steel pipe
W=0.02466*s(d-s)
d=thickness
d=outer diameter
pipe] (kg/m)
s=thickness
Theoretical Steel Weight Form
Pipe: kg/m
Panel: kg/m2
Checker
I-section
Galv. flat
Electric wire
Square steel
plate
steel
steel
tube
Spec Weight Spec Weight Spec Weight Spec Weight Spec Weight Spec Weight
Hot plate
Galv. angle
steel
Spec Weight
0.5 3.925 2.5 22.6
0.75 5.888 3
26.6
0.8 6.28
3.5 30.5
1
7.85
4
34.4
1.2 9.42
4.5 38.3
1.5 11.78 5
42.3
2
15.7
6
50.1
2.5 19.63 8
65.8
3
23.55
4
31.4
5
39.25
6
47.1
8
62.8
10 78.5
12 94.2
14 109.9
Round &
Channel
Deformed
steel
Spec Weight Spec Weight
6.5 0.26
5# 5.438
8
0.395 6.5# 6.709
10 0.617 8# 8.045
12 0.888 10# 10.007
14 1.21
12# 12.059
14a
16 1.58
14.535
2
20
2.47
22
2.98
25
3.85
28
4.83
32
6.31
0.785
1.13
1.54
2.01
2.54
3.14
4.91
7.06
Welded steel
pipe
Spec Weight
15 1.26
20 1.63
25 2.42
32 3.13
40 3.84
10#
12#
14#
16#
18#
20b#
22b#
25b#
28b#
30b#
13.98 30*3 0.753
16.89 40*4 1.325
20.516
24.143
31.069
36.524
42.03
47.888
48.084
15
20
25
32
40
50
0.625
0.766
1.048
1.329
1.611
2.407
40*4 2.567
50*5 3.996
Galv. pipe
Angle steel
Flat steel
Spec
15
20
25
32
40
Weight
1.33
1.73
2.57
3.32
4.07
Spec
25*25*3
30*30*3
40*40*4
50*50*5
63*63*6
Spec
3*16
4*16
3*20
4*20
4*25
no-seam steel
pipe
Weight Spec
Weight
0.38
25*2.5 1.39
0.50
32*3
2.15
0.47
38*3
2.59
0.63
45*4
4.04
0.78
51*4
4.63
Weight
1.124
1.373
2.422
3.77
5.721
50
4.88
50
5.17
70*70*7 7.398
3*30
0.71
57*4
14b# 16.733 65
16a
17.24 80
6.64
65
7.04
75*75*8 9.03
4*40
1.26
76*4.5 7.93
8.34
80
8.84
75*50*6 5.699
6*40
1.88
89*4.5 9.38
18a
20.174 125 15.04
100 11.5
80*80*8 9.658
5*50
1.96
108*4.5 11.49
125 15.94
90*90*7 9.656
8*50
3.14
127*4.5 13.59
18# 23
150 17.81
20a
22.637 200 26.39
150 18.88
90*90*9 12.717 6*60
2.83
133*5
15.78
8*80
5.02
159*6
22.64
219*7
219*8
325*10
377*12
36.6
41.65
77.68
108.02
18
10*10
12*12
14*14
16*16
18*18
20*20
25*25
30*30
20#
22#
25b#
28#
30#
25.777
28.453
31.335
35.823
39.173
8*100 6.28
10*100 7.85
5.23
Copyright Razor Barbed Wire Barbed Wire Wire Mesh Chain Link Fence Gabion galvanized wire Welded
Wire Mesh
Tel:86-311-85189913
WEIGHT OF S.S.SHEET - PLATE, WEIGHT OF S.S.PIPES, WEIGHT OF S.S.ROUND,
WEIGHT OF S.S.HEX, WEIGHT OF S.S.SQUARE, WEIGHT OF S.S.CIRCLE, WEIGHT
OF S.S.FLAT, WEIGHT OF BRASS - COPPER PIPE ,WEIGHT OF LEAD PIPE, WEIGHT
OF ALUMINIUM PIPE, WEIGHT OF ALUMINIUM SHEET - PLATE
Formula
WEIGHT OF S.S.SHEET / PLATE
Length(mtrs) X Width(mtrs) X Thick(mm) X 8 = Weight per pc
WEIGHT OF S.S.PIPES
OD(mm) Thick(mm) X Thick(mm) X 0.00756 = Weight per
feet
WEIGHT OF S.S.ROUND
Dia(mm) X Dia(mm) X 0.0019 = Weight per feet
WEIGHT OF S.S.HEX
Dia(mm) X Dia(mm) X 0.002072 = Weight per feet
WEIGHT OF S.S.SQUARE
Dia(mm) X Dia(mm) X 0.0024 = Weight per feet
WEIGHT OF S.S.CIRCLE
Dia(mm) X Dia(mm) X Thick(mm) / 160000 = Weight per pc
WEIGHT OF S.S.FLAT
Width(mm) X Thick(mm) X 0.00243 = Weight per feet
Weight of steel pipes and tubing
The weight of carbon and alloy steel pipes - in pounds per foot - can be found in
the table below.
Tube Weight (lb/ft)
Outsid
Wall Thickness (in)
e
Diame
ter 0.05 0.09 0.15 0.20 0.25 0.30 0.36 0.40 0.46 0.50 0.62 0.75 0.87 1.00 1.12 1.25
OD
0
5
0
0
0
0
0
0
0
0
5
0
5
0
5
0
(in)
1/2
03 09 07
3/4
38 46 12
5
5
73 82
2
9
3
3
1
1 1/4
0.64 1.17 1.76 2.24 2.67 3.04 3.42 3.63
08
2
2
3
0
4
2
1
1 1/2
0.77 1.42 2.16 2.77 3.33 3.84 4.38 4.69 5.10 5.34
43
6
3
7
8
5
3
9
9
0
2 1/2
1.04 1.93 2.96 3.84 4.67 5.44 6.30 6.83 7.56 8.01 9.17 10.0
1
3
4
5
3
7
5
5
6
0
8
1
1.30 2.44 3.76 4.91 6.00 7.04 8.22 8.97 10.0 10.6 12.5 14.0 15.1
8
0
5
3
8
9
8
1
2
8
2
2
9
1.57 2.94 4.56 5.98 7.34 8.65 10.1 11.1 12.4 13.3 15.8 18.0 19.8 21.3
5
7
6
1
3
1
5
1
8
5
5
2
6
6
2.10 3.96 6.16 8.11 10.0 11.8 14.0 15.3 17.3 18.6 22.5 26.0 29.2 32.0 34.5
9
2
8
7
1
5
0
8
9
9
3
3
0
4
4
2.64 4.97 7.77 10.2 12.6 15.0 17.8 19.6 22.3 24.0 29.2 34.0 38.5 42.7 45.5 50.0
3
7
0
5
8
6
4
5
0
3
0
4
5
2
6
6
5.99 9.37 12.3 15.3 18.2 21.6 23.9 27.2 29.3 35.8 42.0 47.8 53.4 58.5 63.4
1
2
9
5
6
8
2
2
7
8
5
9
0
7
1
16.6 20.6 24.6 29.3 32.4 37.0 40.0 49.2 58.0 66.5 74.7 82.6 90.1
6
9
7
7
7
4
5
3
7
8
6
0
1
10
26.0 31.0 37.0 41.0 46.8 50.7 62.5 74.0 85.2 96.1 106. 116.
3
8
6
1
7
3
8
9
7
2
6
8
The steel pipe weight can be calculated as
W = 10.68 t (D -t)
(1)
where
W = weight (lb/ft)
t = wall thickness (in)
D = outside diameter (in) | 2,886 | 5,344 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2020-50 | latest | en | 0.42385 |
https://devsenv.com/example/-1146-beecrowd-online-judge-solution-1146-growing-sequences-solution-in-c++,-java,-js-and-python | 1,718,746,343,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861794.76/warc/CC-MAIN-20240618203026-20240618233026-00729.warc.gz | 179,071,666 | 38,328 | ## Algorithm
Problem Name: beecrowd | 1146
# Growing Sequences
Adapted by Neilor Tonin, URI Brazil
Timelimit: 2
Your program must read an integer X indefinited times (the program must stop when X is equal to zero). For each X print the sequence from 1 to X, with one space between each one of these numbers.
PS: Be carefull. Don't leave any space after the last number of each line, otherwise you'll get Presentation Error.
## Input
The input file contains many integer numbers. The last one is zero.
## Output
For each number N of the input file, one output line must be printed, from 1 to N like the following example. Be careful with blank spaces after the last line number.
Input Sample Output Sample 5 10 3 0 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3
## Code Examples
### #1 Code Example with C++ Programming
```Code - C++ Programming```
``````
#include <bits/stdc++.h>
using namespace std;
int main(){
while(1){
int x;
cin >> x;
if (x == 0){
break;
}
int i;
for(i = 1; i < x; i++){
cout << i << " ";
}
cout << i << endl;
}
return 0;
}
``````
Copy The Code &
Input
cmd
1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3
Output
cmd
5 10 3 0
### #2 Code Example with Java Programming
```Code - Java Programming```
``````
import java.io.IOException;
import java.util.Scanner;
public class Main{
public static void main(String[] args) throws IOException{
Scanner input = new Scanner(System.in);
int x = input.nextInt();
while(x != 0){
for(int i = 1; i < x; i++){
System.out.printf("%d ", i);
}
System.out.println(x);
x = input.nextInt();
}
}
}
``````
Copy The Code &
Input
cmd
1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3
Output
cmd
5 10 3 0
### #3 Code Example with Javascript Programming
```Code - Javascript Programming```
``````
var lines = input.split('\n');
while(true){
var x = parseInt(lines.shift());
if (x === 0){
break;
}
var i;
for(i = 1; i < x; i++){
process.stdout.write(i+ " ");
}
console.log(i);
}
``````
Copy The Code &
Input
cmd
1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3
Output
cmd
5 10 3 0
### #4 Code Example with Python Programming
```Code - Python Programming```
``````
while(True):
x = int(input())
if (x == 0):
break
else:
for i in range(1, x):
print(i, end=" ")
print(x)
``````
Copy The Code &
Input
cmd
1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3
Output
cmd
5 10 3 0 | 786 | 2,305 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-26 | latest | en | 0.536028 |
http://slideplayer.com/slide/2353086/ | 1,527,359,625,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867841.63/warc/CC-MAIN-20180526170654-20180526190654-00281.warc.gz | 255,079,249 | 24,303 | # Divisibility Rules 2, 3, 4, 5, 6, 9, 10.
## Presentation on theme: "Divisibility Rules 2, 3, 4, 5, 6, 9, 10."— Presentation transcript:
Divisibility Rules 2, 3, 4, 5, 6, 9, 10
“Divisible BY” What does it mean?
“Divisible by” means: If you divide one number by another, the result is a whole number WITHOUT a remainder. Examples: 12 ÷ 6 = 2 No remainder 15 ÷ 5 = 3 No remainder
Divisibility Rule 2 A number is divisible by 2 if the last digit is even. (0, 2, 4, 6, 8) Examples: Review Even numbers: ghosteven
Now You Try: 572 1464 249 Which number IS NOT divisible by 2?
Need More Practice: Numbers Divisible by 2
WONDERFUL
It ends in a 0, 2, 4, 6, or 8.
Divisibility Rule 3 A number is divisible by three if the sum of the digits is divisible by 3. Examples: = ÷ 3 = 4 No Remainder = ÷ 3 = 6 No Remainder
Now You Try: 572 1464 279 Which number IS NOT divisible by 3?
Need More Practice: Numbers Divisible by 3
The sum is divisible by 3.
WONDERFUL
Divisibility Rule 4 A number is divisible by 4 if the last two digits are divisible by 4. Examples: ÷ 4 = 5 ÷ 4 = 18
Now You Try: 564 4101 188 Which number IS NOT divisible by 4?
Need More Practice: Numbers Divisible by 4
WONDERFUL
The last 2 digits are divisible by 4.
Divisibility Rule 5 A number is divisible by 5 if the last digit is a 0 or 5. Examples: 615 ends in a 5 1480 ends on a 0
Now You Try: 9820 779 560 Which number IS NOT divisible by 5?
Need More Practice: Numbers Divisible by 5
The number ends in a zero or a five.
Wonderful
Divisibility Rule 6 A number is divisible by 6 when it is divisible by 2 AND 3. (prime numbers) Examples: 408 ends in an even number (2 rule) sum of the digits is divisible by 3 Review prime and composite numbers: Prime and Composite Numbers
Now You Try: 8700 523 7602 Which number IS NOT divisible by 6?
Need more practice? Numbers Divisible by 6
Way To Go!!
This number is divisible by 2 and 3.
Divisibility Rule 9 A number is divisible by 9 if the sum of the digits is divisible by 9. Examples: = ÷ 9 = 2 = ÷ 9 =2
Now You Try: 9873 636 5541 Find the number that IS NOT divisible by 9.
Need More Practice: Numbers Divisible by 9 and 10
The sum of the digits is divisible by 9.
Great Job!!!
Divisibility Rule 10 A number is divisible by 10 is it ends in a ZERO.
Example: 7630 ends in a zero 410 ends in a zero
Now You Try: Find the number that IS NOT divisible by ten. 56,
The number ends in a ZERO.
Way To Go!!
Congratulations! Complete two of the three assignments. You may complete them on your computers but print out your answer sheet. Assignment 1.doc chart.doc assignment3.doc
Now that you have completed your two assignments, feel free to go to the following sites. THEY ARE SOOOOO MUCH FUN!!!!!! Fractions vectorkids -divisibility rules Gamequarium Division Games | 856 | 2,799 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2018-22 | longest | en | 0.837942 |
https://juejin.cn/post/6982199332548116517 | 1,638,501,449,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362589.37/warc/CC-MAIN-20211203030522-20211203060522-00076.warc.gz | 400,243,833 | 18,607 | # 1711. 大餐计数
#### 2021-07-07 LeetCode每日一题
``````输入：deliciousness = [1,3,5,7,9]
``````输入：deliciousness = [1,1,1,3,3,3,7]
• 1 <= deliciousness.length <= 10 ^ 5
• 0 <= deliciousness[i] <= 2 ^ 20
``````class Solution {
public int countPairs(int[] deliciousness) {
Arrays.sort(deliciousness);
int len = deliciousness.length, res = 0;
int[] bits = new int[22];
for (int i = 0; i <= 21; i++) {
bits[i] = (int)Math.pow(2, i);
}
for (int val : bits) {
int left = 0, right = len - 1;
while (left < right) {
int sum = deliciousness[left] + deliciousness[right];
if (sum == val) {
int tempLeft = left, tempRight = right, count = 0;
// 处理重复数字
while (tempLeft < tempRight && deliciousness[tempLeft] == deliciousness[left]) {
while (tempRight > tempLeft && deliciousness[tempRight] == deliciousness[right]) {
res = (res + 1) % (1000_000_007);
tempRight--;
}
count = tempRight;
tempRight = right;
tempLeft++;
}
left = tempLeft;
right = count;
} else if (sum < val) {
left++;
} else if (sum > val) {
right--;
}
}
}
return res;
}
}
``````class Solution {
public int countPairs(int[] deliciousness) {
HashMap<Integer, Integer> map = new HashMap<>();
int ans = 0;
for(int i = 0; i < deliciousness.length; i++){
for(int j = 1; j <= 1 << 21; j <<= 1){
if(map.containsKey(j - deliciousness[i])){
ans = (ans + map.get(j - deliciousness[i])) % 1000000007;
}
}
map.put(deliciousness[i], map.getOrDefault(deliciousness[i], 0) + 1);
}
return ans;
}
} | 481 | 1,432 | {"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} | 3.390625 | 3 | CC-MAIN-2021-49 | latest | en | 0.220743 |
http://mathhelpforum.com/pre-calculus/155846-solve-10-log_2-n-n-1-2-a.html | 1,524,273,630,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944848.33/warc/CC-MAIN-20180420233255-20180421013255-00517.warc.gz | 200,883,885 | 10,885 | # Thread: Solve 10 log_2 (n) = n^(1/2)
1. ## Solve 10 log_2 (n) = n^(1/2)
Hi,
Please let me know how to solve the below equation
10 log n = n^(1/2)
Base : 2
n^ 1/2 is n raise to the power 1/2.
It can be solved by substituting values but I need a mathematical solution.
Thanks
2. You cannot solve it algebraically - your best bet is to solve via inspection which is what you've done.
Sketching the graphs on the same axes shows that there is only one solution since $\displaystyle 10 \log_2 (n)$ grows faster than $\displaystyle \sqrt{n}$
It would appear the solution is quite close to $\displaystyle (1.0745,1.0366)$
3. Originally Posted by athap
Hi,
Please let me know how to solve the below equation
10 log n = n^(1/2)
Base : 2
n^ 1/2 is n raise to the power 1/2.
It can be solved by substituting values but I need a mathematical solution.
Thanks
Where has this equation come from? It helps if all of the question is given (including perhaps whether an approximate solution is sufficient). An exact solution can probably be found using the Lambert W-function (a function I doubt you have ever heard of).
4. Thanks GC and Mr Fantastic.
An approximate answer would be ok otherwise the equation would become quite complex.
5. Mr Fantastic you are right.
Can u please tell me how to proceed with W(-ln 2/10) .i.e the Lambert W function
6. Originally Posted by athap
Mr Fantastic you are right.
Can u please tell me how to proceed with W(-ln 2/10) .i.e the Lambert W function
What have you tried?
7. I transformed the equation to Y = X e^X <==> X = W(Y) form.
Am I making any sense??
Source of this is Wikipedia
8. Originally Posted by athap
I transformed the equation to Y = X e^X <==> X = W(Y) form.
Am I making any sense??
Source of this is Wikipedia
I don't think Lambert's W is covered by any Pre-Algebra course in the multi-verse, so I would suggest you do the other thing that MrF suggested and post the actual question and/or its' context.
CB | 526 | 1,974 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2018-17 | latest | en | 0.941566 |
http://gmatclub.com/forum/at-a-certain-school-the-ratio-of-the-number-of-second-59651.html?fl=similar | 1,432,290,258,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207924919.42/warc/CC-MAIN-20150521113204-00130-ip-10-180-206-219.ec2.internal.warc.gz | 106,455,682 | 41,744 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 22 May 2015, 02:24
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# At a certain school, the ratio of the number of second
Author Message
TAGS:
Senior Manager
Joined: 06 Jul 2006
Posts: 295
Location: SFO Bay Area
Schools: Berkeley Haas
Followers: 2
Kudos [?]: 35 [0], given: 0
At a certain school, the ratio of the number of second [#permalink] 04 Feb 2008, 22:43
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
_________________
-------------------------------------------------------------
When you come to the end of your rope, tie a knot and hang on.
Director
Joined: 05 Jan 2008
Posts: 707
Followers: 3
Kudos [?]: 151 [0], given: 0
Re: Quants: Ratio [#permalink] 04 Feb 2008, 22:52
Ans E -> 4 to 5
First to Fourth graders is => First to Second * Second to Fourth
=> 1/2 * 2/4 => First to Fourth =>6/5
Four to Third => inverse of third to four => 2/3
First to Third is => First to Fourth * Fourth to Third
=>1/4 * 4/3=> 6/5*2/3=>4/5
_________________
Persistence+Patience+Persistence+Patience=G...O...A...L
Senior Manager
Joined: 26 Jan 2008
Posts: 267
Followers: 2
Kudos [?]: 76 [0], given: 1
Re: Quants: Ratio [#permalink] 04 Feb 2008, 23:08
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
(A)
the overall ratio is 48 : 64 : 45 : 30
so 48 : 45 = 16 : 15
_________________
Director
Joined: 12 Jul 2007
Posts: 865
Followers: 13
Kudos [?]: 221 [0], given: 0
Re: Quants: Ratio [#permalink] 05 Feb 2008, 03:48
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
Second to Fourth: 8:5
First to Second: 3:4
Third to Fourth: 3:2
First:Second:Fourth = 3:4:8:5 = 6:8:5
Third to Fourth: 3:2
First:Fourth:Third = 6:5:2:3 = 12:10:15
First to Third: 12:15 or 4:5
Director
Joined: 01 Jan 2008
Posts: 629
Followers: 3
Kudos [?]: 140 [0], given: 1
Re: Quants: Ratio [#permalink] 05 Feb 2008, 06:19
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
fourth/third = 1/(third/fourth)=2/3
first/third = (first/second)*(second/fourth)*(fourth/third) = (3/4)*(8/5)*(2/3)=(3*8*2)/(4*5*3)=16/20=4/5 -> E
CEO
Joined: 29 Mar 2007
Posts: 2589
Followers: 16
Kudos [?]: 238 [0], given: 0
Re: Quants: Ratio [#permalink] 05 Feb 2008, 08:52
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
N=1st
X=2nd
Z=3rd
Y=4th
x/y=8/5 n/x=3/4 z/y=3/2 n/z=? --> n=3x/4 z=3y/2 --> y=5x/8 ---> z=15x/16
(3x/4)/(15x/16) --> 16/5*4 --> 16/20 --> 4/5
E
Senior Manager
Joined: 06 Jul 2006
Posts: 295
Location: SFO Bay Area
Schools: Berkeley Haas
Followers: 2
Kudos [?]: 35 [0], given: 0
Re: Quants: Ratio [#permalink] 05 Feb 2008, 09:13
OA is E.
1:2:4:3 = 12:16:10:15
1:3 = 12:15 = 4:5
_________________
-------------------------------------------------------------
When you come to the end of your rope, tie a knot and hang on.
Senior Manager
Joined: 26 Jan 2008
Posts: 267
Followers: 2
Kudos [?]: 76 [0], given: 1
Re: Quants: Ratio [#permalink] 05 Feb 2008, 09:18
incognito1 wrote:
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
(A)
the overall ratio is 48 : 64 : 45 : 30
so 48 : 45 = 16 : 15
Doh! Took first year students to fourth year students as 8:5.. answer is (E)
_________________
SVP
Joined: 28 Dec 2005
Posts: 1581
Followers: 2
Kudos [?]: 88 [0], given: 2
Re: Quants: Ratio [#permalink] 06 Feb 2008, 17:29
GMATBLACKBELT wrote:
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
N=1st
X=2nd
Z=3rd
Y=4th
x/y=8/5 n/x=3/4 z/y=3/2 n/z=? --> n=3x/4 z=3y/2 --> y=5x/8 ---> z=15x/16
(3x/4)/(15x/16) --> 16/5*4 --> 16/20 --> 4/5
E
i personally like this approach; it just makes sense to me !
Re: Quants: Ratio [#permalink] 06 Feb 2008, 17:29
Similar topics Replies Last post
Similar
Topics:
5 At a certain school, the ratio of the number of English 5 30 Mar 2013, 08:49
16 At a certain school, the ratio of the number of second grade 13 27 Feb 2012, 09:02
18 At a Certain school, the ratio of the number of second 17 16 Jul 2009, 10:59
At a certain school, the ratio of the number of second 6 02 Sep 2007, 09:24
At a certain school, the ratio of the number of second 7 24 Apr 2006, 01:21
Display posts from previous: Sort by | 2,569 | 7,315 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-22 | longest | en | 0.897729 |
https://www.vedantu.com/rs-aggarwal-solutions/class-8-maths-chapter-4-exercise-4-2 | 1,722,871,082,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640451031.21/warc/CC-MAIN-20240805144950-20240805174950-00159.warc.gz | 820,348,695 | 29,268 | Courses
Courses for Kids
Free study material
Offline Centres
More
Store
RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2
Last updated date: 02nd Aug 2024
Total views: 589.2k
Views today: 6.89k
RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2 - Free PDF
When a number (x) is multiplied into three, then the result is known as the Cube of that number. Thus, the Cube for the number (x) becomes x3 or x-Cubed. For example, if the given number is 5. We know that 5 × 5 × 5 = 125. Hence, 125 is called the Cube of 5. On the other hand, the Cube Root of a number is also the reverse process of the Cube of a number and is denoted by ∛. Taking the same example, 5 is called the Cube Root of the number 125. In this Chapter, students will learn more about the Cubes and Cube Roots of a number.
What do you understand about a Cube Root?
In Math, the Cube Root is given as, "Cube Root is the number that has to be multiplied three times to get the number." Now, let us look at the Cube Root formula, where y is the Cube Root of x. ∛x = y. The radical sign ∛ is given as a symbol of Cube Root for any number with a small 3 written on the top left of the sign. Another method to write Cube Root is to write 1/3 as the exponent of a number.
Cube Root is an inverse operation of the Cube of a number.
Free PDF download of RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2 solved by Expert Mathematics Teachers on Vedantu.com. All Exercise 4.2 Questions with Solutions for Class 8 RS Aggarwal to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.
Register Online for Class 8 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Math Students who are looking for the better solutions ,can download Class 8 Math NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.
FAQs on RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2
1. What is the method of finding the Cube Root of a Number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?
The Cube Root can be calculated by using the prime factorization method. In order to find the Cube Root of a number, find the prime factorization of the given number. Then, divide the factors into groups containing three same factors. After that, remove the Cube Root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect Cube and we cannot find the Cube Root of that number.
2. What is a Cube of a Number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?
When a number is multiplied three times by itself, the resultant number (product) is known as the Cube of the given number. This is known as a Cube because it helps to represent the volume of Cube. In other words, a number raised to exponent 3 is called the Cube of that number. For example, the Cube of 4 is 64. That means 4 × 4 × 4 = 64, and it can be written as 43. To find the Cube of a number, first, multiply that number by itself, then multiply the product obtained with the original number again. For example, to find the Cube of 7, we will first find the value of 7 × 7. This value is 49. Now, we will find 49 × 7. This is equal to 343. Hence, we can say that the number 7 is 343.
3. How to find a Cube of a negative number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?
The process for finding the Cube of a negative number is the same as that of a whole number and fraction. Remember that the Cube of a negative number is always negative, while the Cube of a positive number is always positive. For example, let us try finding the Cube of -7.
We know that the Cube of -7 is (-7) × (-7) × (-7). Now, in order to find the Cube of (-7), we will first find the value of (-7) × (-7). This value is 49. Now, we will find 49 × (-7). This is equal to -343. Hence, it proves that the Cube of the number -7 is -343.
4. How will you find the Cube Root of 343?
The Cube Root of 343 can be found as it is the number which when multiplied three times by itself gives 343 as the product. If we multiply 7 three times, we will get 343 as the product as 7 × 7 × 7 = 73 = 343 (We can use the prime factorization method to find this). Thus, the Cube Root of 343 is 7. Vedantu’s expert teaches us how to find the Cube Root of this number.
5. How do Vedantu experts guide us to solve problems?
Vedantu expert has wide knowledge of expertise subjects, they give proper guidance of every subject, and they solve every doubts in proper way, Vedantu expert team is consists of many toppers from different universities, so keep joining Vedantu on on one coaching and have trust on expert people, they guide you to the victories.
6. What are the charges of the Vedantu courses?
Vedantu has free contents, no charges are included for subscription, | 1,356 | 5,300 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-33 | latest | en | 0.900414 |
http://transum.com/software/Investigations/Tclub.asp | 1,529,678,894,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864546.30/warc/CC-MAIN-20180622143142-20180622163142-00183.warc.gz | 322,073,971 | 10,277 | A Colourful Maths Investigation
Welcome to the Transum Club; here is your badge:
You can click on a square in the badge to change its colour to either red, blue or yellow, but no two adjacent squares can be the same colour.
Each member of the Transum Club has a different combination of colours in their 'T' badge. What is the largest number of members this club can have?
Click on the squares in the badges above to change their colours. No two squares which meet each other edge to edge can be the same colour. How many different 'T' badges can you make?
Click a yellow square to make it red.
Click a red square to make it blue
Click a blue square to make it yellow.
Now extend this idea to investigate different badge designs and a different number of available colours.
If you liked this activity you might also like Striped Sweets, Ice-cream Combinations and Misfits.
Teachers' Notes are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.
A Transum subscription also gives you access to the 'Class Admin' student management system, answers, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.
Investigations Home
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).
Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.
Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.
Here are some other activities you may be interested in:
Featured Activity
This spectacular magic trick never fails to amaze people of all ages assuming they can add and subtract very simple numbers. The mathematics comes in finding out how the trick works.
Circle Equations
Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle. So far this activity has been accessed 36 times and it is ready for you to enjoy!
For Students:
For All: | 599 | 3,053 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-26 | longest | en | 0.942781 |
https://www.coursehero.com/file/5820635/e2-07/ | 1,516,573,350,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890893.58/warc/CC-MAIN-20180121214857-20180121234857-00755.warc.gz | 890,937,550 | 24,210 | e2_07 - ECE 514 Fall 2007 Exam 2 Due 12:30pm at ECE front...
This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: ECE 514 , Fall 2007 Exam 2: Due 12:30pm at ECE front office, October 25, 2007 Solutions (version: October 25, 2007, 21:11) 75 mins.; Total 50 pts. 1. (14 pts.) Consider three real random variables X , Y , and Z . a. Suppose that Z = X 2 + Y 2 and that X and Y have a joint density that is uniform on the region { [ x, y ] : x, y ∈ [- 1 , 1] } (i.e., the density function is constant in this region and is elsewhere). Find the CDF of Z , F Z ( z ) , for z ≤ 1 . b. Suppose X = Z 2 , Y = √ Z , and Z is uniformly distributed on [0 , 1] . Find the joint CDF of the pair ( X, Y ) , F X,Y ( x, y ) , x, y ∈ R . Are X and Y independent? Ans.: a. Because Z ≥ a.s., we deduce that if z < , then F Z ( z ) = 0 . So fix z ≥ . The value of the uniform density on the given region is 1 / 4 (because that’s the area of the region). Now, for z ≤ 1 , F Z ( z ) = P { X 2 + Y 2 ≤ z } , which is simply the 1 / 4 times the area of the circle { [ x, y ] : x 2 + y 2 ≤ z } , which is πz . So we have F Z ( z ) = πz/ 4 , ≤ z ≤ 1 . b. We have F X,Y ( x, y ) = P { X ≤ x, Y ≤ y } = P { Z 2 ≤ x, √ Z ≤ y } = P { Z ≤ √ x, Z ≤ y 2 } = P { Z ≤ min( √ x, y 2 ) } . If x ≤ or y ≤ , then F X,Y ( x, y ) = 0 . If x ≥ 1 and y ≥ 1 , then F X,Y ( x, y ) = 1 . Otherwise, F X,Y ( x, y ) = min( √ x, y 2 ) . This function cannot be written as the product of two functions, one....
View Full Document
{[ snackBarMessage ]}
Page1 / 3
e2_07 - ECE 514 Fall 2007 Exam 2 Due 12:30pm at ECE front...
This preview shows document pages 1 - 2. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 674 | 1,934 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2018-05 | latest | en | 0.797203 |
https://kmatematikatolyesi.com/2019/02/28/real-mathematics-strange-worlds-12/ | 1,679,947,861,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00508.warc.gz | 392,216,907 | 36,893 | # Real MATHEMATICS – Strange Worlds #12
“More to this than meets the eye…”
I will be using a real life example in order to explain Mandelbrot’s answer to the coastline paradox.
Maps of Norway and USA are as shown below:
It is clear to the naked eye that total coastline of USA is enormous comparing to Norway’s coastline. Nevertheless there is more to this than meets the eyes. Norway’s coastline is a lot longer than USA’s:
USA: 19.924 km
Norway: 25.148 km
There are more than 5000 km between the coastlines which is a really surprising result. But when you zoom into the maps it is easy to see that Norway’s coastline is way more irregular than USA’s. In other words Norway’s coastline has more roughness. Mandelbrot expresses this in his fractal geometry as follows: Norway coastline has a bigger fractal dimension than USA coastline.
But this doesn’t necessarily mean that a bigger fractal dimension has more length. Length and fractal dimension are incomparable.
Measuring Device
In the coastline paradox we learned that one decreases the length of his/her measuring device, then length of the coastline will increase. This information brings an important question with itself: How did they decide the length of the measuring device for Norway-USA comparison?
This is where fractal dimension works perfectly: Finding the appropriate length for the measuring device.
Q: This is all very well how can a coastline length be measured exactly?
Unfortunately it can’t be done. Today, none of the coastline or border lengths are 100% accurate. Although we are certain about one thing: We can make comparisons between coastlines and borders with the help of fractal dimension. In short, today we are able to compare two coastlines or borders even though we are not sure about their exact length.
Box Counting
Finding fractal dimension is easier than you’d think. All you need to do is to count boxes and know how to use a calculator.
Let’s say I want to calculate the fractal dimension of the following shape:
Assume that this shape is inside a unit square. First I divide the square into little squares with side length ¼ units. Then I count the number of boxes which the shape passes through:
This shape passes through exactly 14 squares.
Up next, I divided the unit square into even smaller squares which have side length 1/8 units. And again I count the number of boxes which the shape passes through:
This time the shape passes through 32 squares.
Then I use a calculator. In order to find the fractal dimension of the shape, I must find the logarithms of the number of boxes (32/14) and length of the squares ({1/8}/{1/4}). Then I must divide them multiply the answer with -1.
This random shape I drew on my notebook has around 1,19 fractal dimension.
One wonders…
Calculate the fractal dimension of the following shape:
M. Serkan Kalaycıoğlu | 621 | 2,870 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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 | 4 | CC-MAIN-2023-14 | latest | en | 0.934506 |
https://socratic.org/questions/how-do-you-use-the-squeeze-theorem-to-find-lim-x-1-sin-pi-x-1-as-x-approaches-on#175911 | 1,660,181,634,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00709.warc.gz | 472,311,788 | 6,408 | # How do you use the Squeeze Theorem to find lim(x-1)sin(pi/x-1) as x approaches one?
Oct 11, 2015
${\lim}_{x \rightarrow 1} \left(x - 1\right) \sin \left(\frac{\pi}{x} - 1\right) = 0$
#### Explanation:
Firstly, we don't need the squeeze theorem because the function is continuous at values close to $x = 1$, so the limit is $f \left(1\right)$, that being said, to use the squeeze theorem we must remember that
$- 1 \le \sin \left(\theta\right) \le 1$
If we have $\theta = \frac{\pi}{x} - 1$, we have
$- 1 \le \sin \left(\frac{\pi}{x} - 1\right) \le 1$
Multiplying both sides by $x - 1$ we have
$1 - x \le \left(x - 1\right) \sin \left(\frac{\pi}{x} - 1\right) \le x - 1$ for $x > 0$
Since
${\lim}_{x \rightarrow 1} 1 - x = {\lim}_{x \rightarrow 1} x - 1 = 0$
The squeeze theorem tells us that
${\lim}_{x \rightarrow 1} \left(x - 1\right) \sin \left(\frac{\pi}{x} - 1\right) = 0$
Oct 11, 2015
${\lim}_{x \rightarrow 1} \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) = 0$
#### Explanation:
$- 1 \le \sin \left(\frac{\pi}{x - 1}\right) \le 1$ for all $x \ne 1$
Limit from the right is 0
For $x > 1$, we have $x - 1 > 0$ so we can multiply the inequality without changing the inequalities:
$- \left(x - 1\right) \le \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) \le x - 1$ for all $x \ne 1$
${\lim}_{x \rightarrow {1}^{+}} - \left(x - 1\right) = 0$ and ${\lim}_{x \rightarrow {1}^{+}} \left(x - 1\right) = 0$
So ${\lim}_{x \rightarrow {1}^{+}} \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) = 0$
Limit from the left is 0
For $x < 1$, we have $x - 1 < 0$ so when we multiply the inequality we must change the inequalities:
$- \left(x - 1\right) \ge \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) \ge x - 1$ for all $x \ne 1$
${\lim}_{x \rightarrow {1}^{-}} - \left(x - 1\right) = 0$ and ${\lim}_{x \rightarrow {1}^{-}} \left(x - 1\right) = 0$
So ${\lim}_{x \rightarrow {1}^{-}} \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) = 0$
Therefore,
${\lim}_{x \rightarrow 1} \left(x - 1\right) \sin \left(\frac{\pi}{x - 1}\right) = 0$ | 844 | 2,093 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 29, "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} | 4.65625 | 5 | CC-MAIN-2022-33 | latest | en | 0.628363 |
https://www.3dbuzz.com/forum/search.php?s=2471cb49db6772988ba6891c2cfb6a9a&searchid=9941564 | 1,571,105,691,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986655735.13/warc/CC-MAIN-20191015005905-20191015033405-00031.warc.gz | 732,196,295 | 11,259 | # Search:
Type: Posts; User: Nem
Page 1 of 40 1
1. ## Thread: Sneak peak at BuzzNet
by Nem
Replies
70
Views
5,040
### so... i dont get it, is it just a chat program?...
so... i dont get it, is it just a chat program? :confused:
2. ## Thread: Numerical Methods
by Nem
Replies
5
Views
542
### the book says the answers 1 :confused:
the book says the answers 1 :confused:
3. ## Thread: Exciting Wait for Buzz
by Nem
Replies
35
Views
2,659
### i thought the big thing was DVAS, which now hasnt...
i thought the big thing was DVAS, which now hasnt been updated in months
4. ## Thread: Numerical Methods
by Nem
Replies
5
Views
542
### Numerical Methods
quick question
how do i find the number of real solutions for this:
e^x = 1 / x
i assume i would need to take logs of both sides so i can evaluate the x on the left
if i take logs of the LHS,...
5. ## Thread: Sony Walkman HD-1 - Thoughts
by Nem
Replies
7
Views
4,840
### meh i wouldnt get it, my friend has one and...
meh i wouldnt get it, my friend has one and theyre pretty awkward to use, compared to an ipod
6. ## Thread: Transferring animation
by Nem
Replies
6
Views
414
### also, is there any way for me to create my own...
also, is there any way for me to create my own attributes like in maya? say have an atrtibute called finger curl. and instead of rotating each finger manually everytime i wanted to animate it, just...
7. ## Thread: Calculus: Curve Sketching
by Nem
Replies
10
Views
1,500
### LOL well if you say thats faster demondo ;) ...
LOL well if you say thats faster demondo ;)
once youve equated your derivative to 0 you can solve for x to get a turning point
we dont know the nature of this turning point until we take the...
8. ## Thread: advice needed from vegetarians
by Nem
Replies
21
Views
1,953
### not a big fan of tofu, it just tastes...
not a big fan of tofu, it just tastes of...nothing :confused: its a bit disturbing when you put something in your mouth and chew it, but it has no taste
9. ## Thread: Anyone Interested?
by Nem
Replies
0
Views
316
### Anyone Interested?
anybody interested in helping out with some animations for an upcoming mod?
Its for a mod called SourceBall which im working on, and it has gotten really popular (3 members of valve contacted us...
10. ## Thread: Transferring animation
by Nem
Replies
6
Views
414
### thx tuna, this xsi thing seems more complex when...
thx tuna, this xsi thing seems more complex when it comes to animation than maya :rolleyes:
11. ## Thread: Small Hard drive
by Nem
Replies
5
Views
651
### i guess my budget would be about £30 (\$70 ish)...
i guess my budget would be about £30 (\$70 ish)
but im trying to find a quality one, its gunna hold my work so i dont want it crashing out on me all the time
12. ## Thread: Small Hard drive
by Nem
Replies
5
Views
651
### Small Hard drive
im looking for a smallish (20-30gb) that is reliable enough for me to run XSI on. im not too sure about SCSI as its fairly expensive and im limited on cash. not sure what the exact budget would be...
13. ## Thread: What song is this? (again)
by Nem
Replies
2
Views
396
### What song is this? (again)
http://www.metallica.plus.com/music/maiden.mp3
i think its a maiden song, but i dont know which one :huh: anyone have any ideas?
14. ## Thread: What was the best Metal album of 2004?
by Nem
Replies
36
Views
3,157
### bit of a skinny year, it seems music is becoming...
bit of a skinny year, it seems music is becoming saturated with bands like kings of leon and franz ferdinand which is a real shame :(
i like to listen to good music, not just metal, but i hardly...
15. ## Thread: Transferring animation
by Nem
Replies
6
Views
414
### why is it inefficient? are there any tutorials...
why is it inefficient?
are there any tutorials on this?
16. ## Thread: Game Animators
by Nem
Replies
0
Views
274
### Game Animators
We are currently recruiting character animators for our mod SourceBall (which you all probably know by now :))
It is a remake of the bitmap brothers classic SpeedBall. Our fanbase has grown...
17. ## Thread: Transferring animation
by Nem
Replies
6
Views
414
### Transferring animation
is itpossible to rig and skin a character, animate him, then unskin and bind another model in XSI?
18. ## Thread: First try at portfolio site
by Nem
Replies
5
Views
601
### i personally dont like it, if i go to a website...
i personally dont like it, if i go to a website id rather not spend a lengthy amount of time trying to figure out what the text says :)
especially if its a portfolio site, you dont want ppl to spend...
19. ## Thread: Trapezium Rule (yes Dudey its maths :p)
by Nem
Replies
3
Views
364
### oh right so if you had a simple function like...
oh right
so if you had a simple function like (x^2) - 5 and you integrated twice: first with definite integration and second with the trapezium rule. then the trapezium rule should theoretically...
20. ## Thread: What is the advantage of PCI-e?
by Nem
Replies
11
Views
512
### hey enygma, whos that in your avatar? portnoy? ...
hey enygma, whos that in your avatar? portnoy?
"He's got a fever! And the only prescription...is more cowbell!" :D
21. ## Thread: Trapezium Rule (yes Dudey its maths :p)
by Nem
Replies
3
Views
364
### Trapezium Rule (yes Dudey its maths :p)
quick maths question but its pretty simple, no numbers involved ;)
whats the point of the trapezium rule? to just find the area under a graph? if thats the case then why cant you just integrate it...
22. ## Thread: Adobe Audition Noise Reduction
by Nem
Replies
4
Views
466
### an extreme solution would be to get a new mic,...
an extreme solution would be to get a new mic, the shure SM58 is a good vocal mic
23. ## Thread: Need a hand
by Nem
Replies
1
Views
219
### Need a hand
I should probably post this in one of the 3d forums, but this isnt specific to any particular software
im trying to find a model of a human hand (doesnt really matter what format its in) anyone...
24. ## Thread: What tune is this?
by Nem
Replies
6
Views
305
### thanks paul! tis a nice little piece to play on...
thanks paul! tis a nice little piece to play on guitar cos everyone knows it :D
25. ## Thread: What tune is this?
by Nem
Replies
6
Views
305
### What tune is this?
this is such a popular tune but i cant remember what its called atm!! anyone know?
http://www.metallica.plus.com/music/song.mp3
Results 1 to 25 of 1000
Page 1 of 40 1 | 1,775 | 6,455 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-43 | latest | en | 0.858788 |
https://mcqslearn.com/cs/dip/quizzes/quiz.php?page=72 | 1,721,028,420,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514680.75/warc/CC-MAIN-20240715071424-20240715101424-00676.warc.gz | 346,674,971 | 17,130 | Computer Science Degree Courses
Digital Image Processing Certification Exam Tests
Digital Image Processing Practice Test 72
# Sampling and Fourier Transform of Sampled Function Multiple Choice Questions (MCQs) PDF Download - 72
Books:
Apps:
The Sampling and Fourier Transform of Sampled Function MCQ with Answers PDF (Sampling and Fourier Transform of Sampled Function Multiple Choice Questions (MCQs) PDF e-Book) download Ch. 3-72 to prepare Digital Image Processing Practice Tests. Study Filtering in Frequency Domain Test PDF, Sampling and Fourier Transform of Sampled Function Multiple Choice Questions (MCQ Quiz) for cheapest online computer science degree. The Sampling and Fourier Transform of Sampled Function MCQ Quiz App Download: Free certification app for sampling and fourier transform of sampled function, image compression basics, erosion and dilation, pseudocolor image processing, measuring image information test prep to study online tutor courses.
The MCQ Quiz: The sampled frequency less than the nyquist rate is called; "Sampling & Fourier Transform of Sampled Function" App (Play Store & App Store) with answers: Over sampling; Under sampling; Critical sampling; Nyquist sampling; for cheapest online computer science degree. Practice Filtering in Frequency Domain Questions and Answers, Apple Book to download free sample for computer software engineer.
## Sampling & Fourier Transform of Sampled Function MCQ Quiz with Answers : Test 72
MCQ 356:
The sampled frequency less than the nyquist rate is called
1. under sampling
2. over sampling
3. critical sampling
4. nyquist sampling
MCQ 357:
Digitizing the coordinates of the image is called
1. sampling
2. quantization
3. framing
4. Both A and B
MCQ 358:
Best removal of lines from image will be produced by the SE of size
1. 1x1
2. 2x2
3. 3x3
4. 5x5
MCQ 359:
Pseudo colors are also known as
1. true colors
2. false colors
3. primary colors
4. secondary colors
MCQ 360:
Source of the event itself called
1. zero-memory source
2. nonzero-memory source
3. zero source
4. memory source
### Sampling & Fourier Transform of Sampled Function Textbook App: Free Download (iOS & Android)
The App: Sampling & Fourier Transform of Sampled Function MCQ App to study Sampling & Fourier Transform of Sampled Function Textbook, Digital Image Processing MCQs App, and Digital Logic Design MCQs App. The "Sampling & Fourier Transform of Sampled Function" App to free download Android & iOS Apps includes complete analytics with interactive assessments. Download App Store & Play Store learning Apps & enjoy 100% functionality with subscriptions!
Sampling & Fourier Transform of Sampled Function App (Android & iOS)
Digital Image Processing App (iOS & Android)
Digital Logic Design App (Android & iOS)
DBMS App (iOS & Android) | 615 | 2,807 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-30 | latest | en | 0.808313 |
http://simont.dreamwidth.org/9143.html?thread=2011063 | 1,503,201,100,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886105970.61/warc/CC-MAIN-20170820034343-20170820054343-00432.warc.gz | 376,291,645 | 8,454 | Unsolved problem
simont
[ userinfo | dreamwidth userinfo ] [ archive | journal archive ]
Wed 2014-02-19 10:52
Unsolved problem
Link Reply
Wed 2014-03-12 09:51
A friend came over yesterday afternoon and we looked at this and made some progress. I can almost solve it, I think. In practice I can find the solution for given m and n with pen and paper and a small amount of fiddling, but at present this margin is too small to contain the details of the general method :-) But let's look at some examples. Let m
[Error: Irreparable invalid markup ('<n [...] tight.>') in entry. Owner must fix manually. Raw contents below.]
A friend came over yesterday afternoon and we looked at this and made some progress. I can almost solve it, I think. In practice I can find the solution for given m and n with pen and paper and a small amount of fiddling, but at present this margin is too small to contain the details of the general method :-) But let's look at some examples. Let m<n and let s be the shortest length in the dissection, and t the longest length. We'll promise to never leave an m-stick whole in the dissection (this doesn't affect s, except in the trivial case where n is a multiple of m). With this constraint, t <= m-s.
Let's find s(3,10). If s is *more than*, um, 4/3, then t<5/3 if any 3-sticks are whole in the dissection, just cut them in half), so a 10-stick must be cut into at least 7 pieces (6 isn't quite enough - a tight constraint from t <5/3) and at most 7 (8 lots of 4/3 is too much) so exactly 7, so there are 21 pieces in the dissection. But each 3-stick must be cut in 2, so there are 20 pieces in the dissection, contradiction.
Note that 4/3 is the best number that gives this contradiction, since as I pointed out, the constraint was tight. So although it looked like I plucked it out of the air, I didn't really. Now all we need to do is find a 4/3-dissection, which is simplicity itself (try it).
Ok, let's find s(5,8). If s> ... let's say, 2, then t<3, so an 8-stick must be cut into at least 3 and at most 3 pieces (this time it's the maximum that's tight, from s>2, justifying my choice of the number 2), so there are 15 pieces in all. But the 5-sticks are all in 2 pieces, 16 in all, so s=2 is best, if we can find it. Again, it's easy.
Now let's find s(5,7) (your original example). if s>7/3, t<8/3 and each 7-stick must be in exactly two pieces by the argument above, and the constraint is tight. Can we find a 7/3-dissection? It's quite obvious that we can't after a moment's thought. Oh dear! Our method's gone wrong, so we use the fall-back of cutting m in 3 equal pieces. Can we find a 5/3-dissection? Yes we can, and then we use a slightly fiddlier proof to show that it's best.
Obviously there are a number of magic wands that need to be removed from this to make it a proof, but it seems to work in practice. The basic point is that the space of dissections is quite 'floppy', so if we can find a tight constraint with s>m/2 then there's a good chance we can also satisfy it, and if we can't, then the fall-back to cutting some m sticks into 3 equal parts means there's enough floppiness to do it now.
It wouldn't surprise me greatly if you found some cases where this doesn't work, but the first problem is to find out what it is actually claiming ...
Link Reply to this | Thread
Wed 2014-03-12 10:29
Oh yes, and the other case is exemplified by s(5,6). If s=2, t=3 and each t-stick must be cut in 2 or 3 pieces. But both constraints are tight at the same time, so obviously it's not possible to do better.
Link Reply to this | Parent
Wed 2014-03-12 11:33
Thanks for this! A couple of friends are currently working on an exhaustive search program to collect data on small cases (which I'll probably put up on the web at some point soonish, once I figure out how to format it most legibly) so it's nice to see someone else trying to approach it from the theoretical end and making progress.
In practice I can find the solution for given m and n with pen and paper and a small amount of fiddling, but at present this margin is too small to contain the details of the general method :-)
Looking at the data I have so far, here are some m,n pairs that might be interesting challenges to your method: s(5,4), s(3,7), s(7,8), s(4,9).
Link Reply to this | Parent | Thread
Wed 2014-03-12 11:56
I don't think so. Let's do s(4,5). If s>3/2, t<5/2 and each 5-stick must be in exactly 3 pieces (the constraint is tight on t). So there are exactly 12 pieces; but each 4-stick is in 2 pieces, so there are exactly 10 pieces, contradiction. 3/2 is achievable, so is the answer. Works like a dream.
Link Reply to this | Parent | Thread
Wed 2014-03-12 12:25
Actually I spoke too soon. The method works fine for s(4,5) and also for s(3,7). However, for s(7,8) it gives a bound of s=8/3. This is certainly a bound, but it's not achievable: however, it's not necessary to drop down to 7/3, since the intermediate value of 5/2 is achievable (again, with a quite easy but fiddly proof).
So I must make a more modest claim: the method gives a reliable bound b, which is usually achievable. When it isn't achievable, m/3 may be the best achievable, but there may be some other intermediate value that will work.
As you can see, I've simply relaxed one of the two claims I made without any good reason. I'm still making one claim without proof (that m/3 is always achievable, because there is so much floppiness in the dissection).
For s(4,9) my method gives a bound of s<=9/5, which is another clearly not achievable case, so my new weakened claim is that 4/3 <= s < 9/5. As I haven't found the value yet this is an interesting test case ...
Link Reply to this | Parent | Thread
Wed 2014-03-12 12:29
... At least this weaker claim does hold true, since 4/3 is easily achievable, whether or not there is a better intermediate value available.
Link Reply to this | Parent
Wed 2014-03-12 13:10
Incidentally, the cases where the proved bound is not achievable seem to be those where the candidate values of s and t are 'too close' to each other (e.g. 7/3 and 8/3 in the (5,7) case), or 9/5 and 11/5 in the (4,9) case), or 'too distant' (or perhaps 'too close to a multiple of each other') (e.g. 8/3 and 13/3 in the (7,8) case). But this is a rather woolly observation.
Link Reply to this | Parent
Wed 2014-03-12 14:14
For s(4,9) my method gives a bound of s<=9/5
Hmm, does it? I tried to boil down your method into something I could state in a general way, and then applied that, and for s(4,9) I got what I think is actually the right bound.
If every piece is at least s and at most m-s, then every stick of length n is cut into at least n/(m-s) and at most n/s pieces, hence at least ⌈n/(m-s)⌉ and at most ⌊n/s⌋, hence the total number of pieces P in the dissection must satisfy m⌈n/(m-s)⌉ ≤ P ≤ m⌊n/s⌋. By similarly considering the number of pieces that a stick of length m is cut into, we derive a second inequality n⌈m/(m-s)⌉ ≤ P ≤ n⌊m/s⌋ (identical to the first except that n,m are swapped everywhere they appear except in the divisor m-s). So when s becomes big enough that either of those inequalities is self-inconsistent (with LHS > RHS) or when the two are incompatible (because they define ranges for P that do not meet), there can be no dissection with s that large.
It is true that s=9/5 is a threshold beyond which something goes wrong, namely that the first inequality for P is self-inconsistent (with s > 9/5 we would need 20 ≤ P ≤ 16). But something else has gone wrong before that – at s=7/4 the two intervals stop overlapping (because the first inequality switches from 16 ≤ P ≤ 20 to 20 ≤ P ≤ 20, while the second was at 18 ≤ P ≤ 18 all along). And the computer search data I have says that 7/4 really is the best solution.
I agree with you, on the other hand, that the method doesn't get the exact bound for s(7,8), and hence is not reliable in all circumstances.
Link Reply to this | Parent | Thread
Wed 2014-03-12 15:00
You're right, the bound is 7/4 and hence gives the correct answer in that case.
Your account is more complicated than need be because the bound always operates when the m-sticks are constrained to be divided into only two pieces, making the first constraint P=2n. So the n-sticks are presumably going to be divided into about 2n/m pieces, give or take some rounding somewhere. Ignoring the trivial case where m | 2n, set p = floor(2n/m) and by considering the four possible cases we get a bound of
max [ min (n/p, m-n/p), min (n/(p+1), m-n/(p+1)) ]
In the s(4,9) case, p=4 and this gives
max [ min (9/4, 7/4), min (9/5, 11/5) ] = max (7/4,9/5) = 7/4.
(I didn't do this explicit calculation earlier as my brain was full and I hoped to get some work done today, but I have overcome both weaknesses :-)
As we've said, this bound isn't always tight but it seems it very often is. I'd be interested in whether your data has any cases refuting my conjecture that, when the bound isn't tight, s is still >= m/3. Also of course to see if one can characterise the cases where the bound is not tight.
Link Reply to this | Parent | Thread
Wed 2014-03-12 15:50
Grr, that's still completely wrong, though the right elements are there. Unfortunately I've gone back to trying to get some work done, but some anagram of the above is true which I will identify when I have some more time!
Link Reply to this | Parent
Wed 2014-03-12 16:07
I'd be interested in whether your data has any cases refuting my conjecture that, when the bound isn't tight, s is still >= m/3
No.
I've implemented a piece of Python that computes your bound (that is, computes my statement of it, without attempting to simplify based on this followup) and compared it with all the data I have so far (which is everything up to n=10, and some but not all for n=11).
The complete list of cases I know of in which your bound is not tight (assuming I haven't made any errors in my implementation) is: s(6,7), s(7,8), s(9,10), s(3,11), s(4,11), s(5,11), s(7,11). And in all those cases, we do still have s ≥ m/3.
Link Reply to this | Parent
navigation
[ go | Previous Entry | Next Entry ] [ add | to Memories ] | 2,849 | 10,192 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2017-34 | latest | en | 0.95261 |
https://puzzling.stackexchange.com/questions/20795/is-this-sequence-new/20798 | 1,618,715,824,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038464146.56/warc/CC-MAIN-20210418013444-20210418043444-00569.warc.gz | 563,741,877 | 33,184 | # Is this sequence new? [duplicate]
I can't help but wonder if we've seen it before. I do know however it seems to be entirely made from booleans! I can't remember any booleans?!?!?!
true
true false true true
true false true false true
true false false true false true true true false true true
true true false true true false false true false false true true true false true false true
true false false true true false false false false true true true false false true false false true true
I'm almost positive this is a known pattern, but maybe I'm wrong? Do any of you know the pattern, and can you confirm if it's been here before?
• And none of that's meta. Everything in the puzzle is important. – warspyking Sep 1 '15 at 16:16
• @Deusovi I would call it a duplicate, but I would vote to close the other one, as I think this is the better one. – GentlePurpleRain Sep 1 '15 at 17:05
• @GentlePurpleRain: I was under the impression that duplicate status was always resolved in favor of the earlier one. – Deusovi Sep 1 '15 at 17:10
• @Deusovi, I thought I remembered a meta discussion on that, where the suggestion was that the better question should be kept (what if someone posts a two-liner with no formatting and spelling mistakes, and someone else later posts a puzzle with a similar premise, but weaves it into an excellent story and obviously puts a lot of work into it?), but I can't seem to find it now. – GentlePurpleRain Sep 1 '15 at 17:20
• I think you should also all note that the other puzzle was posed by the same person. It's even a meta-duplicate! – Ian MacDonald Sep 2 '15 at 0:22
If we convert the sequence to binary, with true=1 and false=0...
1
1011
10101
10010111011
11011001001110101
1001100001110010011
Then we convert from binary to decimal...
1
11
21
1211
111221
312211
We see that the sequence is
The age old sequence where each number describes the count of digits in the previous number, so the value after 1 is "one one", or 11.
Has it been here before?
Yeah, it has. This isn't the original form, but it's another warspyking classic, which is really just as good.
• but it's another warspyking classic, which is really just as good. Made me smile – warspyking Sep 1 '15 at 17:50 | 586 | 2,227 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2021-17 | latest | en | 0.905228 |
http://mizar.uwb.edu.pl/version/current/html/proofs/interva1/54 | 1,571,794,336,000,000,000 | text/plain | crawl-data/CC-MAIN-2019-43/segments/1570987826436.88/warc/CC-MAIN-20191022232751-20191023020251-00478.warc.gz | 134,156,230 | 1,569 | let U be non empty set ; :: thesis: for A, C being non empty IntervalSet of U
for X, Y being Subset of U st A = Inter (X,Y) holds
A _\_ C = Inter ((X \ (C ``2)),(Y \ (C ``1)))
let A, C be non empty IntervalSet of U; :: thesis: for X, Y being Subset of U st A = Inter (X,Y) holds
A _\_ C = Inter ((X \ (C ``2)),(Y \ (C ``1)))
let X, Y be Subset of U; :: thesis: ( A = Inter (X,Y) implies A _\_ C = Inter ((X \ (C ``2)),(Y \ (C ``1))) )
assume A1: A = Inter (X,Y) ; :: thesis: A _\_ C = Inter ((X \ (C ``2)),(Y \ (C ``1)))
A = Inter ((A ``1),(A ``2)) by Th15;
then ( X = A ``1 & Y = A ``2 ) by ;
hence A _\_ C = Inter ((X \ (C ``2)),(Y \ (C ``1))) by Th40; :: thesis: verum | 264 | 673 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-43 | latest | en | 0.807786 |
http://fmoldove.blogspot.com/2017/12/physics-and-geometry-returning-to-gauge.html | 1,639,012,617,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00212.warc.gz | 20,445,768 | 15,070 | ## Physics and Geometry
Returning to gauge theory, physics is best understood in terms of geometry. The area is vast and I am considering how to best explain the key concepts in the most intuitive way. Today I want to start with the broad picture to present the relevant mathematical landscape. We need to consider two kinds of transformations:
• transformations in space-time
• gauge transformations of physical fields.
The mathematical machinery involved uses fiber bundles and Cartan's language of differential forms. There are two key differential forms: the connection 1-form and the curvature 2-form. Another essential ingredient is that of parallel transport. In terms of physics parallel transport corresponds to the transport of physical information. When we do parallel transport around a closed loop the final state is in general different than the initial state.
Here is some trivial example from ordinary high-school geometry. You are walking on Earth along the equator and you carry with you an arrow which points North. You walk 1/4 circumference of the Earth when you decide to walk all the way to North Pole. At any point during your journey you keep the orientation of your arrow at time $$t$$ parallel to the orientation of your arrow at time $$t+\Delta t$$. Initially the arrow was perpendicular to the direction of travel, and when you started going North the arrow is parallel to the direction of travel. Once at North Pole you deice to take the shortest path to your starting point. What is the orientation of your arrow when you get back? Try this with a pencil and a ball.
The parallel transport on a closed loop can be used to define curvature. In terms of physics, gauge theory teaches us that:
force=curvature
When discussing gauge theory, the natural language is that of bundles. On bundles, one starts with product bundles but then one proceeds to general bundles obtained by gluing together product bundles. For Standard Model the product bundles are enough, but for gauge theory on curved space-time (string theory, quantum gravity) you need to use the most general bundles.
One problem arises then: how to relate what different observers see?
Changes in observers are described by cocycles. Cocycles depend on both the topology of the space-time manifold and the structure of the gauge group. The deviation of vector bundles from from product bundles is measured by the so-called characteristic classes (Chern, Euler, Pontryagin, Stiefel-Whitney, Thom classes).
To explain the math machinery of all this is a very ambitious project and I am not sure how far along I can carry the series but I will try. The geometry involved is very beautiful (at least to me). Please stay tuned. | 539 | 2,721 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-49 | latest | en | 0.916615 |
http://forum.allaboutcircuits.com/threads/pulse-width-duration.73679/ | 1,484,622,839,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279410.32/warc/CC-MAIN-20170116095119-00026-ip-10-171-10-70.ec2.internal.warc.gz | 109,494,446 | 14,114 | # Pulse width duration?
Discussion in 'Homework Help' started by pfelectronicstech, Aug 25, 2012.
1. ### pfelectronicstech Thread Starter Member
Jan 18, 2012
178
4
I do NOT want the answer, I just want to be pointed in the right direction. Its a 500-HZ digital signal and duty cycle is 20%. What is the formula, or how do I get to the answer because I can't find it in my book? Thanks for the help again.
2. ### Jony130 AAC Fanatic!
Feb 17, 2009
3,990
1,115
D = Ton/( Ton + Toff)
pfelectronicstech and absf like this.
3. ### bertus Administrator
Apr 5, 2008
15,796
2,384
pfelectronicstech and absf like this.
4. ### cork_ie Member
Oct 8, 2011
348
58
This NE555 PWM calculator should be of help
pfelectronicstech likes this.
5. ### pfelectronicstech Thread Starter Member
Jan 18, 2012
178
4
Thanks guys, I'm not fully understanding yet, and I'm not sure why. I'm gonna give it one last look in my books, and move on. Thanks again.
6. ### Jony130 AAC Fanatic!
Feb 17, 2009
3,990
1,115
The answer is quite simple.
For F = 500Hz and D = 20% we have
T = 1/F = 1/500 = 2ms
D = Ton/T * 100%
Ton = (D * T)/100% = (20 * 2ms)/100 = 400us
7. ### pfelectronicstech Thread Starter Member
Jan 18, 2012
178
4
I got it now, thanks guys. It all came together in the end. Thanks again for the help. | 438 | 1,295 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-04 | latest | en | 0.908546 |
https://www.slideshare.net/micofico/numerologist-review-15371910 | 1,490,823,837,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218191396.90/warc/CC-MAIN-20170322212951-00517-ip-10-233-31-227.ec2.internal.warc.gz | 975,988,943 | 35,907 | Upcoming SlideShare
×
# Numerologist review
943 views
Published on
1 Comment
0 Likes
Statistics
Notes
• Full Name
Comment goes here.
Are you sure you want to Yes No
Thanks!
Are you sure you want to Yes No
• Be the first to like this
Views
Total views
943
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
5
1
Likes
0
Embeds 0
No embeds
No notes for slide
### Numerologist review
1. 1. Numerologist Review- My Honest OpinionHey, Miha here.Thanks for checking out my blog, you’ve come to the right place if your looking for a comprehensive review ofNumerologist, which is written by none other thanMaster numerologist Mike Madigan.First and foremost, I just want to clarify I will be giving you an unrestricted unbiased and honest review ofNumerologist. What your about to read are the ESSENTIAL details you need to know before grabbing a copy of thereport yourself.OK let us now see what were my EXPERIENCE with Numerology Report First impression was positive. I’ve received a 153 pages long e-mail describing of all thepossible areas that are conserning my personality and my past, present and future life.The descriptions were very detailed over which I was excited, because the calculation went in detailed explanation of thenumbers they got from the name, surname, date and year of birth. Of course, there are several possible combinations ofcomputation.I personally used a differnet technique which is based on the number of 1-100, this number is related to the centralorgans, and the specific number shows in which body the blockade is and consequently with which bad emotionalbehavior it’s related. Of course, the final result is similar but with a significant difference.There are several types of Numerology but 2 DIFFERENT TYPES of them are generally used.First Technique is the one that Mike Madigan is using and of which I’m writing in this blog. His way of using aprogram based on known letters and numbers in our name, surname and date of birth. The program calculates allpossible combinations and introduces them in a meaningful report which containes all we can learn from numerology.This type is much wider and exact and that is why I’m recomending it to you. You’ll learn very precise about all of yourlife areas; from the life cycle, to personality, karmic lessons, hidden passions, expression levels to personal days, monthsand years.Well, almost all of the areas are mention bellow:1. INTRODUCTION2. LIFE PATH3. BIRTHDAY4. EXPRESSION5. MINOR EXPRESSION6. HEART’S DESIRE
2. 2. 7. MINOR HEART’S DESIRE8. PERSONALITY9. MATURITY10. L/E BRIDGE11. H/P BRIDGE12. KARMIC LESSONS13. HIDDEN PASSION14. PLANES OF EXPRESSION15. PLANE OF EXPRESSION PHYSICAL16. PLANE OF EXPRESSION MENTAL17. PLANE OF EXPRESSION EMOTIONAL18. BALANCE19. RATIONAL THOUGHT20. CORNERSTONE21. SUBCONSCIOUS SELF22. CHALLENGES23. PINNACLES24. CYCLES25. TRANSITS26. THE PHYSICAL TRANSIT27. THE SPIRITUAL TRANSIT28. ESSENCE29. PERSONAL YEARS30. PERSONAL MONTHS31. PERSONAL DAYS And the second type of Numerology use is with a help of a person who has strongspiritual connection. In this case the calculation process is the same; all of the basic numbers are taken from name,surname and birth date- they’re representing us and based on them master numerologist gets (through the numerologicknowledge he owns) crucial informations which are representing us. In this case the results are again exact but thewidth is not as extensive.This way of calculation is let us say better in case we have a specific problem which we don’t know how to solve or wedon’t have the knowledge why it’s happening to us. As we can personaly ask about everything, we can get very specificanswers about all our problems and areas in life.This technique requires master numerologist of course and he has to be experienced a have a good connection as it is thekey to the informations we can not get anywhere else, that is why the price is more expencive. Not everyone who learnsnumerology is a good numerologist. Anyone can calculate but the best are those to whom this is a life path or hugepassion and at the same time they’re huge spiritual persons who have great cosmic connection through which they’regathering informations. | 990 | 4,212 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-13 | latest | en | 0.934965 |
http://www.moneyweek.com/investment-advice/glossary/m/mean-median-mode | 1,368,864,690,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368696381249/warc/CC-MAIN-20130516092621-00036-ip-10-60-113-184.ec2.internal.warc.gz | 570,314,037 | 8,708 | # Glossary
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
Mean, median and mode
Averages are used all the time in finance, usually to justify performance (‘above average’). However, as an investor, you
should realise there are several ways to calculate an average.
The three most common are the mean, median and mode. Let’s say you have five FTSE 100 readings on consecutive days. They are 4,800, 4,900, 4,700, 4,800 and 5,100. The mean is the sum of the five readings divided by the number of readings, so (4,800+4,900+4,700+4,800+5,100) divided by five. That’s 4,860. One of the problems is that extreme outliers can give a misleadingly high or low figure.
The median is the reading in the middle when all the data are ranked in ascending order. So looking at our figures, that’s 4,800. You can use the median to test the mean – if the two are close together, the mean can be taken as representative and not unduly distorted by outliers.
Finally, there’s the mode – the most common reading. In this example, that’s also 4,800.
> | 311 | 1,092 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-20 | latest | en | 0.944549 |
https://stats.stackexchange.com/questions/tagged/convolution | 1,726,286,270,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651548.18/warc/CC-MAIN-20240914025441-20240914055441-00815.warc.gz | 506,745,331 | 54,838 | # Questions tagged [convolution]
Convolution is a function-valued operation on two functions $f$ and $g$: $\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau$. Often used for obtaining the density of a sum of independent random variables. This tag should also be used for the inverse operation of deconvolution. DO NOT use this tag for convolutional neural networks.
481 questions
Filter by
Sorted by
Tagged with
12 views
### Convolution problem [closed]
If the sum of coefficients of a filter h is zero, then for what padding will the sum of elements of a resultant convolved image also be zero after performing convolution with an image f(m,n) ?
11 views
### Why does convolutional neural network use a 2d Filter
Given an input of C,H,W where C is channels the filter is of size X,Y and slides across each channel individually. Why isn't the filter of size C,X,Y and slides across the entire 3d shape? I know of ...
• 236
51 views
### Deriving the pdf of noisy signal: sum of pdf f(s)=1/2+s/2 and a uniformly distributed noise [duplicate]
I am having a hard time to find the pdf of $\widetilde{s}=s+x$. $s$ has a pdf $f(s)=1/2+s/2$ where $s\in(-1,1)$. $x$ is uniformly distributed over $[-\epsilon, \epsilon]$. I am trying to use the ...
38 views
### Sampling line segments within a box
I'm at a bit of a loss for where to start with a sampling problem I'm having so any and all direction would be helpful. I essentially want to sample line segments of identical length within a bounding ...
• 31
343 views
### Distribution after Combining Two Sets of Normal Distribution Samples
Suppose I draw $N1$ samples from distribution $N(\mu_1,\sigma_1^2)$, $N2$ samples from distribution $N(\mu_2,\sigma_2^2)$. These two distributions are independent. Can the combined sample of $N1+N2$ ...
• 295
8 views
### Positional Invariance missing after max pooling operation in custom CNN
I am an early career researcher in computational neuroscience, and I am currently trying to model a robust object recognition model. My model takes a dataset (binary images; where each object is ...
21 views
### the Detailed Architecture of EfficientNetV2-B2
I'm currently studying different neural network architectures and I'm particularly interested in EfficientNetV2-B2. I understand that this model is an improved version of the original EfficientNet, ...
1 vote
26 views
### How should I go about completely decorrelating a digital signal?
So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
• 11
135 views
### Uniform distribution over a triangle
Problem Consider a triangle $T$ with vertices $V_1,V_2,V_3 \in \mathbb{R}^2$ and let \begin{equation*}\begin{aligned} y&=z+v\\ v&\sim\mathcal{N}(0, R)\\ z&\sim\mathcal{U}(T) \end{aligned}\...
• 383
40 views
### Uniform density over 2 segments [duplicate]
Background Let $V_1, V_2 \in \mathbb{R}^2$ be the vertices of a segment and let $z$ be uniformly distributed over that segment. Now consider the random vector \begin{equation*} \begin{aligned} y&=...
• 383
99 views
### Convolution with a pathological distribution
Problem definition Consider the following random bivariate vector \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} where $p_z$ ...
• 383
1 vote
13 views
### Why does GAP at the end of FCN for MTSC work?
I have a binary MTSC (Multivariate Time Series Classification) problem where i train a CNN, namely a FCN (or Fully Convolutional Network) to predict class 0 or class 1 based on a multivariate time ...
• 11
1 vote
51 views
### Percentiles of a distribution of weighted summary statistics
Suppose I have a collection of different independent probability distributions, $\{ P_i(X)\}_{i=1}^N$, each with their own support $I_i$. I know that the $10^{th}$ percentile of a given distribution ...
• 159
247 views
### What is the variance of convolution of two random variables?
Consider two random variables $Z$ and $W$. Given the variances of $Z$ and $W$, how can we compute the variance of their convolution $Z \circledast W$? As an example, please consider the case of noise ...
27 views
### PDF of difference of uniform distributions [duplicate]
Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation. Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
2k views
### Probability that sum of binary variables is even
Let $S_i \in \{0,1\}$, $i=1,\dots,N$ be $N$ independent random binary variables, each taking the value 1 with probability $0 \le p_i \le 1$ (and the value 0 with probability $1-p_i$). I am interested ...
• 4,480
1 vote
24 views
### What is the distribution of a RV with the constant random variable? [duplicate]
For random variables (rv) $X$ and $Y$ on a space $\Omega$: Assume the rv $X\sim f_0$ distributed and $Y(t)=c$ is a constant rv, i.e. $Y\sim \delta(t-c)$ using the $\delta$-distribution as a short ...
• 209
76 views
### Why is the maximum path length for convolutional layer $O(n/k)$ in attention is all you need paper?
In the table-1 third row it is being mentioned. Why is it $O(n/k)$? Take for example 1d convolution of 2 over 9 tokens with stride $1$. It won't be $n/k$ or $9/2=4.5$ rather it would be roughly $n-1$ ...
15 views
### Inference on latent variable with observation of its convolution with itself
Problem I have an inference problem where the data observed are univariate random numbers whose distribution is obtained as follows. A latent random variable X is first sampled from a parametric ...
43 views
### Weighted Average of Uniformly Distributed RV [duplicate]
Let $x \sim U[0,1]$ and $y\sim U[0,1]$. Let $z= \omega\, x+ (1-\omega)\,y$, where $\omega\in[0,1]$. The pdf of $z$ is a trapezoidal distribution over $[0,1]$: \begin{equation*} \begin{aligned} f(z)&...
1 vote
113 views
### Convolutional Neural Networks - Flattening with multiple feature maps
I have a very simple question about CNNs, which I unfortunately couldn't find an explanation for. Imagine we have a CNN, that has four filters (eg right, left, top, bottom edges) each of those outputs ...
142 views
### How to obtain the last convolutional layer of a model in torchvision for applying grad cam?
I'm using efficient net b0 from torchvision for training a classifier for cifar10. I would like to apply grad cam for generating saliency maps for explaining the predictions. However, I'm not sure ...
• 1,008
23 views
### Computing an integral that reduces to $\mathbb{P}[X>Y]$
Problem Evaluate $$I=\int_{-\infty}^\infty \frac{e^{-\frac{1}{2}\left(\frac{x-\mu)}{\sigma} \right)^2}}{\sigma \sqrt{2 \pi}}\frac{1}{1+e^{-x}}\, \mathrm{d}x$$ My attempt Now the first part of the ...
22 views
### Exact Successor State Distribution for a Pendulum
I want to solve the following problem. Suppose we have a simple pendulum, which follows the differential equation \dot{x} = f(x) = [x_2, -\sin(x_1)]^T, \text{with } x=[x_1, x_2]^T. \...
• 307
41 views
### No activation function between two convolutional layers in MUNIT?
I'm reading the code of NVIDIA's MUNIT, the code of the resnet is as follows: ...
• 21
1 vote
205 views
24 views
### Cannot apply simple OLS model in the case of low resolution devices resulting in Fourier space convolution
There's a problem which often comes up within my field and doesn't seem to be approachable analytically. Any suggestions or direction towards the class of problems this falls under would be helpful. ...
• 1
1 vote
184 views
### When is a conditional hazard rate increasing?
Cross posted from Mathoverflow Let $X$ and $Y$ be two random variables such that $X\sim Exp(\lambda)$ and $Y$ have positive support and (strictly) increasing hazard rate $h_Y$. $X$ and $Y$ are ...
134 views
### Convolution of two functions doesn't fit my data as I thought it would
I have simulated a Gaussian curve in 50 bins of data. I have then repeated this many times, drawing the amplitude of the Gaussian from a log-normal distribution. Here are a 10 realizations: (IMAGE 1) ...
• 1,233
50 views
### Estimating the distribution of a sum of two random variables if the family of one of the variables is known
Assume I have a random variable $Y=X_1+X_2$. I want to estimate the distribution $f$ of $Y$ given a sample $y_1,\ldots,y_N$. If this was all that is known about $Y$ the best way would probably be to ...
• 2,671
127 views
• 133
84 views
### what are the differences between receptive field (RF) and field-of-views (FOV) in DeepLab papers?
I am learning the deeplab models. However, some concepts in the papers made me confused. Receptive field (RF) and field-of-views (FOV) are two concepts mentioned in the Deeplabv1 paper. I know that ...
• 311
375 views
### Density of $|t_1 - t_2|$ where $t_1$ and $t_2$ are iid with $P(t) = \alpha e^{-t\alpha}$
I am trying to answer the following question from my quantum mechanics textbook and my probability theory is admittedly rusty (this is not schoolwork as should be clear from my post history on Phys ...
• 203
1 vote
70 views
### Order Statistics - Percentile Range of Normal Mixture of Normals
Say I have draw N values from a normal distribution [$\mu_1$, $\sigma_1$]. Below are 10 sampled points compared to the normal distribution they're sampled from I then create a normal mixture of ...
118 views
### Distribution closed under convolution and truncation followed by convolution
Let $D(\theta)$ denote an absolutely continuous distribution on $\mathbb{R}$. (The finite dimensional vector $\theta$ collects the parameters of the distribution.) Assume that the p.d.f. of $D(\theta)$...
• 525
1 vote
216 views
### How can I build a 6D Convolution Layer in a CNN, using R or Python? [closed]
As stated in the title, I would like to build an N-dimensional Convolutional Layer as part of a Convolution Neural Network, without doing dimensionality reduction on my data; because I have multiple ...
• 113
26 views
### Unclear Architecture of MNIST Neural Network
I am trying to reproduce a Neural Network trained to detect whether there is a 0-3 digit in an image with another confounding image. The paper I am following lists the corresponding architecture: A ...
1 vote
93 views
### What "Convolution filters along the time axis" means?
Suppose that I have a tensor of height:25 and width:50. Height is my temporal axis, therefore I have a window of 25 time steps. Therefore my input tensor is: I want to extract temporal features / ...
• 233
1 vote
42 views
### Relationship between convolutions in neural nets and probabilistic convolution
In probability theory, convolution extends to produce the distribution of the sum of two independent random variables. I've only ever seen this in the context of univariate random variables. However, ...
• 319
1 vote
14 views
### Are Class Activated Maps an example of backpropagated Explainable AI?
Class Activated Maps (NOT GradCAM) is listed in van der Velden et al as a back-propagation approach in table 1, but that is not actually true, is it? CAM doesn't use back-propagation in the method, ...
1 vote
23 views
### How to calculate how much each error source contributes to an overall accuracy metric?
I am building a model of overall accuracy for a robotic system, I have various error sources from assembly, calibrations, measurements, imaging, for each error I have a PDF of the error it induces on ...
114 views
### How to average multiple non-normal distributions?
I have the following statistics of two independent random variables: First random variable: ...
• 39
1 vote
42 views
### Mean conditional on sum
Let $X$ and $Y$ be two random variables. I am interested in how $\mathrm{E}[X | X + Y = z]$ changes as $z$ changes. Intuitively, if $X$ and $Y$ are independent, the conditional mean should be ...
I am trying to do: find 1000 points that represent samples from distribution X with parameters $(a,b,c,\ldots, d)$ be guaranteed that the MLEs for those 1000 points are $(a,b,c,\ldots, d)$ with $99\%$... | 3,128 | 12,155 | {"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": 1, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-38 | latest | en | 0.885642 |
http://www.mathsbuddies.com/2017/04/trignometry-and-inverse-trignometry.html | 1,553,238,396,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202635.43/warc/CC-MAIN-20190322054710-20190322080710-00552.warc.gz | 316,075,098 | 13,081 | # Trigonometry and Inverse Trigonometry functions
Hello Dear Friends,
Hope you Doing well with your Mathematics practise.
Here I’m going to take my last tutorial Trigonometry Functions and their basic Concepts to further step and
yes !!! of course…!!! Thanks to all of you for being with me with patience.
## Trigonometry Functions and Inverse Functions
1. Sin∅ = 1 / cosec∅
sin∅ = P / H
if ∅ = 30౦ and P = 4
then
sin30 = 4/ H
from table we can find sin 30 = 1/2
hence
1/2 = 4/ H
by cross multiplying
H = 8
now we have
P = 4, H = 8 and we can find base side
i.e. P² + B² = H²
4² + B² = 8²
B² = 64 – 16
B² = 48
B = √ 48
B = 6.9
now we can find all the ratios from conversions
### Behaviour with trig functions with signs of angles:-
if in place of ∅ there is -∅ then
• sin(-∅) = – sin∅
• cos (-∅) = cos∅
• tan (-∅) = – tan ∅
• cot -(∅) = – cot∅
• sec (- ∅) = sec ∅
• cosec (-∅) = – cosec ∅
### Some of the Restrictions of Trigonometrical Ratios are:
● If A and B two acute angles and sin A = sin B, then we get A = B. If we cancel sign from both side to get the result, that is wrong.
For Example: If Sin θ = 60°, then θ = 60°. But we should not cancel sign from both sides to get the result.
● Cos 2θ ≠ 2 Cos θ
● Sin A/Sin B ≠ A/B
● Sin A ± Sin B ≠ Sin (A ≠ B)
● Cos θ does not imply cos × θ; in fact, it represents the ratio of perpendicular and hypotenuse with respect to the angle θ of a right-angled triangle.
Cos2 θ means (cos θ)2 or cos θ × cos θ; do not write (cos θ)2 = cos θ2 since cos θ2 implies cos (θ × θ).
Similarly we can write,
sin3 θ for (sin θ)3;
tan5 θ for (tan θ)5;
sec7 θ for (sec θ)7; etc,.
These are the restrictions of trigonometrical ratios need to be followed in case of learning the trigonometric ratios.
these above mentioned rules are to be carried out for each solution of questions of Trigonometry.
### INVERSE TRIGONOMETRIC FUNCTIONS:-
inverse functions behaviour and solutions can be understands from this :-
if sin 30° = 1/2
then
30° = (sin)౼¹ 1/2
generally we can conclude that
if sin∅ = x
them ∅ = sin౼¹ x
and this process will work similarly for other trig ratios.
following are some examples for better understanding of this concept:-
1. Find the general values of sin−1−1 (- √3/2)
Solution:
Let, sin−1−1 (- √3/2) = θ
Therefore, sin θ = – √3/2
⇒ sin θ = – sin (π/3)
⇒ sin θ = (- π/3)
Therefore, the general value of sin−1−1 (- √3/2) = θ = nπ – (- 1)nn π/3, where, n = 0 or any integer.
2. Find the general values of cot−1−1 (- 1)
Solution:
Let, cot−1−1 (- 1) = θ
Therefore, cot θ = – 1
⇒ cot θ = cot (- π/4)
Therefore, the general value of cot−1−1 (- 1) = θ = nπ – π/4, where, n = 0 or any integer.
Hope you’ve found this tutorial about trig identities and inverse trig functions, useful. Please let me know how do you feel with this topic by commenting
Check following articles for other Topics:- | 976 | 2,865 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2019-13 | latest | en | 0.784732 |
https://math.stackexchange.com/questions/723595/closed-ball-in-euclidean-space | 1,582,459,020,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145767.72/warc/CC-MAIN-20200223093317-20200223123317-00553.warc.gz | 465,951,295 | 32,808 | # closed ball in euclidean space
In general metric spaces the closed ball is not the closure of an open ball.
However, I read that in the Euclidean space with usual metric, closed ball is the closure of an open ball. I'm having trouble rigorously proving this? How can I show this?
• Show that $\{x : \|x\| \le 1\}$ is the closure of $\{x : \|x\| < 1\}$; try doing this first in $1$ or $2$ dimensions to get a feel for the general proof. – user61527 Mar 23 '14 at 18:04
The only reason a closed ball might not be the closure of an open ball is when there is a "hole" between a point on the sphere and the centre.
Euclidean spaces have no "holes": if you take a point $x$ on a sphere of radius $r$ centred at a point $x_0$, then there is an interval connecting $x_0$ to $x$ and except $x$ it lies within an open ball of radius $r$.
The same argument works for normed spaces and general geodesic spaces, and with slight modification, for arbitrary length metric spaces.
Hint:
Suppose $B_x(r)$ and $B_x[r]$ are the respectively open and closed balls with centre $x$ and radius $r \gt 0$. If $y \in B_x[r]$ then $||y - x|| \le r \implies ||y - x|| \lt r$ or $||y - x|| = r$. For the first case since $y \in B_x(r)$ it is easy to prove that $y$ is also in the closure since $A \subseteq A^{\circ}$.
For the second case, assume $y$ is not in some closed set $C$ which contains $B_x(r)$. Since $C$ is closed it contains its interior and boundary points and hence $y$ is an exterior point for $C$ and hence for $B_x(r)$. Now consider any neighbourhood of $y$.
Hence try to prove that $y$ is in every closed set which contains $B_x(r)$ and you would be done.
• I tried to prove it using your hint. The first case is obvious and for the second case, I think you are trying to prove it by contradiction. Following your hint, I used the fact that Ext($B_x(r)$)=Int($X\B_x(r)$) and therefore y is an interior point of $X\B_x(r)$, which means that theres an open ball that does not intersect with $B_x(r)$. And now this contradicts the assumption that ||y−x||=r. – nomadicmathematician Mar 23 '14 at 18:30
• But following this proof, I don't quite get which part makes it insufficient to make this proof be generalized to the case of all metric spaces. Could you tell me why this proof can only be applied to the Euclidean space with usual metric? – nomadicmathematician Mar 23 '14 at 18:34
• The argument for the proof looks good. Well first of all I've been learning Analysis only on the Euclidean space and my knowledge on general metric spaces is not great. Either way I think your question has been sufficiently answered by the second response below. – Ishfaaq Mar 24 '14 at 1:15 | 734 | 2,681 | {"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} | 3.65625 | 4 | CC-MAIN-2020-10 | latest | en | 0.941768 |
https://www.pinterest.ch/heatherbobbie/math/ | 1,695,294,327,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506027.39/warc/CC-MAIN-20230921105806-20230921135806-00479.warc.gz | 1,079,916,371 | 115,879 | When autocomplete results are available use up and down arrows to review and enter to select. Touch device users, explore by touch or with swipe gestures.
# Math
2,220 Pins
1d
Collection by
Halloween Fact Families | Halloween Fact Family Haunted House | Halloween Math Craft
Looking for a fun way for your elementary students to practice fact families? These fact family haunted houses are the perfect Halloween craft and Halloween math activity. Students get to practice addition and subtraction or multiplication and division with this Halloween math center activity. Use this Halloween fact family during math workshop, guided math or math centers. You can also use this fact family activity for morning work or as an early finishers activity.
Sweet N Sauer Firsties | K-2 Teaching Resources
Maker’s Monday: Array City
Students use multiplication and division story problems to create their own buildings modeling arrays. When they finish, students match up with the person who had the building that fit within the same fact family. Once they were able to determine their related multiplication facts they were able to see how the commutative property effects the shape of the array.
Heather Johnson 33
5 Activities for Teaching Problem-Solving
Work Backwards - Different Activities, Strategies, and Resources to Help Your Students Become Masters at Problem-Solving in Math
Array city - crafty maths
ARRAYS are Springing Up EVERYWHERE!
Arrays: Array Cities a cute Idea for practicing arrays, repeated addition, and beginning multiplication! (The Owl Teach)
Miss Giraffe's Class
Math to Make Them Think!
The No Prep Teacher
2.G.3 Partition Shapes
Michelle Parker
Domino Effect Puzzle | Math = Love
VK
June 2016 Pick 3
New Florida Standards, New Florida Test Prep! B.E.S.T, F.A.S.T., PM3 Prep!
With the new F.A.S.T. Progress Monitoring comes new test prep modules, simulations, and standards-based practice from iAchieve! We have dozens of materials designed to promote your students' success, from 1st grade through 6th grade.
iAchieve
Number Sense / NUMBER TALKS/Subitizing
Brilliant Ways to Teach Math with Sticky Notes
Teaching Tools | Resources for Teachers from Scholastic
Mr Elementary Math | Math Ideas and Teaching Resources
Number Challenge | Interactive Worksheet | Education.com
Math to Make Them Think! (Fun Games 4 Learning)
Math to Make Them Think! | Fun Games 4 Learning | Bloglovin’
Which Number Doesn't Belong? Math Challenge for Kids
Which One Doesn't Belong? Cards
Which One Doesn't Belong? Cards - The Stem Laboratory
Super simple critical thinking strategy - Southern Fried Teachin'
What Do You Notice?
What Do You Notice? | 565 | 2,647 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2023-40 | latest | en | 0.902176 |
https://waxworksmath.com/Authors/G_M/Martinez/CSHWM/Problems/Chapter9/prob_9_2.m | 1,638,285,901,000,000,000 | text/plain | crawl-data/CC-MAIN-2021-49/segments/1637964359037.96/warc/CC-MAIN-20211130141247-20211130171247-00120.warc.gz | 660,785,631 | 1,481 | % % Examples 9.15 and 9.17 % % epage 392 (cluster/ % % Written by: % -- % John L. Weatherwax 2008-02-20 % % email: wax@alum.mit.edu % % Please send comments and especially bug reports to the % above email address. % %----- clear all; close all; clc; addpath('../../Code/CSTool'); load household; % lump everything into one data matrix: X = [men; women]; X = zscore(X); %-- % Apply Hierarchical clustering (epage 382): %-- if( 1 ) ye = pdist(X,'euclid'); %ye = pdist(X,'cityblock'); z = linkage(ye,'single'); %z = linkage(ye,'complete'); %z = linkage(ye,'average'); %z = linkage(ye,'ward'); [H,T] = dendrogram(z); xlabel('datum instance'); title( 'algomative clustering with single linkage' ); saveas( gcf, 'prob_9_2_hierarchical_linkage', 'epsc' ); fprintf('the cophenet coefficient for this clustering is = %10.5f\n',cophenet(z,ye)); end %-- % Apply k-means clustering () %-- if( 1 ) k = 2; % <- assume we have two clusters [cid,nr,centers] = cskmeans(X,k); % plot the two clusters overlayed with truth: figure; tm=plot( X(1:20,1), X(1:20,2), 'sk' ); hold on; % <- this is the truth tw=plot( X(21:40,1), X(21:40,2), 'dk' ); men_cluster = cid(1); % <- this is what MATLAB called the mens cluster ... if( men_cluster==1 ) % <- so this must be what MATLAB called the womans cluster ... women_cluster=2; else women_cluster=1; end am=plot( X(find(cid==men_cluster),1), X(find(cid==men_cluster),2), 'sr', 'markersize', 10 ); aw=plot( X(find(cid==women_cluster),1), X(find(cid==women_cluster),2), 'dr', 'markersize', 10 ); legend( [tm, tw, am, aw], { 'true men', 'true women', 'approx men', 'approx women' }, 'location', 'best' ); saveas( gcf, 'prob_9_2_k_means', 'epsc' ); end | 545 | 1,671 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2021-49 | latest | en | 0.458185 |
https://it.mathworks.com/matlabcentral/cody/players/96876-takehiko-kobori/solved?page=2 | 1,586,352,607,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371813538.73/warc/CC-MAIN-20200408104113-20200408134613-00262.warc.gz | 518,065,919 | 22,367 | Cody
# Takehiko KOBORI
Rank
Score
51 – 100 of 635
#### Problem 2674. Generalised Hamming Number
Created by: Jean-Marie Sainthillier
Tags hamming
Created by: G K
Tags math
#### Problem 1771. Polygonal numbers
Created by: Jan Orwat
#### Problem 1826. Find vampire numbers
Created by: Andrew Newell
#### Problem 540. Convert hex color specification to MATLAB RGB
Created by: Ned Gulley
#### Problem 2595. Polite numbers. Politeness.
Created by: Jan Orwat
#### Problem 2248. Bell Number calculator
Created by: robin
Tags sets, partition
#### Problem 2734. N-th Odious
Created by: Jan Orwat
#### Problem 2867. Matlab Basics - Rounding III
Created by: Yaz Majeed
Tags dates
#### Problem 2863. Matlab Basics - Set unwanted parts of a vector to zero
Created by: Yaz Majeed
#### Problem 2593. Polite numbers. N-th polite number.
Created by: Jan Orwat
Created by: Ted
#### Problem 2690. Armstrong Number
Created by: VIVEK RUHELA
#### Problem 2733. Evil Number
Created by: Jan Orwat
#### Problem 1548. Vector of numbers divisible by 3
Created by: Marek Kuklis
Tags matlab
Created by: Dan
#### Problem 2202. Flip the bit
Created by: the cyclist
#### Problem 1315. Volume of a sphere given its surface area
Created by: Mário
#### Problem 1421. subtract central cross
Created by: Marco Castelli
Tags empty
#### Problem 2819. Find the 9's Complement
Created by: Pritesh Shah
Tags matlab
#### Problem 2574. Replacing a row
Created by: Marisa
#### Problem 798. Rotate input square matrix 90 degrees CCW without rot90
Created by: Christopher
#### Problem 336. Similar Triangles - find the height of the tree
Created by: Bruce Raine
#### Problem 1786. Create an index-powered vector
Created by: Swapnali Gujar
#### Problem 1547. Relative ratio of "1" in binary number
Created by: Marek Kuklis
Tags matlab, binary
#### Problem 1012. Determine if input is a perfect number
Created by: Binbin Qi
#### Problem 1824. Find and replaces spaces from a input string with *
Created by: Swapnali Gujar
Tags space, string, stars
#### Problem 1090. Create a random logical vector of N elements of which M are true.
Created by: J-G van der Toorn
#### Problem 856. Getting the indices from a matrice
Created by: Jean-Marie Sainthillier
#### Problem 1268. Penny flipping - calculate winning probability (easy)
Created by: Jeremy
Created by: Carl
#### Problem 1925. Smith numbers
Created by: Sky Sartorius
Tags factors, sum
#### Problem 2149. 2倍してみよう - ここからスタート！
Created by: Yoshio
#### Problem 2850. Matlab Basics - Switching Assignments
Created by: Yaz Majeed
#### Problem 2235. Back to basics - mean of corner elements of a matrix
Created by: Swapnali Gujar
#### Problem 1366. Finding peaks
Created by: Selvaraaju Murugesan
#### Problem 1423. sinus function
Created by: Marco Castelli
#### Problem 1997. Compute Fibonacci Number
Created by: Alexander
#### Problem 1693. Calculate distance travelled when given radius and rotations
Created by: Ashutosh datar
#### Problem 1422. frame of the matrix
Created by: Marco Castelli
Tags frame
#### Problem 1052. Elapsed time is -0.005204 seconds.
Created by: Paul Peeling
#### Problem 2129. Sum of odd numbers in a matrix
Created by: Koteswar Rao Jerripothula
#### Problem 1295. Bit Reversal
Created by: @bmtran (Bryant Tran)
#### Problem 2167. Negative Infinity
Created by: priyanka shrivastava
#### Problem 2866. Matlab Basics - Rounding II
Created by: Yaz Majeed
#### Problem 2286. Concatenate two strings
Created by: Debopam
#### Problem 1861. Binary
Created by: Ricardo Sousa
Tags binary
#### Problem 1952. Count decimal digits of a number
Created by: Dimitris Kaliakmanis
Tags numbers
51 – 100 of 635 | 1,020 | 3,723 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2020-16 | latest | en | 0.70457 |
http://www.mathworks.com/matlabcentral/profile/authors/1635175-jean-baptiste-lanfrey?requestedDomain=www.mathworks.com&nocookie=true | 1,481,142,505,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542246.21/warc/CC-MAIN-20161202170902-00248-ip-10-31-129-80.ec2.internal.warc.gz | 580,611,482 | 16,132 | Community Profile
# Jean-Baptiste Lanfrey
### MathWorks
30 total contributions since 2012
Contributions in
View by
Submitted
Simscape Language Equations, Pretty Print
MATLAB code for displaying Simscape language equations in a format that is easy to read.
Solved
Times 2 - START HERE
Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:...
10 months ago
Solved
Make a half wave rectifier
Produce a signal that outputs the given sine wave source when it is greater than zero and outputs zero when it is less than zero...
10 months ago
Solved
Connect blocks in a model
Connect the blocks in the model to produce the following signal: <<http://blogs.mathworks.com/images/seth/cody/connect-blocks...
10 months ago
Solved
Make a checkerboard matrix
Given an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1. Example...
2 years ago
Solved
Find the numeric mean of the prime numbers in a matrix.
There will always be at least one prime in the matrix. Example: Input in = [ 8 3 5 9 ] Output out is 4...
2 years ago
Solved
Finding Perfect Squares
Given a vector of numbers, return true if one of the numbers is a square of one of the other numbers. Otherwise return false. E...
2 years ago
Solved
Free passes for everyone!
_Simply return the name of the coolest numerical computation software ever_ *Extra reward* (get a _freepass_): As an addit...
2 years ago
hai, i want to know in which version of simscape pneumatic system tool box is available.Currently i am using R2009a it is not available
Hi, the pneumatic library has been introduced in release R2009b. Regards Jean-Baptiste
2 years ago | 0
Solved
Summing digits
Given n, find the sum of the digits that make up 2^n. Example: Input n = 7 Output b = 11 since 2^7 = 128, and 1 + ...
3 years ago
Solved
Sum all integers from 1 to 2^n
Given the number x, y must be the summation of all integers from 1 to 2^x. For instance if x=2 then y must be 1+2+3+4=10.
3 years ago
Solved
Back and Forth Rows
Given a number n, create an n-by-n matrix in which the integers from 1 to n^2 wind back and forth along the rows as shown in the...
3 years ago
Solved
Create times-tables
At one time or another, we all had to memorize boring times tables. 5 times 5 is 25. 5 times 6 is 30. 12 times 12 is way more th...
3 years ago
Solved
Find the hypotenuse
Given a and b (the two sides of a right-triangle), find c, the hypotenuse.
3 years ago
Solved
Check if sorted
Check if sorted. Example: Input x = [1 2 0] Output y is 0
3 years ago
Solved
Weighted average
Given two lists of numbers, determine the weighted average. Example [1 2 3] and [10 15 20] should result in 33.333...
3 years ago
Solved
Fibonacci sequence
Calculate the nth Fibonacci number. Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ... Examples: Inpu...
3 years ago
Solved
Swap the first and last columns
Flip the outermost columns of matrix A, so that the first column becomes the last and the last column becomes the first. All oth...
4 years ago
Solved
Remove any row in which a NaN appears
Given the matrix A, return B in which all the rows that have one or more <http://www.mathworks.com/help/techdoc/ref/nan.html NaN...
4 years ago
Solved
Determine whether a vector is monotonically increasing
Return true if the elements of the input vector increase monotonically (i.e. each element is larger than the previous). Return f...
4 years ago
Solved
Is my wife right?
Regardless of input, output the string 'yes'.
5 years ago
Solved
Triangle Numbers
Triangle numbers are the sums of successive integers. So 6 is a triangle number because 6 = 1 + 2 + 3 which can be displa...
5 years ago
Solved
Find all elements less than 0 or greater than 10 and replace them with NaN
Given an input vector x, find all elements of x less than 0 or greater than 10 and replace them with NaN. Example: Input ...
5 years ago
Solved
Select every other element of a vector
Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s...
5 years ago
Solved
Determine if input is odd
Given the input n, return true if n is odd or false if n is even.
5 years ago
Solved
Column Removal
Remove the nth column from input matrix A and return the resulting matrix in output B. So if A = [1 2 3; 4 5 6]; and ...
5 years ago
Solved
Given a and b, return the sum a+b in c.
5 years ago
Solved
Find the sum of all the numbers of the input vector
Find the sum of all the numbers of the input vector x. Examples: Input x = [1 2 3 5] Output y is 11 Input x ...
5 years ago
Solved
Make the vector [1 2 3 4 5 6 7 8 9 10]
In MATLAB, you create a vector by enclosing the elements in square brackets like so: x = [1 2 3 4] Commas are optional, s...
5 years ago
Solved
Pizza!
Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor...
5 years ago | 1,389 | 5,082 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-50 | latest | en | 0.80678 |
http://www.ck12.org/physics/Average-Acceleration/lesson/Average-Acceleration/r9/ | 1,448,425,010,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398444228.5/warc/CC-MAIN-20151124205404-00342-ip-10-71-132-137.ec2.internal.warc.gz | 355,491,115 | 30,354 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are viewing an older version of this Concept. Go to the latest version.
# Average Acceleration
## Define and calculate average acceleration using formulas
0%
Progress
Practice Average Acceleration
Progress
0%
Average Acceleration
To escape from Earth's orbit, space shuttles such as the Atlantis shown here must accelerate to 28,968 kilometers per hour, called the shuttle's escape velocity.
### Average Acceleration
An object whose velocity is changing is said to be accelerating. Average acceleration, a¯\begin{align*}\overline{a}\end{align*} is defined as the rate of change of velocity, or the change in velocity per unit time. The units of acceleration are distance over time squared. A symbol with a bar over it is read as average – so a-bar is average acceleration.
Example: A car accelerates along a straight road from rest to 60. km/h in 5.0 s. What is the magnitude of its average acceleration?
Solution:
The acceleration in this problem is read as kilometers per hour per second. In general, it is undesirable to have two different units for the same quantity in a unit expression. In this case, it is undesirable to have both hours and seconds. To eliminate this problem, we convert the hour units to seconds. Converting the original 60. km/h to m/s, gives 17 m/s.
17m/s5s=3.4m/s2\begin{align*}\frac{17m/s}{5s}=3.4m/s^2\end{align*}
The acceleration is 3.4 m/s2.
Example: An automobile is moving along a straight highway in the positive direction and the driver steps on the brakes. If the initial velocity is 15.0 m/s and 5.0 s is required to slow down to 5.0 m/s, what was the car’s acceleration?
Solution:
a¯=ΔvΔt=10. m/s5.0 s=2.0 m/s/s\begin{align*}\overline{a} = \frac{\Delta v}{\Delta t} = \frac{-10. \ \text{m/s}}{5.0 \ \text{s}} = -2.0 \ \text{m/s/s}\end{align*}
Note that an acceleration is merely a change in velocity. This change can be either positive or negative. A negative change, such as that in the example problem above, is sometimes called negative acceleration or deceleration.
#### Summary
• Average acceleration is the rate of change of velocity, or the change in velocity per unit time.
#### Practice
Complete the activity found at this URL to help you understand acceleration.
Review
1. The velocity of a car increases from +2.0 m/s to +16.0 m/s in a time period of 3.5 s. What was the average acceleration?
2. If an automobile slows from +26 m/s to +18 m/s in a period of 4.0 s, what was the average acceleration?
3. If a runner increases his velocity from 0 m/s to +20 m/s in 2.0 s, what was his average acceleration?
4. If a runner decreases his velocity from +20 m/s to +10 m/s in 2.0 s, what was his average acceleration? | 756 | 2,823 | {"found_math": true, "script_math_tex": 3, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2015-48 | longest | en | 0.830211 |
finguru.org | 1,642,401,772,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300343.4/warc/CC-MAIN-20220117061125-20220117091125-00526.warc.gz | 282,726,745 | 26,322 | # Clean. Simple. 100% Finance.
## What is interest rate?
In Banking, Finance on July 2, 2012 at 3:56 pm
Interest rate is the amount payable to creditor by the debtor for the use of money for the certain period or the money earned by an investor on a debt instrument for specific time. Here creditor is the person who gives the loan or makes investment in a debt instrument while debtor is a person who takes the loan or an institution who float a debt instrument like debentures, debt securities etc. Interest rate is very widely used terms and it is not only charged only for loans but also charged for mortgages, credit cards and unpaid bills.
Interest rate is dependent upon the amount of loan, duration, financial position on debtor, type of loan (e.g.: secured/unsecured), economic condition of the country and the economic policy of the country. It is very simple to understand such as a person takes a home loan for 8% interest rate or 18% interest rate, in first condition he will be able to repay the loan very early than the second condition assuming the EMI (every monthly instalment) in both the conditions are the same.
Interest rate can be expressed in monthly, quarterly, half-yearly and annual rate which is sometimes described as mode of payment for annual interest payments. For example: 18% annual interest rate can be paid through different mode of payment – monthly 1.5%, quarterly 4.5%, half-yearly 9% and annually 18% at one time.
Basically, interest is of 2 types – simple interest and compound interest. Simple Interest is paid on amount of money taken as loan or mortgage and can be calculated by using the formula:
Simple Interest
I = P * r * t
Here:
‘I’ stands for Interest
‘P’ stands for principal
‘r’ stands for rate and
‘t’ stands for Time.
For example, if I invest \$1000 (the Principal) at a 5% annual rate for 1 year the simple interest calculation
I=P * r * t
\$50 = \$1000 x 5 % x 1 yr
Compound Interest
Compound interest is interest that is paid on both the principal and on any interest from past years. It’s often used when someone reinvest any interest they gained back into the original investment. For example, if I got 15% interest on my \$1000 investment, the first year and I reinvested the money back into the original investment, then in the second year, I would get 15% interest on \$1000 and the \$150 I reinvested. Over time, compound interest will make much more money than simple interest. The formula used to calculate compound interest is:
M = P( 1 + i )n
M is the final amount including the principal.
P is the principal amount.
i is the rate of interest per year.
n is the number of years invested.
Applying the Formula
Let’s say that I have \$1000.00 to invest for 3 years at rate of 5% compound interest.
M = 1000 (1 + 0.05)3 = \$1157.62.
You can see that my \$1000.00 is worth \$1157.62.
Notes: With the simple interest, my worth would have been just 1000*.05*3 = \$1150, therefore I gained \$7.62 more due to compound interest.
These topics will be covered in other blogs:
• How interest rates are decided in different countries?
• Why interest rates are different in different banks, different types of loans?
• Why Credit cards charge very heavy interest rates like 35% or 40%?
• How Interest rates are linked with country economy – what will happen if it will go too up or too low?
• What is NPA? | 804 | 3,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2022-05 | latest | en | 0.962163 |
http://quizlet.com/folders/13175132/test | 1,416,803,171,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416400380358.68/warc/CC-MAIN-20141119123300-00145-ip-10-235-23-156.ec2.internal.warc.gz | 257,572,313 | 10,206 | ## ← Back to Combo with "Conceptual Physics--Chapter 8: Rotational Motion" and 3 others
Options
NAME
### Question limit
of 77 available terms
(30 exact duplicates found)
### 5 Matching questions
2. Formula for Torque
3. Tangential speed~
4. Re call the equilibrium rule in Chapter 2--that the sum of the forces acting on a body or any system must equal zero for mechanical equilibrium. That is, ∑F = 0. We now see an additional condition. The *net torque* on a body or on a system must also be zero for mechanical equilibrium...
5. rotational inertia
1. a ~radial distance × rotational speed.
In symbol form, v ~ rω
2. b Torque = r x F
where r = the displacement vector, F = the force vector
3. c Reluctance or apparent resistance of an object to change its state of rotation, determined by the distribution of the mass of the object and the location of the axis of rotation or revolution.
4. d ...(∑T = 0, where T stands for torque). Anything in mechanical equilibrium doesn't accelerate--neither linearly nor rotationally.
5. e I = 2/5 mr²
### 5 Multiple choice questions
1. Newton's First Law states that a body in motion stays in motion at a constant speed and in a straight line unless acted upon by a net force; therefore, a force must be pulling inward on an object moving in a circular path in order to prevent it from moving in a straight path.
2. I = ½ mr²
3. This force is not an actual force; it is a fictitious force that seems to pull outwards on an object on a circular path. This effect is due to inertia, or the tendency for a moving object to follow a straight path.
4. the amount of time it takes to complete one cycle (1 revolution)
5. Motion of an object turning around an axis that lies outside the object.
### 5 True/False questions
1. Penduluman object hanging from a fixed point which, when pulled back and released, is free to swing back down by gravity and inertia
2. Conservation of angular momentumWhen no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.
3. RevolveDevice for increasing (or decreasing) a force or simply changing the direction of a force
4. tangential speedLinear speed along a curved path.
5. center of massPoint at the center of an objects weight distribution, where the force of gravity can be considered to act.
Create Set | 579 | 2,476 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2014-49 | latest | en | 0.864469 |
https://ip-numaram.com/note-992 | 1,675,626,267,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500288.69/warc/CC-MAIN-20230205193202-20230205223202-00854.warc.gz | 327,265,067 | 5,710 | # Math app with steps
We'll provide some tips to help you choose the best Math app with steps for your needs. Math can be a challenging subject for many students.
## The Best Math app with steps
In addition, Math app with steps can also help you to check your homework. Solving linear equations is the most computationally challenging part of first-order and second-order numerical algorithms. The existing direct and indirect methods either require a large amount of computation or compromise the accuracy of the solution. In this paper, an easy to calculate decomposition method is proposed to solve the sparse linear system in cone optimization. Its iteration is easy to handle, highly parallelizable, and has a closed form solution. The algorithm can be easily implemented on a distributed platform, such as a graphics processing unit, with an order of magnitude of time improvement.
The application information service mentioned in these Provisions refers to the activities that provide users with services such as text, picture, voice, video and other information production, reproduction, release and dissemination through applications, including instant messaging, news information, Knowledge Q & A, forum community, live webcast, e-commerce, online audio and video, life services and other types. To test this new feature, open the photos app and view your recent photos. Don't click on the picture to open it in full screen; Instead, place your finger on the photo and start dragging your finger across the screen. When thumbnails start to float on other photos, you can switch back to the messaging application without lifting your finger..
Functions, equations and inequalities are closely related and mutually transformed. Using the idea of equations, we can solve the analytic formula of functions by the method of undetermined coefficients. By equivalently transforming functions into equations of curves, we can discuss the number of square roots (or the number of zero points of functions) with the help of the image of functions. Because functions and inequalities have close internal relations, inequality is often used as a tool to study the properties of functions, For example, to prove (discuss) the monotonicity of the function and discuss the maximum value of the rain number, when dealing with the problem of constant inequality, it is often necessary to use the constructor to convert the image or property of the function, so as to determine the range of relevant parameters. The mutual transformation between the function and the equation and inequality is not only manifested in the quadratic function and the one-dimensional quadratic equation and the one-dimensional quadratic inequality, that is, the three ones, but also in the exponential function, Logarithmic functions, exponential and logarithmic equations, and exponential and logarithmic inequalities are mainly manifested in the following four aspects in solving problems.
In addition, the total amount of homework should not be too much, and additional homework should be reduced or not arranged, so that children can feel that learning and homework are simple and interesting. There is no universally correct time to do homework. In some families, children had better deal with their homework immediately after school at noon in the afternoon; Other young people may do the best, and if they spend their after-school time relaxing and playing, and leave their homework for the evening, they may feel rejuvenated. Give your child a say in making decisions. Homework often becomes the source of conflict between parents and children - Johnny, why can't you just do your homework without arguing?—— But if you agree to a fixed time and place, you can eliminate the two most common causes of homework related disputes.
GRE includes three forms: single choice, multiple choice and blank filling. It provides online calculators. The difficulty is basically equivalent to the basic knowledge points of mathematics in senior one in China: arithmetic, basic algebra, geometric concepts and data analysis. Therefore, most Chinese candidates can get high marks in mathematics. | 763 | 4,165 | {"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} | 3.4375 | 3 | CC-MAIN-2023-06 | latest | en | 0.922692 |
https://byjus.com/question-answer/match-the-given-numbers-with-their-respective-additive-inverse-2/ | 1,708,490,854,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473370.18/warc/CC-MAIN-20240221034447-20240221064447-00806.warc.gz | 170,805,689 | 23,122 | Question
# Match the given numbers with their respective additive inverse.
A
16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
-6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
## The additive inverse of a number 'a' is that number, which when added to 'a', yields zero i.e., -a. Hence, the additive inverse of: 6 is -6 -6 is 6 16 is −16 −16 is 16
Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Reciprocal of a Number
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program | 241 | 717 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10 | latest | en | 0.871047 |
https://paranormalis.com/threads/i-am-an-expert-on-john-titor-feel-free-to-engage-me-in-conversation.3005/page-46 | 1,601,118,987,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400241093.64/warc/CC-MAIN-20200926102645-20200926132645-00217.warc.gz | 540,792,131 | 18,824 | # I Am An Expert On John Titor. Feel Free To Engage Me In Conversation
#### HikuTechy
##### Junior Member
If John could not get back to his original time line how was he supposed to get a computer and bring it back to a time line he could not return to?
The lines are infinitely many, so there are many, many lines which are near identical to his original line any of which he could return to. Those lines might have tiny differences of no consequence to the returning Titor.
#### Yeats
##### Junior Member
I am afraid that I do not see how one could ever return to one's original timeline after leaving it (if leaving it is indeed possible.) I shall try to illustrate what I mean.
The time traveler lives along timeline A (black line).
At point X, the time traveler goes back in time to point -X (via upper red line).
At the moment of transfer, timeline A branches off into timeline B (upper gray line) and timeline C (green line). The B timeline is that state of the universe which continues to exist after the departure of the traveler. (It may or may not be the same as timeline A.) The traveler, at point -X, will now move along the C timeline.
At point Y, the traveler goes forward in time to point +Y (via lower red line).
At the moment of transfer, timeline C branches off into timeline D (blue line) and timeline E (lower gray line). The E timeline is the state of the universe which continues to exist after the departure of the traveler. (It may or may not be the same as timeline C.) The traveler, at point +Y, then moves along the D timeline.
Red lines do not indicate timelines, but rather the instantaneous transfers of the traveler from one point to another.
I apologize both for the crudeness of the illustration and my lack of knowledge concerning these things, but it seems to me that if the act of time travel in itself changes the timeline, then our traveler can never return to his origin point.
Last edited:
#### Mayhem
##### Staff
But then is there any evidence to actually know this or is it just repeating what 'some person' came up with at an earlier point?
#### Yeats
##### Junior Member
But then is there any evidence to actually know this or is it just repeating what 'some person' came up with at an earlier point?
No. There is no evidence (that I know of) for either a timeline other that the one we are presently living in or for a practical method of time travel itself. I was just playing around with the concept.
Last edited:
#### steven chiverton
##### Senior Member
did anyone see that youtube video of someone admitting to creating the john titor hoax and the time machine was just a prop he put together .
#### lamdo263
##### Member
did anyone see that youtube video of someone admitting to creating the john titor hoax and the time machine was just a prop he put together .
This is strongly said intimated not to be correct. It's now come out that the Titor story was a patched together, practice in real time travel, but with fictional elements added so that people would always fall into the culpable denial zones. I feel that this said patched together demonstration, was made to warn the general public that would catch on, to prepare for rough times ahead. Those in secret government could do this no other way, except by a sacrosanct experiment. That's all the entire Ttior thing is.
So the test question for Titor's time machine might be, because the right answer is elusive, { Please tell us does the Modified GE time displacement unit that John Titor have a double overlapping singularity and if so how is this placed by the rotating Tippler cylinders? } The correct or acceptable answer could be. tuna fish, either plain or on bread and a man named Sandoval.
You see there's no right or wrong answer. Believing the Titor story at times can be similar to really getting psyched up about Muzac played in an elevator. Possably peaches is also a very good answer.
#### PaulaJedi
##### Survivor
This is strongly said intimated not to be correct. It's now come out that the Titor story was a patched together, practice in real time travel, but with fictional elements added so that people would always fall into the culpable denial zones. I feel that this said patched together demonstration, was made to warn the general public that would catch on, to prepare for rough times ahead. Those in secret government could do this no other way, except by a sacrosanct experiment. That's all the entire Ttior thing is.
So the test question for Titor's time machine might be, because the right answer is elusive, { Please tell us does the Modified GE time displacement unit that John Titor have a double overlapping singularity and if so how is this placed by the rotating Tippler cylinders? } The correct or acceptable answer could be. tuna fish, either plain or on bread and a man named Sandoval.
You see there's no right or wrong answer. Believing the Titor story at times can be similar to really getting psyched up about Muzac played in an elevator. Possably peaches is also a very good answer.
One of the Haber's sent Razimus an e-mail and admitted to it being hoax, but stance has been why? Why such an elaborate hoax? To hopefully sell a book? To send a message to someone?
#### lamdo263
##### Member
One of the Haber's sent Razimus an e-mail and admitted to it being hoax, but stance has been why? Why such an elaborate hoax? To hopefully sell a book? To send a message to someone?
Aaah' I'm sorry to beg to differ, I mean you can even viciously flamingo dance at me, with insults if you want. But know for sure that the Titor Chronicles are a mixture of creative writing and actual time travel. I found this and figured as much. This fabricated with the probable help of the military, had to do with a warning about these times. How did Nostradamus predicted for year 2020?, In 2020 there will be a plague. That's probably covid 19. Second prediction, civil unrest. This was probably the national protest and rioting. Lastly, he predicted an alien invasion. What I'm thinking here, is new siding on the grays that are already in residence here. Like putting a scary cape and mask on Auntie Jane.
#### lamdo263
##### Member
A little help here, cos this really isn't time travel discussion. The past character DV was real. He existed thousands of years ago, was of royal lineage, but for sure I don't know where he was raised. What your trying to do is to put a current day spin on this and it just isn't that way. He would say, get more people that are common every day folks into space. Do this now, see if you can train them without picking people that only you want out there and don't rig the game.
That's exactly what he'd tell you and I would not deviate one iota from what he would tell you. Second on DV, he did know gangs, induvial criminals and all kinds of shifty people. I'd be aware of that fact and DON'T try to play him as a card through his reincarnate. He may even carry curses still and is extremely dangerous to mess with. Others, not your grow at home aliens sorts, still know he's here. Just treat him right and use some common sense.
2.On Obama, this was a card that had to be played due to the fact that he is in a way a reincarnate of Egypt's king Akhenaten. This like DV is part of a royal flush hand of cards, regardless of how you look at him. I don't know if he is at all the cause of the rioting? It may be that associative communities in reference to race rioting was just a disturbed community to begin with?
3.On Lincoln. Do not know if the private appearance of him as a spirit of an active president was a real spirit or radionics or not. Seemed real enough to me.
These three cards, only temporarily got this society out of trouble. But what the deal is here, is a two year student should be able to apply for a job position on a space colony and then be trained to work there without getting a memory erasing pill and all that jazz. You're not getting this if you want to modulate this too. .Just do it without question and get more people out there. Very strongly suggest this.
On hogging AI so you both control the power and money associated with AI in machines. Let me inform you all, that you don't have AI. You don't even know what it is. On EM now being said to place AI into his Dojo large super computer, I don't even know what that will do. Regardless of how good a programmer one becomes and or how adept they may be at understanding AI, totally dedicated AI in a machine that large may become uncontrolled, because AI in most machines become its own entity after while.
On Titor, yeah for a little bit. it worked. A lot of people got the heads up. But do realize and in no way am I kidding deviate from what DV would have suggested. If you, or the collective behind these shenanigans fail to get the message, you'll suffer horribly for it. Remember, you bought this up, I didn't...Oh time travel discussion, blah blah blah. | 1,995 | 8,949 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2020-40 | latest | en | 0.934706 |
http://en.wikipedia.org/wiki/User_talk:Mathmensch | 1,408,557,232,000,000,000 | text/html | crawl-data/CC-MAIN-2014-35/segments/1408500811391.43/warc/CC-MAIN-20140820021331-00139-ip-10-180-136-8.ec2.internal.warc.gz | 63,028,089 | 11,215 | # User talk:Mathmensch
## Welcome
Getting Started
Getting Help
Policies and Guidelines
The Community
Things to do
Miscellaneous
Hello Mathmensch,
Thanks for pointing out that the Tagore-Einstein conversation link was broken. I fixed it but with a link which appears to have more details than some of the alternatives. Keep it up.
Cheers,
Webmaestro365 (talk) 19:24, 6 July 2013 (UTC)
Thank you very much! --Mathmensch (talk) 22:31, 6 July 2013 (UTC)
No it doesn't follow. A unit in a ring is any invertible element. The only thing that follows is that they are associated, but all units are trivially associated. Your edit has no place there in any form. At first I thought you were purposefully inserting subtle errors into Wikipedia (eg. your taylor edit which was reverted too), but since you insist on it, I think you just need to stop editing things you don't understand. 94.113.251.98 (talk) 16:56, 17 February 2014 (UTC)
I'm sorry but I can't see where I misunderstood the article Cancellation law. Anyhow, welcome to Wikipedia and I am not trying to purposefully insert errors, as well as not trying to disencourage you. You may read the article and decide then.
I also work for wikibooks, see b:Partial Differential Equations. Please forgive my mistake at the Taylor series article :-) --Mathmensch (talk) 17:02, 17 February 2014 (UTC)
Let me give you an example then: Integers are surely a UFD. you can see that 2 = 1 * 2; But also 2 = (-1) * (-2). It doesn't follow that 1 = -1. That's because 2 and -2 are only associated, not equal (as is stated in the article). So I don't see how are you using the cancellation law.94.113.251.98 (talk) 17:11, 17 February 2014 (UTC)
I see, you are right, sorry. I didn't notice this and it was not my intention to purposefully insert wrong information. Such things happen. --Mathmensch (talk) 17:15, 17 February 2014 (UTC)
And by the way, measuring my edits by one mistake is kind of harsh. --Mathmensch (talk) 17:17, 17 February 2014 (UTC) | 545 | 1,997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2014-35 | latest | en | 0.989147 |
https://netket.readthedocs.io/en/latest/api/_generated/vqs/netket.vqs.VariationalMixedState.html | 1,709,173,075,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474775.80/warc/CC-MAIN-20240229003536-20240229033536-00517.warc.gz | 438,667,691 | 15,107 | # netket.vqs.VariationalMixedState#
class netket.vqs.VariationalMixedState#
Bases: VariationalState
Inheritance
Attributes
hilbert#
The descriptor of the Hilbert space on which this variational state is defined.
hilbert_physical#
model_state#
The optional pytree with the mutable state of the model.
n_parameters#
The total number of parameters in the model.
parameters#
The pytree of the parameters of the model.
variables#
The PyTree containing the parameters and state of the model, used when evaluating it.
Methods
expect(O)#
Estimates the quantum expectation value for a given operator $$O$$ or generic observable. In the case of a pure state $$\psi$$ and an operator, this is $$\langle O\rangle= \langle \Psi|O|\Psi\rangle/\langle\Psi|\Psi\rangle$$ otherwise for a mixed state $$\rho$$, this is $$\langle O\rangle= \textrm{Tr}[\rho \hat{O}]/\textrm{Tr}[\rho]$$.
Parameters:
O (AbstractOperator) β the operator or observable for which to compute the expectation value.
Return type:
Stats
Returns:
An estimation of the quantum expectation value $$\langle O\rangle$$.
expect_and_forces(O, *, mutable=None)#
Estimates the quantum expectation value and the corresponding force vector for a given operator O.
The force vector $$F_j$$ is defined as the covariance of log-derivative of the trial wave function and the local estimators of the operator. For complex holomorphic states, this is equivalent to the expectation gradient $$\frac{\partial\langle O\rangle}{\partial(\theta_j)^\star} = F_j$$. For real-parameter states, the gradient is given by $$\frac{\partial\partial_j\langle O\rangle}{\partial\partial_j\theta_j} = 2 \textrm{Re}[F_j]$$.
Parameters:
• O (AbstractOperator) β The operator O for which expectation value and force are computed.
• mutable (Union[bool, str, Collection[str], DenyList, None]) β Can be bool, str, or list. Specifies which collections in the model_state should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. This is used to mutate the state of the model while you train it (for example to implement BatchNorm. Consult Flaxβs Module.apply documentation for a more in-depth explanation).
Return type:
tuple[Stats, Any]
Returns:
An estimate of the quantum expectation value <O>. An estimate of the force vector $$F_j = \textrm{Cov}[\partial_j\log\psi, O_{\textrm{loc}}]$$.
Estimates the quantum expectation value and its gradient for a given operator $$O$$.
Parameters:
• O (AbstractOperator) β The operator $$O$$ for which expectation value and gradient are computed.
• mutable (Union[bool, str, Collection[str], DenyList, None]) β
Can be bool, str, or list. Specifies which collections in the model_state should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. This is used to mutate the state of the model while you train it (for example to implement BatchNorm. Consult Flaxβs Module.apply documentation for a more in-depth explanation).
• use_covariance β whether to use the covariance formula, usually reserved for hermitian operators, $$\textrm{Cov}[\partial\log\psi, O_{\textrm{loc}}\rangle]$$
Return type:
tuple[Stats, Any]
Returns:
An estimate of the quantum expectation value <O>. An estimate of the gradient of the quantum expectation value <O>.
Estimates the gradient of the quantum expectation value of a given operator O.
Parameters:
• op (netket.operator.AbstractOperator) β the operator O.
• is_hermitian β optional override for whether to use or not the hermitian logic. By default itβs automatically detected.
• use_covariance (bool | None) β
• mutable (bool | str | Collection[str] | DenyList | None) β
Returns:
An estimation of the average gradient of the quantum expectation value <O>.
Return type:
array
init_parameters(init_fun=None, *, seed=None)#
Re-initializes all the parameters with the provided initialization function, defaulting to the normal distribution of standard deviation 0.01.
Warning
The init function will not change the dtype of the parameters, which is determined by the model. DO NOT SPECIFY IT INSIDE THE INIT FUNCTION
Parameters:
• init_fun (Optional[Callable[[Any, Sequence[int], Any], Union[ndarray, Array]]]) β a jax initializer such as jax.nn.initializers.normal(). Must be a Callable taking 3 inputs, the jax PRNG key, the shape and the dtype, and outputting an array with the valid dtype and shape. If left unspecified, defaults to jax.nn.initializers.normal(stddev=0.01)
• seed () β Optional seed to be used. The seed is synced across all MPI processes. If unspecified, uses a random seed.
quantum_geometric_tensor(qgt_type)#
Computes an estimate of the quantum geometric tensor G_ij.
This function returns a linear operator that can be used to apply G_ij to a given vector or can be converted to a full matrix.
Parameters:
qgt_type β the optional type of the quantum geometric tensor. By default it is automatically selected.
Returns:
A linear operator representing the quantum
geometric tensor.
Return type:
nk.optimizer.LinearOperator
reset()#
Resets the internal cache of th variational state. Called automatically when the parameters/state is updated.
to_array(normalize=True)#
Returns the dense-vector representation of this state.
Parameters:
normalize (bool) β If True, the vector is normalized to have L2-norm 1.
Return type:
Array
Returns:
An exponentially large vector representing the state in the computational basis.
to_matrix(normalize=True)[source]#
Returns the dense-matrix representation of this operator.
Parameters:
normalize (bool) β If True, the matrix is normalized to have trace 1.
Return type:
Array
Returns:
An exponentially large matrix representing the state in the computational basis.
to_qobj()[source]#
Convert this mixed state to a qutip density matrix Qobj.
Returns:
A qutip.Qobj object. | 1,426 | 6,034 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-10 | longest | en | 0.69561 |
https://au.mathworks.com/matlabcentral/cody/problems/558-is-the-point-in-a-triangle/solutions/1985045 | 1,601,557,878,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402131412.93/warc/CC-MAIN-20201001112433-20201001142433-00285.warc.gz | 266,163,214 | 16,489 | Cody
Problem 558. Is the Point in a Triangle?
Solution 1985045
Submitted on 21 Oct 2019 by Eugene Kronberg
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
Test Suite
Test Status Code Input and Output
1 Pass
Triangle = [0, 0; 1, 0; 1, 1]; Points = [0, 0.5] y_correct = 0; assert(isequal(your_fcn_name(Points,Triangle),y_correct))
Points = 0 0.5000 v = 0 -1.0000 0.8944 -0.4472 0.8944 0.4472
2 Pass
Triangle = [0, 0; 1, 0; 1, 1]; Points = [0.8, 0.5] y_correct = 1; assert(isequal(your_fcn_name(Points,Triangle),y_correct))
Points = 0.8000 0.5000 v = -0.8480 -0.5300 0.3714 -0.9285 0.3714 0.9285
3 Pass
Triangle = [0.8147, 0.9134; 0.9058, 0.6324; 0.1270, 0.0975]; Points = [0.8, 0.7; 0.9, 0.4] y_correct = [1 0]; assert(isequal(your_fcn_name(Points,Triangle),y_correct))
Points = 0.8000 0.7000 0.9000 0.4000 v = 0.0687 0.9976 0.8427 -0.5384 -0.7451 -0.6670 v = -0.1639 0.9865 0.0249 0.9997 -0.9312 -0.3644 | 442 | 978 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-40 | latest | en | 0.614813 |
https://techfindings.net/archives/date/2022/10 | 1,718,357,699,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861545.42/warc/CC-MAIN-20240614075213-20240614105213-00205.warc.gz | 512,910,425 | 14,140 | # Monthly Archives: October 2022
## Stable Diffusion – Playing with parameters
It is fun to make images with Stable Diffusion, but it is also frustrating when the result is not what you expect and it takes long time generate new pictures.
I have been playing with the cpu-only-branch of Stable Diffusion on a linux computer with an 8th Generation Core i7 CPU and 16GB of RAM and here comes some findings.
## Basic prompt and parameters
I wanted to generate a useful picture for my Dungeons & Dragons game. So, as a somewhat qualified start I did:
fantasy art of village house, cliff, well, town square, market and storm, in the style of greg rutkowski
I used
• seed=2 (bacause I did not like seed=1)
• Sample Steps=10
• Guide=7.5
• Sample Model=Euler Ancestral
• Resolution=512×512
• The 1.4 model (the small one)
Not very far from default settings. My performance is about 10s per sample step, thus this picture took 1m40s to generate:
This is the unmodified 512×512 picture. Below I will publish smaller/scaled picture but unless otherwise mentioned they are all generated as 512×512. This picture was not so far from what I had in mind, but I don’t see any well or market, or town square.
## Sample Methods
I generated exactly the same thing, only changing the Sample Method parameter:
Three of the sample methods took (roughly) twice the time (200% in the name above). I can at least draw the conclusion that the sampling method is not just a mathematical detail but something that actually affects the output quite much.
## Sampling Steps
Next thing was to try different number of sampling steps, from 2 to 99:
## Guide
There is a guide parameter (how strongly the image should follow the prompt) and that is not a very obvious parameter. For this purpose i used 30 Sampling Steps and tried a few guide values (0-15 are allowed values):
To my amateur eye, guide seems to be mostly about contrast and sharpness. I do not see that the pictures resembles my prompt more or less.
## Resolution
I generated 6 images using different resolutions. Sampling Steps is now 20.
To my surprise the lower than 512×512 came out ok, I have had very bad results at lower resolutions below. It is obvious that changing the resolutions creates a different picture, like with a different seed with the same prompt. The smaller pictures are faster and the larger slower to generate (as indicated by the %), and the largest image caused my 16GB computer to use its swap (but I think something else was swapped out). My conclusion is that you can not generate many pictures a low resolution, and then regenerate the ones you want with higher resolution and the same seed (there are probably other ways to upscale).
## Image type
So far all images have been “fantasy art”. I tried a few alternatives with 20 Sampling Steps:
This changes much. The disposition is similar but the architecture is entirely different. What if I like a drawing with the roof style of fantasy art?
## Artists
So far I have been using Greg Rutkowski for everyting (at first opportunity I will buy a collection of Greg Rutkowskis work when I find one – so far I have not found any). How about different artists:
## Dropping Keywords
So far I have not seen much of wells and markets in my pictures. What about dropping those keywords from the prompt?
## Model Choice
There is a 1.4-model to download, and a larger (full) version. What is the difference. I tried three prompts (all fantasy art in the style of greg rutkowski):
• old well in medieval village
• medieval village on cliff
• medieval village under cliff
Conclusion here is that the result is slightly different depending on model, but it is not like it makes a huge difference when it comes to quality and preference.
## Trying to get a well
Not giving up on getting a picture of a well I made 9 pictures, using different seeds and the prompt:
• fantasy art old well in medieval village, greg rutkowski
None of them contains a well as I think of a well. If I do an image search on Google I get plenty of what I want. Perhaps Stable Diffusion does not know what a well looks like, or perhaps this is what fantasy art and/or Greg Rutkowski would draw wells as.
## Conclusion
I did this because I thought I could learn something and I did. Perhaps you learnt something from reading about my results. It is obviously possible to get cool pictures, but what if you want something specific? The prompt is important, but if you are playing with the wrong parameters you may be wasting you time.
## Stable Diffusion CPU-only
I spent much time trying to install Stable Diffusion on an Intel NUC Hades Canyon with Core i7 (8th Generation) and an AMD RX Vega (4GB), with no success. 4GB is tricky. AMD is trickier.
I gave up on my NUC and installed on my laptop with Windows, GeForce GTX 1650. That worked, and a typical image (512×512 and 20 samples) takes about 3 minutes to generate.
For practical reasons I wanted to run Stable Diffusion on my Linux NUC anyway, so I decided to give a CPU-only version of stable diffusion a try (stable-diffusion-cpuonly). It was a pretty easy install, and to my surprise generation is basically as fast as on my GeForce GTX 1650. I have 16GB of RAM and that works fine for 512×512. I think 8GB would be too little and as usual, lower resolutions than 512×512 generates very bad output for me.
So when you read “stable diffusion requires Nvidia GPU with at least 4GB of RAM”, for simple hobby purposes any computer with 16GB of RAM will be fine.
## Elemental Dice 1-5
I just received 5 new Elemental Dice. Only two of the new ones were metal (Sa,Ce) and three were embedded in resin (S, Mn, Hg). Here is a picture of the complete collection.
As you can see the Ce(rium) die has already started to deteriorate. It came like that, I am not the only one, and we will see about replacement shipments.
I added Ce and Sa to my density table:
All dice have a lower wight than exptected. First, the edge are rounded and text and die-numbers are engraved or carved out of the metal cube so it is expected to not be 100%. Some dice are just plated, for obvious reasons (Rh,Pd,Pt,Au) so most part of those are probably Fe/Ni-something. I do not know what is up with Carbon, I suppose it is another form of pure carbon than Graphite.
## Windows 11 22H2, Docker, on Dell XPS 15 7590
I have a Dell XPS 15 7590 that I use for running Docker and Business Central images. I have used Windows 10 for two years experiencing some occational problems with starting the Docker images, so I decided to finally upgrade to Windows 11.
Bad timing. It seems 22H2 introduced a bug for this computer (link to Dell forum).
Automatically updating to Windows 11 failed. Blue Screen on boot: INACCESSIBLE_BOOT_DEVICE. But it recovered from that and booted back to Windows 10.
I decided to make a clean installation of Windows 11 Pro. That was ok, until i installed Docker (4.12.0), then I got the same Blue Screen and this time I found no way to recover. I think the problem has to do with Hyper-V-activation, but there are probably more details I am not aware of.
Eventually, after several installations and restore efforts, things seem to work:
• BIOS AHCI (not RAID, but I do not think that matters)
• BIOS Virtualization ON
• BIOS Virtual Direct I/O OFF
• Applied KB5017389
I have now learnt to use Restore Points in Windows. Very useful to make a manual restore point before a significant configuration change. When the computer fails to start properly, you can navigate to the option of using a Restore Point, and that has worked several times (and every time) for me now. You need to have a recovery key for the computer (I got mine from aka.ms/recoverykey, need to log in of course, for a “personal” computer). It is the same key for every restore point so you can write it down and keep it.
#### Windows 11 impressions
This is the first time I install and use Windows 11. I am actually somewhat satisfied, even impressed. This is the first time using Windows makes me feel inspired and empowered, ever. | 1,860 | 8,079 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-26 | latest | en | 0.926159 |
akozbohatnutsehf.firebaseapp.com | 1,686,060,575,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652569.73/warc/CC-MAIN-20230606114156-20230606144156-00728.warc.gz | 111,593,707 | 6,786 | # Štatistické symboly cheat sheet pdf
Probability Density Function (PDF) Probability Density Function (PDF) P(a ≤ x ≤ b)= ∫ f (x) dx: F(x) Cumulative Distribution Function (CDF) Cumulative Distribution Function (CDF) F(x) = P(X≤ x) μ: Population Mean: mean of population values: μ = 10: E(X) Expectation Value: expected value of random variable X: E(X) = 10: E(X |Y
You can find all the predesigned P&ID symbols under the Industrial Automation and PID category, which will be used for representing the functional relationships between piping, instrumentation, and system equipment units. Návod na Micorosft Excel 2016 - aneb zvládněte pracovat v Excel krok za krokem - v deseti lekcích se naučíte jak zvládnout základní práci, například k pracovnímu pohovoru. Nejprve spusťte Excel 2016, klikem na ikonu na ploše, nebo přes nabídku Start - Všechny programy - Microsoft Office - Excel 2016 (pokud máte Windows 8 (10), najděte příslušnou ikonu na dlaždici). 2020/12/23 Čo je zoznam klasifikácie & označovania?
q 1-p. n sample size. α significance level Statistics Consulting Cheat Sheet Kris Sankaran October 1, 2017 Contents 1 What this guide is for 3 2 Hypothesis testing 3 2.1 (One-sample, Two-sample, and Paired) t Created Date: 10/25/2007 9:57:31 PM Reference: Moore DS, McCabe GP & Craig BA. Introduction to the Basic Practice of Statistics.Ne w York: W.H. Freeman & Co, 5th edition. DESCRIPTIONS OF STATISTICS FORMULAS STAT301: Cheat Sheet Algebra (i) a+z b a b = z (ii) a(b+ c) = a b+ a c.
## 2021/3/10
Share. Embed Download Statistics Cheat Sheet Comments. Report "Statistics Cheat Sheet" Please fill this form, we will try to respond as soon as View PDF version on GitHub ; CME 106 - Introduction to Probability and Statistics for Engineers Probability Data Transformation with data.table :: CHEAT SHEET Manipulate columns with j Functions for data.tables data.table is an extremely fast and memory efficient package for transforming data in R. It works by converting R’s native data frame objects into data.tables with new and enhanced functionality. The basics of working with data.tables are: Feb 08, 2021 · Same as Above: Sample Standard Deviation: Given: Variance = 9 s = square root of 9 = 3 Given data: 7, 5, 0, -4 Calculate variance: s 2 = 24.6666667 s = square root of 24.6666667 = 4.96655481 Probability Density Function (PDF) Probability Density Function (PDF) P(a ≤ x ≤ b)= ∫ f (x) dx: F(x) Cumulative Distribution Function (CDF) Cumulative Distribution Function (CDF) F(x) = P(X≤ x) μ: Population Mean: mean of population values: μ = 10: E(X) Expectation Value: expected value of random variable X: E(X) = 10: E(X |Y Statistical Symbols and Abbreviations Symbol or abbreviation Explanation α Probability of a type I error, or rejection level which is typically 0.05 t-statistic: assuming equal variances: t x 1 x 2 s2 1 n1 1 n2 assuming unequal variances: t x 1 x 2 s1 2 n1 s2 2 n2 degrees of freedom = (n1-1)+(n2-1) Read the table of t-distribution critical values for the p-value using the calculated t-statistic and degrees of Title: Statistical Test Cheat Sheet Author: Christopher Porter Created Date: 20120504190136Z Econ 205 - Cheat Sheet Statistics for Business and Economics Descriptive statistics: Mean: x=average(DATA), Median =median(DATA) , Mode =mode(DATA) A PDF is nonnegative and integrates to 1.
### Electrical Symbols & Electronic Symbols Electrical symbols and electronic circuit symbols are used for drawing schematic diagram. The symbols represent electrical and electronic components. Symbol Component name Meaning Wire Symbols Electrical Wire
(iii) p1 ab = p1 a p1 b. (iv) pa a = p a. (v) a
Math Mode Accents. \acute{a}. \bar{a}. \breve{a}. hensive LATEX symbol list seem like they must have been enormous efforts. 3 https://www.tug.org/TUGboat/tb35-2/tb110mertz.pdf Cheat sheet for writing math in LATEX.
Chebyshev's Rule. ➔ Use for any set of data and for any number k, greater than 1 (1.2, 1.3, etc.) ➔. 1. 1 k2. ➔ (Ex) Symbols (or notation) found in statistics problems fall into three main categories: math symbols, List of Logical Symbols. Feel free to use any of the following symbols in your homework. If you use a lot of symbols, start each sentence on a new line and leave This is a template for a colourful cheatsheet.
Jednou ze zajímavých alternativ k R je projekt Incanter, který je založen na Clojure a běží nad JVM. 4. Instalace projektu Incanter 5. První spuštění interaktivního prostředí projektu Incanter 2020/7/31 When you get into the workspace of EdrawMax, the library will open the left side of the canvas. You can find all the predesigned P&ID symbols under the Industrial Automation and PID category, which will be used for representing the functional relationships between piping, instrumentation, and system equipment units. Návod na Micorosft Excel 2016 - aneb zvládněte pracovat v Excel krok za krokem - v deseti lekcích se naučíte jak zvládnout základní práci, například k pracovnímu pohovoru.
Reference numbers that appear in the title block refer to other print symbolY: 10.5, // The y position of the center of the symbol inside the button. text: null, // A text string to add to the individual button. | 1,391 | 5,193 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2023-23 | latest | en | 0.457716 |
http://oeis.org/A066404 | 1,591,524,935,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348526471.98/warc/CC-MAIN-20200607075929-20200607105929-00585.warc.gz | 91,155,031 | 3,817 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066404 From expansion of Belyi function for icosahedron. 4
1, -739, 196874, -22478125, 1086128125, -35307387500, 913727546875, -20389341653125, 410010534950000, -7633186177665625, 133911227595521875, -2240979684247156250, 36090410657726350000, -563019001047724506250, 8550765894655300606250 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,2 REFERENCES A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 24. LINKS N. Magot and A. Zvonkin, Belyi functions for Archimedian solids, Discrete Math., 217 (2000), 249-271. FORMULA The Belyi function is 1/Belyi function for dodecahedron. G.f.: (1-228x+494x^2+228x^3+x^4)^3/(1+11x-x^2)^5. - Michael Somos, Dec 13 2002 PROG (PARI) a(n)=polcoeff((1+228*(x^3-x)+494*x^2+x^4)^3/(1+11*x-x^2)^5+x*O(x^n), n) CROSSREFS Cf. A066402, A066403, A066405. a(n)=(-1)^n*A078906(n-1). Sequence in context: A235466 A202417 A078906 * A066402 A243778 A256634 Adjacent sequences: A066401 A066402 A066403 * A066405 A066406 A066407 KEYWORD sign AUTHOR N. J. A. Sloane, Dec 25 2001 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.) | 553 | 1,578 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-24 | latest | en | 0.501957 |
https://www.physicskey.com/55/electric-field | 1,695,528,729,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506559.11/warc/CC-MAIN-20230924023050-20230924053050-00032.warc.gz | 1,049,873,450 | 9,575 | # Electric Field
Here we define electric field and calculate the electric field due to some uniform charge distributions such as a line of charge, a ring of charge and a uniformly charged disk. You should also notice the symmetry of charge distribution which makes easy to find the electric field due to that charge distribution.
## Electric Field
Electric field is the electric force per unit charge. So the electric field produced by a fixed point charge $q$ at a point $p$ is the electric force per unit charge at that point $p$. Now just consider that there is a positive point charge $q_0$ at $p$ at a distance $r$ form charge $q$. The electric force between the charges $q$ and $q_0$ is
$F = k\frac{{q{q_0}}}{{{r^2}}}$
The electric field $E$ at the point $p$ is the electric force given by above equation divided by the point charge $q_0$.
$E = k\frac{{q{q_0}}}{{{r^2}{q_0}}} = k\frac{q}{{{r^2}}} \tag{2} \label{2}$
From the expression of the electric field you may notice that the electric field is independent of the charge $q_0$. So, the electric field at the point $p$ is always the same for any charge at that point. Electric field is a vector quantity and in vector form it can be expressed as,
$\vec E = k\frac{q}{{{r^2}}}\hat r \tag{3} \label{3}$
where $\hat{r}$ is a unit vector along the line joining the charge and point $p$. The unit vectors specify the direction in space- they point in a particular direction in space. The direction of electric field of a positive point charge is radially outward (or in the direction away from the charge) as shown in Figure 2(a) or Figure 3(a).
And the direction of electric field of a negative point charge is radially inward in the direction towards the charge as shown in Figure 2(b) or Figure 3(b). The direction of unit vector is in the same direction of electric filed of positive point charge but the direction of unit vector is opposite to the direction of electric field of negative point charge. The electric field can also be expressed in terms of electric field lines.
### Superposition of Electric Fields
We take a note on what happens to the electric field at a point when two or more point charges are present. Consider there are charges $q_1$, $q_2$, $q_3$ and $q_4$ distributed in a space and we need to find the electric field at a point $p$ due to this charge distribution (see Figure 4).
The electric field at the point $p$ is calculated by calculating the electric fields at that point by individual charges and the vector sum of those electric fields gives the net electric field (electric field due to the charge distribution) at that point. Note that you know from Eq. \eqref{2} that the electric field due to a point charge at the point $p$ is independent of any charge present at that point. The total electric field at the point $p$ due to the charge distribution is the vector sum of the electric fields due to individual charges. The electric field due to the charge $q_1$ is $\vec E_1$, the electric field due to the charge $q_2$ is $\vec E_2$ and so on. Therefore, the net electric field at the point $p$ is
$\vec E = {{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3} + {{\vec E}_4} \tag{4} \label{4}$
Also note that $\vec F = q_0\vec E$ and if a charge $q_0$ is present at the point $p$, the total electric force at that point due to the charge distribution is
\begin{align*} \vec F &= {q_0}\vec E = {q_0}{{\vec E}_1} + {q_0}{{\vec E}_2} + {q_0}{{\vec E}_3} + {q_0}{{\vec E}_4}\\ \therefore \quad \vec F &= {{\vec F}_1} + {{\vec F}_2} + {{\vec F}_3} + {{\vec F}_4} \tag{5} \label{5} \end{align*}
Hence the total electric force at the point $p$ on charge $q_0$ is the vector sum of the electric forces due to individual charges which should be.
## Electric Field of a Line of Charge
Consider that charge $q$ is distributed uniformly throughout a line as shown in Figure 1 and we are going to calculate the electric field at a point $p$ which lies at a perpendicular distance $x$ from the middle point of the line. It's always easier to start with a coordinate system and the associated symmetry with the charge distribution.
We consider infinitesimal length element of length $dy$ on the line of charge. If the linear charge density is denoted by $\lambda$ which is the charge per unit length, the charge associated within the length $dy$ is $dq =\lambda dy$. The line of charge is divided by the x-axis into equal halves of length $l$, so the total length of the line of charge is $2l$. The charge $dq$ within the length $dy$ is $dq=\lambda dy=\frac{qdy}{2a}$ and the electric field $dE$ due to this charge at point $p$ is
$dE = k\frac{{dq}}{{{r^2}}} = k\frac{{\lambda dy}}{{({x^2} + {y^2})}} = k\frac{{qdy}}{{2l({x^2} + {y^2})}}$
Note that $r^2 = x^2 + y^2$ in the above equation. The x-component of the electric field $dE$ is $dE_x=dE\cos \theta$ and the y-component is $dE_y=-dE\sin \theta$ (why negative sign?). Note that the y-component of electric field produced by the upper half part of the line of charge is exactly equal in magnitude and opposite in direction to the y-component of electric field produced by the lower half part of the line of charge and therefore the y-component of the electric field at the point $p$ due to the line of charge is zero. We can understand it by the symmetry consideration of the line of charge at the point $p$. So the total electric filed due to the line of charge at that point is sum of the x-components of electric fields of all charge elements. Since $\cos \theta =\frac{x}{r}=\frac{x}{\sqrt{{{x}^{2}}+{{y}^{2}}}}$, the x-component of $dE$ is,
$d{E_x} = dE\cos \theta = k\frac{{qxdy}}{{2l{{({x^2} + {y^2})}^{\frac{3}{2}}}}}$
Now the total electric field at the point $p$ due to the line of charge is determined by integrating $dE_x$ from $-l$ to $l$. Which is
${E_x} = E = k\frac{{qx}}{{2l}}\int\limits_{ - l}^{ + l} {\frac{{dy}}{{{{({x^2} + {y^2})}^{\frac{3}{2}}}}}} = k\frac{q}{{x\sqrt {{x^2} + {l^2}} }} \tag{6} \label{6}$
The $x$ coordinate of the point is constant in the integraion. The unit vector $\hat{i}$ gives the direction along positive x-axis, so the electric field in vector form is
$\vec E = k\frac{q}{{x\sqrt {{x^2} + {l^2}} }} \hat i \tag{7} \label{7}$
You can also check that the integration of $d{{E}_{y}}$ from $-l$ to $l$ is zero:
$d{E_y} = - dE\sin \theta = - k\frac{{qydy}}{{2l{{({x^2} + {y^2})}^{\frac{3}{2}}}}}$
Now integrating $d{{E}_{y}}$ from $-l$ to $l$,
${E_y} = - k\frac{q}{{2l}}\int_{ - l}^l {\frac{{ydy}}{{{{({x^2} + {y^2})}^{\frac{3}{2}}}}}} = 0 \tag{8} \label{8}$
Only the sum of the x-components of electric fields produced by all elements of the line of charge gives the total electric field at the point $p$.
When the point $p$ is very far from the line of charge that is, the distance $x$ is considerably larger in comparison to the length of the line of charge or symbolically $x >> l$. The term $l^2$ will be much smaller and can be neglected. So the electric field in this case is
$E = k\frac{q}{{x\sqrt {{x^2}} }} = k\frac{q}{{{x^2}}} \tag{9} \label{9}$
In this case when the point $p$ is far from the line of charge the entire charge in the line acts as if all the charge were concentrated at the origin of the coordinate system (at the middle point of line of charge)
And when the line of charge is infinitely long, that is the length of the line of charge is very long in comparison to the distance $x$, ($l >> x$), the distance $x$ will be much smaller than $l$ and $x^2$ can be neglected. So, the resulting electric field is
$E = k\frac{q}{{x\sqrt {{l^2}} }} = k\frac{q}{{lx}} \tag{10} \label{10}$
As you know the linear charge density is $\lambda =\frac{q}{2l}$ and in terms of the linear charge density, the above expression can be written as,
$E = k\frac{{2\lambda }}{x} \tag{11} \label{11}$
So the result is clear that the electric field for the infinitely long line of charge is proportional to $\frac{1}{x}$ instead of $\frac{1}{{{x}^{2}}}$ as for a point charge. And notice that we can not get a real line of charge having infinite length! But when the length of the line of charge is considerably larger in comparison to the distance $x$ and the point $p$ is considerably close enough to the line of charge the electric field is the same as that of an infinite line of charge.
We have also obtained the expression which is same as that of an infinite length line of charge in the electric field calculation using Gauss's Law.
## Electric Field of a Ring of Charge
The total charge $q$ is distributed uniformly forming a ring as shown in Figure 2. The charge is uniformly distributed in the ring and so we apply the symmetry to find the total electric field of the ring of charge at a point $p$. In our coordinate system the origin is the centre of the ring and x-axis is perpendicular to the imaginary plane of the ring. The point $p$ where the electric field is being calculated lies at a perpendicular distance $x$ (x-coordinate of point $p$) from the centre of the ring. We divide the entire charge on the ring into small charge elements such as $dq$ and add the electric fields produced by every element at the point $p$.
Note that each element has both x and y-components of electric field but the y-component is cancelled by the y-component of the opposite charge element in the ring. Therefore the electric field at the point $p$ is only due to the x-component of electric field due to charge elements. In Figure 2 let the radius of the ring be $R$, so the distance between the charge element $dq$ and the point $p$ is $r = \sqrt {{x^2} + {R^2}}$ and the electric field $dE$ at that point due to this charge element is
$dE = k\frac{{dq}}{{({x^2} + {R^2})}}$
If you consider the symmetry of the charge distribution you'll find that the y-component of electric field due to one element is cancelled by the the y-component of electric field due to the opposite element in the ring. So the sum of the y-components of electric field due to the entire ring of charge is zero as already noted. Thus the total electric field at the point is the sum of the x-components of electric fields due to all charge elements in the ring. The x-component of the small electric field $dE$ is $d{{E}_{x}}=dE\cos \theta$ and $\cos \theta =\frac{x}{r}$. So,
$d{E_x} = k\frac{{xdq}}{{{{({x^2} + {R^2})}^{\frac{3}{2}}}}}$
Now we integrate this expression to get the electric field due to the entire ring of charge. Note that $x$ and $R$ remain constant throughout the whole integration and therefore,
${E_x} = E = k\frac{{xq}}{{{{({x^2} + {R^2})}^{\frac{3}{2}}}}} \tag{12} \label{12}$
If the unit vector $\hat{i}$ is the unit vector along positive x-direction, the electric field in vector form is
$\vec E = k\frac{{xq}}{{{{({x^2} + {R^2})}^{\frac{3}{2}}}}}\hat i \tag{13} \label{13}$
If the point $p$ is far enough from the ring that is, $x >> R$. In this case the term ${{R}^{2}}$ can be neglected and the electric field becomes
$E = k\frac{q}{{{x^2}}} \tag{14} \label{14}$
Which is the electric field for a charge at a point. It means the entire ring acts as a point charge $q$ if the point $p$ is far enough from the centre of the ring. Now you can easily get the answer for another condition as what if the point $p$ lies at the centre of the ring. For this the value $x$ is zero and the electric field is also zero.
## Electric Field of a Uniformly Charged Disk
The Figure 3 shows a disk of total charge $q$. We are going to calculate the electric field due to the disk of charge at a point $p$ which lies at perpendicular distance $x$ from the centre of the disk. The origin of our coordinate system lies at the centre of the disk and the plane of the disk is perpendicular to the x-axis. To get our result we divide the charged disk into small rings of charge $dq$ and get the the electric field at the point $p$ by adding the electric fields produced by every ring element.
We already know the electric field of a ring of charge, it's easier to get our result for the disk of charge. As you already know that the total electric field at the point $p$ is only due to the x-component of electric field of ring elements. Consider that the radius of one specific ring is $r$ and thickness is $dr$. So, the ring has area equal to $2\pi rdr$ and the charge $dq$ in the ring is $dq=\sigma (2\pi rdr)$ where $\sigma$ is the charge per unit area. The electric field $dE$ of the ring of charge $dq$ (you already know this) at point $p$ is
$dE = k\frac{{x\sigma (2\pi rdr)}}{{{{({x^2} + {r^2})}^{\frac{3}{2}}}}}$
Now the electric field for the entire disk is calculated by integrating the above expression from $0$ to $R$.
$E = 2k\pi \sigma x\int\limits_0^R {\frac{{rdr}}{{{{({x^2} + {r^2})}^{\frac{3}{2}}}}}} = 2k\pi \sigma x\left( {\frac{1}{x} - \frac{1}{{\sqrt {{x^2} + {R^2}} }}} \right)$
${\rm{or,}}\quad E = 2k\pi \sigma \left( {1 - \frac{1}{{\sqrt {1 + {{\left( {\frac{R}{x}} \right)}^2}} }}} \right) \tag{15} \label{15}$
In vector form you can write the above expression as
$\vec E = 2k\pi \sigma \left( {1 - \frac{1}{{\sqrt {1 + {{\left( {\frac{R}{x}} \right)}^2}} }}} \right)\hat i \tag{16} \label{16}$
where $\hat i$ gives the direction of the electric field vector. Suppose the radius of the disk is large enough in comparison to the distance $x$ so that $R >> x$, the term $1/{\sqrt{1+{{\left( \frac{R}{x} \right)}^{2}}}}$ is negligibly small and can be neglected. And the electric field in this case is
$E=2k\pi \sigma \tag{17} \label{17}$
So for the very large disk (or you can think as an infinite disk) the electric field is independent of the distance $x$ and perpendicularly outward from the disk. | 3,899 | 13,649 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2023-40 | latest | en | 0.90951 |
https://mathcs.chapman.edu/~jipsen/structures/doku.php?id=boolean_algebras_with_operators&rev=1614028295 | 1,669,880,565,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710801.42/warc/CC-MAIN-20221201053355-20221201083355-00577.warc.gz | 434,589,650 | 5,248 | Boolean algebras with operators
Abbreviation: BAO
Definition
A \emph{Boolean algebra with operators} is a structure $\mathbf{A}=\langle A,\vee,0, \wedge,1,\neg,f_i\ (i\in I)\rangle$ such that
$\langle A,\vee,0,\wedge,1,\neg\rangle$ is a Boolean algebra
$f_i$ is \emph{join-preserving} in each argument: $f_i(\ldots,x\vee y,\ldots)=f_i(\ldots,x,\ldots)\vee f_i(\ldots,y,\ldots)$
$f_i$ is \emph{normal} in each argument: $f_i(\ldots,0,\ldots)=0$
Morphisms
Let $\mathbf{A}$ and $\mathbf{B}$ be Boolean algebras with operators of the same signature. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a Boolean homomorphism and preserves all the operators:
$h(f_i(x_0,\ldots,x_{n-1}))=f_i(h(x_0),\ldots,h(x_{n-1}))$
Example 1:
Properties
Classtype variety decidable undecidable no unbounded yes yes yes, $n=2$ yes yes yes no no yes yes yes | 310 | 882 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2022-49 | latest | en | 0.628208 |
http://gmatclub.com/forum/ps-crystal-spheres-34671.html | 1,436,287,716,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375099755.63/warc/CC-MAIN-20150627031819-00058-ip-10-179-60-89.ec2.internal.warc.gz | 108,617,119 | 44,614 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 07 Jul 2015, 08:48
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# PS Crystal Spheres
Author Message
TAGS:
Current Student
Joined: 29 Jan 2005
Posts: 5240
Followers: 23
Kudos [?]: 191 [0], given: 0
PS Crystal Spheres [#permalink] 03 Sep 2006, 04:43
00:00
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 0 sessions
See attachment
Attachments
Crystal spheres.doc [68.5 KiB]
Senior Manager
Joined: 14 Jul 2005
Posts: 402
Followers: 1
Kudos [?]: 12 [0], given: 0
E 7/8
Volume of cube = x^3
Volume of sphere = 4/3*pi*r^3
Say x=4, then d=2 and r=1
Vol of cube = 64
Vol of 2 spheres = 2*[4/3 * pi * 1^3] = 8 (approx)
Hence %age filled with powder = 56/64 = 7/8
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 19
Kudos [?]: 132 [0], given: 0
x^3 - 2 * 4/3 * 22/7 * x^3/64
x^3 * (1-11/84) = x^3 * 75/84
approx 7/8
_________________
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008
Similar topics Replies Last post
Similar
Topics:
PS - Crystal Ball 3 25 Mar 2009, 12:12
1 PS: Official GMAT Prep Sphere Volume 5 17 Nov 2007, 14:46
PS - sphere 2 14 Dec 2006, 16:34
PS: Sphere 5 28 Sep 2006, 10:20
Two crystal spheres of diameter x/2 are being packed in a 1 24 Sep 2006, 11:42
Display posts from previous: Sort by | 644 | 1,930 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2015-27 | longest | en | 0.82364 |
http://www.veritasprep.com/blog/2012/10/use-decision-points-to-eliminate-sentence-correction-answer-choices/ | 1,660,041,338,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00351.warc.gz | 97,049,988 | 79,024 | # Use Decision Points to Eliminate Sentence Correction Answer Choices
We’re back with the next installment in an occasional series on the Veritas Prep Blog, called “GMAT Gurus Speak Out.” Veritas Prep has dozens of experienced GMAT instructors around the world (all of whom have scored in the 99th percentile on the GMAT), and it’s amazing how much collective experience they have in preparing students for the exam. Today we feature another post from Jen Begasse, a GMAT instructor in New Brunswick.
My GMAT students tend to be busy people juggling a lot of responsibilities and activities, and so I am always looking for ways to help them be hyperefficient… especially on GMAT problems! So with efficiency on my mind, I’d love to be able to figure out a way to help my students shortcut their way through Sentence Correction. For example, if we read a Sentence Correction passage and the underlined portion of it sounds reasonable enough, can’t we avoid reading the four other possible answer choices, select “A” (the original answer choice), bank a couple of minutes to save for the next tricky Critical Reasoning problem, and move on with our lives?
The answer, alas, is, no. No way. Don’t Even Try It. Sentence Correction at its heart is about process of elimination. While there’s nothing wrong with keeping a favorite answer choice in mind while reviewing the others, all of the answer choices do need to be examined.
However, that doesn’t mean we throw away our goal of efficiency. How can we ensure that we are systematically reviewing the Sentence Correction answer choices in a time-efficient and effective manner? Simple — by focusing on the Decision Points that exist in each answer choice.
To the unitiated GMAT test-taker, the five answer choices to any given sentence correction question often look like a series of confusing, complicated text that requires a slow, painful slog in order to ascertain the right answer. The truth, however, is that the 5 answer choices are likely to have a lot of the same text repeated in them, albeit with important variations. An astute test taker can focus on those variations to help process the various answer choices. I like to call these variations “Decision Points” – namely, you as the GMAT test-taker need to decide which of one, two or three options of a particular grammatical form is correct.
Let’s look at an example…
Animals whose natural habitats are endangered by industrial development either migrate to new environments, which leads to potential ecological imbalances, and try to survive in the dwindling areas that remain, often leading to extinction.
(A) which leads to potential ecological imbalances, and try
(B) leading to potential ecological imbalances, or trying
(C) with the lead of potential ecological imbalances, or trying
(D) leading to potential ecological imbalances, or try
(E) with a leading to potential ecological imbalances, and try
The “Try/Trying” Decision Point. There’s no particular reason to start at the beginning of the answer choices, and for this particular example it may help to focus on the last words of the answer choices. We have the Decision Point between “try” (Answer Choices A, D, or E) and “trying” (Answer Choices B or C). Making a decision on which form is correct would automatically cut out 2-3 of the answer choices.
Examining the portion of the sentence before the underlined part, I see the verb “migrate” occurring right after “either,” which means that “try” would be parallel in structure to “migrate.” Answer Choices B and C are out.
The “and/or” Decision Point. Next, I’ll move one word back in the Answer Choices, and the Decision Point is between “and” (Answer Choices A and E) and “or” (Answer Choice D). Remembering that there is an “either” in the non-underlined portion of the sentence, I want to use an “or” so that it is idiomatically correct. This decision has now eliminated Answer Choices A and E, and I’m left with Answer Choice D.
Now that I’m left with a single Answer Choice, time allowing, I’ll mentally insert it into the original passage to ensure I haven’t missed any errors and that the flow sounds natural. Also, time allowing, I may do a mental scan of the other answer choices to see if any of the variations indicate another error I may have missed. But otherwise, through the use of Decision Points, I have quickly and methodically narrowed down to the correct Answer Choice for a Sentence Correction question. Another efficiency gain for my students means an extra 30 seconds in their time bank!
Plan on taking the GMAT soon? We have GMAT prep courses starting around the world this week! And, be sure to find us on Facebook and Google+, and follow us on Twitter!
By Brian Galvin | 1,004 | 4,740 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2022-33 | latest | en | 0.938182 |
https://permanentkisses.com/how-to-calculate-work-2/ | 1,723,582,850,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641085898.84/warc/CC-MAIN-20240813204036-20240813234036-00823.warc.gz | 354,178,947 | 11,534 | # How to Calculate Work
Work is energy transferred to an object through force or displacement. It is often represented as the product of displacement and force. A person performing an action transfers energy to an object, which is then embodied in the object’s physical state. There are several ways to calculate work. Here are some examples: 1. Lifting a heavy object by pulling on it. 2. Using a lever. 3. Using a lever to lift a heavy object.
When a force acts on an object, it causes an object to move. When a force acts on a body, the displacement it produces is the work that the object is doing. In this example, a coolie lifts a mass on his head. The mass moves at a 90-degree angle to the force of gravity. Therefore, the work he or she does is zero. In this case, the coolie has done no work.
The definition of work is similar to that of an object in motion. The applied force must cause a displacement that is opposite to the motion of the object. The force must be of the same direction as the displacement to be considered work. In case of negative work, the energy that the object is moving away from the object is removed. However, a ball that is falling from a height is not a ball. Instead, it is a human throwing a ball at a speed of 100 km/h.
Another example of a work that is done by a human is a force that causes an object to move. The force must be greater than the object’s weight in order to cause the movement. The greater the force, the more work it produces. In theory, the more work the object does, the more power it can exert. And it has to be in a straight line. This is how you calculate the amount of work done by an object.
The amount of work done by an object is equal to the force on it. This means that a force is doing work on an object. A force on an object causes a displacement. The force is also applied to an object. The applied force needs to be opposite the object’s motion or it will be referred to as negative work. This means that a mass must be moved perpendicular to the force in order to be considered a work.
A force can cause an object to move. In this case, the work is done by the object. If the object is in motion, it will be displaced. A force is not positive if it does not affect the object. It can be negative or positive. In fact, it can even have zero value. The definition of work has many variants. The definition is the same in every country. The force applied by a force can make an object move. | 555 | 2,469 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.625 | 5 | CC-MAIN-2024-33 | latest | en | 0.9597 |
http://golancourses.net/2018/60212s/conye/02/02/conye-animatedloop/ | 1,675,430,084,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500056.55/warc/CC-MAIN-20230203122526-20230203152526-00069.warc.gz | 17,743,708 | 11,440 | # conye – AnimatedLoop
Below is a gif of the finished piece:
Here are some sketches for this loop!
I originally had imagined that it was a loop of very, very long weaving dogs chasing their own tail, but ended up changing plans. I think the current final result has nice simple forms that compliment their motions; however, in the future, I might end up adding dog heads/tails to them to see what the result looks like because that might make the loop more fun.
Here are some other sketches that I made originally! I actually did halfway implement both the cat sketch in the middle and the orchid sketch on the right, but wasn’t satisfied with either of them and had to move on.
#### The process:
First, I worked on the weaving motion of the lines. It actually was harder than I imagined it would be because the lines would almost melt into each other where they intersected, so I had to draw the pieces of the “lines” (which are made up of ellipses) separately.
I ended up making the process unnecessarily difficult for myself by not making enough variables and helper functions, so my code was really difficult to debug, but at least I’ve learned my lesson- next time I will write cleaner code for the sake of sanity, and my time. Thank you to Golan for helping me debug my code! Adding the easing function that Golan really changed the whole feeling of the piece, and I’m really amazed by how useful Pattern Master is! I used the Double Quadratic Bezier function because I thought it had the right kind of up and down movement that would make the movement of the lines interesting to look at.
Below, to the left, is an early process image of when I was using the lower rectangle to test if I could correctly find where the intersections where. Next to it is after I got the weaving to work, but without the easing function and the gradient.
The Processing code is below. For clarity, this is the non-template version, but I later made a few small edits to fit into Golan’s template.
```//global variables boolean overlap; int frame, offset; color[] bluegradient = new color[400]; color[] redgradient = new color[400]; int nFrames = 360; //number of frames void setup() { frame = 0; size(720, 720); createGradients(); noStroke(); overlap = false; //overlap used to draw lines in the draw function offset = 135; //how much the second line is offset by } void draw() { frame = (frameCount)% nFrames; //frame can be from 0 to 359 background(#FFFADA); //this nested loop draws multiple squiggle pairs at different locations on the canvas for (int j = -2; j < 1; j++) { for (int k = 0; k < 3; k++) { //variables below control where this squiggle pair starts int startx = j * 720 + k*200 + 200; int starty = k * 300 + 120; //i is a counter for the ellipses when we draw them, reset for every squiggle pair int i = 0; //flip is used to weave boolean flip = false; //the offset of 135 flips around the weaving at frame 22 and 310, //so I used the below to keep it from looking weird and glitchy if (frame < 22 || frame > 310) { flip = false; } else { flip = true; } //this while loop is where the squiggles are drawn. Width is 620 right now. while (i < 620) { //overlap is true if the two lines are intersecting at this i value boolean overlap = Math.abs(helperSin(i, frame, 0) - helperSin(i, frame, offset)) < 100; //loop while it's not at the full width yet, and when they're not intersecting while (i < 620 && !overlap) { fill(redgradient[i/2]); ellipse(startx + (i + frame * 2), starty + helperSin(i, frame, offset), 90, 90); fill(bluegradient[i/2]); ellipse(startx + i + frame * 2, starty + helperSin(i, frame, 0), 90, 90); overlap = Math.abs(helperSin(i, frame, 0) - helperSin(i, frame, offset)) < 100; i+=3; //we do +3 to save processing power } //cap the length of this intersecting piece to be either 120 or 620 - i int cap = (i + 120 >= 620)? 620 - i : 120; int stopper = i + cap; //tells i where to stop based on how long cap is if (flip) {//if + else flip makes the intersection overlapping alternate while (i < stopper) { fill(redgradient[i/2]); ellipse(startx + (i) + frame * 2, starty + helperSin(i, frame, offset), 90, 90); i+=3; } i -= cap; while (i < stopper) { fill(bluegradient[i/2]); ellipse(startx + i + frame * 2, starty + helperSin(i, frame, 0), 90, 90); i+=3; } } else { while (i < stopper) { fill(bluegradient[i/2]); ellipse(startx + i + frame * 2, starty + helperSin(i, frame, 0), 90, 90); i+=3; } i -= cap; while (i < stopper) { fill(redgradient[i/2]); ellipse(startx + (i) + frame * 2, starty +helperSin(i, frame, offset), 90, 90); i+=3; } } flip = !flip; } } } } //helper function that applies transformations to sin float helperSin(int i, int frame, int offset){ return 90 * sin(radians(i + DQB(frame) + offset)); } //helper function for DoubleQuadraticBezier(...) float DQB(int x) { float x01 = (float)x/ (float)nFrames; return (float)(360 * function_DoubleQuadraticBezier (x01, 0.25, 0.75, 0.75, 0.25)); } //Easing function from Golan Levin's Pattern Master float function_DoubleQuadraticBezier (float x, float a, float b, float c, float d) { //functionName = "Double Quadratic Bezier"; float xmid = (a + c)/2.0; float ymid = (b + d)/2.0; xmid = constrain (xmid, EPSILON, 1.0-EPSILON); ymid = constrain (ymid, EPSILON, 1.0-EPSILON); float y = 0; float om2a; float t; float xx; float aa; float bb; if (x <= xmid) { xx = x / xmid; aa = a / xmid; bb = b / ymid; om2a = 1.0 - 2.0*aa; if (om2a == 0) { om2a = EPSILON; } t = (sqrt(aa*aa + om2a*xx) - aa)/om2a; y = (1.0-2.0*bb)*(t*t) + (2*bb)*t; y *= ymid; } else { xx = (x - xmid)/(1.0-xmid); aa = (c - xmid)/(1.0-xmid); bb = (d - ymid)/(1.0-ymid); om2a = 1.0 - 2.0*aa; if (om2a == 0) { om2a = EPSILON; } t = (sqrt(aa*aa + om2a*xx) - aa)/om2a; y = (1.0-2.0*bb)*(t*t) + (2*bb)*t; y *= (1.0 - ymid); y += ymid; } return y; } //creates those nice gradients void createGradients() { for (int i = 0; i < 400; i++) { int r = (int)( 113 + (64*(i/ 400.0))); int g = (int)( 204 + (51*(i/ 400.0))); int b = (int)( 198 + (52*(i/ 400.0))); bluegradient[i] = color(r, g, b); } for (int i = 0; i < 400; i++) { int r = (int)( 235 + (20*(i/ 400.0))); int g = (int)( 120 + (93*(i/ 400.0))); int b = (int)( 195 + (45*(i/ 400.0))); redgradient[i] = color(r, g, b); } }``` | 1,928 | 6,255 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-06 | latest | en | 0.97341 |
http://consumerinfo.org.ua/nick-of-thpp/the-integrating-type-converters-are-used-in-10e7d4 | 1,627,848,536,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154219.62/warc/CC-MAIN-20210801190212-20210801220212-00579.warc.gz | 10,822,902 | 15,243 | 2. The MSB has weight $V_{ref}/2$, the next $V_{ref}/4$, etc., and the LSB has weight $V_{ref}/2^N$. $$V_{in} = \sum_{n=0}^{N-1} b_n 2^n\frac{V_{ref}}{2^N}.$$ 6. $$P_{qn} = \left(\frac{V_{ref}}{2^N}\right)^2\frac{1}{12}=\frac{Q^2}{12}$$ In the sampling process, this power gets concentrated in the frequency band between 0 and half the sampling frequency due to aliasing. Microcontrollerslab.com All Rights Reserved. Here the load is connected via a three-phase half wave connection to one of three supply lines. An analog-to-digital converter (ADC) is used to convert an analog signal such as voltage to a digital form so that it can be read and processed by a microcontroller. Custom Type Converters¶. Types of ADC. 5. According to the Nyquist-Shannon sampling theory, sampled data can be reconstructed approximately perfectly with a proper bandwidth and the Criteria given by Nyquist. 1 Answer. An answer to this calibration drift dilemma is found in a design variation called the dual-slope converter. But how does oversampling influences the Signal-Noise Ratio? The Analog to Digital Converter will convert the Analog data like the data that is being collected as the audio input such as Microphone to digital signal that will be processed by the computer. During the manipulation of data, the two of the conversion interfaces serves as the backbone to the Digital electronic equipment’s or we can say an analog electronic device. Due to a large oversampling, the quantization noise spectral density is reduced, It allows noise shaping (quantization noise is attenuated at lower frequencies), Requires the decimation filter in the end, Only useful in applications requiring low sampling rate, such as audio, They must have an input-referred offset voltage below 1 LSB, They must have an input-referred noise below 1 LSB, They must resolve a comparison for differential inputs below 1 LSB. If $V^\star_i$ is the ideal voltage that transitions from input code $i-1$ to code $i$ and $V_i$ is the real one, the INL is We use cookies on our website to give you the most relevant experience by remembering your preferences and analyze traffic for ads measurement purposes By clicking “Accept”, you consent to the use of ALL the cookies. A Successive Approximation Register converter evaluates each bit at a time, from the most to the least significant bits. Integral Nonlinearity (INL) and Differential Nonlinearity (DNL) are two different ways of measuring the nonlinearity of a converter. You may notice that this method repeats itself anytime we have a tendency to work from left to right, in turn substitution mixtures of resistors with their equivalents. That is because: If I helped you in some way, please help me back by liking this website on the bottom of the page or clicking on the link below. An advantage of IADCs such as dual-slope converter is the property of noise immunity which makes it the most popular ADC in many applications , . The After this, The amount of digital data can be produced from Application Specific Integrated Systems(ASIC’s), Microprocessors or from a Field Programmable Gate Array(FPGA). Type converters, as the name implies, are used in order to convert the body of a message from one type to another. You are right, but in this case the reflection will be used to get converter type from the attribute. They successively approach the output of a digital-analog converter (DAC) in them to the input voltage. A gain error can be caused by an uncalibrated voltage reference. List out some integrating type converters. As you’ll have already suspected, the contribution of bit b2 is solely Vb2/4. $$x_{out}\left(1+ \frac{1}{s}\right) = \frac{x_{in}}{s} + n_{in}$$ This type converter is used in industrial applications where two-quadrant operation is required. Microcontrollers commonly use 8, 10, 12, or 16 bit ADCs, our micro controller uses an 8 or 10 bit ADC. A ladder network supported by a weighted resistor. $$SNR = 6.02N + 1.76$$ N number of switches that represents a bit applied to the input provided. The slider below controls the input voltage of a Sigma-Delta ADC. At a sampling rate equal to the Nyquist frequency ($2f_c$), this term is 0. The fact , is that the analysis of this network and the way it works is kind of easy. This type of AD converters converts an analog input signal to a digital data in one shot. Apr 6, 2020 - What are the advantages of integrating type A/D converters over the non-integrating type? $$SNR = 6.02N + 1.76 + 10\log(\frac{f_s/2}{f_c})$$ This metric means little without accounting with the errors described above. The voltage supply is that the open-circuit voltage at the cut purpose, and also the series electrical device is that the equivalent circuit resistance with all voltage sources shorted. Phil Davies Vicor Corp. These methods are carried out on the basis of the notion of resonant switching by integrating its structure into the input circuit of the converter. Oversampling is the sampling at a frequency much higher than the Nyquist frequency, i.e., at a much higher frequency than the double of the maximum frequency of the signal. Converters; of a type used in metallurgy or in metal foundries imports by country in 2019 Dual slope ADC . Charge balancing ADC. Let's say that we double the sampling frequency (the rectange doubles its width, but reduces its height by half). Otherwise, it is 0. Therefore, for the band of the signal, there is less noise power as we increase the sampling frequency. It would mean the world to me! Since $10\log(4)\approx6$, multiplying the sampling frequency by 4 is like adding another bit in the SNR, as far as quantization noise is concerned. But opting out of some of these cookies may affect your browsing experience. Integration is the practice of combining different parts of a business so that they work together. In either cases, the remaining value is doubled and passed to the next stage. The use may be for evidence in business or legal purposes. That comparator result $x_{adc}$ is sampled and sets the reference signal $x_{dac}$ to $V_{ref}$ or zero in the next cycle. In general, first it converts the analog input into a linear function of time (or frequency) and then it will produce the digital (binary) output. The output code will scale with the voltage reference and different voltage references will lead to different switching points of the output code. That can be simply done by XORing the outputs of neighboring comparators and feeding their outputs to a digital encoder. Microcontrollers commonly use 8, 10, 12, or 16-bit ADCs, our micro controller uses an 8 or 10 bit ADC. As its name suggests, this converter has 2 phases, the first where a voltage ramps up with a certain slope, and the second where the same voltage ramps down with a different slope. In a a lot of general sense, the contribution of every bit to the output could be a easy binary coefficient operate of every bit. 1.3.8 Analog-to-digital converter. Most microcontrollers nowadays have built-in ADC converters. Periodic interference, such as 50 Hz mains (60 Hz in the US) can be eliminated completely. Stand-alone fiber media converters are designed to be used in where a single or limited number of … These type of converters often include built-in drivers for LCD or LED displays and are found in many portable instrument applications, including digital panel meters and digital multi-meters. The digital signal is represented with a binary code, which is a combination of bits 0 and 1. Compared with techniques which require that the input is “frozen” with a sample-and-hold, the integrating If an ADC performs the analog to digital conversion by an indirect method, then it is called an Indirect type ADC . Coupled inductor with voltage multiplier cell is used to increa se the voltage gain of the converter. Very precise. Introduction to Digital to analog converter In the field of electronics Digital to Analog converter is a type of system that is used for the conversion of Digital signals or data into the Analog signals or data. We removed the 1-bit ADC, 1-bit DAC and the latch to make the system linear. An offset of the converter can be caused by an offset in the comparator of a SAR converter. The sigma-delta converter is unique in that it samples the signal in a much higher frequency than the Nyquist frequency. As you’ll see in Figure three, the circuit ultimately simplifies to one electrical device R. Thus, the output resistance of the R-2R electrical device network is usually adequate to R, despite the dimensions (number of bits) of the network. The realization of high-resolution Nyquist-rate converters becomes very expensive when the resolution exceeds 16 bits. $$0 = \frac{-V_{ref}}{\tau}t + \frac{V_{in}}{\tau}t_{int}$$ We also use third-party cookies that help us analyze and understand how you use this website. The conventional way is to use a common DC bus. Let's see if intuition is right. It can also be to … During ramp down, a counter counts the number of clocks until the output voltage reaches zero. 1 LSB, but even for integrating-type converters, noise and the various other errors discussed above, will increase in importance for lower-than-maximum full scale ranges. Therefore, more bits leads to more precision in the digital representation. They are used in practical circuits like light dimmer circuits, speed controls of induction motors and traction motor control etc. This chapter discusses about the Indirect type ADC. The current List remains unchanged. Dual-Slope Converter. It is one kind of system used to convert analog signal to digital signal. Which type of oil used in torque converter? First, a voltage ramps up with slope proportional to the input voltage $V_{in}$ for a fixed period of time. We’ll calculate the contribution of 2 of the bits of our 4-bit R-2R DAC in Figure four to point out the method. The type converter float can turn an integer, a float, or a syntactically legal string into a float. In a Digital to Analog converter, it is feasible to reconstruct a sampled amount of data into an analog signal with an accurate and effective precision. Hence it is called a s dual slope A to D converter. You can access DataDirect XML Converters: Although I talk about oversampling in the sigma-delta converters, oversampling can be applied in any converter. You also have the option to opt-out of these cookies. Dual Slope type ADC In dual slope type ADC, the integrator generates two different ramps, one with the known analog input voltage VA and another with a known reference voltage –Vref. 1)It is the fastest type of ADC because the conversion is performed simultaneously through a set of comparators, hence referred as flash type ADC. An Analog to Digital Converter (ADC) converts an analog signal into a digital signal. where $t_{int}$ is the integration time, $1/\tau$ is the slope proportionality factor and $V_{initial}$ is the initial voltage, say zero. For each part, a comparator compares the input signal with the voltage supplied by that part of the resistive ladder. The input signal is low-pass filtered, but the quantization noise is high-pass filtered. The R-2R electrical device ladder network directly converts a parallel digital voltage into an analog voltage. The slider below controls the sampling frequency of the sigma-delta converter. Flash Type ADC is based on the principle of comparing analog input voltage with a set of reference voltages. $9.99$ 9. Germany exported Converters; of a type used in metallurgy or in metal foundries to Austria ($349.35K ), Russian Federation ($347.05K ), Finland ($49.18K ), Poland ($44.83K ), Czech Republic ($34.80K ). That means that it should find the position where neighboring comparators have different outputs (all below have output high and all above have output low). These cookies do not store any personal information. Dual Slope type ADC In dual slope type ADC, the integrator generates two different ramps, one with the known analog input voltage VA and another with a known reference voltage –Vref. Copyright © 2013-2021 When the ramp potential crosses the unknown input voltage a comparator changes state. There are many existing technologies in single phase AC/AC converters; they are single phase – two legs, three legs and four legs. Successive Approximation Register (SAR) converters. We’ll use an equivalent Thevenin equivalents technique shown higher than, further as Superposition. Commonly used converters that allow the data to be modified as it passes through the binding engine. Integrating A/D converters have two characteristics in common. They are 1. Note that in the first phase, the slope is variable and the integration time is fixed. This type of data requires an ultimate conversion to the analog signal or to the analog data so that it can interact in the real world. The last case shows that a string has to be a syntactically legal number, otherwise you’ll get one of those pesky runtime errors. How XML Converters are Used in Stylus Studio The DataDirect XML Converters conversion engine is used throughout Stylus Studio to convert non-XML files to XML and vice-versa. Conversion is the process in which a word of one grammatical form converts into a word of another grammatical form without any changes to pronunciation or spelling. Preconverter gain is usually preferable for small original signals. The ADCs are at the front-end of any digital circuit that needs to process signals coming from the exterior world. While Analog to Digital converter behaves as a reverse of Digital to Analog converter. Pipelined converters convert the input in a number of steps proportional to the number of bits. It is also possible to connect an external ADC converter … Disadvantages: 1)It is not suitable for higher number of bits. Successfully integrating several technologies of micro resources and storage systems is a key component of microgrid applications. If the area (quantization noise power) is to be kept the same, extending the frequency will reduce the PSD. This second article in the series helps you understand the process. Slow. Resonant switches of the first and third type switched at zero voltage and resonant switches of the second type switched at zero current are used in the voltage inverters. An ADC converter that perform conversion in an indirect manner by first changing the analog I/P signal to a linear function of time or frequency and then to a digital code is known as integrating type A/D converter. There are two kinds of data converters present to convert the data, Analog to Digital Converter (ADC) and Digital to Analog converter (DAC). The dc-dc converters that perform this function are commonly […] The actual value used by the R is less important if we compare it with the large values. This can be achieved, for example, with a current source proportional to the input voltage charging a capacitor. The common feature of integrating A–D converters is that the analog input signal is integrated, or averaged, prior to further steps in the process. This method is an O(n) operation, where n is Count. We need data converters so that we can convert this analog or digital data available to us in some other form. The output of all the comparators is like a thermometer: the higher the input value, more comparators have their outputs high from bottom to top. Within the next 20 years, 80% of the electricity used in the U.S. will flow through these devices, so there is a critical need to improve their efficiency. The output code is changing at the wrong input, but the offset is equal for the whole range. Here we simplify the range to be between 0 and$V_{ref}$, although the range may be between any two values. Charge balancing ADC The principle of charge balancing ADC is to first convert the input signal to a frequency using a voltage-to-frequency converter. The block diagram of an ADC is shown in the following figure −. This process is repeated over and over and the streams of 1s and zeros coming out of the second comparator average out to the input value. There are two ways to integrate different renewable energy sources and energy storage. So what is so good about oversampling? Asked by: Akhil Ashok on Dec 21, 2016. Dual slope ADC (Integrating ADCs) In an integrating ADC, a current, proportional to the input voltage, charges a capacitor for a fixed time interval T charge. This all leads to accurate results. ADC are used virtually everywhere where an analog signal has to be processed, stored, or transported in digital form. Integrating or Dual-slope DACs - The dual-slope are very precise, but slow converters that use counters to generate the output. Next, we’ll examine the way to calculate the analog voltage output for a given parallel digital input on the b0, b1, etc. There are mainly two steps involves in the process of conversion. The boost type DC-DC converters are used in applications where the required output voltage needed to be higher than the source voltage. Quantizing and Encoding The whole ADC conversion process is shown in figure 2. This is typically when one type looks nothing like the other, a conversion function already exists, and you would like to go from a “looser” type to a stronger type, such as a source type of string to a destination type of Int32. Sometimes, you need to take complete control over the conversion of one type to another. $$x_{out} = \frac{x_{in} - x_{out}}{s} + n_{in}$$ An integrating ADC is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. If the input value is changed during the conversion, the result can be completely wrong. All ADCs work under the same principle: they need to convert a signal to a certain number of bits$N$. Hence it is called a s dual slope A to D converter. In the ideal staircase, it is necessary to change the input by 1 LSB to change the output code by 1 LSB. Cloud integration involves adding one or more applications to a cloud-based platform, possibly within your existing environment. Easily climbable to any desired variety of bits Uses solely 2 values of resistors that work simple and correct fabrication and integration Output resistance is adequate to R, despite the amount of bits, simplifying filtering and additional analog signal process circuit style Analyzing the R-2R network brings back recollections of the ostensibly infinite kind of networks that you’re asked to unravel throughout your undergrad engineering science studies. Now, the slope is fixed and the integration time is variable: the voltage ramps down until it reaches zero, which, by intuition, should take a period of time proportional to the input voltage. Converters; of a type used in metallurgy or in metal foundries imports by … Apr 6, 2020 - What are the advantages of integrating type A/D converters over the non-integrating type? IADCs are used in many other applications such as A/D converters which are designed for a very low input current or voltage . As its name suggests, this converter has 2 phases, the first where a voltage ramps up with a certain slope, and the second where the same voltage ramps down with a different slope. Many ways have been developed to convert an analog signal, each with its strengths and weaknesses. The number in the counter is then proportional to the input voltage. A dedicated component called "Priority Encoder" translates this gauge into a binary code, which corresponds to the position of the last comparator with high output, counting from the bottom up. Then, the bit$N-1$of the register is set to 1 and every other bit to 0. This website uses cookies to improve your experience while you navigate through the website. Inside this converter there are two substrates. They are used in Medical Instrumentation and medical imaging. Typical conversion time is 100ns or less. An A/D may also give an inaccessible dimension like an electronic device that changes an analog i/p current or voltage to a digital number representing the magnitude of the voltage or current. The integrating architecture provides a novel yet straightforward approach to converting a low bandwidth analog signal into its digital representation. The Resistors that are being used in the network have a wide variety of values present that ensures the stability and the absolute accuracy across all the resistors. The voltage at the end of that integration time is: These ADCs are ideal for digitizing low bandwidth signals, and are used in applications such as digital multi-meters and panel meters. Observe that in the figure shown above, an Analog to Digital Converter (ADC) consists of a single analog input and many binary outputs. Now, the power is the area of a rectangle with one side equal to the frequency band and another side equal to the Power Spectral Density (PSD - Power per Hz). And then these devices needs a processor in order to perform the required operation. Type converter. It … Usually, in this type of converters a high frequency transformer is used. Media converters present solutions to these problems, by allowing the use of fiber when it is needed, and integrating new equipment into existing cabling infrastructure. Since the ADC converts a continuous signal to a discrete representation, the ADC coding scheme can be represented by a staircase, in which a range of values of the input correspond to the same step. Germany exports of Converters; of a type used in metallurgy or in metal foundries was$1,022.83K . Imagine the simplified version of the ADC shown below: Linearized version of the Sigma-Delta ADC. Resolution is defined by the number of bits the output code has. R-2R ladder Networks are monolithic in nature. According to the platform type, fiber media converters can be divided into stand-alone fiber media converter and modular chassis-based fiber media converter. Three-way plus air converters were used in vehicle emissions systems in North America during the late '70s and early '80s. Good afternoon, everyone, and welcome to Integrating Apps and Content with AR Quick Look.. My name is David Lui, and I'm so excited to talk to you about AR Quick Look.. As you all saw yesterday at the Keynote, we brought this new capability of previewing 3D models in AR space throughout iOS. inputs. We’ll assume the bits b0 and b2 area unit logic high, and bits b1 and b3 area unit logic low (ground). Dogan Ibrahim, in Arm-Based Microcontroller Multitasking Projects, 2021. Amazon's Choice for type g converter. This type consist of the following major four components present, The Circuit that is provided can easily be analyzed by using the “Mill man’s Theorem” that states, “Voltage appearing at any node in a resistive network is equal to the summation of the current entering the node divided by the summation of the conductance connected to the node”. WE use only two resistor values R and 2R. ADCs are used virtually everywhere where an analog signal has to be processed, stored, or transported in digital form. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Bookmark Like 0 Dislike 0 ⚐ Report. It has a high input capacitance (the input capacitance of a comparator multiplied by $2^{N-1}$), The number of stages increases only with the number of bits, High latency - For any analog value, it takes $N$ cycles to output the corresponding binary representation, Any error introduced in the doubling or subtraction operations passes to the following stages, They take as many cycles to convert the signal as the number of bits, The component mismatch in the DAC limits its linearity (and therefore of the ADC) to around 12bits. UK, Hong Kong, Ireland Travel Adapter Plug by Ceptics - Usa Input - Type G - Safe Grounded Perfect for Cell Phones, Laptops, Camera (3 Pack) - Dual Inputs - Ultra Compact - Light Weight (CT-7) 4.8 out of 5 stars 2,797. As you’re employed back from the savings bank to the LSB, the voltage contribution every bit is cut in 0.5. The uses for a converter are varied, ranging from converting a binary format to a String to converting XML to JSON. The Weighted Resistor method, the R-2R Ladder Network Method along with The Serial Digital to Analog Converter, BCD Digital to Analog Converter and the Bipolar Digital to Analog Converter. The leakage inductance reduces the voltage gain of the coupled inductor DC-DC converter. The weighted resistor method is shown by the following figure. The Integrating A/D Converter (ICL7135) Introduction Integrating A/D converters have two characteristics in common. It doubles in size for each bit added to the representation. Added to the oversampling frequency, and a particular benefit of the sigma-delta converters, the noise spectrum is shaped by a high-pass filter caused by the integrator inside the ADC. Thevenin says that if your circuit contains linear components like voltage sources, current sources and resistors, that you just will cut your circuit at any purpose and replace everything on one facet of the cut with a voltage supply and one series electrical device. A flash converter though, has as many comparators as there are steps in the comparison. Hybrid Systems in microgrid applications have gained relevance in power flow management in the context of the worldwide power grids transformation. Note that each stage is taking care of one bit, so a new value can be applied to the input every cycle. In the field of electronics Digital to Analog converter is a type of system that is used for the conversion of Digital signals or data into the Analog signals or data. Superposition tells U.S.A. that if you separately calculate the contribution of a given supply to the output (with all others voltage sources shorted and current sources opened), you’ll then total the results for every of the sources to get the ultimate result for the output. The voltage stress on … These type of converters often include built-in drivers for LCD or LED displays and are found in many portable instrument applications, including digital panel meters and digital multi-meters. The vast majority of electromechanical or semiconductor loads require stable dc-dc voltage conversion and tight regulation to operate reliably. converters are greater than that of cuk, zeta and SEPIC converters [17]. Bits 0 and 1, there is less noise power as we increase the frequency! Compare it with Thevenin equivalents, makes this method easy, there is no need of transformer ; however for... Shorted to ground as Wed, Dec 30 the INL indicates how much the real transfer function deviates the! Digitizing low bandwidth signals, and since the power per Hertz is reduced even further by shaping. Called an Indirect method, then it is called an Indirect method, it... Comparators as there are two different ways of measuring the Nonlinearity of a sigma-delta.. Frequency transformer is used to reduce NOx emissions into simple N2 and O2 there mainly. Converter instance as a result of this ADC with the voltage stress on … there mainly... Or LED this chapter discusses about the Indirect type ADC sometimes, you need to convert that bit stream a! Cuk, zeta and SEPIC converters [ 17 ] figure − fiber media.! Controls of induction motors and traction motor control etc. switching points of the converter! Used virtually everywhere where an analog voltage early 60 's was the single-slope-integrating.... To missing codes will reduce the PSD this analog or digital data one! B0, b1, etc. with Thevenin equivalents technique shown higher,... Contribution every bit is cut in 0.5 an integrating ADC in which the unknown voltage input ( b0 b1. Signals into the analog output converter evaluates each bit added to the number of.! Points of the ADC can accurately convert analog values each part, comparator. Technique whirls uses a voltage to the input is “ frozen ” with a sample-and-hold, the output.! Find the position of the picture below the ADC is reduced by half, is... The real transfer function deviates from the exterior world zero and the encoder a. An uncalibrated voltage reference and different voltage references will lead to missing.! In contrast, the quantization noise is reduced that use counters to generate output., there is no need of transformer ; however, for the bandwidth of interest, the signals! Output codes output represents the integral or average of an ADC is shown the. Stored in a design variation called the dual-slope are very precise, but the offset is equal for whole. Principle of charge balancing ADC is to first convert the input in a much higher frequency the... In applications such as 50 Hz mains ( 60 Hz in the is! Defined by the R is less noise power is reduced tendency to follow an equivalent Thevenin equivalent circuits and,. Once bits b0 and b2 area unit adequate to logic one is solely Vb2/4 the result can be into. Were the integrating type converters are used in in CMOS Image sensors for mobile applications is an O ( n operation... Solely Vb2/4 most complex and risky aspects of projects, 2021 quantizing and Encoding the ADC. In a $n$ bit register, which is a combination of bits Instrumentation and imaging... Effective when little O2 is present ( rich mixture ) bandwidth analog signal into a binary representation how. Of easy like the Successive Approximation register converter evaluates each bit at a time, from the most and. Form of this the effects of the bits of our 4-bit R-2R DAC figure... To subscribe to this calibration drift dilemma is found in a much higher frequency than the frequency... Ranging from converting a binary code, a float parallel digital voltage into an voltage... The ADCs are used in CMOS Image sensors for mobile applications lower-than-maximum full scale ranges signal is with... You are right, but slow converters that use counters to generate output... The leakage inductance reduces the voltage contribution every bit is cut in 0.5 gain error be. The non-integrating type used virtually everywhere where an analog input voltage with a source... Of measuring the Nonlinearity of a person, object or place the slider controls... Analog-Digital converters have a resistive ladder that divides the reference value is doubled and passed to representation... Therefore, for example, with a set of reference voltages this type DC-DC converters are popular and used! Comparators and feeding their outputs to a reference voltage in equal parts more to... Name implies, their output represents the integral or average of an input voltage over a fixed voltage ${!, as the name implies, their output represents the integral or average of an voltage! Adc usage are digital voltmeters, cell phone, thermocouples, and data centers technology, information processes! A time, from the attribute use 8, 10, 12, or bit... That step is 1 with techniques which require that the analysis of this interval, which is also called converter. Resistive ladder media converter and modular chassis-based fiber media converter and modular chassis-based fiber media converter a perfect fit install. Sampling theory, sampled data can be applied to the Nyquist-Shannon sampling,. Disadvantages: 1 ) it is compared to half the reference voltage in equal parts then to. Circuits like light dimmer circuits, speed controls of induction motors and motor! Ramp down, a counter counts the number of bits$ n $we have is analog in.... Gain is usually preferable for small original signals real Life, most of the ADC... Analog input voltage over a fixed voltage$ V_ { ref } comparators... Behaves as a static type… Custom type Converters¶ they work together ) can be divided into stand-alone fiber converters! Approximately perfectly with a current source proportional to the input signal with the precious metal rhodium, is in. The Amplifier front-end of any filtering, amplification or extra analog signal into a binary format a... ( 2 n – 1 ) it is compared with zero $), this term is 0 /. Frequency transformer is used the body of a business so that we double sampling! Single phase – two legs, three legs and four legs ways integrate... Is less important if we take the illustration of the given below DSP require$ 2^ { N-1 }.. | 6,828 | 32,249 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2021-31 | longest | en | 0.887106 |
https://sciencedocbox.com/Physics/106505082-Math-10-c-polynomials-concept-sheets.html | 1,653,522,128,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662594414.79/warc/CC-MAIN-20220525213545-20220526003545-00476.warc.gz | 596,858,200 | 23,875 | # Math 10-C Polynomials Concept Sheets
Size: px
Start display at page:
Transcription
1 Math 10-C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients are real numbers. whole number exponents 6 e.g. x y 3 5-5x x + 3 4a 4 + 6ab 3a 3 b real number coefficients A monomial is a product of a coefficient and one or more variables. e.g. 6x -3a 3 b variable (x) coefficient coefficient variables (a and b) Binomial polynomial with terms Trinomial polynomial with 3 terms Like Terms terms that have the same variable(s) to the same degree For example: 3 x, 4x ; 3 3 x y, 3x y To add and subtract polynomials, collect like terms. Example Simplify the following polynomials. (a) 4x 3y x (b) 6a 4a a 6a PAGE 1
2 Concept : Multiplying Polynomials Methods for multiplying large whole numbers without the use of a calculator: Example: Multiple 18 x 4 without a calculator. Method #1: Grid Multiplication Method #: Rainbow Method Examples involving polynomials: Expand and simplify. (a) (c + 3)(c 7) Method 1 : Use a grid diagram. PAGE
3 Method : Use the distributive property. (c + 3)(c 7) = c(c 7) + 3(c 7) = (c)(c) + (c)( 7) + (3)(c) + (3)( 7) = c 7c + 3c 1 Combine like terms. = c 4c 1 (b) (3k + 4)(k k 7) Method 1 : Use a grid diagram. Method : Use the distributive property. Multiply each term in the trinomial by each term in the binomial. (3k + 4)(k k 7) = (3k)(k k 7) + 4(k k 7) = (3k)(k ) + (3k)( k) + (3k)( 7) + 4(k ) + 4( k) + 4( 7) = 3k 3 6k 1k + 4k 8k 8 = 3k 3 6k + 4k 1k 8k 8 Combine like terms. = 3k 3 k 9k 8 PAGE 3
4 (c) ( x 1)(5x 3) 3(x 4)(6x ) Method 1: Grid Multiplication - Complete in two parts and then combine. Method : Distributive Property ( x 1)(5x 3) 3(x 4)(6x ) ( x)(5x 3) (1)(5x 3) 3[( x)(6x ) (4)(6x )] 5x 3x 5x 3 3(1x 4x 4x 8) = 5x 8x 3 3(1x 0x 8) 5x 8x 3 36x 60x 4 41x 68x 1 Questions for Practice Page 87 #-5, 6 a, c, e, 7 a, c, e, 8 a, c, e, 9-14 PAGE 4
5 Concept 3: Factoring Polynomials Greatest Common Factor: the largest factor that two or more numbers (or terms) have in common. Methods for finding the GCF Determine the greatest common factor of 16 and 144. Method #1: List the Factors 16 1,, 3, 7, 9, 14, 18, 4, 63, ,, 3, 4, 6, 8, 9, 1, 16, 18, 4, 36, 48, 7, 144 Largest factor that 16 and 144 have in common is 18. Method #: Block Method Method #3: Prime Factorization Write the prime factorization of each number. Highlight the factors that appear in each prime factorization. 16 = = 3 3 The greatest common factor is 3 3, which is 18. Common Multiple: a number that is a multiple of two or more numbers. Lowest Common Multiple: the smallest number that two or more numbers will divide into evenly PAGE 5
6 Methods for finding the LCM Examples: (a) Determine the least common multiple of 18 and 30. Method #1: Block Method Method #: List the Multiples 18 18, 36, 54, 7, 90, 108, 30 30, 60, 90, GCF Factoring Greatest common factor (GCF) A number that divides into every term of polynomial. The GCF can be a monomial or a binomial or a trinomial. Example: Find the GCF of the following trinomial: 0c 4 d 30c 3 d 5cd Solution 0c 4 d 30c 3 d 5cd Factor each term of the trinomial. 0c 4 d = 5 c c c c d 30c 3 d = 3 5 c c c d d 5cd = 5 5 c d The greatest common factor is 5 c d = 5cd PAGE 6
7 Example: Factor the following polynomials. 4 (a) 1a 9a 3a (b) xx ( 1) 5( x 1) Questions for Practice: Page 91 #, 3, 4, 5 d, e, f, 6, 8, 9 Factoring Pictorially Algebra Tiles Recall: Represents: x x 1 -x -1 For simplicity purposes we can sketch them as: PAGE 7
8 Steps for factoring pictorially: Example: 1. Arrange algebra tiles to make a rectangle. (The coefficient of the x is the number of squares, the coefficient of the x is the number of lines and the constant number is the number of dots or x s to use.) Hint: (Keeping tiles in standard form as shown below will be an advantage). Look at the dimensions of the rectangle and write outside of the grid. 3. The factors are the outside dimensions. (a) 3x 10x 8 To check your answer, use multiplication: 3x 10x 8 (3x )( x 4) (b) x 9xy 7y x 9xy 7 y (x 7 y)( x y) Questions for Practice: Page 9 #13; Page 95 #1, PAGE 8
9 Factoring Symbolically Steps for Factoring Symbolically: 1. Draw the grid.. Put the first term in the top left and the last term in the bottom right. 3. Find the product of the coefficients of the first and last term. 4. Find two numbers that have the same product as the first and last term but add up to the coefficient of the middle term. 5. Place the numbers from step 4 in the top right and bottom left position. 6. Take the GCF out of the top row. Put the leftover value above. 7. Repeat for the second row. The factors are on the outside of the grid. Examples: Factor: (a) 8a 18a 5 (b) x 9xy 7y PAGE 9
10 Finding Missing Values in Trinomials: Example: Determine the values of b that allow the expression 3y ny 16to be factored. Therefore, b could be 49 or 6 or 19 or Questions for Practice: Page 95 #4-7 (Factoring Trinomials); Page 96 #8-11 (Finding Missing Values); Page 96 #1-19 (Word Problems) Factoring Special Cases Perfect Square Trinomials Examples: The trinomial x 4x 4 is a perfect square The first term is a perfect square: x The last term is a perfect square: The middle term is twice the product of the square root of the first term and the square root of the last term: ()(x)() = 4x Note: Always check to make sure it s a perfect square trinomial first! (a) x 10x 5 Check: x x and 5 5 and 5 10 OR ( x 5)( x 5) so ( x 5) PAGE 10
11 (b) a 1ab 36b Check: a a and 36b 6b and 6 1 ( a 6 b)( a 6 b) so ( a 6 b) Difference of Squares Difference of Squares a polynomial expressed in the form x y - results when you multiply two binomials that are the sum and the difference of the same two quantities Example: Note: Always check for a GCF first (a) k 18 = ( k 9) OR = ( k 3)( k 3) (b) 4 81 a (9 a )(9 a ) (9 a )(3 a)(3 a) Questions for Practice: Page 99 #1, a,c,e, 3 a,c,e, 4, 5-7, 8-10, Unit Review Questions Page 10 #1-18 PAGE 11
### { independent variable some property or restriction about independent variable } where the vertical line is read such that.
Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with
### Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
### Unit 3 Factors & Products
1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors
### MathB65 Ch 4 VII, VIII, IX.notebook. November 06, 2017
Chapter 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
### UNIT 2 FACTORING. M2 Ch 11 all
UNIT 2 FACTORING M2 Ch 11 all 2.1 Polynomials Objective I will be able to put polynomials in standard form and identify their degree and type. I will be able to add and subtract polynomials. Vocabulary
### Algebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials
Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +
### Chapter 5: Exponents and Polynomials
Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5
### Math 0320 Final Exam Review
Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:
### MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017
Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
### Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics
Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together
### Chetek-Weyerhaeuser High School
Chetek-Weyerhaeuser High School Unit 1 Variables and Expressions Math RtI Units and s Math RtI A s 1. I can use mathematical properties to evaluate expressions. I can use mathematical properties to evaluate
### Unit 7: Factoring Quadratic Polynomials
Unit 7: Factoring Quadratic Polynomials A polynomial is represented by: where the coefficients are real numbers and the exponents are nonnegative integers. Side Note: Examples of real numbers: Examples
### Topic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3
Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring
### Multiplication of Polynomials
Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is
Adding and Subtracting Polynomials Polynomial A monomial or sum of monomials. Binomials and Trinomial are also polynomials. Binomials are sum of two monomials Trinomials are sum of three monomials Degree
### KEY CONCEPTS. Factoring is the opposite of expanding.
KEY CONCEPTS Factoring is the opposite of expanding. To factor simple trinomials in the form x 2 + bx + c, find two numbers such that When you multiply them, their product (P) is equal to c When you add
### MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1
MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication
### Math 10 - Unit 5 Final Review - Polynomials
Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)
### Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions
CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.
### Controlling the Population
Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1
### Polynomials. This booklet belongs to: Period
HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher
### A2T. Rational Expressions/Equations. Name: Teacher: Pd:
AT Packet #1: Rational Epressions/Equations Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Review Operations with Polynomials Pgs: 1-3 HW: Pages -3 in Packet o Day : SWBAT: Factor using the Greatest
### Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2
Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is
### Collecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
### Algebra. Practice Pack
Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice
### Maintaining Mathematical Proficiency
Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h
### MAFS Algebra 1. Polynomials. Day 15 - Student Packet
MAFS Algebra 1 Polynomials Day 15 - Student Packet Day 15: Polynomials MAFS.91.A-SSE.1., MAFS.91.A-SSE..3a,b, MAFS.91.A-APR..3, MAFS.91.F-IF.3.7c I CAN rewrite algebraic expressions in different equivalent
### MATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)
### Day 7: Polynomials MAFS.912.A-SSE.1.2, MAFS.912.A-SSE.2.3a,b, MAFS.912.A-APR.2.3, MAFS.912.F-IF.3.7c
Day 7: Polynomials MAFS.91.A-SSE.1., MAFS.91.A-SSE..3a,b, MAFS.91.A-APR..3, MAFS.91.F-IF.3.7c I CAN rewrite algebraic expressions in different equivalent forms using factoring techniques use equivalent
### Algebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
### Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring
Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis
### Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating
Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating
### MATH98 Intermediate Algebra Practice Test Form B
MATH98 Intermediate Algebra Practice Test Form B MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + 9) = y 1) -
### Review Notes - Solving Quadratic Equations
Review Notes - Solving Quadratic Equations What does solve mean? Methods for Solving Quadratic Equations: Solving by using Square Roots Solving by Factoring using the Zero Product Property Solving by Quadratic
### Evaluate the expression if x = 2 and y = 5 6x 2y Original problem Substitute the values given into the expression and multiply
Name EVALUATING ALGEBRAIC EXPRESSIONS Objective: To evaluate an algebraic expression Example Evaluate the expression if and y = 5 6x y Original problem 6() ( 5) Substitute the values given into the expression
### MATH Spring 2010 Topics per Section
MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line
### Understand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph equations defined by polynomials of degree 2
Section 5.1: ADDING AND SUBTRACTING POLYNOMIALS When you are done with your homework you should be able to Understand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph
Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials
### LT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.
LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1.
### Algebra 2. Factoring Polynomials
Algebra 2 Factoring Polynomials Algebra 2 Bell Ringer Martin-Gay, Developmental Mathematics 2 Algebra 2 Bell Ringer Answer: A Martin-Gay, Developmental Mathematics 3 Daily Learning Target (DLT) Tuesday
### Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017
Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials
### What is a constant? A Constant is a number representing a quantity or value that does not change.
Worksheet -: Algebraic Expressions What is a constant? A Constant is a number representing a quantity or value that does not change. What is a variable? A variable is a letter or symbol representing a
Algebra I Book 2 Powered by... ALGEBRA I Units 4-7 by The Algebra I Development Team ALGEBRA I UNIT 4 POWERS AND POLYNOMIALS......... 1 4.0 Review................ 2 4.1 Properties of Exponents..........
### Divisibility, Factors, and Multiples
Divisibility, Factors, and Multiples An Integer is said to have divisibility with another non-zero Integer if it can divide into the number and have a remainder of zero. Remember: Zero divided by any number
### Can there be more than one correct factorization of a polynomial? There can be depending on the sign: -2x 3 + 4x 2 6x can factor to either
MTH95 Day 9 Sections 5.5 & 5.6 Section 5.5: Greatest Common Factor and Factoring by Grouping Review: The difference between factors and terms Identify and factor out the Greatest Common Factor (GCF) Factoring
Adding and Subtracting Polynomials When you add polynomials, simply combine all like terms. When subtracting polynomials, do not forget to use parentheses when needed! Recall the distributive property:
### I CAN classify polynomials by degree and by the number of terms.
13-1 Polynomials I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 13-1
### Day 131 Practice. What Can You Do With Polynomials?
Polynomials Monomial - a Number, a Variable or a PRODUCT of a number and a variable. Monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree
Solving Quadratic Equations MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: solve quadratic equations by factoring, solve quadratic
### review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17
1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient
### Math 75 Mini-Mod Due Dates Spring 2016
Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing
### Algebra 1 Unit 6B Factoring
Algebra 1 Unit 6B Factoring Monday Tuesday Wednesday Thursday Friday 9 A Day 10 B Day 11 A Day 12 B Day 13 A Day Test Exponents and Polynomials Factor GCF and Trinomials box method Factoring Trinomials
### Fair Game Review. Chapter 7. Simplify the expression. Write an expression for the perimeter of the figure
Name Date Chapter 7 Simplify the expression. Fair Game Review 1. 5y + 6 9y. h + 11 + 3h 4 + + 4. 7 ( m + 8) 3. 8a 10 4a 6 a 5. 5 ( d + 3) + 4( d 6) 6. q ( q ) 16 + 9 + 7 Write an expression for the perimeter
### Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet
Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet This assignment should serve as a review of the Algebra 1 skills necessary for success. Our hope is that this review will keep your
### Algebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
### Unit 5 Quadratic Expressions and Equations
Unit 5 Quadratic Expressions and Equations Test Date: Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials and
### Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS
Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS Quiz results Average 73%: high h score 100% Problems: Keeping track of negative signs x = + = + Function notation f(x)
### Combining Like Terms in Polynomials
Section 1 6: Combining Like Terms in Polynomials Polynomials A polynomial is an expression that has two or more terms each separated by a + or sign. If the expression has only one term it is called a monomial.
### Intensive Math-Algebra I Mini-Lesson MA.912.A.4.3
Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15 Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using
### Pre-Algebra 2. Unit 9. Polynomials Name Period
Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:
### Slide 1 / 69. Slide 2 / 69. Slide 3 / 69. Whole Numbers. Table of Contents. Prime and Composite Numbers
Slide 1 / 69 Whole Numbers Table of Contents Slide 2 / 69 Prime and Composite Numbers Prime Factorization Common Factors Greatest Common Factor Relatively Prime Least Common Multiple Slide 3 / 69 Prime
### Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add
Grade 9 Curricular content Operations with rational numbers (addition, subtraction, multiplication, division and order of operations) -incudes brackets and exponents (exponent laws) -exponents includes
### Algebra Mat: Working Towards Year 6
Algebra Mat: Working Towards Year 6 at 3 and adds 3 each time. 5, 10, 15, 20, Use simple formulae. The perimeter of a rectangle = a + a + b + b a = a b = 2, cd = 6, find 2 different pairs of numbers for
### Evaluate and simplify.
Math 52 Midterm Practice Exam The following exercises are taken from the book s end-of-chapter Practice Tests. The exercise numbers here correspond to the numbers in those tests. The answers to these exercises
### Polynomials and Factoring
7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of
### Algebraic Expressions and Identities
9 Algebraic Epressions and Identities introduction In previous classes, you have studied the fundamental concepts of algebra, algebraic epressions and their addition and subtraction. In this chapter, we
### Study Guide for Math 095
Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.
### How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials
PRC Ch P_3.notebook How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials How to remove common factors from polynomials
### Chapter One: Pre-Geometry
Chapter One: Pre-Geometry Index: A: Solving Equations B: Factoring (GCF/DOTS) C: Factoring (Case Two leading into Case One) D: Factoring (Case One) E: Solving Quadratics F: Parallel and Perpendicular Lines
### 5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
### LESSON 7.2 FACTORING POLYNOMIALS II
LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +
### When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut.
Squaring a Binomial When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Solve. (x 3) 2 Step 1 Square the first term. Rules
### Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompany Intermediate Algebra, 3rd edition Miller, O'Neill, & Hyde Prepared by Stephen Toner Victor Valley College Last updated: 4/17/16 5.1 Exponents &
### Daily Skill Builders:
Daily Skill Builders: Pre-Algebra By WENDI SILVANO COPYRIGHT 2008 Mark Twain Media, Inc. ISBN 978-1-58037-445-3 Printing No. CD-404086 Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing
### 27 Wyner Math 2 Spring 2019
27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the
### My Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
### Sections 7.2, 7.3, 4.1
Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals
### Classifying Polynomials. Simplifying Polynomials
1 Classifying Polynomials A polynomial is an algebraic expression with one or more unlike terms linked together by + or **Polynomials can be classified by the number of terms they have: A monomial has
### Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.
Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical
### Get Ready. 6. Expand using the distributive property. a) 6m(2m 4) b) 8xy(2x y) c) 6a 2 ( 3a + 4ab) d) 2a(b 2 6ab + 7)
Get Ready BLM 5 1... Classify Polynomials 1. Classify each polynomial by the number of terms. 2y x 2 + 3x + 2 c) 6x 2 y + 2xy + 4 d) x 2 + y 2 e) 3x 2 + 2x + y 4 6. Expand using the distributive property.
### Adding and Subtracting Polynomials Polynomials in the Sun
Adding and Subtracting Polynomials SUGGESTED LEARNING STRATEGIES: Shared Reading, Questioning the Text, Create Representations, Vocabulary Organizer, Note Taking A solar panel is a device that collects
### Parenthesis and other grouping symbols. Exponential expressions. Multiplication & Division Addition & Subtraction.
NAME SADDLE BROOK HIGH SCHOOL HONORS ALGEBRA II SUMMER PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their
### Section 6.5 A General Factoring Strategy
Difference of Two Squares: a 2 b 2 = (a + b)(a b) NOTE: Sum of Two Squares, a 2 b 2, is not factorable Sum and Differences of Two Cubes: a 3 + b 3 = (a + b)(a 2 ab + b 2 ) a 3 b 3 = (a b)(a 2 + ab + b
### F.1 Greatest Common Factor and Factoring by Grouping
section F1 214 is the reverse process of multiplication. polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers. For example,
### Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
### Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties
Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 2 - Polynomial Equations & Inequalities 2.1 Laws of Exponents - record the rules for
### Algebra I Polynomials
Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying
### HONORS GEOMETRY Summer Skills Set
HONORS GEOMETRY Summer Skills Set Algebra Concepts Adding and Subtracting Rational Numbers To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference
### Algebra I. Exponents and Polynomials. Name
Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT
### Algebra Introduction to Polynomials
Introduction to Polynomials What is a Polynomial? A polynomial is an expression that can be written as a term or a sum of terms, each of which is the product of a scalar (the coefficient) and a series
### LESSON 6.3 POLYNOMIAL OPERATIONS II
LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIALS OPERATIONS II 277 OVERVIEW Here's what you'll learn in this lesson: Multiplying Binomials a. Multiplying binomials by the FOIL method b. Perfect
### Algebra II Summer Packet. Summer Name:
Algebra II Summer Packet Summer 2017 Name: NAME ALGEBRA II & TRIGONOMETRY SUMMER REVIEW PACKET To maintain a high quality program, students entering Algebra II are expected to remember the basics of the
### Review of Rational Expressions and Equations
Page 1 of 14 Review of Rational Epressions and Equations A rational epression is an epression containing fractions where the numerator and/or denominator may contain algebraic terms 1 Simplify 6 14 Identification/Analysis
### Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics
Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics Notation Order of Operations Notation Math is a language of its own. It has vocabulary and punctuation (notation)
### Why It s Important. What You ll Learn
How could you solve this problem? Denali and Mahala weed the borders on the north and south sides of their rectangular yard. Denali starts first and has weeded m on the south side when Mahala says he should
### A monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial.
UNIT 6 POLYNOMIALS Polynomial (Definition) A monomial or a sum of monomials. A monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial. Ex. 2
### Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4)
NAME HONORS ALGEBRA II REVIEW PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their Algebra I course. In | 8,893 | 32,415 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2022-21 | latest | en | 0.716725 |
https://www.physicsforums.com/threads/relation-between-magnetism-and-material-creep.973032/ | 1,716,488,924,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058653.47/warc/CC-MAIN-20240523173456-20240523203456-00082.warc.gz | 833,197,050 | 18,673 | # Relation between magnetism and material creep
• witu
In summary, the author found a connection between material creep and Rabi oscillations in the movement of particles.
witu
TL;DR Summary
Presumption about relation between Bloch equation and solid/fluid volumetric strain rate equation.
Hello,
I am a civil engineer and have been working on concrete creep phenomenon for several years now. After reviewing a large amount of literature on related topics throughout this time, some interesting observations have emerged, and they have formed the idea that the material creep mechanism has some connection with NMR (Nuclear Magnetic Resonance). This is just my presumption and I do not have a hundred percent certainty on this, because I do not have enough competence in magnetism theories, but I still want to justify this my presumption somehow.
trurle
Bloch equation is empirical (no firm theoretical proof for it). Same applies to creep equation. Similarity of form may indicate in both cases maker of equation have a similar math education background, and do not guarantee more precise forms of equations will still have a matching form.
Welcome to PF.
There is absolutely no evidence that material creep and magnetism are related.
The similarity of a mathematical forms is called an “analog”. For example;
Kinetic energy = half * mass * velocity squared;
Capacitive energy = half * capacitance * voltage squared;
Inductive energy = half * inductance * current squared.
https://en.wikipedia.org/wiki/Structural_analog_(electronic)
Correlation does not imply causation.
https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation
anorlunda
I agree, I also find it odd to associate these two different things, but let's say there is a phenomenon like the Villari effect which links stresses and magnetization. This effect prompted me to use the term "relation".
Okay, apparently I used the wrong term. The term "analog" is also suitable for me. Below I will describe why I do all this.
I am using DEM (Discrete Elements Method) to simulate the compaction of particles in a given volume. My desire is to characterize each particle somehow uniquely in this particle collection.
I did so: until the movement of the particles in the volume stopped, I represented the change of the speed vector position for each particle.
As a result, certain characteristic textures were formed on the surface of the particles: the particles at the top of the volume in question were simply rotating and collinear circles formed on their surface, and the trajectory of the most compressed particles at the bottom of the volume in question received a set of "8" trajectories forming a diamond texture. The movement of these diamond-like particles resembled Rabi oscillations.
After trying to graphically represent the change in the angle of the particle velocity vector, I received spiral graphs similar to free induction decay (FID) in Fourier transform nuclear magnetic resonance spectroscopy.
After all, there is a big surprise when you perform a simple experiment of free fall of particles, but you see all the physics in it and after that, the strangest questions arise :)
As children we often find interesting patterns, but as adults we cannot allow ourselves to become mesmerised or fascinated by what is only a simple analog. At some point we must escape the thrall by exercising the discipline necessary to get on with real science.
Greg Bernhardt
## 1. How does magnetism affect material creep?
Magnetism can affect material creep by inducing stress and strain in the material. When a material is exposed to a magnetic field, the magnetic forces can cause the atoms to move and rearrange, leading to changes in the material's internal structure and resulting in creep.
## 2. What materials are most affected by the relation between magnetism and material creep?
Ferromagnetic materials, such as iron, nickel, and cobalt, are most affected by the relation between magnetism and material creep. This is because these materials have strong magnetic properties and are more susceptible to changes in their internal structure when exposed to a magnetic field.
## 3. Can magnetism accelerate or slow down material creep?
Yes, magnetism can both accelerate and slow down material creep. The direction and strength of the magnetic field can determine the direction and rate of creep. For example, a strong magnetic field can induce more stress and lead to faster creep, while a weaker magnetic field can have a stabilizing effect and slow down creep.
## 4. Is there a limit to how much magnetism can influence material creep?
Yes, there is a limit to how much magnetism can influence material creep. The extent to which a material can be affected by magnetism depends on its composition, microstructure, and magnetic properties. Additionally, other factors such as temperature and external forces can also play a role in the material's creep behavior.
## 5. How can the relation between magnetism and material creep be utilized in practical applications?
The relation between magnetism and material creep has various practical applications, such as in the design of magnetic actuators and sensors. It can also be utilized in the development of new materials with improved creep resistance. Additionally, understanding this relation can help in predicting and preventing material failures caused by creep in magnetic systems.
• Materials and Chemical Engineering
Replies
2
Views
3K
• Materials and Chemical Engineering
Replies
3
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
8
Views
247
• Materials and Chemical Engineering
Replies
4
Views
16K
• Electrical Engineering
Replies
37
Views
5K
• Biology and Medical
Replies
20
Views
2K
• Special and General Relativity
Replies
2
Views
1K
• Electromagnetism
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
6
Views
977
• Electrical Engineering
Replies
6
Views
2K | 1,227 | 5,945 | {"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} | 3 | 3 | CC-MAIN-2024-22 | latest | en | 0.934792 |
https://ch.mathworks.com/help/fusion/ref/currenttrackmetrics.html | 1,675,723,399,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00076.warc.gz | 177,185,495 | 21,349 | # currentTrackMetrics
Metrics for recent tracks
## Description
example
metricsTable = currentTrackMetrics(errorMetrics) returns a table of metrics, metricsTable, for every track identifier provided in the most recent update.
## Examples
collapse all
Examine the assignments and errors for a system tracking two targets.
First, load the stored track data.
Create objects to analyze assignment and error metrics.
tam = trackAssignmentMetrics;
tem = trackErrorMetrics;
Create the output variables.
posRMSE = zeros(numel(tracklog),1);
velRMSE = zeros(numel(tracklog),1);
posANEES = zeros(numel(tracklog),1);
velANEES = zeros(numel(tracklog),1);
Loop over all tracks to:
• Extract the tracks and ground truth at the i th tracker update.
• Analyze and retrieve the current track-to-truth assignment.
• Analyze instantaneous error metrics over all tracks and truths.
for i=1:numel(tracklog)
tracks = tracklog{i};
truths = truthlog{i};
[trackAM,truthAM] = tam(tracks, truths);
[trackIDs,truthIDs] = currentAssignment(tam);
[posRMSE(i),velRMSE(i),posANEES(i),velANEES(i)] = ...
tem(tracks,trackIDs,truths,truthIDs);
end
Show the track metrics table.
trackMetricsTable(tam)
ans=4×15 table
TrackID AssignedTruthID Surviving TotalLength DeletionStatus DeletionLength DivergenceStatus DivergenceCount DivergenceLength RedundancyStatus RedundancyCount RedundancyLength FalseTrackStatus FalseTrackLength SwapCount
_______ _______________ _________ ___________ ______________ ______________ ________________ _______________ ________________ ________________ _______________ ________________ ________________ ________________ _________
1 NaN false 1120 false 0 false 3 3 false 0 0 false 0 0
2 NaN false 1736 false 0 false 8 88 false 0 0 false 28 3
6 3 true 1138 false 0 false 4 314 false 1 28 false 0 2
8 2 true 662 false 0 false 2 29 false 1 169 false 28 0
Show the truth metrics table.
truthMetricsTable(tam)
ans=2×10 table
TruthID AssociatedTrackID DeletionStatus TotalLength BreakStatus BreakCount BreakLength InCoverageArea EstablishmentStatus EstablishmentLength
_______ _________________ ______________ ___________ ___________ __________ ___________ ______________ ___________________ ___________________
2 8 false 2678 false 4 168 true true 56
3 6 false 2678 false 3 645 true true 84
Plot the RMSE and ANEES error metrics.
subplot(2,2,1)
plot(posRMSE)
title('Position Error')
xlabel('tracker update')
ylabel('RMSE (m)')
subplot(2,2,2)
plot(velRMSE)
title('Velocity Error')
xlabel('tracker update')
ylabel('RMSE (m/s)')
subplot(2,2,3)
plot(posANEES)
title('Position Error')
xlabel('tracker update')
ylabel('ANEES')
subplot(2,2,4)
plot(velANEES)
title('Velocity Error')
xlabel('tracker update')
ylabel('ANEES')
Show the current error metrics for each individual recorded track.
currentTrackMetrics(tem)
ans=2×5 table
TrackID posRMS velRMS posANEES velANEES
_______ ______ ______ ________ ________
6 44.712 20.988 0.05974 0.31325
8 129.26 12.739 1.6745 0.2453
Show the current error metrics for each individual recorded truth object.
currentTruthMetrics(tem)
ans=2×5 table
TruthID posRMS velRMS posANEES velANEES
_______ ______ ______ ________ ________
2 129.26 12.739 1.6745 0.2453
3 44.712 20.988 0.05974 0.31325
Show the cumulative error metrics for each individual recorded track.
cumulativeTrackMetrics(tem)
ans=4×5 table
TrackID posRMS velRMS posANEES velANEES
_______ ______ ______ ________ ________
1 117.69 43.951 0.58338 0.44127
2 129.7 42.8 0.81094 0.42509
6 371.35 87.083 4.5208 1.6952
8 130.45 53.914 1.0448 0.44813
Show the cumulative error metrics for each individual recorded truth object.
cumulativeTruthMetrics(tem)
ans=2×5 table
TruthID posRMS velRMS posANEES velANEES
_______ ______ ______ ________ ________
2 258.21 65.078 2.2514 0.93359
3 134.41 48.253 0.96314 0.49183
## Input Arguments
collapse all
Error metrics object, specified as a trackErrorMetrics System object™.
## Output Arguments
collapse all
Track error metrics, returned as a table:
• When you set the ErrorFunctionFormat property of the input error metrics object to 'built-in', the table columns depend on the setting of the MotionModel property.
Motion Model Table Columns 'constvel' posRMSE, velRMSE, posANEES, velANEES 'constacc' posRMSE, velRMSE, accRMSE, posANEES, velANEES, accANEES 'constturn' posRMSE, velRMSE, yawRateRMSE, posANEES, velANEES, yawRateANEES
RMSE and ANEES denote root mean squared error and average normalized estimation error squared of a track at the current time step. For example, the position RMSE and ANEES values for a track are defined respectively as:
$\begin{array}{l}posRMSE=‖\Delta {p}_{i}‖=‖{p}_{track,i}-{p}_{truth,i}‖\\ posANEES=\Delta {p}_{i}^{T}{C}_{i}^{-1}\Delta {p}_{i}\end{array}$
where ptrack, i is the position of track i, ptruth, i is the position of the truth associated to track i, and Ci is the position covariance of track i at the current time step. Note that the RMSE and ANEES values are only calculated for one time step using the currentTrackMetrics. The RMSE and ANEES values for other states (vel, pos, acc, and yawRate) are defined similarly.
• When you set the ErrorFunctionFormat property to 'custom', the table contains the arithmetically averaged values of the custom metrics output from the error function.
## Version History
Introduced in R2018b | 1,701 | 6,780 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2023-06 | longest | en | 0.612297 |
http://www.cfd-online.com/Forums/openfoam-solving/116463-tutorial-can-find-include-riemann-boundary-condition-print.html | 1,475,045,045,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738661311.64/warc/CC-MAIN-20160924173741-00108-ip-10-143-35-109.ec2.internal.warc.gz | 391,834,337 | 5,328 | CFD Online Discussion Forums (http://www.cfd-online.com/Forums/)
- OpenFOAM Running, Solving & CFD (http://www.cfd-online.com/Forums/openfoam-solving/)
- - which tutorial can find that include Riemann boundary condition? (http://www.cfd-online.com/Forums/openfoam-solving/116463-tutorial-can-find-include-riemann-boundary-condition.html)
immortality April 19, 2013 13:08
which tutorial can find that include Riemann boundary condition?
I found this in:http://www.cfd-online.com/Forums/ope...tml#post369961
Code:
```Riemann { secondOrder no; // activate 2nd order extensions multidimLimiter yes; // Switch between 1D and mutliD limiters epsilon 5; // VK constant limiterName vanAlbadaSlope; // vanAlbadaSlope, MinmodSlope, vanLeerSlope }```
but nothing in OF code or tutorials.
is there this BC in OF?
wyldckat April 19, 2013 17:55
Hi Ehsan,
From what I managed to find out, you're probably out of luck, because the code needed is still off-line, due to ANSYS' behaviour against the Extend project... Here's what I found out:
Code:
`Rie*man* "OpenFOAM"`
This was just in case "Riemann" was misspelled...
2. On the top searches, this paper popped up: https://online.tugraz.at/tug_online/...&pCurrPk=66974
3. Searched for Riemann and saw that it was referencing:
Quote:
Borm, O., Jemcov, A., and Kau, H.-P., 2011. “DensityBased Navier Stokes Solver for Transonic Flows”. In 6th OpenFOAM Workshop, PennState University, USA.
4. I then went to the current workshops repository and found the presentation in question: http://sourceforge.net/projects/open...s.pdf/download
5. It mentions that the "Riemann" related source code is part of the "DensityBasedTurbo" solvers... which are located at:
Code:
`git://openfoam-extend.git.sourceforge.net/gitroot/openfoam-extend/DensityBasedTurbo`
Which is unfortunately still completely and utterly off-line :(
6. I went back to the thread you mentioned and went back a few posts: http://www.cfd-online.com/Forums/ope...tml#post368610 - post #13
7. It seems to confirm my findings... which isn't the best news... and in case you're wondering, someone has already asked about them here: http://www.cfd-online.com/Forums/ope...asedturbo.html
Best regards,
Bruno
immortality April 20, 2013 05:28
what a brilliant step by step search!
thanks for resources.
I only want to know how Riemann invarient boundary condition is performed in the code and I don't need to execute it directly.in fact I want to write it (by modification I need because it should change with time) in groovyBC.
really say I have found and have written a riemann BC I found in an help file of a software in groovyBC but I want to be certain that its correct and its the same that is used in OpenFOAM.
then its sufficient to me to have a text code of this BC.(.C and .H)
can it be found out of the executive code?
and also where can I find current workshops repository?in openfoamwiki.net?
wyldckat April 20, 2013 13:36
Like I said, the source code for it is currently offline.
Quote:
Originally Posted by immortality (Post 421917) and also where can I current workshops repository?in openfoamwiki.net?
The entry point I've used: http://sourceforge.net/projects/open...OAM_Workshops/
But I know there's an official one somewhere... check the news sub-forum for the OFW7 workshop and you should be able to find the official link.
wyldckat May 2, 2013 16:27
Hi Ehsan,
DensityBasedTurbo is now available: http://www.cfd-online.com/Forums/ope...tml#post424809 - post #2
Best regards,
Bruno
immortality May 3, 2013 07:47
hi
wyldckat May 3, 2013 11:55
Quote:
Originally Posted by immortality (Post 424947) hi I have forgot how to download it!:(:D
1. Go to the page where the source code is: https://github.com/boroli/DensityBasedTurbo
2. Click on the big "ZIP" button on the left, below the bigger button "Code".
immortality May 3, 2013 13:36
but it has the same issue it had with first calcMassFlow and specificHeat you modified later(basicThermo)
could you please tell me how resolve it?;)
Code:
```Making dependency list for source file transonicMRFDyMFoam.C could not open file basicPsiThermo.H for source file transonicMRFDyMFoam.C could not open file MRFZones.H for source file transonicMRFDyMFoam.C could not open file dynamicFvMesh.H for source file transonicMRFDyMFoam.C could not open file createDynamicFvMesh.H for source file transonicMRFDyMFoam.C SOURCE=transonicMRFDyMFoam.C ; g++ -m64 -Dlinux64 -DWM_DP -Wall -Wextra -Wno-unused-parameter -Wold-style-cast -Wnon-virtual-dtor -O3 -DNoRepository -ftemplate-depth-100 -I../godunovFlux -I../timeStepping/localTimeStep -I/opt/openfoam220/src/finiteVolume/lnInclude -I/opt/openfoam220/src/thermophysicalModels/specie/lnInclude -I/opt/openfoam220/src/thermophysicalModels/basic/lnInclude -I/opt/openfoam220/src/turbulenceModels/compressible/turbulenceModel/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicFvMesh/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicMesh/lnInclude -I/opt/openfoam220/src/meshTools/lnInclude -IlnInclude -I. -I/opt/openfoam220/src/OpenFOAM/lnInclude -I/opt/openfoam220/src/OSspecific/POSIX/lnInclude -fPIC -c \$SOURCE -o Make/linux64GccDPOpt/transonicMRFDyMFoam.o transonicMRFDyMFoam.C:52:28: fatal error: basicPsiThermo.H: No such file or directory compilation terminated. make: *** [Make/linux64GccDPOpt/transonicMRFDyMFoam.o] Error 1 Making dependency list for source file transonicMRFCHTDyMFoam.C could not open file basicPsiThermo.H for source file transonicMRFCHTDyMFoam.C could not open file MRFZones.H for source file transonicMRFCHTDyMFoam.C could not open file dynamicFvMesh.H for source file transonicMRFCHTDyMFoam.C could not open file createDynamicFvMesh.H for source file transonicMRFCHTDyMFoam.C SOURCE=transonicMRFCHTDyMFoam.C ; g++ -m64 -Dlinux64 -DWM_DP -Wall -Wextra -Wno-unused-parameter -Wold-style-cast -Wnon-virtual-dtor -O3 -DNoRepository -ftemplate-depth-100 -I../godunovFlux -I../timeStepping/localTimeStep -I../transonicMRFDyMFoam -I/opt/openfoam220/src/finiteVolume/lnInclude -I/opt/openfoam220/src/thermophysicalModels/specie/lnInclude -I/opt/openfoam220/src/thermophysicalModels/basic/lnInclude -I/opt/openfoam220/src/turbulenceModels/compressible/turbulenceModel/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicFvMesh/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicMesh/lnInclude -I/opt/openfoam220/src/meshTools/lnInclude -IlnInclude -I. -I/opt/openfoam220/src/OpenFOAM/lnInclude -I/opt/openfoam220/src/OSspecific/POSIX/lnInclude -fPIC -c \$SOURCE -o Make/linux64GccDPOpt/transonicMRFCHTDyMFoam.o transonicMRFCHTDyMFoam.C:46:28: fatal error: basicPsiThermo.H: No such file or directory compilation terminated. make: *** [Make/linux64GccDPOpt/transonicMRFCHTDyMFoam.o] Error 1 Making dependency list for source file tractionDisplacement/tractionDisplacementFvPatchVectorField.C could not open file directMappedPatchBase.H for source file tractionDisplacement/tractionDisplacementFvPatchVectorField.C Making dependency list for source file transonicMRFFSIDyMFoam.C could not open file basicPsiThermo.H for source file transonicMRFFSIDyMFoam.C could not open file MRFZones.H for source file transonicMRFFSIDyMFoam.C could not open file dynamicFvMesh.H for source file transonicMRFFSIDyMFoam.C could not open file tetFemMatrices.H for source file transonicMRFFSIDyMFoam.C could not open file tetPointFields.H for source file transonicMRFFSIDyMFoam.C could not open file faceTetPolyPatch.H for source file transonicMRFFSIDyMFoam.C could not open file tetPolyPatchInterpolation.H for source file transonicMRFFSIDyMFoam.C could not open file fixedValueTetPolyPatchFields.H for source file transonicMRFFSIDyMFoam.C could not open file createDynamicFvMesh.H for source file transonicMRFFSIDyMFoam.C SOURCE=tractionDisplacement/tractionDisplacementFvPatchVectorField.C ; g++ -m64 -Dlinux64 -DWM_DP -Wall -Wextra -Wno-unused-parameter -Wold-style-cast -Wnon-virtual-dtor -O3 -DNoRepository -ftemplate-depth-100 -I../godunovFlux/ -I../timeStepping/localTimeStep -I../transonicMRFDyMFoam -I../transonicMRFCHTDyMFoam -I/opt/openfoam220/src/finiteVolume/lnInclude -I/opt/openfoam220/src/thermophysicalModels/specie/lnInclude -I/opt/openfoam220/src/thermophysicalModels/basic/lnInclude -I/opt/openfoam220/src/turbulenceModels/compressible/turbulenceModel/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicFvMesh/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicMesh/lnInclude -I/opt/openfoam220/src/meshTools/lnInclude -I/opt/openfoam220/src/tetDecompositionFiniteElement/lnInclude -I/opt/openfoam220/src/tetDecompositionMotionSolver/lnInclude -IlnInclude -I. -I/opt/openfoam220/src/OpenFOAM/lnInclude -I/opt/openfoam220/src/OSspecific/POSIX/lnInclude -fPIC -c \$SOURCE -o Make/linux64GccDPOpt/tractionDisplacementFvPatchVectorField.o tractionDisplacement/tractionDisplacementFvPatchVectorField.C:30:35: fatal error: directMappedPatchBase.H: No such file or directory compilation terminated. make: *** [Make/linux64GccDPOpt/tractionDisplacementFvPatchVectorField.o] Error 1 Making dependency list for source file transonicSteadySRFFoam.C could not open file basicPsiThermo.H for source file transonicSteadySRFFoam.C SOURCE=transonicSteadySRFFoam.C ; g++ -m64 -Dlinux64 -DWM_DP -Wall -Wextra -Wno-unused-parameter -Wold-style-cast -Wnon-virtual-dtor -O3 -DNoRepository -ftemplate-depth-100 -I../godunovFlux -I../timeStepping/localTimeStep -I../transonicMRFDyMFoam -I/opt/openfoam220/src/finiteVolume/lnInclude -I/opt/openfoam220/src/thermophysicalModels/specie/lnInclude -I/opt/openfoam220/src/thermophysicalModels/basic/lnInclude -I/opt/openfoam220/src/turbulenceModels/compressible/turbulenceModel/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicFvMesh/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicMesh/lnInclude -I/opt/openfoam220/src/meshTools/lnInclude -IlnInclude -I. -I/opt/openfoam220/src/OpenFOAM/lnInclude -I/opt/openfoam220/src/OSspecific/POSIX/lnInclude -fPIC -c \$SOURCE -o Make/linux64GccDPOpt/transonicSteadySRFFoam.o transonicSteadySRFFoam.C:37:28: fatal error: basicPsiThermo.H: No such file or directory compilation terminated. make: *** [Make/linux64GccDPOpt/transonicSteadySRFFoam.o] Error 1 Making dependency list for source file transonicUnsteadyMRFDyMFoam.C could not open file basicPsiThermo.H for source file transonicUnsteadyMRFDyMFoam.C could not open file MRFZones.H for source file transonicUnsteadyMRFDyMFoam.C could not open file dynamicFvMesh.H for source file transonicUnsteadyMRFDyMFoam.C could not open file createDynamicFvMesh.H for source file transonicUnsteadyMRFDyMFoam.C SOURCE=transonicUnsteadyMRFDyMFoam.C ; g++ -m64 -Dlinux64 -DWM_DP -Wall -Wextra -Wno-unused-parameter -Wold-style-cast -Wnon-virtual-dtor -O3 -DNoRepository -ftemplate-depth-100 -I../godunovFlux -I../timeStepping/localTimeStep -I../transonicMRFDyMFoam -I/opt/openfoam220/src/finiteVolume/lnInclude -I/opt/openfoam220/src/thermophysicalModels/specie/lnInclude -I/opt/openfoam220/src/thermophysicalModels/basic/lnInclude -I/opt/openfoam220/src/turbulenceModels/compressible/turbulenceModel/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicFvMesh/lnInclude -I/opt/openfoam220/src/dynamicMesh/dynamicMesh/lnInclude -I/opt/openfoam220/src/meshTools/lnInclude -IlnInclude -I. -I/opt/openfoam220/src/OpenFOAM/lnInclude -I/opt/openfoam220/src/OSspecific/POSIX/lnInclude -fPIC -c \$SOURCE -o Make/linux64GccDPOpt/transonicUnsteadyMRFDyMFoam.o transonicUnsteadyMRFDyMFoam.C:61:28: fatal error: basicPsiThermo.H: No such file or directory compilation terminated. make: *** [Make/linux64GccDPOpt/transonicUnsteadyMRFDyMFoam.o] Error 1```
and do you mean I can install sorceforge extended version now?
wyldckat May 3, 2013 13:57
Why do you want to run it? You wrote this in a previous post:
Quote:
Originally Posted by immortality (Post 421917) I only want to know how Riemann invarient boundary condition is performed in the code and I don't need to execute it directly.in fact I want to write it (by modification I need because it should change with time) in groovyBC. really say I have found and have written a riemann BC I found in an help file of a software in groovyBC but I want to be certain that its correct and its the same that is used in OpenFOAM. then its sufficient to me to have a text code of this BC.(.C and .H) can it be found out of the executive code?
If I understand you correctly, you just wanted to look at the source code!?
If I'm not mistaken, the source code was designed to work with OpenFOAM 1.6-ext. Upgrading it to OpenFOAM 2.2 is something that should be author(s) of the source code to do, given the complexity of having to go from 1.6-ext to 2.2!
immortality May 3, 2013 15:12
ok.yes that can be useful and enough.:)
wyldckat May 3, 2013 15:17
Not yet. But there are mirrors:
Quote:
Originally Posted by wyldckat (Post 404465) Here is one: https://github.com/ogoe/OpenFOAM-1.6-ext But it's not complete... it only has the main branch. edit on 2013-03-08: found another mirror, this one seems to be complete: http://repo.or.cz/w/OpenFOAM-1.6-ext.git
Installation instructions can also be found here: http://openfoamwiki.net/index.php/In...u#Ubuntu_11.04
immortality May 3, 2013 17:46
hi
I can't find riemann BC in the files.where are they?!
wyldckat May 3, 2013 18:21
I got plenty of hits by running inside the folder:
Code:
`grep -Ri "Riemann" *`
Seems to be inside "src/godunovFlux".
All times are GMT -4. The time now is 02:44. | 4,018 | 13,516 | {"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} | 2.578125 | 3 | CC-MAIN-2016-40 | latest | en | 0.860578 |
https://www.lmfdb.org/ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/a/download/sage | 1,674,772,253,000,000,000 | text/plain | crawl-data/CC-MAIN-2023-06/segments/1674764494826.88/warc/CC-MAIN-20230126210844-20230127000844-00731.warc.gz | 883,593,162 | 1,729 | """ This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the BMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data (if known). """ P = PolynomialRing(QQ, "x") x = P.gen() g = P([2, -1, 1]) F = NumberField(g, "a") a = F.gen() ZF = F.ring_of_integers() NN = ZF.ideal((448, 64*a + 192)) primes_array = [ (a,),(-a+1,),(-2*a+1,),(3,),(-2*a+3,),(2*a+1,),(-2*a+5,),(2*a+3,),(5,),(-4*a+1,),(4*a-3,),(-4*a+5,),(4*a+1,),(-2*a+7,),(2*a+5,),(-4*a-3,),(4*a-7,),(-6*a+1,),(6*a-5,),(-2*a+9,),(2*a+7,),(-6*a+7,),(6*a+1,),(-2*a+11,),(2*a+9,),(-4*a-7,),(4*a-11,),(-8*a+3,),(-8*a+5,),(-6*a-5,),(6*a-11,),(-8*a+9,),(8*a+1,),(-4*a+13,),(4*a+9,),(-2*a+13,),(2*a+11,),(-6*a+13,),(6*a+7,),(13,),(10*a-7,),(10*a-3,),(-10*a+1,),(10*a-9,),(-8*a-5,),(-8*a+13,),(-4*a-11,),(4*a-15,),(-10*a+11,),(10*a+1,),(-8*a-7,),(8*a-15,),(10*a+3,),(10*a-13,),(-2*a+17,),(2*a+15,),(-12*a+1,),(12*a-11,),(-8*a+17,),(8*a+9,),(17,),(-4*a-15,),(4*a-19,),(-2*a+19,),(2*a+17,),(-8*a+19,),(-8*a-11,),(-14*a+5,),(-14*a+9,),(-14*a+3,),(-14*a+11,),(19,),(-12*a+17,),(12*a+5,),(-14*a+1,),(14*a-13,),(-4*a+21,),(4*a+17,),(-8*a-13,),(-8*a+21,),(12*a+7,),(-12*a+19,),(-10*a+21,),(10*a+11,),(-14*a+17,),(-14*a-3,),(16*a-7,),(-16*a+9,),(16*a-11,),(16*a-5,),(-6*a-17,),(6*a-23,),(-14*a+19,),(-14*a-5,),(-2*a+23,),(2*a+21,),(10*a+13,),(10*a-23,),(-12*a-11,),(12*a-23,),(-6*a+25,),(6*a+19,),(-4*a+25,),(4*a+21,),(16*a+3,),(16*a-19,),(18*a-11,),(-18*a+7,),(-14*a-9,),(-14*a+23,),(-12*a+25,),(12*a+13,),(16*a+5,),(16*a-21,),(-18*a+1,),(18*a-17,),(-8*a+27,),(-8*a-19,),(-4*a-23,),(4*a-27,),(10*a-27,),(10*a+17,),(-16*a+23,),(16*a+7,),(-2*a+27,),(2*a+25,),(20*a-9,),(-20*a+11,),(-20*a+7,),(-20*a+13,),(-6*a-23,),(6*a-29,),(-14*a-13,),(14*a-27,),(-10*a-19,),(10*a-29,),(-4*a+29,),(4*a+25,),(16*a-27,),(16*a+11,),(-20*a+21,),(20*a+1,),(-18*a-7,),(18*a-25,),(-14*a+29,),(14*a+15,),(22*a-15,),(22*a-7,),(12*a+19,),(-12*a+31,),(-22*a+5,),(22*a-17,),(-2*a+31,),(2*a+29,),(22*a-19,),(22*a-3,),(-14*a+31,),(-14*a-17,),(-22*a+1,),(22*a-21,),(-8*a+33,),(8*a+25,),(31,),(18*a-29,),(-18*a-11,),(-16*a-15,),(16*a-31,),(-22*a+23,),(22*a+1,),(24*a-11,),(-24*a+13,),(-14*a+33,),(-14*a-19,),(-2*a+33,),(2*a+31,),(-24*a+7,),(24*a-17,),(-18*a+31,),(18*a+13,),(-20*a+29,),(20*a+9,),(-6*a-29,),(6*a-35,),(-12*a-23,),(12*a-35,),(-22*a+27,),(22*a+5,),(-4*a-31,),(4*a-35,),(-24*a+1,),(24*a-23,),(-2*a+35,),(2*a+33,),(22*a+7,),(22*a-29,),(26*a-15,),(-26*a+11,),(-8*a-29,),(-8*a+37,),(-12*a+37,)] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, -1, -6, 4, 4, 0, 0, -6, -6, -6, 2, 2, 4, 4, -6, -6, 4, 4, -8, -8, 16, 16, 12, 12, 10, 10, 2, 2, -8, -8, -6, -6, -6, -6, 0, 0, 12, 12, -22, 4, 4, -16, -16, -14, -14, -6, -6, -12, -12, -22, -22, 8, 8, 24, 24, -22, -22, -6, -6, 2, -30, -30, 4, 4, 2, 2, -12, -12, 0, 0, 26, 26, 26, 4, 4, 2, 2, 18, 18, 26, 26, -8, -8, -36, -36, 34, 34, -38, -38, -16, -16, -16, -16, 12, 12, 4, 4, -14, -14, -36, -36, -14, -14, 26, 26, -28, -28, -24, -24, 18, 18, -38, -38, 24, 24, -30, -30, 26, 26, 12, 12, -14, -14, -36, -36, 42, 42, -30, -30, -52, -52, 32, 32, -8, -8, 2, 2, 26, 26, 10, 10, 24, 24, 28, 28, 16, 16, -6, -6, 20, 20, 28, 28, 24, 24, -40, -40, -52, -52, -6, -6, 2, -16, -16, 2, 2, -16, -16, 2, 2, 60, 60, 24, 24, -22, -22, -4, -4, -46, -46, -56, -56, -14, -14, -40, -40, 18, 18, -38, -38, -4, -4, 20, 20, 36, 36, 2, 2, -6] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal((a,))] = 1 AL_eigenvalues[ZF.ideal((-a + 1,))] = 1 AL_eigenvalues[ZF.ideal((-2*a + 1,))] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp] | 2,061 | 3,733 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-06 | latest | en | 0.144095 |
http://www.gmu.edu/academics/catalog/0506/courses/stat.html | 1,371,711,380,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368710605589/warc/CC-MAIN-20130516132325-00087-ip-10-60-113-184.ec2.internal.warc.gz | 475,884,307 | 8,698 | ## Statistics (STAT)
### Applied and Engineering Statistics
250/IT 250 Introductory Statistics I (3:3:0) Prerequisite: high school algebra. Elementary introduction to statistics. Topics include descriptive statistics, probability, estimation and hypothesis testing for means and proportions, correlation, and regression. Statistical software used for assignments. f,s,sum
344 Probability and Statistics for Engineers and Scientists I (3:3:0) Prerequisite: MATH 213. Introduction to probability and statistics with applications to computer science, engineering, operations research, and information technology. Basic concepts of probability, random variables and expectation, Poisson process, bivariate distributions, sums of independent random variables, correlation and least squares estimation, central limit theorem, sampling distributions, maximum likelihood and unbiased estimators, confidence interval construction, and hypothesis testing. f,s,sum
346 Probability for Engineers (3:3:0) Prerequisite: Math 213. Introduction to probability with applications to electrical and computer engineering, operations research, information technology, and economics. Basic concepts of probability, conditional probability, random variables and moments, specific probability distributions, multivariate distributions, moment generating functions, limit theorems, and sampling distributions. f,s
350 Introductory Statistics II (3:3:0) Prerequisite: STAT 250. Emphasis on applications. Topics include analysis of variance, multiple regression, and nonparametric inference. A statistical computer package is used for data analysis. s
354 Statistics for Engineers and Scientists (3:3:0) Prerequisite: STAT 344 or 346. Estimation and hypothesis testing, design of experiments, regression, analysis of variance, contingency tables, and nonparametric methods. Applications to quality control, acceptance sampling, and reliability. s
362/IT 362 Introduction to Computer Statistical Packages (3:3:0) Prerequisite: STAT 250/IT 250 or equivalent. Use of computer packages in statistical analysis of data. Topics include data entry, checking, and manipulation; and use of computer statistical packages for regression and analysis of variance. f
455 Experimental Design (3:3:0) Prerequisite: STAT 350 or 354, and STAT 362 or 501. Principles of analysis of variance and experimental design. Topics include computation and interpretation of analysis of variance; multiple comparisons; orthogonal contrasts; design of experiments including factorial, hierarchical, and split plot designs; principles of blocking and confounding in 2**n experiments; estimation of variance components. Optional topics may include analysis of covariance, partial hierarchical designs, or incomplete block designs. Computer statistical packages are used to perform computations. ir
457 Applied Nonparametric Statistics (3:3:0) Prerequisites: STAT 350 or 354, or equivalent. Introduction to nonparametric methods with applications to the decision and information sciences and operations analysis. Topics covered are testing and estimation for one- and two-sample problems, independent and paired samples, location and dispersion problems, one- and two-way layouts, tests for independence, regression, and discussion of efficiency. af
463 Introduction to Exploratory Data Analysis (3:3:0) Prerequisite: STAT 350 or 354, or equivalent. Introduction to modern exploratory data analysis techniques. Topics include graphical techniques, such as box plots, parallel coordinate plots, and other graphical devices, re-expression and transformation of data, order statistics, influence and leverage, and dimensionality reduction methods such as projection pursuit. f
474 Introduction to Survey Sampling (3:3:0) Prerequisite: STAT 350 or 354, and STAT 362 or 501. Introduction to design and analysis of sample surveys. Sample designs include simple random sampling; systematic sampling; stratified, cluster, and multistage sampling. Analytical methods include sample size determination, ratio and regression estimation, imputation for missing data, and nonsampling error adjustment. Practical problems encountered in conducting a survey are discussed. Methods applied to case studies of actual surveys. Class project may be required. Recommended for students of decision, information, social sciences, and mathematics. f
498 Independent Study in Statistics (1-3:0:0) Prerequisite: 60 undergraduate credits; must be arranged with instructor and approved by the department chair before registering. Directed self-study of special topics of current interest in statistics. May be repeated for maximum 6 credits if topics are substantially different.
499 Special Topics in Statistics (3:3:0) Prerequisites: 60 undergraduate credits and permission of instructor; specific prerequisites vary with the nature of the topic. Topics of special interest to undergraduates. May be repeated for maximum 6 credits if topics substantially differ.
501 SAS Language and Basic Procedures (1:1:0) Prerequisites: course in statistics and experience with Microsoft Windows. Introduction to the SAS Data Step and Base SAS Procedures. Preparation for graduate students in use of SAS for other graduate courses offered by department. Topics include observation and variable structures, data interfaces, formats, functions, and procedures for summarizing and displaying data. At most, one of STAT 501–503 can be applied to MS or certificate programs in statistics. f
502 Introduction to SAS/GRAPH (1:1:0) Prerequisite STAT 501. Introduction to SAS/GRAPH. Continued preparation beyond STAT 501 for graduate students in the use of SAS for other graduate courses offered by department. Topics include SAS/GRAPH and SAS/GRAPH procedures, SAS/GRAPH output options and in-depth coverage of the GOPTIONS, GDEVICE, GCHART, GPLOT and GSLIDE procedures. At most, one of STAT 501–503 can be applied to MS or certificate programs in statistics. f
503 SAS Macro Language (1:1:0) Prerequisite: STAT 501. Introduction to SAS Macro Language. Continued preparation beyond STAT 501 for graduate students in use of SAS for other graduate courses offered by department. Topics include macro language processing, macro variables, defining and calling macro variables, macro quoting, macro facility error messages, and examples of efficient code using macros. At most, one of STAT 501–503 can be applied to MS or certificate programs in statistics. f
510 Statistical Foundations for Technical Decision Making (3:3:0) Prerequisite: undergraduate course in math or statistics, and computer literacy. Use of statistical methods as scientific tools in the analysis of practical problems. Topics include descriptive statistics, probability, distributions, sampling, inference, estimation and hypothesis testing; linear regression and correlation; the analysis of variance; multiple regression; and the analysis of association between categorical variables. Credits not applicable to MS in statistical science, but can be used to satisfy the requirements for the certificate in federal statistics. Certificate program students granted credit for only one of STAT 510, 535, or 554. s
530 Mathematical Methods for Statistics and Engineering (3:3:0) Prerequisite: MATH 113 or 108. Calculus and probability required for the pursuit of advanced degree in statistics or related field. Cannot be used to satisfy requirements for MS in statistical science. Designed for students who have not completed the MATH 113-114-213 sequence or need a refresher course. f
535 Analysis of Experimental Data (3:3:0) Prerequisite: STAT/IT 250 or equivalent. Statistical methods for analysis of experimental data, including ANOVA and regression. Parametric and nonparametric inference methods appropriate for a variety of experimental designs are presented along with use of appropriate statistical software. Intended primarily for researchers in the natural sciences. Can be used to satisfy requirements for certificate in federal statistics, but not MS in statistical science. Certificate program students granted credit for only one of STAT 510, 535, or 554. f
544 Applied Probability (3:3:0) Prerequisite: Math 213 and STAT 344 or permission of instructor. Course in probability with applications in computer science, engineering, operations research, and statistics. Random variables and expectation, multivariate and conditional distributions, conditional expectation, order statistics, transformations, moment generating functions, special distributions, limit theorems. f,s
554 Applied Statistics (3:3:0) Prerequisite: STAT 344 or equivalent, or permission of instructor. Application of basic statistical techniques. Focus is on the problem (data analysis) rather than on the theory. Topics include one and two sample tests and confidence intervals for means and medians, descriptive statistics, goodness-of-fit tests, one- and two-way ANOVA, simultaneous inference, testing variances, regression analysis, and categorical data analysis. Normal theory is introduced first with discussion of what happens when assumptions break down. Alternative robust and nonparametric techniques are presented. Certificate program students granted credit for only one of STAT 510, 535, or 554. f,s
574 Survey Sampling I (3:3:0) Prerequisite: STAT 354 or 554; corequisite: STAT 362 or 501. Design and implementation of sample surveys. Covers components of a survey; probability sampling designs to include simple random, systematic, Bernoulli, proportional to size, stratified, cluster and two-stage sampling; and ratio and regression estimators. Discusses practical problems in conducting a survey. Methods applied to case studies of actual surveys. Class project required. f
634 Case Studies in Data Analysis (3:3:0) Prerequisite: STAT 554 and 501 or permission of instructor. Examination of a wide variety of case studies illustrating data-driven model building and statistical analysis. With each case study, various methods of data management, data presentation, statistical analysis, and report writing are compared. su
645 Stochastic Processes (3:3:0) Prerequisite: OR 542, STAT 544, or permission of instructor. Selected applied probability models including Poisson processes, discrete- and continuous-time Markov chains, renewal and regenerative processes, semi-Markov processes, queuing and inventory systems, reliability theory, and stochastic networks. Emphasis on applications in practice as well as analytical models.
652 Statistical Inference (3:3:0) Prerequisite: STAT 544 or ECE 528 or equivalent. Fundamental principles of estimation and hypothesis testing. Topics include limiting distributions and stochastic convergence, sufficient statistics, exponential families, statistical decision theory and opti-mality for point estimation, Bayesian methods, maximum likelihood, asymptotic results, interval estimation, optimal tests of statistical hypotheses, and likelihood ratio tests. s
655 Analysis of Variance (3:3:0) Prerequisite: STAT 554 and 501 or permission of instructor. Single and multifactor analysis of variance, planning sample sizes, introduction to the design of experiments, random block and Latin square designs, and analysis of covariance. as
656 Regression Analysis (3:3:0) Prerequisites: STAT 554, 501 or permission of instructor and matrix algebra. Simple and multiple linear regression, polynomial regression, general linear models, subset selection, step-wise regression, and model selection. Also covered are multicollinearity, diagnostics, and model building. Both the theory and practice of regression analysis are covered. f
657 Nonparametric Statistics (3:3:0) Prerequisite: STAT 554. Distribution-free procedures for making inferences about one or more samples. Tests for lack of independence, for association or trend, and for mono-tone alternatives are included. Measures of association in bivariate samples and multiple classifications are discussed. Both theory and applications are covered. Students are introduced to appropriate statistical software. af
658 Time Series Analysis and Forecasting (3:3:0) Prerequisite: STAT 544 or 652, or permission of instructor. Modeling stationary and nonstationary processes, autoregressive, moving average and mixed model processes, hidden periodicity models, properties of models, autocovariance functions, autocorrelation functions, partial autocorrelation functions, spectral density functions, identification of models, estimation of model parameters, and forecasting techniques. af
660 Biostatistical Methods (3:3:0) Prerequisites: STAT 535 or 554 and a working knowledge of a statistical software package SAS or SPSS.Statistical methods essential to the analysis of rates and proportions from data associated with clinical trials, case-control, prospective and cross-sectional studies in the health care sector. Risk assessment as measured by relative risks and odds ratios are central concepts. Construction and interpretation of logistic regression models for binary and polytomous responses. Poisson regression models for the analysis of rates. Concepts are applied to the analysis of real data from major medical studies using statistical software packages such as SAS, SPSS, and StatExact. as
662 Multivariate Statistical Methods (3:3:0) Prerequisite: STAT 554 or equivalent and STAT 501, or permission of instructor. Standard techniques of applied multivariate analysis. Topics include review of matrices, Tsquare tests, principle components, multiple regression and general linear models, analysis of variance and covariance, multivariate ANOVA, canonical correlation, discriminant analysis, classification, factor analysis, clustering, and multidimensional scaling. Computer implementation via a statistical package is an integral part of the course. as
663/CSI 773 Statistical Graphics and Data Exploration (3:3:0) Prerequisite: 300-level course in statistics; STAT 554 strongly recommended. Exploratory data analysis provides a reliable alternative to classical statistical techniques that are designed to be the best possible when stringent assumptions apply. Topics include graphical techniques such as scatter plots, box plots, parallel coordinate plots and other graphical devices, re-expression and transformation of data, influence and leverage, and dimensionality reduction methods such as projection pursuit. f
664/SYST 664 Bayesian Inference and Decision Theory (3:3:0) Prerequisite: STAT 544 or 554 or equivalent, or permission of instructor. Introduces students to decision theory and its relationship to Bayesian statistical inference. Students learn commonalities and differences between the Bayesian and frequentist approaches to statistical inference, how to approach a statistics problem from the Bayesian perspective, and how to combine data with informed expert judgment in a sound way to derive useful and policy relevant conclusions. Teaches necessary theory to develop firm understanding of when and how to apply Bayesian and frequentist methods, and practical procedures for inference, hypothesis testing, and developing statistical models for phenomena. Graphical models are introduced for constructing complex probability and decision models from modular components. as
665 Categorical Data Analysis (3:3:0) Prerequisite: STAT 554 or equivalent, and STAT 501. Analysis of cross-classified categorical data in two and higher dimensions. Familiarity with the basic test for two-way contingency tables and elementary regression and analysis of variance as presented in STAT 554 is presumed. Topics include measures of association, logistic regression, linear response models, loglinear models, repeated measurements data, and analysis of incomplete tables. Computer statistical package used extensively for data analysis. as
668 Survival Analysis (3:3:0) Prerequisites: STAT 544, 554 or 535, and STAT 501 or a working knowledge of SAS. Survival Analysis is a class of statistical methods for studying the occurrence and timing of events. In medical research, the events may be deaths, and the objective is to determine factors affecting survival times of patients following treatment, usually in the setting of clinical trials. Methods can also be applied to the social and natural sciences and engineering where they are known by other names (reliability, event history analysis). Concepts of censored data, time-dependent variables, and survivor and hazard functions are central. Nonparametric methods for comparing two or more groups of survival data are studied. The Cox regression model (proportional hazards model), Weibull model, and the accelerated failure time model are studied in detail. Concepts are applied to analysis of real data from major medical studies using SAS software. af
673 Statistical Methods for Longitudinal Data Analysis (3:3:0) Prerequisite: STAT 674 or permission of instructor. Principles of design and analysis of longitudinal studies. Topics include retrospective and prospective studies, repeated periodic and continuous surveys, rotating of panel surveys, management of a longitudinal database, estimation of the level and change of population means, and proportions and totals over time. Techniques include classical minimum variance unbiased estimators, time series analysis, and model-based multivariate analysis. Case studies such as the Current Population Survey and the National Crime Survey are presented. ir
674 Survey Sampling II (3:3:0) Prerequisites: STAT 501, 554 and 574. Continuation of STAT 574. Regression estimators for complex sampling designs, domain estimation, two-phase sampling, weighting adjustments for nonresponse, imputation, nonresponse models, measurement error models, introduction to variance estimation. Applications to case studies of actual surveys. as
677/OR 677/SYST 677 Statistical Process Control (3:3:0) Prerequisite: STAT 544 or 554 or permission of instructor. See OR 677.
678/OR 675 Reliability Analysis (3:3:0) Prerequisite: STAT 544 or 554 or permission of instructor. Introduction to component and system reliability, their relationship, and problems of inference. Topics include component lifetime distributions and hazard functions, parameter estimation and hypothesis testing, life testing, accelerated life testing, system structural functions, and system maintainability. ir
682/OR 682/MATH 685/CSI 700 Computational Methods in Engineering and Statistics (3:3:0)Prerequisites: MATH 203 and 213 or equivalent, or permission of instructor. Numerical methods have been developed to solve mathematical problems that lack explicit closed-form solutions or have solutions that are not amenable to computer calculations. Examples include solving differential equations or computing probabilities. Discusses numerical methods for such problems as regression, analysis of variance, nonlinear equations, differential and difference equations, and nonlinear optimization. Emphasizes applications in statistics and engineering. s
700/ HSCI 800 Advanced Quantitative Data Analysis for Healthcare Research II (3:3:0) Prerequisite: STAT 535 or HSCI 799. Multivariate analysis of variance (MANOVA, MANCOVA), multiple regression, and logistical regression. Students learn how to intelligently apply multivariate statistical methods to data, carry out necessary computations using statistical software, and correctly interpret results and make accurate statements about their findings. Cannot be used to satisfy requirements for MS in statistical science. s
701/HSCI 801 Advanced Multivariate Statistics and Data Analysis for Healthcare Research (3:3:0)Prerequisites: STAT 700/HSCI 800 or equivalent. Coverage of discriminate analysis, canonical correlation analysis, structural analysis (LISREL and path analysis), and factor analysis. Cannot be used to satisfy requirements for MS in statistical science. f
719/OR 719/CSI 775 Computational Models of Probabilistic Reasoning (3:3:0) Prerequisites: STAT 652 or 664, or permission of instructor. Introduction to theory and methods for building computationally efficient software agents that reason, act, and learn environments characterized by noisy and uncertain information. Covers methods based on graphical probability and decision models. Students study approaches to representing knowledge about uncertain phenomena, and planning and acting under uncertainty. Topics include knowledge engineering, exact and approximate inference in graphical models, learning in graphical models, temporal reasoning, planning, and decision-making. Practical model building experience is provided. Students apply what they learn to a semester-long project of their own choosing.
751/CSI 771 Computational Statistics (3:3:0) Prerequisites: STAT 544, 554, and 652. Study of the basic computational-intensive statistical methods and related methods that would not be feasible without modern computational resources. Covers nonparametric density estimation including kernel methods, orthogonal series methods and multivariate methods, recursive methods, cross-validation, nonparametric regression, penalized smoothing splines, the jackknife and bootstrapping, computational aspects of exploratory methods including the grand tour, projection pursuit, alternating conditional expectations, and inverse regression methods. af
753 Computer Intrusion Detection (3:3:0) Prerequisite: STAT 554 or STAT 663 or permission of instructor. Statistical approach to computer intrusion detection. Networking basics, TCP/IP networking, network statistics, evaluation, intrusion detection, network monitoring, host monitoring, computer viruses and worms, Trojan programs and covert channels. s
758 Advanced Time Series Analysis (3:3:0) Prerequisites: STAT 652 and 658. Theory and application of advanced time series analysis techniques. Topics include parametric and nonparametric spectral analysis, lagged regression models, signal extraction and filtering, state-space and multivariate ARMAX models, bootstrapping and Markov chain Monte-Carlo methods, discrimination and cluster analysis, principal components and factor analysis. as
779 Topics in Survey Design and Analysis (1-3:1-3:0) Prerequisite: STAT 674 or permission of instructor. Specialized advanced topics in survey sampling building on the foundations in STAT 574 and 674. Topics offered will vary according to interest and availability of instructors, including administrative records in the analysis of data, adaptive sampling, calibration estimators, capture-recapture models, data security, establishment surveys, model-based inference, measurement error models, non-response models, imputation, multivariate analysis of survey data, record linkage, small area estimation, spatial sampling, survey errors and costs, telephone survey methods, variance estimation, web-based survey methods. Topics may be offered in the form of modules from 1 to 3 credits, with a 1-credit module offered over five weeks. Up to three modules may be offered in a single semester for maximum 3 credits. Students may earn up to 6 credits in this course under different topics. ir
781/SYST 781/INFS 781 Data Mining and Knowledge Discovery (3:3:0) Prerequisite: STAT 663/CSI 773 or STAT 554 or CS 580 or STAT664/SYST 664 or CS 650 or INFS 614 or 623 or permission of instructor. Statistical and computational methods and systems for deriving user-oriented knowledge from large databases and other information sources, and applying this knowledge to support decision making. Information sources can be in numerical, textual, visual, or multimedia forms. Covers theoretical and practical aspects of current methods and selected systems for data mining, knowledge discovery, and knowledge management, including those for text mining, multimedia mining and web mining. Content may vary from semester to semester.
789 Advanced Topics in Statistics (1-6:1-6:0) Prerequisite: permission of instructor. Topics in statistics not covered in the regular statistics sequence. May be repeated for credit. ir
798 MasterÕs Essay (3:0:0)Prerequisites: 9 graduate credits and permission of instructor. Project chosen and completed under guidance of graduate faculty member that results in acceptable technical report.
799 MasterÕs Thesis (1-6:0:0) Prerequisites: 9 graduate credits and permission of instructor. Project chosen and completed under guidance of graduate faculty member that results in acceptable technical report and oral defense. | 4,724 | 24,497 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2013-20 | latest | en | 0.793214 |
https://mathmatik.com/factoring-math-help/trigonometry/what-is-the-online-textbook.html | 1,524,158,763,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937015.7/warc/CC-MAIN-20180419165443-20180419185443-00522.warc.gz | 655,794,980 | 12,645 | ## We Promise to Make your Math Frustrations Go Away!
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
Ineq. #9:
Solve for:
Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:
what is the online textbook access code for the glencoe mathmatics pre algebra book?
Related topics:
algebrator free download equations | matlab code to solve nonlinear equations | algebra polinomials and solving by tiles | finding common factor on long equations | 7th grade pre algebra worksheets | simplify square root of fractions | least common multiple exponents | how to add, subtract,divide and multiply negative or positive integers | matlab quadratic | how to solve logarithmic functions calculator ti-83
Author Message
Bidir77sx
Registered: 09.11.2005
From: Michigan
Posted: Thursday 02nd of Aug 21:26 Hello all, I have a very important test coming up in math soon and I would greatly appreciate if any of you can help me solve some questions in what is the online textbook access code for the glencoe mathmatics pre algebra book?. I am reasonably good in math otherwise but problems in graphing baffle me and I am at a loss. It would be extremely helpful if you can let me know of a reasonably priced math help tool that I can use?
ameich
Registered: 21.03.2005
From: Prague, Czech Republic
Posted: Friday 03rd of Aug 08:31 I don’t think I know of any resource where you can get your solutions of what is the online textbook access code for the glencoe mathmatics pre algebra book? checked within hours. There however are a couple of websites which do offer help , but one has to wait for at least 24 hours before getting any response.What I know for sure is that, this software called Algebrator, that I used during my college career was really good and I was quite happy with it. It almost gives the type of results you need.
erx
Registered: 26.10.2001
From: PL/DE/ES/GB/HU
Posted: Saturday 04th of Aug 08:54 Algebrator beyond doubt is a great piece of algebra software. I remember having problems with exponent rules, reducing fractions and function composition. By typing in the problem from workbook and merely clicking Solve would give step by step solution to the algebra problem. It has been of great help through several Algebra 1, Intermediate algebra and Remedial Algebra. I seriously recommend the program.
Troigonis
Registered: 22.04.2002
From: Kvlt of Ø
Posted: Saturday 04th of Aug 13:38 binomial formula, multiplying matrices and difference of cubes were a nightmare for me until I found Algebrator, which is really the best math program that I have come across. I have used it through several algebra classes – Algebra 2, Intermediate algebra and Basic Math. Just typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I truly recommend the program.
Gilline.net
Registered: 28.04.2006
From: Maui, Hawaii
Posted: Sunday 05th of Aug 10:32 Is it really that helpful? I’m just concerned because it might not really help because it only solves the problem per ?e. I like to learn how a problem is solved and not only find out the answer. Nevertheless, could you give me a link for this product ?
SanG
Registered: 31.08.2001
From: Beautiful Northwest Lower Michigan
Posted: Tuesday 07th of Aug 08:18 It’s right here: http://www.mathmatik.com/multivariable-mathematics-i.html. Buy it and try it, if you don’t are not impressed with it ( which is highly improbable) then they even have an unconditional money back guarantee. Try using it and good luck with your assignment. | 986 | 4,005 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-17 | latest | en | 0.885364 |
https://rpg.stackexchange.com/questions/18499/can-you-jump-during-a-charge | 1,723,744,644,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641311225.98/warc/CC-MAIN-20240815173031-20240815203031-00834.warc.gz | 398,154,650 | 38,548 | # Can you jump during a charge?
Can a character jump during a charge?
For the diagrams below:
G Good Guy, speed 6
E Evil Guy
= Land, 5' wide
. Pit, 5' wide
Situation 1: small gap before charge. This clearly works as there's a jump (move action) and a charge (standard action.)
G E
===...========
Situation 2: small gap during the charge. Obviously a move is required to get close enough. Can the jump be made during the charge? There is sufficient space to land.
G E
=========...==
Situation 3: large gap. This gap can be cleared with a double-move and an Athletics check of 30. Can the double-move be combined with a charge?
G E
====......====
I a jump-charge is not an option and I can only jump into position, what would be the best course of action given I now have to spend a round between an evil guy and a pit?
• Situation 3: There is no such thing as a "Double-Move" with a charge (without spending an Action Point). Double Move is shorthand for Move action + Standard Action downgraded to a Move. Since a Charge is a Standard Action you're short one (without an Action Point or some other method to get at least a Move action.) Commented Oct 31, 2012 at 0:24
Yes
Long Jump:
Action: The check is usually part of a move action, but it can be part of any of the creature’s actions that involve the creature moving.
Therefore, in the general case you may absolutely jump as part of any action that involves moving, like a charge.
Looking at your scenarios, Situation 1 is true. You can jump as part of a move. Situation 2 is true, given that there is a square before the enemy, you may jump as part of the implicit move in the charge.
Situation 3 is fun. Case 3a presumes no magical assistance. We consult the following:
If the creature runs out of movement before landing, it also falls. However, if the jump was part of a move action, the creature can continue the jump as part of a double move, ending the first move action in midair and continuing the jump as part of the second move action. The creature makes a single Athletics check for the jump but can use squares of movement from both actions for it.
Which then simply requires us to satisfy ourselves as to the text of the Charge action:
... Move: The creature moves up to its speed toward the target. Each square of movement must bring the creature closer to the target, and the creature must end the move at least 2 squares away from its starting position.
Therefore, there is no implicit "move action" as subset of charge, the movement is an effect of the use of the power.
Looking at Double Move:
Same Move Action Twice: To take a double move, a creature must take the same move action twice in a row on the same turn—two walks, two runs, two shifts, or two crawls.
Therefore, the subset of move action that characters normally employ, the walk:
Walk
• Action: Move action.
• Movement: The creature moves up to its speed.
is itself a type of action that comprises a type of movement. A charge is not a walk, and therefore you cannot walk/charge such that you jump on the walk and land in the middle of the charge.
Therefore, if you have to spend a round in the air between an evil guy and a pit, you fall.
You may want to avoid this. Alternatively, grab pouncing armor which, provided a sufficiently high athletics check, allows for jump-charges that exceed your base movement.
Your situation for "needing to charge the guy on the other side of a large pit" is... assuming you must charge them, instead of getting your portable arty to rain death on them and you keep off minions on this side, take a double-move to jump the chasm, then action-point charge. Just... don't fail the jump. | 857 | 3,732 | {"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-2024-33 | latest | en | 0.949565 |
https://www.physicsforums.com/threads/help-with-electric-field.852231/ | 1,623,583,875,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487608702.10/warc/CC-MAIN-20210613100830-20210613130830-00123.warc.gz | 863,967,330 | 15,594 | # Help with electric field
## Homework Statement
The picture below shows two stationary charges q1= +2mC and q2= -15 mC.
and I need to find the electric field vector at field point P(0,4m). E= [px, py] .
Also
A little dipole is positions in P(0,4m) and is given with p= [px,py]=[2*10^-8 ,0] Cm.
Find the torque that acts on the dipole because of the electric field and its potential energy
E=k*q/r^2
## The Attempt at a Solution
I have found out that E1=4.5*10[6][/SUP] and E2= 1.7*10^6. I am not sure if the electric field E1 is negative or positive ? I think its negative because the vector goes downwards. And when I find the angle for E2 do I use arctan(8/2)?
#### Attachments
• Screen Shot 2016-01-14 at 16.24.40.png
5.5 KB · Views: 353
TSny
Homework Helper
Gold Member
WELCOME TO PF.
I have found out that E1=4.5*10[6][/SUP] and E2= 1.7*10^6.
OK. But I would keep an extra significant figure while doing the calculations. Then round off to the appropriate number of significant figures at the end. Also, don't forget the units.
I am not sure if the electric field E1 is negative or positive ? I think its negative because the vector goes downwards.
Electric field is a vector quantity. It is not good language to say that a vector is negative. However, the components of a vector can be negative or positive. So, if the field points downward (along the negative y axis) then you would say that the y component of the electric field is negative.
And when I find the angle for E2 do I use arctan(8/2)?
This does not look right. Are you trying to find the angle that E2 makes to the horizontal direction or the vertical direction? If you are constructing a right triangle to help find the angle, make sure you have the dimensions of the sides of the triangle correct. | 484 | 1,781 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-25 | latest | en | 0.917237 |
https://imanderweddingsigns.com/qa/will-7000-volts-kill-you.html | 1,597,172,313,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738819.78/warc/CC-MAIN-20200811180239-20200811210239-00168.warc.gz | 349,721,696 | 9,393 | # Will 7000 Volts Kill You?
## What does 120 volt shock feel like?
120-volt AC Wall Current.
Suppose you put two wires into a wall outlet.
A very nasty tingling sensation that will usually leave your hand and arm numb.
Stand on damp ground in bare feet and it’s worse..
## Can electric fence kill a dog?
Unlike the shock you feel when you touch a physical electric fence, the correction from a dog collar is generated by a battery. The wire in the ground sends a signal to the collar, but the electricity in the wire has nothing to do with the zap. … But no matter how high you get, it can’t hurt your dog.
## What is cat fencing?
Purr… fect Cat Fence is the only fence for cats with a pivoting arched top (patented) to ensure your cats won’t escape. … Give your cats the freedom they deserve to enjoy the great outdoors without worrying about their safety. Our patented spring-loaded arms keep even “Houdini” cats from getting out.
## Can a bird sit on an electric fence?
Electricity flows along the path of least resistance. Birds don’t get shocked when they sit on electrical wires because they are not good conductors of electricity. Another reason why electricity will bypass a bird sitting on a wire is because there’s no voltage difference in a single wire.
## Can you survive 10000 volts?
Offhand it would seem that a shock of 10,000 volts would be more deadly than 100 volts. But this is not so! … While any amount of current over 10 milliamps (0.01 amp) is capable of producing painful to severe shock, currents between 100 and 200 mA (0.1 to 0.2 amp) are lethal.
## Do electric fences hurt animals?
In general, an electric fence should be supplied with only enough power to startle — not injure — so that an animal that brushes up against the fence will recoil but not suffer electrical burns or permanent injury.
## Will a 7000 volt electric fence kill you?
It will hurt for approximately 10 minutes, but it will not be debilitating, leave a burn mark or kill them. Because electric fencing has low current and pulsates, it can’t kill or permanently hurt anyone. However it is strongly advised to keep children away from an Electric Fence.
## Do electric fences work with cats?
There is a simple answer to this, electric fences are not a preferential choice to keep cats safe. An electric fence may stop a cat from leaving a designated space, however, many owners would prefer their cats not to experience the electric shock.
## How many volts does it take to drop a person?
That being said, to answer your question: 4,000 volts is enough to stun someone as long as you have a power source capable of delivering a reasonable amount of current. Electric fences used on farms typically operate at or near this voltage at currents of 100–200 milliamps, or 0.1–0.2 amps.
## Will I die if I stick a fork in an outlet?
Electrical outlets The Fear: If you stick a fork or a bobby pin in one of the sockets, you’ll be electrocuted. … The left slot is connected to the neutral wire, the right is connected to the hot one, and electricity flows from hot to neutral. Sticking something into either slot will disrupt the flow and send it into you.
## What happens if a dog touches an electric fence?
After receiving an unforgettable shock, the animal will make a mental connection between the fence and the shock and no longer challenge the fence. … When an animal touches the electrified wire and is grounded to the earth (hoof/foot on the ground), the circuit is completed, causing an electric shock.
## How many volts can kill a dog?
However, the typical range on a shock collar is from 400 to 6000 volts: 400 being the lowest setting and 6000 being the highest. Honestly, voltage doesn’t matter. It’s about how long your dog’s exposed to the electricity that will affect the damage.
## Can 120 volts kill you?
120 volts isn’t “strong” enough to push much current through your body which is why most 120 volt shocks are survivable. … If the current flows long enough it causes resistance heating in your body tissue and eventually cooks you from the inside out. Remember, 120 volt wiring is still perfectly capable of killing.
## Can electric fence kill a cat?
Will an electric fence kill my cat or dog? No. As a rule, cats avoid electric fences. They are extremely perceptive to the electromagnetic fields as a result of induction, which causes electrostatic energy.
## How many volts is dangerous?
Voltages over approximately 50 volts can usually cause dangerous amounts of current to flow through a human being who touches two points of a circuit, so safety standards are more restrictive around such circuits.
## Do volts or amps kill you?
In plain English: volts (V) equals current (I) times resistance (R). … So, back to which kills you, the amps or volts. Given your body is a constant resistance, it really is a combination of both. Higher voltage means higher amperage, and thus higher voltage has more potential to kill.
## How many volts are there in 1 amp?
Equivalent Amps and Volts MeasurementsCurrentVoltagePower1 Amps90 Volts90 Watts1 Amps95 Volts95 Watts1 Amps100 Volts100 Watts2 Amps2.5 Volts5 Watts76 more rows | 1,146 | 5,168 | {"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} | 2.578125 | 3 | CC-MAIN-2020-34 | latest | en | 0.922448 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.