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://www.unitconverters.net/power/terajoule-second-to-calorie-it-second.htm
| 1,719,024,117,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00564.warc.gz
| 927,387,394
| 3,641
|
Home / Power Conversion / Convert Terajoule/second to Calorie (IT)/second
# Convert Terajoule/second to Calorie (IT)/second
Please provide values below to convert terajoule/second [TJ/s] to calorie (IT)/second [cal/s], or vice versa.
From: terajoule/second To: calorie (IT)/second
### Terajoule/second to Calorie (IT)/second Conversion Table
Terajoule/second [TJ/s]Calorie (IT)/second [cal/s]
0.01 TJ/s2388458966.275 cal/s
0.1 TJ/s23884589662.75 cal/s
1 TJ/s238845896627.5 cal/s
2 TJ/s477691793254.99 cal/s
3 TJ/s716537689882.49 cal/s
5 TJ/s1194229483137.5 cal/s
10 TJ/s2388458966275 cal/s
20 TJ/s4776917932549.9 cal/s
50 TJ/s11942294831375 cal/s
100 TJ/s23884589662750 cal/s
1000 TJ/s2.388458966275E+14 cal/s
### How to Convert Terajoule/second to Calorie (IT)/second
1 TJ/s = 238845896627.5 cal/s
1 cal/s = 4.1868E-12 TJ/s
Example: convert 15 TJ/s to cal/s:
15 TJ/s = 15 × 238845896627.5 cal/s = 3582688449412.4 cal/s
| 344
| 928
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-26
|
latest
|
en
| 0.49045
|
https://electronics.stackexchange.com/questions/409621/how-to-calculate-poles-for-a-high-order-system
| 1,714,024,894,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712297284704.94/warc/CC-MAIN-20240425032156-20240425062156-00768.warc.gz
| 196,978,886
| 41,152
|
# How to calculate poles for a high order system?
I have a fourth order system which is fully controllable and observable, which needs to satisfy certain design criteria.
I am trying to design a full-state feedback controller for the following system:
$$\frac{-0.00198s + 2}{s^4 + 0.1201s^3 + 12.22s^2 + 0.4201s + 2}$$
Design Requirements:
<5% Overshoot
<2s settling time
The schematic of this type of control system is shown below where $$\K\$$ is a matrix of control gains. Note that here we feedback all of the system's states, rather than using the system's outputs for feedback.
A related example, State-Space Methods for Controller Design.
While I am aware how to design second order systems using the above design requirements, I am struggling when it comes to higher order systems.
Below I present equations and working for finding poles for a second order system. Apologies if wording is hard to decipher.
Poles for 2nd order @ -2.6 +- i*2.39
One would then proceed to use MATLAB place function as follows:
p2 = [-2.6 + 1i*2.39, -2.6 - 1i*2.39];
K = place(A,B,p2);
Acl = A - B*K;
mysys = ss(Acl,B,C,D);
Since this method only yields two poles, how can I satisfy my design requirements if I have a fourth order system?
This can also be thought of as designing a full state feedback controller to obtain the specific transient one requires. Closed loops dynamics and more specifically eigenvalues of matrix Acl have a lot to do with finding the desired poles. I am yet to fully understand how. Any suggestions would be appreciated.
• Are you permitted to turn this into a pair of 2nd order, with one band-pass and one low-pass?
– jonk
Nov 29, 2018 at 21:23
• @jonk I would like to keep the system at 4th order. Using settling time and overshoot equations, one can extract a pair of complex poles. The other 2 poles might be obtained using a totally different method than the one presented above. I would also like to make the distinction between pole placement and pole calculation. I am not asking about pole placement per se (this is shown in MATLAB code), but how to find the poles required to satisfy the system requirements. Once calculated, one could proceed with pole placement.
– rrz0
Nov 29, 2018 at 21:28
• I've not tackled this, directly. I'm a hobbyist and I would decompose everything down to 2nd order (and 1st order, if odd-ordered.) Looking at this as a math exercise, and not having any electronics training let alone for 4th order filters, I'd be looking at the amplitude response to get your overshoot equation. This would be a derivative of an 8th order, so a solution to a 7th order equation which must be zero at the peak, as I see it. Interesting problem, though. I don't have the time now to sit down with it but I hope to do so when I do, if someone else doesn't answer this. I already +1 it.
– jonk
Nov 29, 2018 at 21:37
• This isn’t really an EE question. It’s all about solving a double quadratic equation and lies firmly in maths now matter how interesting it might be. One thought; solve it in excel or something similar by trial and error of two multiplied 2nd order equations. Nov 29, 2018 at 21:44
• Google "Dominant pole". If it's a control problem you want to shove one pair of poles out to being significantly faster, then just design the second set of poles to your specifications. Alternately, start with a specification for a pole pair that would give you 2s settling and 2.5% overshoot, and set both pairs to that. Then see if you can tweak things a bit. Nov 29, 2018 at 21:49
A second order system is relatively simple. It is straight forward to determine the overshoot and the settling time. This is not the case for a higher order system.
I will limit the discussion to linear systems having linear controllers.
For a higher order system you generally construct a cost function. There are many ways to do so. A good place to start is with the linear quadratic regulator (lqr in MATLAB). For your SISO system it will have the form $$\int_0^\infty (x^\top Q x + R u^2 + 2 x^\top N u) \ \mathrm{d} t.$$ A good place to start is to set $$\int_0^\infty (x^\top x + R u^2) \ \mathrm{d} t.$$ Then you can vary R until you get a satisfactory response. The lqr function in MATLAB will give you the feedback matrix.
Because you are after low overshoot and fast settling times the LQR is not really the best tool you can use. Instead the ITAE (integrated time absolute error) minimizes $$\int_0^\infty |e| t \ \mathrm{d}t.$$ This way you penalize errors more the further away they occur.
For a fourth order system your target transfer function is $$\frac{\omega_0^4}{s^4 + 2.1 \omega_0 s^3 + 3.4 \omega_0^2 s^2 + 2.7 \omega _0^3 s + \omega_0^4}.$$ You can find more information on page 21 here.
Setting omega to 10 yields
For your system you do not need to control the zeros because the s term is small. If it were larger, you would need to remove the zeros.
• Many thanks for your answer. I have never used the ITAE to penalize errors as you describe. Could you kindly expand on how you got the target transfer function? Did you use MATLAB functions?
– rrz0
Dec 1, 2018 at 11:12
• @Rrz0 there isn’t a function to give you the poles in MATLAB. You need to write an optimization program to calculate them. Dec 1, 2018 at 11:15
• @Rrz0 I think the poles I have are actually wrong. I’ll edit my answer to correct the mistake. Dec 1, 2018 at 11:18
• @Rrz0 I added a good reference to get you started on ITAE. If you look around, there was a MATLAB script to calculate the ITAE coefficients floating around a few year ago. The ITAE is just one method. You can use any cost function you want. I gave it more as an example of how to select the target transfer function. Dec 1, 2018 at 11:44
| 1,493
| 5,748
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.4375
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.921905
|
https://brilliant.org/problems/water-in-a-sphere/
| 1,477,127,032,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-44/segments/1476988718866.34/warc/CC-MAIN-20161020183838-00215-ip-10-171-6-4.ec2.internal.warc.gz
| 828,666,615
| 15,187
|
# Water in a sphere..
Level pending
A hollow sphere is filled with water weighing as much as the sphere. It then does pure rolling.
The ratio of the $$KE$$ of the system when the water is liquid to that when it is solid is of the form $$\frac{a}{b}$$ where $$a$$ and $$b$$ are co prime integers.
Find $$a+b$$
$$\textbf{Assumption}$$
$$\bullet$$ The velocity of the system in both the cases is same.
×
Problem Loading...
Note Loading...
Set Loading...
| 119
| 460
|
{"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}
| 2.640625
| 3
|
CC-MAIN-2016-44
|
longest
|
en
| 0.925008
|
https://brainmass.com/statistics/normal-distribution/simulation-using-crystal-ball-optquest-57959
| 1,503,155,562,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-34/segments/1502886105455.37/warc/CC-MAIN-20170819143637-20170819163637-00644.warc.gz
| 744,749,911
| 19,158
|
Share
Explore BrainMass
# Simulation using Crystal Ball / OptQuest
This problem requires the use "Crystal Ball", the popular commercial spreadsheet add-in. For clarity, it is distributed by Decisioneering, Inc. This problem specifically requires that Excel and "Crystal Ball" (and OptQuest as applicable) be used - and not any other software choices. The link below directs you to a free 7-day trial: http://www.decisioneering.com/downloadform.html
Question:
Jim Jarrington owns a magazine stand at the Ovalstone business center in Roanoke, Virginia. He buys his magazines wholesale at \$0.50 per magazine and sells them for \$0.75. Jim has wondered about the optimal number of magazines to order each day. Based on history, he has found that demand (even though it is discrete) can be modeled by a normal distribution with a mean of 50 and standard deviation of 5. When he has more magazines than customers, he can recycle all the extra magazines the next day and receive \$0.05 per magazine. On the other hand, if he has more customers than magazines, he loses some goodwill in addition to the lost profit on the potential sale of \$0.25. Jim estimates the incremental lost goodwill costs five days' worth of business (that is, dissatisfied customers will go to a competitor the next week, but come back to the week after that).
Part A:
Create a spreadsheet model to determine the optimal number of magazines to order each day. Use 500 replications and round the demand values generated by the normal random number generator (RNG) to the closest integer value.
Part B:
Construct a 95% confidence interval for the expected payoff from the optimal decision.
Note: Please provide an explanation, so the student is able to understand the logic and application of the logic within the context of this problem and the software used.
#### Solution Summary
A simulation using Crystal Ball is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
\$2.19
| 431
| 2,053
|
{"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}
| 3.296875
| 3
|
CC-MAIN-2017-34
|
longest
|
en
| 0.926038
|
https://www.physicsforums.com/threads/time-and-work.383534/#post-2608304
| 1,632,531,154,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780057584.91/warc/CC-MAIN-20210924231621-20210925021621-00321.warc.gz
| 935,739,937
| 14,351
|
# Time and work
## Homework Statement
The problem is as follows
" 2 pipes fill cistern with water in 4 and 6 hours respectively.If the first pipe in 4 and 6 hours
respectively . if the first pipe be opened first and the pipes be opened alternatively one at a time for 1 hour each, in how many hours will the cistern be filled up"
My attempt:
I first took that in 1 hour first pipe fills 1/4th of tank and second pipe 1/6 thof tank
.: in 2 hours they fill 1/4+1/6= 5/12th of tank
in 1hour they fill 5/24 th of tank
.: they fill the tank in 24/5 hours
But the problem is my book's answer is 19 hours.I don't know how that is possible because if they alone fill it in 4 and 6 hours then if they are working together the time should be less.
| 212
| 739
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.796875
| 4
|
CC-MAIN-2021-39
|
latest
|
en
| 0.934996
|
https://nrich.maths.org/public/topic.php?code=-99&cl=2&cldcmpid=6288
| 1,576,352,125,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-51/segments/1575541288287.53/warc/CC-MAIN-20191214174719-20191214202719-00298.warc.gz
| 478,990,617
| 9,554
|
# Resources tagged with: Working systematically
Filter by: Content type:
Age range:
Challenge level:
### There are 338 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically
### Isosceles Triangles
##### Age 11 to 14 Challenge Level:
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
### Sociable Cards
##### Age 11 to 14 Challenge Level:
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
### Number Sandwiches
##### Age 7 to 14 Challenge Level:
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
### Inky Cube
##### Age 7 to 14 Challenge Level:
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
### Product Sudoku
##### Age 11 to 14 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
### Coded Hundred Square
##### Age 7 to 11 Challenge Level:
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
### First Connect Three
##### Age 7 to 14 Challenge Level:
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
##### Age 11 to 14 Challenge Level:
How many different symmetrical shapes can you make by shading triangles or squares?
### Extra Challenges from Madras
##### Age 11 to 14 Challenge Level:
A few extra challenges set by some young NRICH members.
### Factor Lines
##### Age 7 to 14 Challenge Level:
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
### Tetrahedra Tester
##### Age 11 to 14 Challenge Level:
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
##### Age 5 to 11 Challenge Level:
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
### Pair Sums
##### Age 11 to 14 Challenge Level:
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
### Window Frames
##### Age 5 to 14 Challenge Level:
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
### Twinkle Twinkle
##### Age 7 to 14 Challenge Level:
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
### Difference
##### Age 7 to 11 Challenge Level:
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
### Magic Potting Sheds
##### Age 11 to 14 Challenge Level:
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
### M, M and M
##### Age 11 to 14 Challenge Level:
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
### Fence It
##### Age 11 to 14 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
### A Square of Numbers
##### Age 7 to 11 Challenge Level:
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
##### Age 11 to 14 Challenge Level:
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
### Junior Frogs
##### Age 5 to 11 Challenge Level:
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
### Cuboids
##### Age 11 to 14 Challenge Level:
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
### Triangles to Tetrahedra
##### Age 11 to 14 Challenge Level:
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
### Number Daisy
##### Age 11 to 14 Challenge Level:
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
### Ratio Sudoku 3
##### Age 11 to 16 Challenge Level:
A Sudoku with clues as ratios or fractions.
### Broken Toaster
##### Age 7 to 11 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
### Cinema Problem
##### Age 11 to 14 Challenge Level:
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
### Multiples Grid
##### Age 7 to 11 Challenge Level:
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
### Seasonal Twin Sudokus
##### Age 11 to 16 Challenge Level:
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
### Weights
##### Age 11 to 14 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
### A Right Charlie
##### Age 7 to 11 Challenge Level:
Can you use this information to work out Charlie's house number?
### Single Track
##### Age 7 to 11 Challenge Level:
What is the best way to shunt these carriages so that each train can continue its journey?
### Red Even
##### Age 7 to 11 Challenge Level:
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
### Teddy Town
##### Age 5 to 14 Challenge Level:
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
### Dicey Perimeter, Dicey Area
##### Age 7 to 11 Challenge Level:
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
### Two and Two
##### Age 11 to 14 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
### Shunting Puzzle
##### Age 7 to 11 Challenge Level:
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
### Knight's Swap
##### Age 7 to 11 Challenge Level:
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
### Paw Prints
##### Age 7 to 11 Challenge Level:
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
### Map Folding
##### Age 7 to 11 Challenge Level:
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
### Code Breaker
##### Age 7 to 11 Challenge Level:
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
### One to Fifteen
##### Age 7 to 11 Challenge Level:
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
##### Age 7 to 11 Challenge Level:
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
### Square Corners
##### Age 7 to 11 Challenge Level:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
### Sealed Solution
##### Age 7 to 11 Challenge Level:
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
### Reach 100
##### Age 7 to 14 Challenge Level:
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
### Triangles All Around
##### Age 7 to 11 Challenge Level:
Can you find all the different triangles on these peg boards, and find their angles?
### Colour in the Square
##### Age 7 to 16 Challenge Level:
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
### Sitting Round the Party Tables
##### Age 5 to 11 Challenge Level:
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
| 2,221
| 9,201
|
{"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}
| 3.8125
| 4
|
CC-MAIN-2019-51
|
longest
|
en
| 0.86419
|
https://es.mathworks.com/matlabcentral/answers/1772810-how-to-create-a-list-of-random-number-with-a-minimum-difference-between-each-number?s_tid=prof_contriblnk
| 1,713,250,267,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296817073.16/warc/CC-MAIN-20240416062523-20240416092523-00248.warc.gz
| 222,896,015
| 30,781
|
# how to create a list of random number with a minimum difference between each number?
20 visualizaciones (últimos 30 días)
Raghav Rathi el 2 de Ag. de 2022
Comentada: Raghav Rathi el 2 de Ag. de 2022
Hi,
I am trying to create a list of 'n' random numbers within a range(1,m) and the difference between adjacent numbers need to be at least 'd'.
The list needs to be sorted and no repetion allowed.
I can do the same in python using
% r = m - ((m - 1) * (n - 1))
% = 30 - ((3-1) * (6-1)) = 30 - 2*5 = 20
%[(d-1)*i + x for i, x in enumerate(sorted(random.sample(range(r), n)))]
print([2*i + x for i, x in enumerate(sorted(random.sample(range(20), 6)))])
>>[2, 5, 14, 20, 24, 28]
In the above code, I am trying to generate a sorted list of 6 random numbers from 0-30, with a minimum difference between each adjacent element of at least 3.
Can some one plese suggest me how can I do something similar in matlab?
##### 11 comentariosMostrar 9 comentarios más antiguosOcultar 9 comentarios más antiguos
Torsten el 2 de Ag. de 2022
So [2 14 4 28 20 4] (not ordered, repetitions allowed) (d=3, n=6 and m = 30) would be acceptable in your test case ?
Raghav Rathi el 2 de Ag. de 2022
Sorry for the confussion again, by either I meant, it can either be increasing or decresing.
If you take [2 14 4 28 20 4], after sorting it will be [2 4 4 14 20 28 ], and the difference between 1st 3 elements is less than 3 so it wont be acceptable. if it was [2 5 8 14 20 28 ] then it would be acceptable.
Iniciar sesión para comentar.
### Respuestas (1)
David Hill el 2 de Ag. de 2022
Editada: David Hill el 2 de Ag. de 2022
You can brute force it.
m=200;%randomn numbers between 1-200
n=50;%array length
d=20;%minimum distance
a=randi(m,100000,n);%make sifficiently large
D=abs(diff(a,[],2));
idx=D>=d;
f=find(sum(idx,2)==n-1);
randNums=a(f,:);%rows of array having randomn numbers with adjacent elements being at least d apart
##### 4 comentariosMostrar 2 comentarios más antiguosOcultar 2 comentarios más antiguos
David Hill el 2 de Ag. de 2022
Below works but the randomn numbers will be skewed towards the high-side of the interval.
m=2000;
n=10;
d=5;
r=1:m;
R=[];
while 1
for k=1:n
if length(r)+k<n||isempty(r)
r=1:m;
R=[];
break;
end
p=randperm(length(r),1);
R=[R,r(p)];
r=r(r>(r(p)+d));
end
if ~isempty(R)
break;
end
end
Raghav Rathi el 2 de Ag. de 2022
Thank you David.
Iniciar sesión para comentar.
### Categorías
Más información sobre Logical en Help Center y File Exchange.
R2022a
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by
| 842
| 2,620
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.34375
| 3
|
CC-MAIN-2024-18
|
latest
|
en
| 0.554999
|
http://www.coderanch.com/t/382769/java/java/permutation-combination
| 1,462,542,260,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-18/segments/1461861812410.28/warc/CC-MAIN-20160428164332-00152-ip-10-239-7-51.ec2.internal.warc.gz
| 447,943,607
| 9,523
|
Win a copy of Re-engineering Legacy Software this week in the Refactoring forum
or Docker in Action in the Cloud/Virtualization forum!
# permutation combination problem
sitaram panse
Greenhorn
Posts: 3
JTable with 5 column and n rows.
After filling the table with values i've got an array of object of cell values .
I want to perform the permutation combination on this Object[] [] to fetch the all possible combinations of n(row)-5(column-fix) elements.
suppose i have 5 rows and 5 columns in the table then it should generate all possible combinations i.e(120) without repeating the elements. result should be such that from each column only one elements would be selected at a time. each individual combination will have exact 5 elemnts. Sequence of elements will not be considered.
The permutation should be the maximal possible combination of the attributes with each other.
Object[][] data={{ "A1","B1","C1" ,"D1","E1" },{ "A2","B2","C2" ,"D2","E2" },{ "A3","B3","C3" ,"D3","E3" },{ "A4","B4","C4" ,"D4","E4" },{ "A5","B5","C5" ,"D5","E5" }};
For Example:
Result should be like this each (combination must be unique):
1st column will always have A's, 2nd column will always have B's, 3rd C's, 4th D's and 5th E's......
A1B1C1D1E1....Correct combs
A1B2C1D1E1
A2B1C1D1E1
A2B2C1D1E1
.........................
B1A1C1D1E1...wrong combination( At 1st place only A should be entertain)
........................ and so on....
Can i get some help or code snippet to generate this?
Jim Yingst
Wanderer
Sheriff
Posts: 18671
Normally permutations and combinations are two different things, and it's confusing to refer to this as a "permutation combination". What you have here seems to be a combinations problem, with additional constraints, so I'll just use the term combinations.
It looks to me like there are not 120 combinations here, but 3125. That is, there are 5 choices for the first positions, 5 choices for the second, 5 for the third, etc. 5 * 5 * 5 * 5 * 5 = 3125. Since each position is drawn from a separate sample set (1st column is always an A, 2nd always a B, etc) there is no need to divide by anything to eliminate duplicates.
It seems like it should be fairly straightforward to solve this with some nested for loops - five of them. Or you could do this with a recursive solution, if you prefer. Whichever makes more sense to you. I'd prefer the nested loops:
For simplicity, while working on this you may want to start with a smaller table, e.g. 2 x 2 or 3 x 3. Because it may be difficult to check 3125 rows for accuracy. But checking 4 or 27 is easier.
sitaram panse
Greenhorn
Posts: 3
Actualy i also tried the same with one D array.
I have a 2D array like Object[n][m] where m=5 (Fixed), but n could be anything.
so the combination of elements should be generated according to no. of rows.
For Example:
Object[][] data={{ "A1","B1","C1" ,"D1","E1" },{ "A2","B2","C2" ,"D2","E2" },{ "A3","B3","C3" ,"D3","E3" },{ "A4","B4","C4" ,"D4","E4" },{ "A5","B5","C5" ,"D5","E5" }};
Result should be like this each (combination must be unique):
1st column will always have A's, 2nd column will always have B's, 3rd C's, 4th D's and 5th E's......
A1B1C1D1E1....Correct combs
A1B2C1D1E1
A2B1C1D1E1
A2B2C1D1E1
.........................
B1A1C1D1E1...wrong combination( At 1st place only A should be entertain)
........................ and so on....
I'll appriciate your help on this.
| 1,004
| 3,402
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.515625
| 3
|
CC-MAIN-2016-18
|
longest
|
en
| 0.889814
|
https://byjus.com/question-answer/a-stone-a-is-dropped-from-rest-from-height-h-above-ground-a-second-stone-7/
| 1,713,890,316,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296818732.46/warc/CC-MAIN-20240423162023-20240423192023-00424.warc.gz
| 133,433,849
| 29,411
|
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question
# A stone A is dropped from rest from height h above ground. A second stone B is simultaneously thrown vertically up with velocity v. Find v so that B meets midway between their initial positions.
A
gh
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2gh
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3gh
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4gh
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
## The correct option is A √ghLet time of travel of each stone =t Distance travelled by each stone =h2 Taking upward direction as positive Using second equation of motion, For stone A, −h2=−12gt2 ⇒t=√hg For stone B, h2=vt−12gt2 Putting t=√hg, we get v=√gh Alternate sol: For stone B w.r.t A, Srel=h, urel=v−0=v m/s, arel=0 Using second equation of motion, Srel=urelt+12at2 ⇒h=vt ⇒t=hv……(1) For the body dropped from height h, h2=12gt2⇒t=√hg……(2) From (1) and (2) √hg=hv⇒v=√hg
Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Relative Motion
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program
| 397
| 1,220
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.546875
| 4
|
CC-MAIN-2024-18
|
latest
|
en
| 0.820684
|
http://www.physicsforums.com/showthread.php?s=48467ac63f4fddcc2ba1e471d0020a80&p=3999492
| 1,369,258,796,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-20/segments/1368702448584/warc/CC-MAIN-20130516110728-00037-ip-10-60-113-184.ec2.internal.warc.gz
| 645,011,532
| 7,279
|
## Door and energy efficiency
Quote by luis20 Thanks! How did you get (pi^2)/8?
By mistake... I dropped a 2 exponent along the way. It's actually (pi^2)/12, so the hinged door is better.
Calculate the kinetic energy of the two doors. The one for the rotating door is $\frac{1}{2}Iω^{2}$ where $I=\int^{l}_{0}ρx^{2}dx$ with ρ linear density and $l$ width of the door.
I was writing a lengthier answer when I hit something on the page and lost it all so you'll forgive me if I let you do the details :)
Recognitions:
Homework Help
| 152
| 532
|
{"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}
| 2.53125
| 3
|
CC-MAIN-2013-20
|
latest
|
en
| 0.918752
|
https://www.mathbix.com/converter/weight/pounds-to-grams
| 1,653,319,400,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662558030.43/warc/CC-MAIN-20220523132100-20220523162100-00450.warc.gz
| 989,429,206
| 4,427
|
You Might Also Like
Pound (lb) To Grams (g) Converter
Conversion Rule
M(g) = M(lb) x 453.592
[ Where, M is a variable in lb and g ]
Examples
Example 1. Convert 0.7 pound to grams.
Solution!
• 1 lb = 453.592 g.
• 0.7 lb = 0.7 x 453.592 g.
• 0.7 lb = 317.5144 g.
Example 2. Convert 3 pound to grams.
Solution!
• 1 lb = 453.592 g.
• 3 lb = 3 x 453.592 g.
• 3 lb = 1360.776 g.
Example 3. Convert 1.7 pound to grams.
Solution!
• 1 lb = 453.592 g.
• 1.7 lb = 1.7 x 453.592.
• 1.7 lb = 771.1064 g.
lb To g Conversion Table
0.1 lb = 45.3592 g 2 lb = 907.184 g 0.2 lb = 90.7184 g 3 lb = 1360.776 g 0.3 lb = 136.0776 g 4 lb = 1814.368 g 0.4 lb = 181.4368 g 5 lb = 2267.96 g 0.5 lb = 226.796 g 6 lb = 2721.552 g 0.6 lb = 272.1552 g 7 lb = 3175.144 g 0.7 lb = 317.5144 g 8 lb = 3628.736 g 0.8 lb = 362.8736 g 9 lb = 4082.328 g 0.9 lb = 408.2328 g 10 lb = 4535.92 g 1 lb = 453.592 g 100 lb = 45359.2 g
How To Convert
| 440
| 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}
| 3.546875
| 4
|
CC-MAIN-2022-21
|
latest
|
en
| 0.336743
|
artqulture.com
| 1,501,073,393,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-30/segments/1500549426161.99/warc/CC-MAIN-20170726122153-20170726142153-00269.warc.gz
| 607,001,928
| 37,086
|
How much for that painting?
Is the economic value of art based on airy fairy numbers that collectors and galleries pluck from the air?
Let us evaluate from a simple starting point – where it all begins, in the artist’s studio.
An unknown artist (let us call him Andy) has been painting for years. He had set up a small street-side stall with his paintings displayed. Some of them are deemed ‘interesting’ by a walker-by. Due to the subjectivity of art in current times, it would be irrelevant whether the art is “good” or not as price does not have a linear correlation to “good” or “beauty” (and beauty was never ever clearly defined anyway but let us leave that for another discussion). Mr. Walkerby buys them, at USD80 each.
Andy priced each piece based on:
1. Material cost. (e.g. USD10)
2. The number of hours he spent (5hours) and how many burgers he would like to eat in a day (2 burgers and drinks), in order to continue painting (e.g.USD15)
3. His rent, utilities, overheads. (e.g.USD5)
4. How many more hours it will take for him to draw and sell another painting (1+2+3) – this is a sustainability factor. Some call it, profit margin. (e.g.USD40)
So the piece he is selling would come up to USD80. And Andy can survive another day to work, and possibly save.
If Andy wanted to save more, buy more and/or better materials, spend more time on the paintings, the price of his paintings goes up.
Mr.Walkerby then puts the paintings up for sale at his little shop- where he pays overheads for. He sells the paintings at USD160 each to cover costs, and his No.4.
Mr. Retail who buys from Mr. Walkerby then keeps 2 pieces, and puts the rest up for sale, also at a margin.
If Andy never knows about the “Retail” price of his painting, he will continue selling his pieces at USD80, with increases each year depending on inflation.
If Andy realizes that his paintings are sold at a margin on top of margins, he may decide that he wants to charge what the “Retail” price is charging (maybe he needs a new sweater).
Suppose scenario 2 happens – three things could happen:
A. Mr. Walkerby will not buy them anymore as they are considered expensive.
B. Mr. Walkerby buys more, as he thinks that there is still demand.
C. Mr. Retail buys directly from Andy.
If A. happens, Andy has overestimated his popularity.
If B. happens, the demand will depend on whether Mr. Retail thinks there is still demand at the higher price.
If C. happens, Andy gains. Mr. Retail will need to work hard to sell the art which will be at a higher price.
All artists need a Mr. Walkerby and Mr. Retail to become “established” – a subjective term coined by those who needed to justify their no.4.
What is clear from this illustration is that once art goes through the hands of a trader (which we call galleries), expect higher prices. Also expect rave reviews, art shows, marketing and publicity, champagne launches.
The cycle goes on and on. Artists that make the news are the B and C scenario types. The thing is, the more expensive the piece, you will note that the galleries are also in expensive locations, paying expensive employees to run expensive shows and talks. Then everybody wants a piece of it once a famous gallery or critique declares the piece “marvelous”. And the bidding starts.
That same painting, when put on the street and gone unnoticed by Mr. Walkerby, could still have been worth USD80.
And we haven’t even gone into the topic of auctioneers, collectors, agencies, lessors yet! That is for another article.
Here is also an interesting write up that we can learn a thing or two from – a blunt account from the business themselves about a print for sale – http://www.artbusiness.com/appsellart.html
More articles on the value of art, and our experiences, soon.
Advertisements
| 869
| 3,791
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.328125
| 3
|
CC-MAIN-2017-30
|
longest
|
en
| 0.973891
|
http://www.convertit.com/Go/SmartPages/Measurement/Converter.ASP?From=wk
| 1,563,953,036,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-30/segments/1563195531106.93/warc/CC-MAIN-20190724061728-20190724083728-00354.warc.gz
| 188,417,953
| 3,518
|
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```week = 604800 second (time) ``` Related Measurements: Try converting from "wk" to autumn, century, day, fiscal yr (fiscal year), hour, leap yr (leap year), millenium, novennial, olympiad, quindecennial, quinquennial, s (second), sidereal day, sidereal month, sidereal yr (sidereal year), spring, summer, synodic month, weekend, winter, or any combination of units which equate to "time" and represent time. Sample Conversions: wk = .07806691 autumn, .01917808 calendar yr (calendar year), .00191654 decade, .01944444 fiscal yr (fiscal year), .5 fortnight, 168 hour, 10,080 minute, .22998438 month, .00212948 novennial, .02555382 pregnancy, .00383307 quinquennial, .00273791 septennial, 7.02 sidereal day, .01916462 sidereal yr (sidereal year), .07483296 summer, .23704225 synodic month, 1 week, 3.5 weekend, .07861488 winter, .01916536 yr (year).
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!
| 399
| 1,453
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-30
|
longest
|
en
| 0.683398
|
https://studysoup.com/tsg/52244/thomas-calculus-early-transcendentals-13th-edition-chapter-5-problem-1qgy
| 1,575,814,823,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-51/segments/1575540510336.29/warc/CC-MAIN-20191208122818-20191208150818-00557.warc.gz
| 557,729,545
| 11,441
|
# How can you sometimes estimate quantities like distance
## Problem 1QGY Chapter 5
Thomas' Calculus: Early Transcendentals | 13th Edition
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants
Thomas' Calculus: Early Transcendentals | 13th Edition
4 5 0 408 Reviews
17
1
Problem 1QGY
How can you sometimes estimate quantities like distance traveled, area, and average value with finite sums? Why might you want to do so?
Step-by-Step Solution:
Step 1 of 3
Step 2 of 3
Step 3 of 3
##### ISBN: 9780321884077
This full solution covers the following key subjects: area, average, distance, estimate, Finite. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. The answer to “How can you sometimes estimate quantities like distance traveled, area, and average value with finite sums? Why might you want to do so?” is broken down into a number of easy to follow steps, and 23 words. Since the solution to 1QGY from 5 chapter was answered, more than 226 students have viewed the full step-by-step answer. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. The full step-by-step solution to problem: 1QGY from chapter: 5 was answered by , our top Calculus solution expert on 08/01/17, 02:37PM.
#### Related chapters
Unlock Textbook Solution
Enter your email below to unlock your verified solution to:
How can you sometimes estimate quantities like distance
×
Get Full Access to Thomas' Calculus: Early Transcendentals - 13th Edition - Chapter 5 - Problem 1qgy
Get Full Access to Thomas' Calculus: Early Transcendentals - 13th Edition - Chapter 5 - Problem 1qgy
I don't want to reset my password
Need help? Contact support
Need an Account? Is not associated with an account
We're here to help
Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Already have an Account? Is already in use
| 580
| 2,359
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3
| 3
|
CC-MAIN-2019-51
|
latest
|
en
| 0.899365
|
https://brainly.in/question/12523
| 1,484,643,664,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-04/segments/1484560279650.31/warc/CC-MAIN-20170116095119-00487-ip-10-171-10-70.ec2.internal.warc.gz
| 796,041,256
| 9,901
|
# How did newton find the value of 'g' with the help of inverse square law?
1
by nisha11a
• Brainly User
2014-06-05T22:14:19+05:30
how did newton find the value of 'g' with the help of inverse square law?
Solution:
Consider a body of mass = m
According to the law of Gravitation ,
F =GMm/r² ,,,,,,,,,,,,,, (1)
Where F is the force of attraction between the body of mass m and the earth.
G= universal Gravitational Constant
r = distance between the center of masses.
Also ,
we know that earth attracts a body with a force given by
F=mg .......(2)
from 1 and 2 , we gt
mg = GMm/r²
or g =GM/r²
Hope this helps You!!!
| 194
| 656
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.328125
| 3
|
CC-MAIN-2017-04
|
latest
|
en
| 0.848348
|
https://www.thestudentroom.co.uk/showthread.php?t=2217728
| 1,542,236,614,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-47/segments/1542039742316.5/warc/CC-MAIN-20181114211915-20181114233915-00425.warc.gz
| 1,035,173,285
| 45,558
|
You are Here: Home >< Maths
# Mathematics Problem watch
1. I am having trouble with the whole of this question for some reason and I can't understand where I am going wrong.
Two students, Alan and Betty, work part time washing dishes in a local restaurant. After a particularly busy night each is faced with a mountain of identical dinner plates to wash. They both have their own sink to work at. Water is supplied to each sink at 60°C.
This is too hot for Alan who adds cold water until the temperature of the water in the sink is 50°C. Betty, however, has a pair of rubber gloves and can stand the hotter water. The temperature in the kitchen is 20°C.
Both students are studying an engineering degree course at their university and know that a possible mathematical model for the washing up process is
T(n) = p + qe^(-0.02n)
where T °C is the temperature of the water and n is the number of plates washed, while p and q are constants.
(a) Work out the values of p and q
(i) for Alan (ii) for Betty
The students begin washing up and keep going until the water temperature in each sink drops to 25°C.
(b) How many whole plates have been washed.
(i) by Alan (ii) by Betty?
Alan, who has washed fewer plates, resumes the job and continues until Betty’s total has been matched.
(c) What is now the temperature of the water in Alan’s sink?
I understand part (b) which is just using Natural Logs and part (c) which just uses the numbers from the previous 2 parts but part (a) is throwing me off.
As the number of plates washed at the start would be 0, my equation to solve for Alan would be 50 = p + q and for Betty would be 60 = p + q which are incorrect due to 2 unknowns and I cannot figure out how to solve this question.
2. (Original post by D556mm)
...
Hint: Consider
3. (Original post by ghostwalker)
Hint: Consider
So .. 50 = p + qe^(-0.02 * a large value) ?
I tried 1 million and got that 50 = p but then that would mean in the next part that you would have to take a Natural Log of a negative which is undefined
4. (Original post by D556mm)
So .. 50 = p + qe^(-0.02 * a large value) ?
I tried 1 million and got that 50 = p but then that would mean in the next part that you would have to take a Natural Log of a negative which is undefined
So you're telling me that after Alan has done an infinite number of plates the water temperature is still 50!
And you don't need the log of a negative number when doing part b). Post your working, once you've sorted a).
5. I think you need to consider both the limit as n tends to infinity and also the case when n=0. Remember that the water temperature can't fall below room temperature either. That should give you enough information to determine p and q.
6. What I'm getting here is:
n tends to infinity:
50 = p + qe^(-0.02*1000000)
e^(-0.02*1000000) = 0
50 = p + (q*0)
50 = p which would mean q = 0
n tends to 0:
50 = p + qe^(-0.02*0)
e^(-0.02*0) = e^0 = 1
50 = p + (1*q)
50 = p + q (many values for both p and q)
Apologies for all these problems, I've just been stuck on it for the past 2 days and I can't get my head around it at all
7. (Original post by D556mm)
What I'm getting here is:
n tends to infinity:
50 = p + qe^(-0.02*1000000)
e^(-0.02*1000000) = 0
50 = p + (q*0)
50 = p which would mean q = 0
n tends to 0:
50 = p + qe^(-0.02*0)
e^(-0.02*0) = e^0 = 1
50 = p + (1*q)
50 = p + q (many values for both p and q)
Apologies for all these problems, I've just been stuck on it for the past 2 days and I can't get my head around it at all
The temperature of the water after an infinite number of plates have been washed is not 50. Think about it, with each plate washed, the temperature drops a little. What temperature will the water eventually settle to after washing enough plates?
For Alan:
Same for Betty, but note that she has a different T(0) to Alan.
8. (Original post by D556mm)
...
OK, for Alan:
For n=0: Since the water starts at 50 degrees, we have.
50 = p + q.
As n tends to infinity: The water will have cooled down to ambient(room) temperature, so:
20 = p + 0
And solve simultaneously.
9. Ok, I think I got it.
Alan:
p = 20, q = 30
Washes 89.59 dishes = 90 dishes (or would that be rounded down as it is for wholes plates?)
Betty:
p = 20 and q = 40
Washes 103.97 = 104 (again, rounded down or up?)
and finally Alan's temp when matched with the number of dishes that Betty washed (I used 104 as n) would be 23.7°C (3sf)
10. (Original post by D556mm)
...
They seem reasonable. I'm not checking arithmetic at this level. You can plug values back into the appropriate equation to check.
As to whether you round up or down, I don't know. The instructions in the question seem contradictory to me if your decimal part is >= 0.5.
11. Well, Thanks for the help
12. on mine it says give answers to the nearest plate so just round normally
on mine it says give answers to the nearest plate so just round normally
how many thousands of people are trying to solve this problem now???
14. (Original post by davros)
how many thousands of people are trying to solve this problem now???
Makes you wonder if it's assessed.
15. (Original post by ghostwalker)
Makes you wonder if it's assessed.
Plymouth University seems to be a common factor
TSR Support Team
We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.
This forum is supported by:
Updated: January 7, 2013
Today on TSR
### The TSR A-level options discussion thread
Choosing A-levels is hard... we're here to help
### University open days
• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources
### Maths Forum posting guidelines
Not sure where to post? Read the updated guidelines here
### How to use LaTex
Writing equations the easy way
### Study habits of A* students
Top tips from students who have already aced their exams
| 1,617
| 6,082
|
{"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}
| 3.96875
| 4
|
CC-MAIN-2018-47
|
latest
|
en
| 0.973207
|
http://mathforum.org/kb/message.jspa?messageID=7435416
| 1,524,265,472,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-17/segments/1524125944742.25/warc/CC-MAIN-20180420213743-20180420233743-00520.warc.gz
| 202,485,757
| 5,904
|
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by NCTM or The Math Forum.
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic: Pseudoteaching
Replies: 31 Last Post: Apr 19, 2011 9:35 AM
Search Thread: Advanced Search
Messages: [ Previous | Next ]
Jonathan Groves Posts: 2,068 From: Kaplan University, Argosy University, Florida Institute of Technology Registered: 8/18/05
Re: Pseudoteaching
Posted: Apr 19, 2011 8:02 AM
Plain Text Reply
On 4/18/2011 at 2:13 pm, Richard Strausz wrote:
> (Still another post from Dan Meyer. The original post
> and the comments were interesting to read.)
>
> When teaching areas of circles and the relationship
> between length and area, I am looking forward to this
> as a kick-off:
> http://blog.mrmeyer.com/?p=9258
>
> Richard
Richard,
This post reminds me of Jonathan Crabtree's post on here a few
months ago about how students have different intuitions on what
a square twice as big means.
Dan Meyer's post is a good example of a common trick that many
use to exaggerate data. Like many people, I generally perceive
the ratio of areas immediately as a way to judge their relative
sizes rather than the ratios of dimensions. I take it that using
ratios of areas rather than just dimensions is quite common;
otherwise, why would this trick for trying to exaggerate relative
sizes of numbers be as common as it is?
Helping students learn about such tricks is a good lesson for
them.
Jonathan Groves
Date Subject Author
2/22/11 Joshua Fisher
2/22/11 Robert Hansen
2/22/11 Richard Strausz
2/22/11 Joshua Fisher
2/22/11 Robert Hansen
2/22/11 Joshua Fisher
2/23/11 Richard Strausz
2/23/11 Robert Hansen
2/23/11 Richard Strausz
2/23/11 Joshua Fisher
2/23/11 Paul A. Tanner III
2/23/11 Richard Strausz
2/23/11 Robert Hansen
2/23/11 Richard Strausz
2/23/11 Joshua Fisher
2/24/11 Robert Hansen
2/24/11 Richard Strausz
2/24/11 Joshua Fisher
2/24/11 Richard Strausz
2/24/11 Joshua Fisher
2/25/11 Mark Hammond
2/27/11 John Threlkeld
2/25/11 Robert Hansen
2/25/11 Joshua Fisher
2/25/11 Mark Hammond
2/26/11 Robert Hansen
3/1/11 GS Chandy
3/13/11 Richard Strausz
4/18/11 Richard Strausz
4/18/11 Robert Hansen
4/19/11 Jonathan Groves
4/19/11 Richard Strausz
© The Math Forum at NCTM 1994-2018. All Rights Reserved.
| 678
| 2,338
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-17
|
longest
|
en
| 0.887503
|
http://school.outsbook.com/rank/statistics/1865
| 1,555,991,621,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-18/segments/1555578586680.51/warc/CC-MAIN-20190423035013-20190423061013-00420.warc.gz
| 143,742,181
| 5,238
|
Problem Solver Statistics
Statistics
Rank: 105
tausimman minuha
cantonment english school and college
157 117 106 SUBMISSIONS PROBLEMS TRIED PROBLEMS SOLVED
Solved problems (106)
100 - Can You Type It?
101 - Income
102 - Divisor
103 - Mina and Rina
104 - Ages
105 - Book Price
106 - Hostel Meal
107 - Excavate Pond
108 - Dividend
109 - Average Age
110 - Average Run
111 - Father Age
112 - Barahatia Village
113 - Profit Percentage
114 - Loss Percentage
115 - Annum Interest
116 - Interest Rate
117 - Principal Amount
118 - Barahatia Village (II)
119 - Pass
120 - Increase of Population
121 - Quotient
122 - Save Money in Bank
124 - Rice Crop
125 - Hostel Meal (II)
126 - Chair and Table
127 - Victory Day
128 - Twice Number
129 - Subtracted Number
200 - Can you type it (II)??
201 - Motu and Patlu
202 - HELP!!!!!HELP!!!!!!
203 - Diffy
204 - Multi Diffy
205 - Mr. Ant’s Confusing Sum
206 - Subtraction Sum
207 - Car
208 - Square Formula
209 - Professor’s Homework
210 - Professor’s Homework (II)
211 - Consecutive Odd Numbers
212 - Consecutive Even Numbers
213 - Pond Digging
214 - Square Summation
215 - Age Calculation
216 - Motu Patlu Returns
217 - The national flag of Bangladesh
218 - Multi Process
219 - Monkey Vs Bamboo
220 - Midpoint
222 - Acceleration
223 - Slide Calipers
224 - Bus Travelling
226 - Polygons
227 - Help Boltu
228 - Strange Multiplication
229 - The national flag of Bangladesh (II)
233 - Easiest Equation V.2
234 - Split Number
235 - Simply Square
237 - Salesman
238 - Chestnuts
240 - How many Pages?
241 - Too Easy!!!!!!
243 - Pass Exam
244 - Chocolate Bars
245 - Chocolates
246 - Multiplication
248 - Tina's Profit
249 - The national flag of Bangladesh (III)
251 - Equation
254 - Ceiling and Floor
255 - Carpeting
257 - Racing
300 - Very Easy :)
301 - Binary to Decimal
302 - Octal to Decimal
303 - Strange Digits
305 - Mina and Rina Again
306 - Book Price Again
307 - Multi Diffy Again
308 - Consecutive Numbers
309 - Odd Numbers
310 - Even Numbers
311 - Find Big
312 - Find Small
313 - Simply Square Again
315 - Circle
318 - Chocolate Bars Again
319 - Chocolates Again
320 - Multiplication Again
321 - Three Circles
323 - Temperature Conversion
326 - Racing Moto Again
327 - Subtraction Sum Again
329 - Simply Area II
500 - Print “Hello”
501 - Odd Numbers
502 - Even Numbers
508 - Print the Numbers
511 - Print “a”
512 - Print Alphabets
Tried but not yet solved problems (11)
225 - Find Distance
231 - Pond Digging (II)
250 - Racing Moto
252 - Building
256 - Wind Weight
258 - Replace
322 - Trapezium
325 - Equation Again
330 - Diagonal
331 - Diagonal II
| 730
| 2,588
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.453125
| 3
|
CC-MAIN-2019-18
|
latest
|
en
| 0.496624
|
https://www.daniweb.com/programming/software-development/code/371536/rotate-sequences-left-or-right
| 1,726,673,911,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651899.75/warc/CC-MAIN-20240918133146-20240918163146-00562.warc.gz
| 658,904,053
| 16,576
|
# Rotate sequences left or right
Updated 1 Tallied Votes 671 Views
Another quick code over breakfast inspired by 'spying' the other forums.
Gribouillis commented: nice +13
``````""" Rotate sequences right or left
>>> rot_right(arr)
[(7, 4, 1), (8, 5, 2), (9, 6, 3)]
>>> p(rot_right(arr))
(7, 4, 1)
(8, 5, 2)
(9, 6, 3)
----------------------------------------
>>> p(rot_right(rot_right(arr))
)
(9, 8, 7)
(6, 5, 4)
(3, 2, 1)
----------------------------------------
>>> p(rot_right(rot_right(rot_right(arr))))
(3, 6, 9)
(2, 5, 8)
(1, 4, 7)
----------------------------------------
>>> p(rot_right(rot_right(rot_right(rot_right(arr)))))
(1, 2, 3)
(4, 5, 6)
(7, 8, 9)
----------------------------------------
>>> p(rot_right(rot_left(arr)))
(1, 2, 3)
(4, 5, 6)
(7, 8, 9)
----------------------------------------
>>> a =['***',
' * ',
' ']
>>> p(a)
***
*
----------------------------------------
>> p(map(''.join, rot_right(a)))
*
**
*
>>> p(map(''.join, rot_left(a)))
*
**
*
----------------------------------------
>>> p(map(''.join, rot_left(rot_left(a))))
*
***
----------------------------------------
"""
def p(a, sep=40*'-'):
""" print sequences in separate lines and line separation sep """
for line in a: print(line)
print(sep)
def rot_left(a):
return list(zip(*a)[::-1])
def rot_right(a):
return list(zip(*a[::-1]))
if __name__ == '__main__':
arr = [[1,2,3],[4, 5, 6], [7, 8, 9]]
p(arr)
p(rot_right(rot_right(rot_right(arr))))
p(rot_right(rot_right(rot_right(arr))))``````
TrustyTony 888
The sequences does not need to be of square arity for functions to work, here another helper for the 'tetris' case:
``````>>> a = ['***', ' * ']
>>> def strrot(string_seq, rotation=rot_left, fun=''.join, times=1):
for count in range(times):
string_seq = map(fun, rotation(string_seq))
return '\n'.join(string_seq)
>>> strrot(a)
'* \n**\n* '
>>> print strrot(a)
*
**
*
>>> print strrot(a, times=2)
*
***
>>> print strrot(a, times=3)
*
**
*
>>> print strrot(a, rotation=rot_right)
*
**
*
>>> print strrot(a, rotation=rot_right, times=2)
*
***``````
TrustyTony 888
Another interesting aplication for the generalized principle:
``````""" rotating histogram by functions rot_left, rot_left and strrot """
def p(a, sep='', groupsep=40*'-'):
""" print sequences in separate lines and line separation sep """
for line in a: print(sep.join(line))
print(groupsep)
def rot_left(a):
return list(zip(*a)[::-1])
def rot_right(a):
return list(zip(*a[::-1]))
def strrot(string_seq, rotation=rot_left, fun=''.join, times=1):
for count in range(times):
string_seq = map(fun, rotation(string_seq))
return string_seq
if __name__ == '__main__':
histo = """
red ***********
yellow *************
brown ****
"""
histo = histo.split('\n')
histo = [' '.join(''.join(word[::-1]) for word in line.split(' ')) for line in histo]
linemax = len(max(histo, key=len))
histo = [line.ljust(linemax) for line in histo if line]
p(strrot(histo), sep =' ')
""" Output:
*
*
* *
* *
* *
* *
* *
* *
* *
* * *
* * *
* * *
* * *
y
e b
l r
r l o
e o w
d w n
----------------------------------------
"""``````
Gribouillis 1,391
Here is how I would code it to get rid of the 'rotation' argument and make it a little faster
``````def strrot(string_seq, times = 1):
times %= 4
if times % 2:
string_seq = reversed(zip(*string_seq)) if times == 1 else zip(*reversed(string_seq))
return [''.join(t) for t in string_seq]
else:
return reversed([s[::-1] for s in string_seq]) if times else string_seq``````
To rotate right, pass times = -1, or -44445 :)
TrustyTony 888
Thanks fro your analysis Gribouillis, interesting rotation of reversed, zip and * for odd cases. I did little different single if case-like statement vesion of it, so:
``````""" rotating histogram by functions rot_left, rot_left and strrot """
def p(a, sep='', groupsep=40*'-'):
""" print sequences in separate lines and line separation sep """
for line in a: print(sep.join(line))
print(groupsep)
def rot_left(a):
return list(zip(*a)[::-1])
def rot_right(a):
return list(zip(*a[::-1]))
def strrot(string_seq, times = 1):
times &= 0b11
if not times:
return string_seq
elif times == 2:
return list(reversed([s[::-1] for s in string_seq]))
elif times == 3 :
string_seq = zip(*reversed(string_seq))
else:
string_seq = list(reversed(zip(*string_seq)))
return [''.join(t) for t in string_seq]
if __name__ == '__main__':
t = ['***', '* ']
for count in range(1,5):
print('Left rotate %i:\n' % count)
p(strrot(t, times=count))
print(60*'=')
print('Right rotate variations')
p(strrot(t, -44445))
p(strrot(t, -1))
p(strrot(t, 3))``````
The python deque (double ended que) is good for left/right rotation
``````from collections import deque # Double-ended Que
stringToRotate = "hello"
alpha = 'hello' # This is your reference
dq = deque(alpha) # make double ended
amount = 2
dq.rotate(amount)# positive values drags to the right - negative to the left
rotatedString = "" # define for later
for letter in stringToRotate:
if letter in alpha:
index_alpha = alpha.index(letter) # Get original position of letter
rotatedString += dq[index_alpha] # add the rotated letter to string
print rotatedString``````
TrustyTony commented: Inappropriate for 2-d case -3
Be a part of the DaniWeb community
We're a friendly, industry-focused community of developers, IT pros, digital marketers, and technology enthusiasts meeting, networking, learning, and sharing knowledge.
| 1,546
| 5,407
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-38
|
latest
|
en
| 0.400543
|
http://vintagecalculators.com/html/addometer.html
| 1,709,559,523,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947476452.25/warc/CC-MAIN-20240304133241-20240304163241-00406.warc.gz
| 40,767,362
| 4,607
|
Mechanical Calculators
296 x 50 x 15 mm (11.75" x 2.0" x 0.6").
Made in U.S.A. 1900s - 1960s.
For addition the stylus is placed in the hole against the appropriate large, inner number and dialed clockwise.
For subtraction the stylus is placed in the hole against the appropriate small outer number and dialed counter-clockwise.
Carry is automatic, and the instrument is cleared by pulling out the tab at bottom right.
As well as decimal models, versions were also made for working in feet and inches, as above and Sterling currency, as below.
In the standard version the wheels are colour coded for working in currency eg. the two white wheels on the right would be for cents and the rest for dollars, in groups of three. Or the colours can just be ignored and a decimal point inserted mentally as appropriate between the wheels. The addometer above shows the value 87654321, or it could be interpreted as \$876,843-21.
Made by the Reliable Typewriter and Adding Machine Co., Chicago, Illinois, U.S.A.
296 x 50 x 15 mm (11.75" x 2.0" x 0.6").
Made in U.S.A. 1900s - 1960s.
In the feet and inches version the wheel second from the right has numbers to 11 for dealing with inches. The wheel on the right deals with eigths and quarters of an inch. The addometer shows the value 123,456 feet 11 5/8 inches.
Made by the Reliable Typewriter and Adding Machine Co., Chicago, Illinois, U.S.A.
Details as for the Feet and inches Addometer above.
This version was made for use in countries with Pounds-Shillings-Pence, Sterling currency (see the Sterling Currency Calculator section for more details of Sterling currency).
This requires the fitting of special dials:
The 4 white dials on the left are for Pounds; the two red dials are for Shillings (20 Shillings = 1 Pound); the 2nd dial from the right is for Pennies (12 Pennies = 1 Shilling); the dial on the right is for Farthings (from "fourthings" (4 Farthings = 1 Penny).
The calculator in the photograph displays the value:
£1,234 17s 6 3/4d
(1,234 Pounds, 17 Shillings, and 11 3/4 Pence).
Distributed in the UK. by Taylor's, 74 Chancery Lane, London.
| 551
| 2,113
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10
|
latest
|
en
| 0.920694
|
https://tutel.me/c/programming/questions/49858122/how+can+i+run+a+block+of+code+until+get+the+same+result+3+times
| 1,537,830,484,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-39/segments/1537267160842.79/warc/CC-MAIN-20180924224739-20180925005139-00450.warc.gz
| 642,639,742
| 14,430
|
#### [SOLVED] How can I run a block of code until get the same result 3 times?
How can I make this code run until getting 3 "Blue" rolls in a row?
``````var cards = ['Blue', 'Yellow'];
var currentCard = 'Yellow';
while (currentCard !== 'Blue') {
console.log(currentCard);
var randomNumber = Math.floor(Math.random() * 2);
currentCard = cards[randomNumber]
}
console.log('Blue')
``````
#### @Joe Warner 2018-04-16 13:10:25
You can just use a variable to count how many times blue has been rolled then stop when it reaches that amount
If you want it to reset when you get a yellow like you said in a comment below add an else to reset the count :)
I need a block that increases a variable each time I get a blue card and when you get a yellow card you reset it
`````` var cards = ['Blue', 'Yellow'];
var currentCard = 'Yellow';
var blueCount = 0;
while (blueCount < 3) {
console.log(currentCard);
var randomNumber = Math.floor(Math.random() * 2);
currentCard = cards[randomNumber]
if (currentCard === 'Blue') {
blueCount++;
} else {
blueCount = 0;
}
}
console.log('Blue')``````
You can do this without a while loop as well using recursion i'd suggest using recursion my function below isn't the best way to handle it but should give you an idea
``````var cards = ['Blue', 'Yellow'];
function recursiveRoll3(count = 0, card = getRand()) {
if (count === 3) return;
console.log(card)
return card === 'Blue' ?
recursiveRoll3(count += 1) :
recursiveRoll3(0);
}
function getRand() {
return cards[Math.floor(Math.random() * 2)];
}
recursiveRoll3()``````
#### @ansibly 2018-04-16 14:24:25
I read your initial question to mean: I want a function that will tell me how many times it took to 'roll' the color 'Blue' 3 times.
I need a block that increases a variable each time I get a blue card and when you get a yellow card you reset it
...to mean: I want a function that will tell me how many times it took to 'roll' the color 'Blue' 3 times consecutively.
Here are my take on both using recursive functions instead of loops.
``````function roll(list, target, times, hits, rolls) {
if(hits === times) return rolls;
hits = (hits)? hits : 0;
rolls = (rolls)? rolls : 0;
var rand = Math.floor(Math.random() * list.length);
hits = (list[rand] === target)? hits+1 : hits;
return roll(list, target, times, hits, rolls+1);
}
function rollConsecutive(list, target, times, hits, rolls) {
if(hits === times) return rolls;
hits = (hits)? hits : 0;
rolls = (rolls)? rolls : 0;
var rand = Math.floor(Math.random() * list.length);
hits = (list[rand] === target)? hits+1 : 0;
return rollConsecutive(list, target, times, hits, rolls+1);
}
var numberOfTimesToRollColor = roll(['Blue','Yellow'], 'Blue', 3);
console.log(numberOfTimesToRollColor);
var numberOfTimesToRollColorConsecutively = rollConsecutive(['Blue','Yellow'], 'Blue', 3);
console.log(numberOfTimesToRollColorConsecutively);``````
#### @goediaz 2018-04-16 13:34:24
I want to share my approach with you.
``````var cards = ['Blue', 'Yellow'];
var count = 0;
function getACard(randomNumber) {
if (cards[randomNumber] !== 'Blue') {
console.log(cards[randomNumber]);
getRandomNumber();
} else {
count++
console.log('Blue: ' + count);
if (count < 3) {
getRandomNumber();
} else {
return;
}
}
}
function getRandomNumber() {
var randomNumber = Math.floor(Math.random() * 2);
getACard(randomNumber);
}
getRandomNumber();``````
I tried to make it as simple as a could.
Here is a fiddle so you can play with it.
#### @Ron Nabuurs 2018-04-16 13:14:18
You have to save a variable when you get an Blue card. For example you can increase a variable each time you get a blue card. Each time you check if that variable is 3 and if it is you have 3 times blue.
``````var cards = ['Blue', 'Yellow'];
var timesBlue = 0
var currentCard = 'Yellow';
while (timesBlue != 3) {
var randomNumber = Math.floor(Math.random() * 2);
currentCard = cards[randomNumber]
console.log(currentCard);
if (currentCard == 'Blue') {
timesBlue++;
}
}``````
#### @b3nc1 2018-04-16 13:13:42
`````` var cards = ['Blue', 'Yellow'];
var currentCard = 'Yellow';
var counter = 0;
while (counter < 3) {
console.log(currentCard);
var randomNumber = Math.floor(Math.random() * 2);
currentCard = cards[randomNumber]
if(currentCard === 'Blue'){
counter++
}
}
console.log('Blue')
``````
#### @b3nc1 2018-04-16 13:52:21
i was writing it and you were just faster
### [SOLVED] How can I get last characters of a string using JavaScript
• 2011-05-03 18:12:18
• user695663
• 709236 View
• 562 Score
• Tags: javascript
### [SOLVED] javnumber generator
• 2017-02-03 12:00:46
• Tom Wilson
• 39 View
• -4 Score
• Tags: javascript
### [SOLVED] How to rewrite code without using jquery?
• 2013-11-14 18:33:11
• Jolanta Smaga
• 100 View
• 0 Score
| 1,365
| 4,773
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-39
|
longest
|
en
| 0.818305
|
https://pbsfonline.com/question-what-is-baseball-money-line/
| 1,679,866,800,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296946535.82/warc/CC-MAIN-20230326204136-20230326234136-00734.warc.gz
| 519,256,287
| 20,809
|
This is the most popular way people bet on baseball. A money line wager is pretty straight forward. You are simply placing a bet on who you think will win the game. Odds are displayed with the away team listed first or on top and the home team listed second or on the bottom.
## How good is +200 odds?
For example, a bet placed at +200 in American odds (2/1 in fractional or 3.00 in decimal) has a 33.33 percent implied winning probability. A bet placed at -200 in American odds (1/2 in fractional or 1.50 in decimal) has a 66.67 percent implied winning probability.
## What does +200 mean in odds?
When odds are expressed with a + or a – followed by a number, they are American money line odds: +200 signifies the amount a bettor could win if wagering \$100. If the bet works out, the player would receive a total payout of \$300 (\$200 net profit + \$100 initial stake).
## How do you know which team is favored?
If there is a minus sign next to a team’s spread, that suggests that they are favored and have to win by or cover that amount. If there is a positive sign, that tells you that they are the underdog and they are getting points.
## How do I win a bet every time?
How to Always Win Sports Betting | 5 Step Guide You Must See.
## What is the most profitable sport to bet on?
With that in mind, here is my own personal list of the most profitable sports to bet on:
1. College Basketball. For me, this is a no-brainer.
2. NBA. The NBA is Thunderdome.
3. MLB. This is another numbers game.
4. NFL.
5. Soccer.
6. College Football.
7. Horse Racing.
8. WNBA.
## How much do I win if I bet \$100 on odds?
The number on the left represents your winnings and the number on the right represents your stake. For example: 2/1 odds means you’ll win \$2 for every \$1 you bet. A \$100 bet at 2/1 odds would win \$200, for a total payout of \$300.
## What happens if you bet \$100 on a money line?
This means that the bettor would have risked \$400 and ultimately gained \$100. The positive number shows how much would be gained on a successful \$100 bet. A +300 money line, for instance, would mean that if you place a successful bet of \$100, you would win \$300.
## What are +100 odds?
A +100 odds line, on the other hand, means that you have the opportunity to win the same amount that you are wagering. Making a \$100 wager at +100 odds means that you could win \$100 on that bet. Worth noting is that sportsbooks are always looking to make money, and sports betting is a form of gambling.
## How do you read baseball odds?
Baseball odds are shown using a “Money Line.” The Money Line: Odds for a game based on \$1. A “minus” (-) preceding the number indicates the team is a favorite. A “plus” (+) preceding the number indicates the team is an underdog.
## What does +450 mean in odds?
So, a -450 number would mean that you would have to bet \$450 in order to win \$100 in profit back. On the other hand, an odds number with a “plus” in front of it means that the team or player is an underdog.
## What do odds of +350 mean?
A +350 underdog means you risk only \$100, but you win \$350. You either lose \$100 or win \$350, or push. American Odds can easily be converted into other odds such as decimal or fraction, using our free online calculator.
## How do you figure out odds?
Probability can be expressed as 9/30 = 3/10 = 30% – the number of favorable outcomes over the number of total possible outcomes. A simple formula for calculating odds from probability is O = P / (1 – P). A formula for calculating probability from odds is P = O / (O + 1).
## How do you predict a draw using odds?
How to Predict a Draw in Football Match (4 Tips Revealed)
## Can I bet on both teams to win?
There are no rules normally stopping you backing both teams on betting exchanges, where you can also back and lay the same selection, which is basically the same as backing both selections. People that normally do this are known as betting exchange traders or simply betting traders.
## What is the easiest bet to win?
The 5 Easiest Football Bets to Win
• First Half Over/Under. A variation on the Over/Under bet is First (or Second) Half Over/Under.
• Double Chance. Another easy football bet is Double Chance, which allows you to bet on two of three possible outcomes for the match.
• Draw No Bet.
• Both Teams to Score.
## How can I bet without losing?
How Do You Bet Without Losing?
1. Plenty of Research. The most important aspect of becoming a successful sports bettor is to do plenty of research.
2. Use a Handicapper. Another helpful tip to remember when betting on sports is to use a handicapper to help guide you.
3. Show Restraint.
4. No Parlays.
## Which is the best market to bet on?
Best Betting Markets in Football
• Match Odds. The Match Odds market is by far the most popular.
• Double Chance. The Double Chance market is a spinoff of the Match Odds market.
• Draw No Bet.
• Correct Score.
• Over/Under.
• Both Teams to Score.
• Asian Handicap.
## What’s the easiest sport to bet on?
What’s the Easiest Sport to Bet On?
• College Basketball – Easiest Sport for Beating the Book.
• NFL Football – Most Accessible Sport to Bet On.
• MLB Baseball – Best Sport for Beginning Sports Bettors.
• Conclusion.
## What sport is gambled on the most?
Football
In the US, football is undoubtedly the most popular sport for wagers. And globally, the game is the second-most betted-upon. Wagers on the NFL make up nearly half of all sports bets placed in the US.
## What percentage of sports gamblers win?
Winning Percentages
Professional sports bettors rarely sustain a long-term winning percentage higher than 55 percent, and it’s often as low as 53 or 54 percent.
## What does plus 1000 odds mean?
The bigger the number after the plus sign, the bigger of an underdog that the team or person is to win. So, if a team is +1000 to win, this would mean that you would win \$1000 in profit with a bet of \$100 – if they won, of course.
## What does 80 to 1 odds pay?
Rich Strike, a late entrant in the grandest horse race, went off at 80-1 odds. Meaning a \$10 Win bet on the Derby winner would’ve returned \$818.
## What does 40 to 1 odds pay?
MyTopSportsbooks Conversion Table for common Odds
UK EU Bet
39/1 40.00 \$100
40/1 41.00 \$100
41/1 42.00 \$100
42/1 43.00 \$100
## What is a 2 leg parlay?
The first type of parlay is a standard parlay. To be considered a parlay, a bet must have two or more legs. You can add as many legs as you want to a parlay. The more legs you add, the higher your potential payout on a sportsbook. More legs bring more risk, and that’s why the payout is more substantial.
## How much does a parlay bet cost?
Typical payouts for up to 10 team parlay bet
Number Odds Payout
2 Team Parlay 2.6 to 1 \$360
3 Team Parlay 6 to 1 \$700
4 Team Parlay 11 to 1 \$1,200
5 Team Parlay 22 to 1 \$2,300
## What is a 3 way moneyline in baseball?
Three-Way Moneylines, Made Simple. Whereas a typical moneyline bet involves a bet on one of two options, three-way moneyline betting involves three options. When wagering on a three-way moneyline, you can bet either Team A to win, Team B to win, or for the event to end in a tie (sometimes referred to as a ‘draw’).
## What does a +7 spread mean?
What does +7 spread mean? If the spread is seven points for a game, it means the underdog is getting seven points, noted as +7 on the odds. A team posted at -7 is the favorite and is laying seven points.
## Do you lose money on negative odds?
One of the most frequently asked questions about negative odds is, “Do you lose money on negative odds?” The answer is no. Your profit on those odds is just less than it would be compared to positive odds. Negative odds denote favored teams.
| 1,930
| 7,747
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.015625
| 3
|
CC-MAIN-2023-14
|
latest
|
en
| 0.951378
|
https://www.scribd.com/document/81208018/Aps-Notess
| 1,569,164,264,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-39/segments/1568514575515.93/warc/CC-MAIN-20190922135356-20190922161356-00428.warc.gz
| 1,038,229,398
| 89,645
|
You are on page 1of 35
## Lecture Notes and Problem Sets
Peter Hst
Torbjrn Helvik
Eugenia Malinnikova
Contents
1. Basic problem solving techniques 3
1.1. Induction 3
1.2. Combinatorial proofs 3
1.3. Inclusion-Exclusion 4
1.4. The Pigeon-hole principle 5
2. Abstract algebra 6
2.1. Groups 6
2.2. Other structures 7
3. Polynomials over C 9
3.1. Denition, Ring of polynomials 9
3.2. Polynomials over complex numbers 10
3.3. Dierent ways to determine polynomial 12
4. Linear algebra 14
4.1. Linear, or vector, spaces 14
4.2. Linear operators 14
4.3. Determinants 16
4.4. Representation of a matrix 18
5. Matrix calculus 21
5.1. A matrix is a linear map 21
5.2. The characteristic polynomial 22
5.3. Diagonalization 23
5.4. A few more tricks 23
5.5. Non-negative matrices 24
6. Sequences and series 25
6.1. Sequences and limits 25
6.2. Series 26
7. Problem sets 30
7.1. Basics 30
7.2. Abstract algebra 30
7.3. Polynomials over C 31
7.4. Linear algebra 31
7.5. Matrix calculus 32
7.6. Sequences and series 33
7.7. Calculus 33
8. Hints 35
8.1. Basics 35
8.2. Abstract algebra 35
8.3. Polynomials over C 35
8.4. Linear algebra 35
1. Basic problem solving techniques
by Peter Hst
Polya divides problem solving into four stages, Understanding the problem, Devising a plan,
Carrying out the plan and Looking back. Of these stages I would here like to focus on the
second and fourth.
In a standard mathematical proof you will see a neatly written presentation of how to solve
the problem at hand. This is the result of Polyas stage three. However, to understand where
the solution came from clearly stage two is more important. In the group discussions in this
course we will undertake the dicult endeavor of discussing our solutions as they occurred in
Stage 2. Some practical tricks to achieve this are an informed uninterest in the details (and
results!) of carrying out the plan, and notes in the solution marking what led one to the ideas.
Another stage frequently neglected is the looking back. In this course this function will be
naturally covered by the discussions in the tutor groups. However, to get the most out of these
discussions every participant should be prepared to analyze the problems, which in particular
involves having tried to solve them.
1.1. Induction. Formally induction is quite a simple technique: you verify the initial condition
P
0
and the implication P
n
P
n+1
, and remember to use the magic words follows by induction.
The diculty is nding the right proposition and the index on which to work the induction.
Of course, we can also do induction on several indices at the same time (in this case you should
be especially careful about circular reasoning) or of more complex indices, such as n+m or
nm.
Closely related to induction is recursion. In recursion we want to nd some object, and
reduce this task to nding one of a set of sub-object. For instance, consider a rectangular
subset of a square lattice, say R
m,n
= (0, 0), . . . , (0, n), (1, 0), . . . , (m, n), and all paths going
up and to the right connecting the corners of R
m,n
. We want to count the number of such
paths, say r
m,n
. We can split the set of paths into two disjoint sets, those that pass through
(0, 1) and those that pass through (1, 0). Thus we see that
r
m,n
= r
m,n1
+ r
m1,n
.
This is the same recursion as satised by the binomial coecients, and since the initial condi-
tions (r
i,1
= r
1,i
= 1) are also the same, we conclude that
r
m,n
=
_
m + n
m
_
.
1.2. Combinatorial proofs. We continue with our rectangular lattice and give bijective or
combinatorial proofs of the equation
r
m,n
=
_
m + n
m
_
=
n
k=0
_
n
k
__
m
k
_
.
For simplicity of notation we assume that n m throughout this section.
By a combinatorial or bijective proof we mean that both sides of the equation are interpreted
as cardinalities of sets and the equality is shown by nding a bijection between the sets. In
many cases the sets will actually be the same (and the bijection the identity) and the work
goes into the interpretation.
For the above equality we already have the interpretation of the left-hand-side, it is the
number of up-right paths connecting the lower-left corner to the upper-right corner. Fix k n
and choose a k-element subset M of 0, . . . , n 1 and a k-element subset N of 1, . . . , m.
3
We dene a bijection from pairs (M, N) to paths as follows. We go right from (0, 0) to (M
1
, 0),
where M
1
is the smallest element in M. Then we go up from (M
1
, 0) to (M
1
, N
1
), where N
1
is the smallest element in N. Then we got right to (M
2
, N
1
) etc. From (M
k
, N
k
) we go right
all the way to (m, N
k
) and then up to (m, n). Thus we have a path from (0, 0) to (m, n) for
every pair (M, N). To comlpete the proof, we need to check that this correspondence denes
a bijection, but this is left for the reader.
We can dene another bijection on the same set to prove the same inequality as follows. Let
D denote the diagonal at distance n from (0, 0), i.e. D = (n, 0), (n 1, 1), . . . , (0, n). Now
the number of paths from (0, 0) to (n k, k) equals
_
n
k
_
. The number of paths from (n k, k)
to (m, n) equals
_
m
mk
_
=
_
m
k
_
. So the number of paths through (n k, k) equals
_
n
k
__
m
k
_
and
since every path passes through one and only one of the points in D, we see that the total
number of paths is
n
k=0
_
n
k
__
m
k
_
.
We leave it to the reader to give combinatorial proofs of the following identities, which are
derived from the formula
(1 +x)
n
=
n
k=0
_
n
k
_
x
k
by setting x = 1, setting x = 1 and by dierentiating and setting x = 1, respectively:
(1.1)
n
k=0
_
n
k
_
= 2
n
,
n
k=0
(1)
k
_
n
k
_
= 0,
n
k=0
k
_
n
k
_
= n2
n1
.
1.3. Inclusion-Exclusion. Although not covered during the lecture, the principle of inclusion
and exclusion is directly related to combinatorial proofs. The idea is that we constructed our
bijection poorly, so that some elements were counted multiple times (inclusion). We correct the
situation by removing the over-counted elements (exclusion). Typically, we will also over-do
the removal, so we go for another inclusion, then exclusion etc.
As an example, lets consider the classical derangement problem: n people go to the restau-
rant and leave their coats in a coat-check. There is some mix-up with the tags, and they get
back random coats. What is the probability that someone gets the right coat back?
Now we estimate the ways in which at least one person gets the right coat. For each
k = 1, . . . , n we give person k his or her coat, and assign the other coats randomly in (n 1)!
ways. Obviously, in each case at least one person gets the right coat, and there are a total of n!
such assignments. However, several assignments are multiply counted, namely, an assignment
in which exactly k people get the right coat is counted k times. So we generate assignments
by choosing two-people subsets, giving these people the right coats, and distributing the rest
randomly. There are
_
n
2
_
(n 2)! such assignments, but again multiple counts. This time we
count a set with k correct assignments
_
k
2
_
times. When we subtract the latter set of assignments
from the former, we see that those assignments where exactly 1 or 2 people get the right coat
are correctly counted, whereas those where exactly k people get the right coat are counted
k
_
k
2
_
times. Now we see that we can continue this process of generating assignments and
alternatively adding and subtracting them. When we do this also for = 3, . . . n, we see that
the assignments for which exactly k people get the right coat are counted
k
i=1
(1)
i+1
_
k
i
_
= 1
4
time, by the second formula in (1.1). So in the nal tally, every assignment is counted the right
number of times, which means that the total number of ways in which at least one person gets
the right coat is
n!
_
n
2
_
(n 2)! +
_
n
3
_
(n 3)! . . . + (1)
i
_
n
1
_
+ (1)
i+1
= n!
_
1
1
2!
+
1
3!
. . . + (1)
i
1
(n 1)!
+ (1)
i+1
1
n!
_
=
_
n!
e
_
.
where [x] is the integer closest to x. The last expression follows since the sum is just the rst
terms in the Taylor expansion of e
1
. So the probability asked for is
_
n!
e
1
n!
.
1.4. The Pigeon-hole principle. The pigeon-hole principle is very simple: it says that if
f : M N is a mapping of nite sets M, N, and M has more elements than N, then f is not
an injection, i.e. there exists m
1
, m
2
M such that f(m
1
) = f(m
2
). Stated another way, if
you put n + 1 letters in n pigeon-holes, then at least one pigeon-hole will contain at least two
letters. Of course the diculty in using this principle is in determining what the pigeon-holes
and letters are in a particular problem.
5
2. Abstract algebra
typed by Peter Hst
based on notes by Alexei Roudakov
2.1. Groups.
2.1.1. Abstract groups. We start our study of algebra by dening an operation which can serve
for instance as a model of addition. Let G be a set and : GG G. We say that (G, ) is
a group if
(1) there exists a neutral element e G, i.e. a e = e a = a for all a G;
(2) every element has an inverse, i.e. for every a G there exists b G such that a b = e;
(3) the operation is associative, i.e. a (b c) = (a b) c for all a, b, c G.
The inverse of the element a is denoted by a
1
.
Note that in general we have a b ,= b a, i.e. the group is non-commutative. However, if
ab = e, then also ba = e (prove this). Often a group is written multiplicatively, which means
that we denote the operation by instead of , and use the usual conventions of omitting this
sign, so a b is written ab. We say that a group is commutative or abelian if ab = ba for every
pair of elements.
Some examples of groups are: (Z, +), (Q, +),
_
(0, ),
_
. For a natural number k we can
dene a group Z
k
whose elements are the numbers 1, . . . , k with the operation + dened as
addition modulo k. These groups are all commutative
We can also construct new groups from old. For instance, let G be a group and S be a set.
Consider the set M = f
## f : S G. This set is made to a group by dening the element
f
M
g to be the function from S to G which maps a S to f(a)
G
g(a). We call this a
point-wise evaluation.
Exercise: Let G be a nite group with the property that g
2
= g g = e for every g G.
Show that the number of elements of G is a power of 2.
2.1.2. Permutation groups. Let next S be a nite set. Then a bijection of S to itself is called
a permutation. Note that the composition of two permutations is a permutation. We denote
the group of permutations of 1, . . . , n by S
n
. We use the notation (a
1
a
2
. . . a
k
) for the
permutation with (a
i
) = a
i+1
, (a
k
) = a
1
and (a) = a for all other elements. Permutations
of the type (a b) are called transpositions.
Exercise: Let S
n
and =
1
k
=
1
m
, where the sigmas and taus are
transpositions. Show that (1)
k
= (1)
m
.
We can represent a permutation graphically in R
2
as follows: for S
n
connect (i, 1) with
(j, 1) if and only if (i) = j. The connections should be by a smooth curve which stays
between the lines (x, 1) and (x, 1). (The curves should be drawn so that two curves are never
tangent, at most two curves meet in any one point, and a curve never intersects itself.) Let l
be the number of intersection points in such a graph.
Exercise: Show that (1)
l
depends only on , not on how we draw the diagram. Thus we
may dene () = (1)
l
.
Mappings that preserve the natural structure in algebra are called homomorphisms (with
appropriate prex when necessary, e.g. group homomorphism). Explicitly, let G and H be
groups and f : G H be a mapping. We say that f is a homomorphism if
(1) f(e
G
) = e
H
;
(2) f(a
G
b) = f(a)
H
f(b), for all a, b G.
6
Exercise: Show that if f is a homomorphism, then f(a
1
) = f(a)
1
.
The set 1, 1 is a group under normal multiplication, with 1 as neutral element.
Exercise: Let : S
n
1, 1 be a homomorphism. Show that is the identity, or =
dened in Exercise 2.1.2.
2.1.3. Thoughts on problems with groups. Since groups carry so little structure, they are quite
elusive. However, certain special classes of groups, e.g. abelian groups which are nitely gen-
erated, are quite easy to understand.
One way of specifying some structure of a group, without giving away too much of its
abstractness, is by specifying a relation. For instance, say we have a
2
= e for every element
of the group. These kind of problems have been quite popular in the competitions, since their
solutions do not require (or benit from) extensive knowledge of algebra.
Relations are particularly important when constructing groups from free groups. We say
that G is a free group with generators A satisfying the following property: if F is a group and
: A F is a mapping, there extends uniquely to a homomorphism of G. An example
should clarify this let G = Z and A = 1. Now the mapping : A F extends to Z
uniquely by (k) = k(1) (we use (k) = (k 1) + (1) = k(1) and proof by induction).
We can construct a free group as follows: we take a set a
1
, . . . , a
n
, which will be our
generators. Our set is made up of nite sequences (usually called words) (b
1
, . . . , b
l
), where
each b
i
is either a
j
or a
1
j
for some j but the sequence should be without a
j
and a
1
j
as
consecutive elements. The operation on this set is that of concatenation, i.e.
(b
1
, . . . , b
l
)(c
1
, . . . , c
l
) = (b
1
, . . . , b
l
, c
1
, . . . , c
l
),
with the understanding that we cancel any a
j
with a a
1
j
that comes next to it, e.g.
(a, b
1
, a, c)(c
1
, a, a) = (a, b
1
, a, a, a).
This denes a group, and the group is freely generated by a
1
, . . . , a
n
.
Once we have a free group G generated by a set a
1
, . . . , a
n
, we can construct other groups
by requiring that a relation hold. A relation is just an element of G set to 1, the neutral
element. For instance, in Z we can dene the relation k = 1: Then we get the group Z
k
dened
previously. As another example consider the free group dened as in the previous paragraph
by generators a and b, and require the relation ab = ba (equivalently, aba
1
b
1
= 1). Then we
can write the elements in our groups in a normal form, with all the as preceeding all the bs,
so our elements are of the form (a, . . . , a, b, . . . , b), which is more conveniantly written ar a
k
b
l
.
In particular, this group is isomorphic to Z
2
.
2.2. Other structures. Groups are very exible, but correspondingly capture only very little
structure. In this section we have a look at two other algebraic strucutes, this time ones with
two operations.
We say that (R, +, ) is a ring if
(1) (R, +) is a commutative group;
(2) there exists a multiplicative identity 1, i.e. 1a = a1 = a for all a R;
(3) multiplication is associative, i.e. a(bc) = (ab)c for all a, b, c R;
(4) the distributive law holds, i.e. a(b+c) = ab+ac and (a+b)c = ac+bc for all a, b, c R.
Notice that addition in a ring is commutative, but multiplication need not be.
The standard example of a (non-commutative) ring is the set of matrices. Of course (Q, +, ),
(R, +, ) and (C, +, ) are all rings. Another example is given by the set of polynomials over a
ring, where addition and multiplication are dened in a point-wise sense. This means that we
just calculate with polynomials as we always have done, only that the coecients are now in
some ring.
7
We can put more structure on our algebraic object by requiring that also multiplication is
as close as possible to a commutative group. We say that (F, +, ) is a eld if
(1) (F, +, ) is a ring;
(2) (F 0, ) is a commutative group
The sets (Q, +, ), (R, +, ) and (C, +, ) are also rings. For a prime number p, calculation
modulo p in Z
p
is also a eld. If k is a composite number (i.e. k has non-trivial divisors), then
Z
k
is a ring, but not a eld: suppose k = mn, where m and n are integers larger than one.
Viewing m and n as elements in Z
k
, we see that mn = 0, so that the elements cannot have
multiplicative inverses (required in a eld). More generally, we see that a Z
k
is invertible if
and only if (a, k) = 1, that is, the numbers are relatively prime.
8
3. Polynomials over C
by Eugenia Malinnikova
3.1. Denition, Ring of polynomials.
3.1.1. Polynomials as functions. By a polynomial we mean a function of the form
P(x) = a
n
x
n
+ a
n1
x
n1
+ ...a
1
x + a
0
.
If a
n
,= then n is called the degree of the polynomial P. To dene the class of functions we
should specify:
the domain of denition,
what coecients are allowed.
First, we consider polynomials with real coecients that are dened on the real line. We
say that a is a root of the polynomial P if P(a) = 0.
Clearly, a polynomial is a smooth function (i.e. it is continuous together with all its deriva-
tives). We will use the standard notation C
## (R) for the class of all smooth functions on real
line R. Polynomials of degree less than or equal to n can be characterized in the following way:
T
n
= f C
(R) : f
(n+1)
0.
Let P be a polynomial of degree n then P is equal to its nth Taylors polynomial. From
calculus we know that
a
k
=
P
(k)
(0)
k!
, P(x) = a
n
x
n
+ o(x
n
) ([x[ ).
Remark 3.1. Sometimes it is convenient to rewrite a polynomial as a linear combination of the
powers of x x
0
for some particular point x
0
P(x) =
n
k=1
b
k
(x x
0
)
k
.
Clearly, b
0
= P(x
0
) and P(x
0
) = 0 if and only if there exists a polynomial Q such that
P(x) = (x x
0
)Q(x).
Remark 3.2. Theorems from calculus can be applied for polynomials as they are smooth (in
particular, continuous) functions.
Exercise: Let P be a polynomial.
a) Prove that P has a real root, provided that the degree of P is odd.
b) Suppose that P has k distinct real roots, show that its derivative has at least k 1 distinct
real roots.
Exercise: a) Prove that each polynomial can be written as the dierence of two positive
polynomials.
b) Prove that each polynomial can be written as the dierence of two decreasing polynomials.
9
3.1.2. Polynomial ring. Let R be a ring. A polynomial P(X) over R is dened as a formal
expression of the form
P(X) = a
n
X
n
+ a
n1
X
n1
+ . . . + a
1
X + a
0
,
where the coecients a
n
, . . . , a
0
are elements of the ring R and X is considered to be a formal
symbol. Summands in the formula above, a
k
X
k
, are called monomials. Polynomials over R
can be added by simply adding the corresponding coecients as elements of R, and multiplied
using the distributive law and the rules aX = Xa for any a R and X
k
X
l
= X
k+l
.
Exercise: Prove that the set of polynomials over R with these operation is a ring. This
ring is denoted by R[X].
3.1.3. Division of polynomials. In this section we consider polynomials over a eld F (one may
assume that F is equal to R (real numbers) or C (complex numbers)).
Let S and T be two polynomials over F, T ,= 0. Then there exist unique polynomials Q and
R such that S = QT + R and deg R < deg T (division with remainder).
If R = 0 we say that T divides S.
Exercise: Divide P(X) = X
3
+ 3X
2
2X + 1 with remainder by
a) X + 2
b) X
2
X + 2.
A polynomial is called irreducible if it is not divisible by any non-constant polynomial of
lesser degree. We will describe irreducible polynomial over R and C in the next section.
3.2. Polynomials over complex numbers.
3.2.1. Roots of quadratic polynomials and complex numbers. Let P(x) = ax
2
+ bx + c be a
quadratic polynomial with real coecients. As we know from school, the number of its real
roots is dened by the sign of the expression b
2
4ac. If it is non-negative then the real roots
are given by the formula
x
1,2
=
b
b
2
4ac
2a
.
Let us consider the polynomial x
2
+ 1. It has no real roots. We will add a formal symbol i
to the eld of real numbers and consider the set of formal expressions of the form x+iy, where
x, y R. This set with two operations
(x
1
+ iy
1
) + (x
2
+ iy
2
) = (x
1
+ x
2
) + i(y
1
+ y
2
)
(x
1
+ iy
1
)(x
2
+ iy
2
) = (x
1
y
1
x
2
y
2
) + i(y
1
x
2
+ x
1
y
2
)
is a eld, we denote it by C, elements of C are called complex numbers. If z = x+iy is a complex
number then x is called the real part of z, y is called the imaginary part of z, and xiy is called
the complex conjugate of z. We will use the following notation x = '(z), y = (z), x iy = z.
Exercise: Check that each quadratic polynomial with complex coecients has two complex
roots (that may coincide).
Another standard interpretation of complex numbers comes from identifying pairs (x, y) with
points of the plane. If we then consider the polar coordinates, we get
x + iy = r cos + ir sin = r(cos + i sin ) =: re
i
.
The advantage of the polar form is that the powers of a complex number are easily calculated
in the polar form:
(re
i
)
n
= r
n
e
in
Exercise: Find all roots of the polynomial z
n
1.
10
3.2.2. Fundamental theorem of algebra and irreducible polynomials.
Theorem 3.3. Any polynomial with complex coecients has a complex root.
Corollary 3.4. Any polynomial P of degree n over C has exactly n (not necessarily distinct)
complex roots and can be written in the form
(3.5) P(z) = a
n
(z
1
) . . . (z
n
).
It follows from the theorem that all polynomials over C of degree greater than one are
reducible. So irreducible polynomials in C[x] are constants and polynomials of degree one.
Exercise: a) Let P be a polynomial with real coecients. Prove that if is a root of P,
then so is
.
b) Describe all irreducible polynomials over R.
It follows from the last exercise that any polynomial P with real coecients can be written
in the form:
P(x) = a
n
m
k=1
(x a
k
)
s
l=1
(x
2
+ p
s
x + q
s
),
where a
k
are the real roots of the polynomial and quadratic polynomials x
2
+p
s
x +q
s
have no
real roots.
Exercise: Let P be a polynomial over R such that P(x) 0 for any x R. Prove that
there exist two polynomials Q and R over R such that P = Q
2
+ R
2
.
(Hint: Use the statement above and the following identity (a
2
+ b
2
)(c
2
+ d
2
) = (ac + bd)
2
+
2
.)
3.2.3. Roots of the derivative. Let A be a set of complex numbers, we consider elements of A
as points on the plane. The convex hull of A is the intersection of all half-planes that contain
A. In other words, the convex hull of A is the smallest convex set that contains A. If A is a
nite set, then its convex hull is a polygon.
The following result on the roots of the derivative of a polynomial is both beautiful and
useful.
Theorem 3.6. Let
1
, . . . ,
n
be all roots of the polynomial P C[z]. Then all roots of P
lie
in the convex hull of
1
, . . . ,
n
.
Proof. Using the denition of the convex hull, we see that it suces to prove that if all roots
of P lie in a half-plane E, then all roots of P
## lie in E. By a linear change of variables,
Q(z) = P(z + ), we see that it is enough to prove this when E is the upper half-plane, i.e.
E = z = x + iy : y 0.
Suppose that (
k
) 0 for k = 1, . . . , n. As we know from the previous subsubsection,
P(z) = a(z
1
) . . . (z
n
). We take the derivative of the product of n functions
P
(z) = a
n
k=1
(z
1
) . . .
(z
k
) . . . (z
n
),
where the hat over a factor means that the factor is omitted. Now the ratio P
/P can be
written in a simple way
(3.7)
P
(z)
P(z)
=
n
k=1
1
z
k
.
11
Assuming that () < 0, we will show that P
## () ,= 0. We apply the above formula
P
()
P()
=
n
k=1
1
k
=
n
k=1
k
[
k
[
2
,
and take the imaginary parts
_
P
()
P()
_
=
n
k=1
k
[
k
[
2
_
=
n
k=1
() +(
k
)
[
k
[
2
> 0.
It follows that P
## () ,= 0 and the theorem is proved.
One can get formula (3.7) by taking the derivative of log P(z). This formula has many
applications, in particular, it is useful in the next exercise.
Exercise: Let P be a polynomial of degree n that has n distinct real roots x
1
, . . . , x
n
.
Prove that
a)
n
k=1
P
(x
k
)
P
(x
k
)
= 0,
b) for any c > 0 the set x R :
P
(x)
P(x)
> c is a union of nitely many disjoint intervals of
total combined lengths
n
c
.
3.3. Dierent ways to determine polynomial.
3.3.1. Roots and Coecients. Any polynomial over C is determined by its leading coecient
and its roots. (We use the convention here that every polynomial of degree n has n complex
roots and formula (3.5) is valid; some of the roots may coincide.) On the other hand each
polynomial is determined by its coecients. The relations between the roots and the coecients
are described below.
Theorem 3.8. (Viet) Suppose that polynomial P(z) =
n
k=0
a
k
z
k
has roots
1
, . . . ,
n
then
a
0
= (1)
n
a
n
n
j=1
j
, a
1
= (1)
n1
a
n
n
k=1
1
. . .
k
. . .
n
,
.
.
.
a
n2
= a
n
j=l
l
, a
n1
= a
n
n
k=1
k
.
In other words, a
k
is equal to (1)
nk
a
n
1
, . . .
n
.
Exercise: Let P(x) = x
n
+a
n1
x
n1
+. . . +a
1
x+a
0
be a polynomial with real coecients.
Suppose that P has n distinct positive roots. Prove that
(a
n1
)
n
> n
n
[a
0
[.
12
3.3.2. Polynomial interpolation. Each polynomial of degree less than n + 1 is determined by
its values at n+1 distinct points. In fact, suppose that two polynomials P
1
and P
2
coincide at
n+1 points and deg P
1
n, deg P
2
n. Then the dierence P
1
P
2
is a polynomial of degree
less than n + 1 that has n + 1 distinct roots, and so P
1
P
2
= 0.
Theorem 3.9 (Lagrange interpolation formula). Let P be a polynomial of degree less than
n + 1 and P(z
j
) = a
j
, j = 1, . . . , n + 1. Then
P(z) =
n+1
j=1
a
j
(z z
1
) . . .
(z z
j
) . . . (z z
n+1
)
(z
j
z
1
) . . .
(z
j
z
j
) . . . (z
j
z
n+1
)
.
It is easy to see that the above polynomial satises P(z
j
) = a
j
and we noted before that
there exists unique polynomial of degree less than n +1 that solves the interpolation problem.
Exercise: (Newton interpolation) There is another way to write down the same polynomial:
P(z) = b
1
+ (z z
1
) (b
2
+ (z z
2
) (. . . (b
n1
+ (z z
n
)b
n
) . . .)) ,
where coecient b
k
depend on a
1
, . . . a
k
and x
1
, . . . , x
k
.
a) Write down formulas for b
1
and b
2
.
b) Find Newton and Lagrange interpolation polynomials for the data P(0) = 3, P(1/2) =
4, P(1) = 6.
13
4. Linear algebra
by Peter Hst
4.1. Linear, or vector, spaces. We start by recalling the basic denitions of vector spaces.
Algebraically, a vector space is made up of a commutative group (V, ), a eld (K, +, ) and a
scalar multiplication : K V V which satisfy the following properties:
(1) a(u + v) = au + av;
(2) (a + b)v = av + bv;
(3) a(bv) = (ab)v; and
(4) 1v = v.
Here a, b K, u, v V , 1 is the unit element of K and 0 is the zero element of V and K. In
this case we say that V is a vector space over K.
Some examples of groups: any eld is a vector space over itself; K
n
is a vector space over
K, for any eld; n-by-n matrices over a eld K, and more generally linear transformations of
a eld K; R is a vector space over Q.
Some further important terms (V is a vector space over K):
a vector subspace of V is a subset V
of V such that (V
## , K) is a vector space in the
inherited operations;
v is a linear combination of v
i
i
if v =
a
i
v
i
, where a
i
K;
the span of a set v
i
i
is the smallest subspace containing all the vectors, or, equivalently,
the set of all nite linear combinations of vectors in v
i
i
;
v
i
i
is linearly independent if any vector in the span of v
i
i
can be written as a linear
combination in exactly one way, or, equivalently, if the equation
a
i
v
i
= 0 has only
the solutions a
1
= . . . = a
k
= 0;
v
i
i
is a basis for V if the set spans V and is linearly independent;
the dimension of V is the number of elements in a basis of V .
4.2. Linear operators. Another very important concept related to vector spaces, emphasized
by the alternative name linear spaces, is that of linear operators. If V and V
## are vector spaces
on K, then we say that the operator T : V V
is linear if
T(au + bv) = aT(u) + bT(v)
for all a, b K and u, v V . Recall that if we have chosen bases for nite vector spaces V
and V
## , then we may represent a linear transformation by a matrix.
Some important words here are (V, V
## are vector spaces over K, T is a linear operator from
V to V
):
the image of T is T(V );
the kernel of T is T
1
(0), i.e. all those elements of V that map to 0;
for nite dimensional V
## , the rank of T is the dimension of the image of T.
To understand the action of a linear operator, it is useful to single out some vectors for this
the operation is especially simple. This leads us to Eigenvectors. We say that v V 0 is
an Eigenvector corresponding to the Eigenvalue K if T(v) = v.
A Euclidean style descriptions of the procedure for determining the Eigenvalues and vectors
follows. Recall the following procedure for calculating the eigenvectors of the matrix
A =
_
7 2
2 2
_
:
14
First, calculate
det(A I) = det
_
7 2
2 2
_
= (7 )(2 ) + 4 = ( 3)( 6).
This gives the eigenvalues
1
= 3 and
2
= 6.
Second, look at the rst eigenvalue, 3. Solve the equation (A 3I)v
1
= 0:
_
4 2
2 1
__
x
y
_
=
_
4x + 2y
2x y
_
=
_
0
0
_
.
Hence v
1
=
_
1
2
_
.
Then, look at the second eigenvalue, 6. Solve the equation (A 6I)v
2
= 0:
_
1 2
2 4
__
x
y
_
=
_
x + 2y
2x 4y
_
=
_
0
0
_
.
Hence v
2
=
_
2
1
_
.
Why does this procedure give all the eigenvectors of the matrix A, i.e. all non-zero vectors
such that Av = v?
Problems.
(1) Find a basis for the image and the kernel of
_
1 3
3 4
_
considered as a linear transformation of a two-dimensional vector space
a) over R,
b) over Z
5
.
(2) Let V be the vector space whose elements are arithmetic sequences, (a, a+k, a+2k, a+
3k, . . .), a, k R. Find a basis of this space and thus determine its dimension. Give an
example of a one-dimensional subspace.
(3) Let L
1
(R
n
) be the set of all continuous functions f : R
n
R for which
_
R
n
[f(x)[ dx < .
Show that L
1
(R
n
) is innite dimensional by nding a subspace with innitely many
basis vectors.
(4) Dene R
+
= x > 0. Show that
_
R
+
_
2
is not a subspace of the vector space R
2
. Let
V be the set of 2-vectors over R
+
, i.e. the elements of V are vectors of the form
_
a
b
_
,
a, b R
+
. We dene an addition on V by
_
a
b
_
_
c
d
_
=
_
ac
bd
_
and a scalar multiplication by
k
_
a
b
_
=
_
a
log k
b
log k
_
.
We dene addition and multiplication in R
+
by l k = lk (i.e. addition corresponds to
ordinary multiplication) and l k = explog(l) log(k). Show that V is a vector space
over R
+
.
15
(5) Let P
0
= (0, y, z) and P
1
= (x, y, z): x + y + z = 0. Let A: R
3
R
3
be a linear
transformation such that A(P
k
) = P
k
. Show that the dimension of the kernel of A is 0
or 1. Give examples which show that both cases can occur.
(6) Let V and W be vector spaces. Suppose that T : V W is a linear transformation
with the following properties:
a) if T(x) = T(y) then x = y (i.e. T is one-to-one, or injective)
b) for any w W there exists v V such that T(v) = w (i.e. T is onto, or surjective).
Show that T is an isomorphism.
(7) Consider the eld Q of rational numbers (i.e. fractions of integers). We consider R as
a vector space over Q.
(a) Find a 2-dimensional subspace of R.
(b) Show that the equation f(x + y) = f(x) + f(y) has a solution not of the form
f(x) = cx on this subspace.
4.3. Determinants. In this section we recall one abstract way of dening the determinant of
a matrix.
Let v
1
, . . . v
n
, x and y be row vectors with n elements (in some eld K, e.g. R). Then det
is dened as the unique function which takes n-tuples of vectors with n components, that is
elements of K
n
, and satises the following conditions:
det is multilinear, i.e.
det(ax + by, v
2
, . . . , v
n
) = a det(x, v
2
, . . . , v
n
) + b det(y, v
2
, . . . , v
n
),
where a, b K and the same holds for all other vectors v
i
.
det is antisymmetric, i.e.
det(v
1
, v
2
, . . . , v
n
) = det(v
2
, v
1
, . . . , v
n
),
and the same for all other swaps of vectors (not necessarily adjacent).
det(I
n
) = 1.
Let us start by checking that det is uniquely determined by these conditions, i.e. that there
are not two dierent functions satisfying them. We make the following observations:
Lemma 4.1. If v
i
= v
j
for i ,= j, then det(v
1
, . . . , v
n
) = 0.
Proof. We use property (2) of the determinant to swap v
i
and v
j
:
det(v
1
, . . . , v
i
, . . . , v
j
, . . . , v
n
) = det(v
1
, . . . , v
j
, . . . , v
i
, . . . , v
n
).
But since v
i
= v
j
we obviously have
det(v
1
, . . . , v
i
, . . . , v
j
, . . . , v
n
) = det(v
1
, . . . , v
j
, . . . , v
i
, . . . , v
n
).
From this the claim directly follows.
Corollary 4.2. Let a K. Then
det(v
1
, . . . , v
i
, . . . , v
n
) = det(v
1
, . . . , v
i
+ av
j
, . . . , v
n
).
Proof. By Property (1) of the determinant,
det(v
1
, . . . , v
i
+ av
j
, . . . , v
n
) = det(v
1
, . . . , v
i
, . . . , v
n
) + a det(v
1
, . . . , v
j
, . . . , v
n
).
But by the previous lemma, the latter term is zero.
Lemma 4.3. If v
i
= 0, then det(v
1
, . . . , v
n
) = 0.
16
Proof. Let a R, a ,= 1. By Property (1),
det(v
1
, . . . , av
i
, . . . , v
n
) = a det(v
1
, . . . , v
i
, . . . , v
n
).
Since v
i
= 0 it follows trivially that av
i
= v
i
. Therefore the two determinants in the previous
equation are the same. Thus the equations is
(a 1) det(v
1
, . . . , v
i
, . . . , v
n
) = 0.
Since a 1 ,= 0, this implies the claim.
We consider the matrix A whose i
th
row is given by v
i
. We denote det(v
1
, . . . , v
n
) also by
det(A).
Theorem 4.4. The function det: (V
n
)
n
R is uniquely determined by the conditions (1)(3).
Proof. We consider the matrix A whose i
th
row is given by v
i
. Let us say that A is brought
to row-reduced echelon form by performing k row swaps, and by dividing the rows by the
constants k
1
, . . . , k
n
(look up the description of the algorithm to produce the row-reduced
echelon form in the book, if necessary). Then each of the row-swaps produces a factor 1 in
front of the determinant (by Property (2)) and division of a row by k
i
produces a factor of k
i
in front (by Property (1)). Subtracting a multiple of the row containing the pivotal element
has no eect of the determinant, by Corollary 4.2.
There are then two possibilities: if the rref is I
n
, then
det(A) = (1)
k
k
1
k
n
det(I
n
) = (1)
k
k
1
k
n
.
If, on the other hand, rref is not I
n
, then it contains at least one zero-row (since A is n-by-n).
Then, by Lemma 4.3, det(A) = 0. We have thus put forth an algorithm for computing the
determinant of any matrix A clearly this implies that the determinant function is uniquely
dened.
In the proof of the previous theorem we saw one of the fundamental properties of the deter-
minant:
Corollary 4.5. The determinant of A is 0 if and only if A is not invertible.
Proof. The square matrix A is invertible if and only if its rref is I
n
. In the previous proof we
saw that this is precisely the case when A is invertible.
Also of great importance is the following product formula for the determinant:
Theorem 4.6. Let A and B be n-by-n square matrices. Then det(AB) = det(A) det(B).
Proof. Suppose rst that B is not invertible. Then det(A) det(B) = 0, so we must show that
det(AB) = 0, as well. Let x be a non-zero vector such that Bx = 0 (exists, since B is not
invertible). Then ABx = A(Bx) = A0 = 0, and so AB is not invertible (since an invertible
matrix does not take a non-zero vector to zero).
If B is invertible, we can consider the function
D(A) =
det(AB)
det(B)
.
We can check that this function satises the conditions (1)(3) above. Since the determinant
was the unique function satisfying these conditions, this implies that D(A) = det(A).
The following results follow directly by applying the formula in the previous theorem.
Corollary 4.7. Let A be an invertible matrix. Then det(A
1
) = (det(A))
1
.
Corollary 4.8. Let A and B be similar n-by-n matrices. Then det(B) = det(A).
17
Proof. There exists an invertible matrix S such that B = S
1
AS (by the denition of begin
similar). Thus
det(B) = det(S
1
AS) = det(S
1
) det(A) det(S) = det(S)
1
det(S) det(A) = det(A).
If T is a linear operator, we know that its matrix in two dierent bases are similar. In view
of the previous corollary, it makes sense to dene the determinant of this operator to be the
determinant of any of these matrices.
Using the multilinearity of the determinant (Property (1)), one can derive the so-called
Laplace expansion for the determinant of a matrix.
4.4. Representation of a matrix. We view a matrix as representing a linear transformation
from a (nite dimensional) vector space to itself when we have chosen a bases for the spaces.
If we choose dierent bases, then the matrix will be dierent. However, the matrices for the
transformation are similar, i.e. A
= SAS
1
for some invertible matrix S. This leads to the
question of choosing S so that A
## is as simple as possible for a given A. In many senses the
Jordan normal form is this simplest representation. We know that not every matrix can be
diagonalized. The Jordan normal form is in some sense the closest you can get to a diagonal
matrix. In order to present the proper context for the JNF, we need to introduce some concepts.
4.4.1. Decomposition. Let V and W be vector spaces. Their direct sum, V W, is dened as
pairs of vectors (v, w), v V , w W with the following addition:
(v
1
, w
1
) (v
2
, w
2
) := (v
1
+ v
2
, w
1
+ w
2
).
(Note that the additions on the right-hand-side are in the vector spaces V and W.)
Exercise: Show that V W is a vector space.
Let S and T be linear operators on V and W, respectively. Then we dene S T by
S T(v w) := (S(v), T(w)).
Exercise: Show that S T is linear operator.
Let T be a linear operator on the nite vector space V . We say that the subspace V
V
is invariant under T if T(V
) V
## . If dim(V ) = n and dim(V
) = m then T is represented by
a block matrix of the form
_
A B
0 C
_
,
where A is m-by-m and C is (n m)-by-(n m). In other words the fact that we know an
invariant subspace gives us signicant structural information about the matrix of the transfor-
mation. Suppose next that T happens to be such a linear operator as to have V
and V
as
invariant subspaces. Suppose further that V
= and V = V
## . Then the matrix of
T in a suitably chosen basis is
_
A O
0 C
_
,
where A and C have the same dimensions as before.
4.4.2. Jordan normal form. We next dene some sort of an iterated Eigenvector: we say that
v lies in the root space R() of the linear operator T if (V I)
m
v = 0 for some m. Clearly, if
v is an Eigenvector corresponding to the Eigenvalue then v R(). It turns out that V can
be decomposed into its root-spaces:
18
Theorem 4.9. Let T be a linear operator on the nite dimensional vector spaces V . Suppose
T has Eigenvalues
1
, . . . ,
k
. Then
V = R(
1
) . . . R(
k
).
In view of what was said in the previous section, this implies that T is represented by a
matrix of block-diagonal type, with one block for each distinct Eigenvalue. It turns out that
we can even do much better than this.
Theorem 4.10 (Jordan Normal Form). Let T be a linear operator on the nite dimensional
vector spaces V . Then T has a representation in block diagonal form where every block has the
form
_
_
_
_
1 0 . . . 0
0 1 . . . 0
0 0 . . . 0
_
_
_
_
,
where the diagonal entries are Eigenvalues of T and the entries immediately above the diagonal
are 1s.
Note that the matrix given in the previous theorem is as a whole of the form with Eigenvalues
on the diagonal and 1s and 0s immediately above the diagonal. Thus T is represented as the
sum of a diagonal operator and a nilpotent operator. (Recall that a linear operator T on the
vector space V is said to be nilpotent if there exists k > 0 such that T
k
(v) = 0 for every v V .)
Exercise: Let V be the space of functions of the form f(x) = e
x
p(x), where p(x) is
polynomial of degree at most n 1. Find a basis of V in which the matrix of the operator
d/dx is the n n Jordan block with on the diagonal.
Problems.
(1) Let A M
R
(n, n). What is the smallest value of n if A
m+1
= 0, but A
m
,= 0. Give an
example when n = 3.
(2) Let A M
R
(n, m) and B M
R
(m, n). If AB is invertible, what can you say about the
relationship between n and m?
(3) Let A and B be square matrices. If AB + A + B = 0, show that A and B commute,
i.e. that AB = BA.
(4) The following are some properties of matrix multiplication:
AI = IA = I,
(AB)C = A(BC), and
AB ,= BA,
where A, B, C, I are n by n matrices, and I denotes the identity. Describe how matrix
multiplication is dened (i.e. the logic of the denition), and why it implies these
properties.
(5) Among all unit vectors
_
_
x
y
z
_
_
R
3
nd the one for which ax +by +cz is maximal, where a, b and c are nonzero constants.
Can you interpret this result in terms of the dot product?
(6) Consider the vector space V of all symmetric 2-by-2 real matrices which have eigenvector
v
1
=
_
1
1
_
(the matrix may or may not have other eigenvectors). We make it an inner
product space by dening
A, B) = tr(A
T
B),
19
where tr denotes the trace, i.e. the sum of the diagonal entries. Find an orthogonal
basis of V .
(7) Find all inner products on the vector space R
2
. (Hint: Recall that every inner product
is represented by a matrix, but not the other way around.)
Find all complex inner products on C
2
. (Hint: Recall that every complex inner
product is represented by a complex matrix, but not the other way around.)
(8) In constructing a model of a certain kind of uid a complicated equation arises involving
traces and determinants of symmetric matrices. In order to show that one of the terms
is negligible compared to the others, the inequality
tr(A) n det(A)
1/n
is needed. Show that it holds for all symmetric n-by-n real matrices A. Recall that the
trace of A, tr(A), is the sum of the elements on the diagonal.
(9) Consider vectors in R
2
with vectors v
1
= (x
1
, y
1
) and v
2
= (x
2
, y
2
). Dene a bilinear
form by
(v
1
, v
2
) = x
1
x
2
+ x
1
y
2
+ x
2
y
1
+ kx
2
y
1
.
For which values of k is this (a) symmetric, (b) bilinear and (c) an inner product.
(10) Dene inner products spaces such that the Cauchy-Schwarz inequality allows you to
arm the following inequalities:
_
n
i=1
v
i
w
i
_
2
_
n
i=1
v
2
i
__
n
i=1
w
2
i
_
.
__
b
a
f(x)g(x) dx
_
2
__
b
a
f(x)
2
dx
___
b
a
g(x)
2
dx
_
.
(11) Consider the space of second degree polynomials. Dene an inner product by the
formula
p, q) =
_
b
a
p(x)q(x) dx.
For which choises, if any, of a, b R is the standard basis 1, x, x
2
orthogonal?
(12) Let V be an inner product space. Suppose v is orthogonal to each of w
1
, . . . , w
k
. Show
that v is orthogonal to spanw
1
, . . . , w
k
. Show also that any set of orthogonal vectors
is linearly independent.
(13) Let e
1
, . . . , e
n
be an orthonormal basis of a Euclidean space. Prove Bessels inequality
k
i=1
v, e
i
)
2
|v|
2
,
and Parsevals identity
v, w) =
n
i=1
v, e
i
)e
i
, w).
20
5. Matrix calculus
by Torbjrn Helvik
5.1. A matrix is a linear map. A m n matrix A denes a linear map R
n
R
m
. The
vector x is mapped to the vector Ax. Conversely, every linear map f : R
n
R
m
can be
represented by a mn matrix A such that f(x) = Ax. Note that A depends on the choice of
basis for R
n
. When not stating otherwise we use the standard euclidian basis. Composition of
linear maps are given by matrix products: If g : R
m
R
k
is represented by B then
(g f)(x) = BAx
There is a simple way of nding the matrix that represents a map f in a given basis. Assume
that f : R
n
R
m
and let (e
i
)
n
i=1
constitute a basis for R
n
. Write x =
i
x
i
e
i
. Then
f(x) = f(
i
x
i
e
i
) =
i
x
i
f(e
i
) = Ax
with the ith column of A being f(e
i
).
Exercise: Find the matrices in the standard basis representing the following operations
on R
3
:
(1) Reection through the xy plane
(2) Rotation by /2 in the xy plane, followed by a rotation by /2 in the yz plane
(3) Projection onto the plane dened by x = y.
Let A be a m n matrix. The rank of A is the number of linearly independent column
vectors of A. This is equal to the number of linearly independent row vectors of A. For the
rest of this section, dene k = rank(A)
We now look at some important subspaces of R
n
and R
m
related to A. Recall that for any
map f : X Y
Im f = y Y : x X with f(x) = y = f(X)
ker f = x X : f(x) = 0 = f
1
(0)
We rst look at the image of A. Taking the product Ax is the same as taking a linear
combination of the columns of A. In fact if we write the columns of A as v
1
, v
2
, . . . , v
n
, then
Ax =
i
x
i
v
i
.
Therefore,
Im A = spanv
1
, . . . , v
n
R
m
This is a k-dimensional linear subspace of R
m
. Let us denote the orthogonal component of
Im A by X, such that R
m
= Im A X. We claim that X = ker A
T
(recall that the kernel is
the subspace consisting of all vectors that is mapped to 0 by the matrix). Indeed, if y Im A
and x ker A
T
, then
z
T
y = z
T
(Ax) = (A
T
z)x = 0
One can also show that dim(ker A
T
) = mk. The same relation is of course valid for Im A
T
and ker A.
To sum up, the four fundamental subspaces of the matrix A are connected in the following
way
R
n
= ImA
T
ker A (dimensions k and n k)
R
m
= ImA ker A
T
(dimensions k and mk)
The rst pair is invariant under row operations on A and the second pair under column oper-
ations.
21
Let A be a square matrix. If there exists a matrix B such that AB = I we call B the inverse
of A and write B = A
1
. In this case, we say that A is invertible (or non-singular). It is also
the case that BA = I.
The following are equivalent
A is invertible
det(A) ,= 0
0 is not an eigenvalue of A
rank(A) = n
The inverse of a 2 2 matrix is given by the formula
_
a b
c d
_
1
=
1
_
d b
c a
_
Inverses of larger matrices can be found by Gauss-Jordan elimination.
Exercise: Let A and B be square matrices. If AB + A + B = 0, show that AB = BA.
5.2. The characteristic polynomial. The characteristic polynomial c
A
(x) of the square nn
matrix A is dened as
c
A
(x) = det(A xI)
The roots of c
A
are the eigenvalues of A. The multiplicity of as a root in c
A
(x) is the
algebraic multiplicity of . The geometric multiplicity of is the dimension of the eigenspace
corresponding to (that is, the dimension of ker(AI)). The geometric multiplicity is never
larger than the algebraic multiplicity.
Lemma 5.1. The geometric multiplicity of = 0 is n k i rank(A) = k.
Exercise: Prove this
Write
c
A
(x) = x
n
+ a
n1
x
n1
+ + a
0
The coecients a
n1
and a
0
of c
T
are particulary useful:
a
n1
= Trace(A) =
i
a
0
= Det(A) =
i
Similar matrices have the same characteristic polynomial:
Lemma 5.2. If B = S
1
AS, with S invertible, then c
B
(x) = c
A
(x)
Also:
Lemma 5.3. If A and B are square, c
AB
(x) = c
BA
(x).
One can look at polynomials of matrices. The following result can be useful:
Lemma 5.4. If p is a polynomial such that p(A) = 0, then p() = 0 for all eigenvalues of
A.
Exercise: Prove this.
The Cayley-Hamilton theorem says that any matrix satises its own characteristic equation:
Theorem 5.5 (Cayley-Hamilton).
c
A
(A) = 0
Exercise: a) Show that for any m N there exists a real m m matrix A such that
A
3
= A + I.
b) Show that det A > 0 for every real mm matrix satisfying A
3
= A + I.
22
5.3. Diagonalization. Let A be a nn matrix with n independent eigenvectors x
1
, . . . , x
n
.
Let S be the matrix with these eigenvectors as column vectors, and let be a diagonal matrix
with the eigenvalues
1
, . . . ,
n
on the diagonal. Then
A = SS
1
This is called the diagonal form of A. A is not diagonalizable if it has less than n independent
eigenvectors. But note that repeated eigenvalues is no problem as long as their algebraic mul-
tiplicity equals their geometric multiplicity. Also, there is no connection between invertibility
and diagonalizability.
Lemma 5.6. A real symmetric matrix can be diagonalized by a orthogonal matrix S
T
S = I,
and a Hermitian matrix can be diagonalized by a unitary matrix (S
H
S = I).
Lemma 5.7. If A and B are diagonalizable, they share the same eigenvector matrix S i AB
= BA.
Note that A
n
= S
n
S
1
, and
n
is found simply by squaring all elements since is diagonal.
This is an important use of the diagonal form.
If some eigenvalues has lower geometric multiplicity than algebraic, A is not diagonalizable.
The best we can do in this case is the Jordan form. If A has s independent eigenvectors, it is
similar to a matrix with s blocks:
M
1
AM = J =
_
_
J
1
J
s
_
_
Each block is a triangular matrix with a single eigenvalue
i
and a single eigenvector:
J
i
=
_
i
1
1
i
_
_
The same eigenvalue
i
may appear in several blocks if it corresponds to several independent
eigenvectors.
Exercise:
Let A and B be square matrices of the same size. If
rank(AB BA) = 1,
show that (AB BA)
2
= 0.
5.4. A few more tricks. The following is general trick that can be helpful. In a matrix
multiplication AB, one can divide A into submatrices of the size nm and B into submatrices
of size m n, and do the multiplication as if these were the elements of the matrix. This is
perhaps best communicated by an example. Let A to F be n n matrices. Then
_
A B
C D
_
_
E
F
_
=
_
AE + BF
CE + DF
_
Also, note that if A is a matrix with row vectors (a
T
1
, a
T
2
, . . . , a
T
n
) and B is a matrix with
column vectors (b
1
, b
2
, . . . , b
n
), then the rows of AB are (a
T
1
B, . . . , a
T
n
B) and the columns of
AB are (Ab
1
, . . . , Ab
n
). This can be utilized to construct matrixes that perform operations
such as permutations on the rows or columns of a matrix C.
23
5.5. Non-negative matrices. NB: This section is not important for the competition, but the
Perron-Frobenius theorem is a strong result that one should know about.
Let A be a k k matrix. We say A is non-negative if a
ij
0 i, j.
Denition 5.8. Let A be a non-negative matrix, and let a
(n)
ij
denote the (i, j)-elements of A
n
.
We say A is
Irreducible if for any pair i, j there is some n > 0, such that a
(n)
ij
> 0.
Irreducible and aperiodic if there is some n > 0, such that a
(n)
ij
> 0 for all pairs i, j.
Theorem 5.9 (Perron-Frobenius Theorem). Let A be a non-negative k k matrix.
(1) A has a real eigenvalue 0, and [[ where is any other eigenvalue. If A is
irreducible then > 0 and if A also is aperiodic, then > [[.
(2) We have min
i
(
k
j=1
a
ij
) max
i
(
k
j=1
a
ij
)
(3) has a non-negative eigenvector u, and a non-negative left eigenvector v.
(4) If A is irreducible, then is a simple root of the characteristic polynomial, and the
corresponding eigenvectors are strictly positive.
(5) If A is irreducible, then is the only eigenvalue of A with a non-negative eigenvector.
(6) If u and v are the right and left eigenvector, normalized such that v u = 1, then
lim
n
1
n
A
n
= uv
Note that his implies that any stochastic matrix has 1 as the largest eigenvalue (a matrix
is stochastic if all row sums are 1).
24
6. Sequences and series
by Eugenia Malinnikova
6.1. Sequences and limits.
6.1.1. Basic facts and examples. We begin with some simple rules and theorems that are useful
when calculating limits:
(1) Each monotone sequence has a limit (either nite or innite).
(2) Let x
n
n
, a
n
n
, b
n
n
be sequences of real numbers such that a
n
x
n
b
n
for each
n. If the limits lim
n
a
n
and lim
n
b
n
exist and are equal, then lim
n
x
n
exists
and
lim
n
x
n
= lim
n
a
n
= lim
n
b
n
.
(3) A sequence x
n
n
has a limit if and only if limsup
n
x
n
= liminf
n
x
n
, where
limsup
n
x
n
= lim
n
sup
kn
x
k
and liminf
n
x
n
= lim
n
inf
kn
x
k
.
(4) If the sequence x
n
n
is dened by x
n
= f(n) for some function f and lim
x
f(x)
exists, then lim
n
x
n
exists and is equal to lim
x
f(x).
Exercise: Calculate lim
n
(
n
2
+ n n).
As usual in such kind of problems we should prove that the limit exists and nd it. Here are
several solutions that use a number of simple rules listed above.
Solution 1: We have
n
2
+ n n =
n
n
2
+ n + n
=
1
_
1 + 1/n + 1
.
Then clearly, lim
n
(
n
2
+ n n) =
1
2
.
Solution 2: It is easy to check that n +
n1
2n
<
n
2
+ n < n +
1
2
. Thus we have
n1
2n
<
n
2
+ n n <
1
2
. Now, clearly, the rst and the last terms converge to
1
2
when n goes to .
Applying the "squeezing" rule we get the limit exists and lim
n
(
n
2
+ n n) =
1
2
Exercise: Let a
n
be a seguence such that a
1
= 1, a
n+1
>
3
2
a
n
.
a) Prove that the sequence
_
2
3
_
n1
a
n
has a nite limit or tends to innity.
b) For any > 1 there exists a sequence with these properties such that
lim
n
_
2
3
_
n1
a
n
= .
Solution: a) The sequence
_
2
3
_
n1
a
n
is increasing since a
n+1
>
3
2
a
n
. Thus it either has
a nite limit or tends to innity.
b) For any > 1 there exists a sequance b
n
such that b
1
= 1, b
n+1
> b
n
and b
n
tends to
when n goes to innity. (Can you write down a formula that denes such a sequence?) Now
let a
n
=
_
3
2
_
n1
b
n
.
Sometimes it is easier to prove that the limit exists rst, and then use that information to
calculate the limit. Moreover we may assume that the limit exists, then calculate it and nally
prove that the assuption is true.
Exercise: We consider the Fibonacci sequence F
0
= 1, F
1
= 1, F
n+1
= F
n
+ F
n1
.
Calculate lim
n
F
n+1
F
n
.
25
Solution: It is clear that the sequence is bounded, 1
F
n+1
F
n
2, if we calculate the rst
few terms we will see that it is not monotone. Suppose that this sequence has a limit . Then
= lim
n
F
n+1
F
n
= lim
n
F
n
+ F
n1
F
n
= lim
n
(1 +
F
n1
F
n
) = 1 +
1
.
Thus is equal to the positive solution of the quadratic equation x
2
x 1 = 0, i.e. =
1
2
(1 +
5).
Now we want to estimate [
F
n+1
F
n
[ =
_
1 +
F
n1
F
n
_
_
1 +
1
. We denote a
n
=
F
n+1
F
n
, then
we have
[a
n
[ =
1
a
n1
=
[ a
n1
[
a
n1
<
[ a
n1
[
.
Thus [a
n
[ tends to zero as n goes to innity and we get lim
n
F
n+1
F
n
= .
Problems.
(1) Calculate lim
n
1
n
+2
n
+...+n
n
n
n
.
(2) Let x
1
=
a, x
n+1
=
a + x
n
for n 1, where a 1. Find lim
n
x
n
.
(3) Let x
1
= 2005, x
n+1
=
1
43x
n
for n 1. Find lim
n
x
n
.
(4) Let a
1
= 1, a
n
=
1
n
n1
k=1
a
k
a
nk
for n 2. Show that
(i) limsup
n
[a
n
[
1/n
< 2
1/2
,
(ii) limsup
n
[a
n
[
1/n
2
3
.
(5) Find lim
N
ln
2
N
N
N2
k=2
1
ln k ln(Nk)
.
6.2. Series.
6.2.1. Basic facts on convergence.
(1) The series
n=1
a
n
converges if and only if for any > 0 there exists N such that
k=n
a
k
,
whenever m n N.
(2) Let = limsup
n
[a
n
[
1
n
. If < 1 then the series
n=1
a
n
conveges, if > 1 then the
series
n=1
a
n
diverges.
(3) If limsup
n
a
n+1
a
n
< 1, then
n=1
a
n
converges.
(4) If a
n
> a
n+1
> 0 and lim
n
a
n
= 0, then the series
n=1
(1)
n
a
n
converges.
Exercise: Does there exist a bijective map : N N such that
n=1
(n)
n
2
< ?
Hint: Consider t
k
=
3
k+1
n=3
k
+1
(n)
n
2
, take terms with (n) 3
k
and prove that t
k
1
9
for
each k.
Exercise: Find out if the series
n=1
(1)
n
a
n
converges or diverges, where
a) a
n
=
10
n
n!
, b) a
n
=
2
n
n!
n
n
, c) a
n
=
sin(n/4)
ln n
.
26
6.2.2. Integral test, Series as Riemann sums. The simplest version of the integral test, that is
used very often to determine if a series is convergent or divergent, is the following:
If f : [1, ) [0, ) is a non-increasing function then
n=1
f(n) < if and only if
_
1
f(x)dx < .
In particular, we use that test to determine for which values of p series
1
n
p
,
1
nln
p
n
converge. Sometimes this test is convinient to combine with some prior estimates of the terms
of a series.
Exercise: Let (n) be the number of digits of (the decimal representation) of n. Find out
if the series
(n)
n
2
converges.
Solution: We note that (n) = k means 10
k1
n < 10
k
. Therefor (n) (ln 10)
10
ln n+
1 and
(n)
n
2
< .
In general, it might be useful to write down a series as a Riemann some for an integral.
(Unformal rule, if you see lim
a
n
, try to compaire
a
n
to some integral.)
Exercise: Find lim
t1
(1 t)
t
n
1+t
n
.
Hint:
t
n
1+t
n
=
e
nln t
1+e
nln t
= (ln t)
1
(e
nln t
+ 1)
1
.
6.2.3. Summation by parts. Let A
n
=
n
k=1
a
k
, then
m
n=1
a
n
b
n
=
m1
1
A
n
(b
n
b
n+1
) + A
m
b
m
.
To prove the above formula write a
n
= A
n
A
n1
, rewrite the sum as two sums as change
the summation index in the second sum to combine terms with A
n
. This calculation explains
two following tests:
The series
n=1
a
n
b
n
converges if
(i)
n=1
a
n
< and b
n
is a monotone bounded sequence,
or
(ii) A
n
=
n
k=1
a
k
are bounded and the sequence b
n
is monotone and tends to zero.
Exercise: Prove that
n=1
sin n
n
< .
Hint: Take a
n
= sin n, b
n
= 1/n and prove that s
n
= a
1
+ ... + a
n
are bounded.
Exercise: Suppose that b
1
b
2
b
3
... and lim
n
b
n
= 0. Show that
n=1
2
n
b
n
<
if and only if
n=1
2
n
(b
n
b
n+1
) < .
Hint:
N
n=1
2
n
b
n
=
N1
n=1
(2
n+1
2)(b
n
b
n+1
)+(2
N+1
2)b
N
, prove rst that
n=1
2
n
(b
n
b
n+1
) < implies lim
N
2
N
b
N
= 0.
6.2.4. Series summation. General methods
(1) If a
n
= b
n+1
b
n
and b = lim
n
b
n
then
n=1
a
n
= b b
1
.
(2) If
n=1
a
n
< then
n=1
a
n
= lim
x1
n=1
a
n
x
n
.
(3) To nd a sum of the form
n=1
a
n
cos nx or
n=1
a
n
sin nx it is useful to write this
sum as a real or imaginary part of the sum
n=1
a
n
z
n
.
Exercise: Find
n=1
a
n
, where
a) a
n
=
1
n(n+m)
, b) a
n
=
1
n2
n
, c) a
n
=
n
2
n!
, d) a
n
=
sin nx
n
.
27
Solution: a) a
n
=
1
m(n+m)
1
mn
,
n=1
a
n
=
1
m
(1 +
1
2
+
1
3
+ ...
1
m
).
b)
n=1
a
n
= lim
x1
n=1
x
n
n2
n
= lim
x1
n=1
_
x
0
t
n1
2
n
dt = lim
x1
_
x
0
1
2 t
dt = ln 2.
Justify the calculation!
c) a
n
=
n
(n1)!
, we write the series as a power series once again, but now nx
n1
is the derivative
of x
n
:
n=1
a
n
= lim
x1
n=1
nx
n1
(n 1)!
= lim
x1
(
n=1
x
n
(n 1)!
)
= lim
x1
(xe
x
)
= 2e.
d) Let z = e
ix
, then sin nx = z
n
and
n=1
a
n
=
_
n=1
z
n
n
_
= (ln(1 z)) = (ln(1 e
ix
).
Further, we have 1 e
ix
= e
ix/2
(e
ix/2
e
ix/2
) = ie
ix/2
sin x/2 and
(ln(1 e
ix
) = ln(ie
ix/2
) =
x
2
.
We get
n=1
sin nx
n
=
x
2
.
Check that all calculations may be justied for x (0, ], nd out why this argument does not
work for x = 0.
Problems.
(1) Suppose that a
n
0 and
n=1
a
n
< . Prove that
n=1
a
n
n
< .
(2) Suppose
n=1
a
n
< . Do the following sums have to converge as well?
a)a
1
+ a
2
+ a
4
+ a
3
+ a
8
+ a
7
+ a
6
+ a
5
+ a
16
+ a
15
+ ... + a
9
+ a
32
+ ...,
b)a
1
+a
2
+a
3
+a
4
+a
5
+a
7
+a
6
+a
8
+a
9
+a
11
+a
13
+a
15
+a
10
+a
12
+a
14
+a
16
+....
(3) Suppose that a
n
> 0,
n=1
a
n
= and s
n
= a
1
+ ... + a
n
. Prove that
a)
n=1
a
n
a
n
+1
= ,
b)
n=1
a
n
s
n
= ,
c)
n=1
a
n
s
2
n
< .
(4) Let
n
n=1
be a sequence of positive real numbers such that lim
n
n
= 0. Find
lim
n
1
n
n
k=1
ln
_
k
n
+
n
_
.
(5) (i) Prove that lim
x
n=1
nx
(n
2
+x)
2
=
1
2
.
(ii)Prove that there is a positive constant c such that for every x [1, ) we have
n=1
nx
(n
2
+ x)
2
1
2
c
x
.
(6) For which x the series
n=1
ln
_
1 +
(1)
n
n
x
_
converges?
28
(7) Show that
n=1
(1)
n1
sin(ln n)
n
## converges if and only if > 0
(8) Find out if the series
n=1
sin nsin n
2
n
converges or not.
(9) Let b
0
= 1,
b
n
= 2 +
_
b
n1
2
_
1 +
_
b
n1
.
Calculate
n=1
2
n
b
n
.
(10) Calculate the sums of the following series
n=1
cosnx
n
.
29
7. Problem sets
NOTE: Many of the following problems were taken from sources such as the International
Mathematics Competition for University Students, or the Putnam Competition. No claim of
originality is made on the parts of the authors, and the problems are included for educational
purposes only.
7.1. Basics.
7.1.1 Let n be a xed positive integer. How many ways are there to write n as a sum of positive
integers, n = a
1
+a
2
+. . . +a
k
, with k an arbitrary positive integer and a
1
a
2
. . .
a
k
a
1
+ 1 For example, with 4 there are four ways: 4, 2 + 2, 1 + 1 + 2, 1 + 1 + 1 + 1.
7.1.2 Let S be an innite set of real numbers such that [s
1
+s
2
+. . . +s
k
[ < 1 for every nite
subset s
1
, s
2
, . . . , s
k
S. Show that S is countable.
7.1.3 a) Show that the unit square can be partitioned into n smaller squares if n is large
enough.
b) Let d > 2. Show that there is a constant N(d) such that, whenever n N(d), a
d-dimensional unit cube can be partitioned into n smaller cubes.
7.1.4 Let A
n
= 1, 2, . . . n, where n 3. Let T be the family of all non-constant functions
f : A
n
A
n
satisfying the following conditions:
(1) f(k) f(k + 1) for k = 1, 2, . . . n 1;
(2) f(k) = f(f(k + 1)) for k = 1, 2, . . . n 1.
Find the number of functions in T.
7.1.5 Let r, s, t be positive integers which are pairwise relative prime. Suppose that a and b are
elements of a commutative multiplicative group with unit e such that a
r
= b
s
= (ab)
t
= e.
Show that a = b = e.
7.1.6 Let X be a set of
_
2k4
k2
_
+ 1 real numbers, k 2. Prove that there exists a monotone
sequence (x
i
)
k
i=1
X such that
[x
i+1
x
1
[ 2[x
i
x
1
[
for all i = 1, . . . , k 1.
7.2. Abstract algebra.
7.2.1 Let G be a group and a be an element in G. The minimal positive integer n such that
a
n
= e is called the order of element a and is denoted ord a. Show that for any a G
a: if gcd(k, ord a) = 1, then ord(a
k
) = ord a;
b: if ord(a) = 2, then ord(aba) = ord b for any b G;
c: ord(ab) = ord(ba) for any b G.
7.2.2 Consider permutations of 1, ..., n. They form a group with composition as the opera-
tion, which is denoted S
n
. As usual S
n
and = (a
1
, ..., a
k
) means (a
i
) = a
i+1
, i =
1, ..., k 1, (a
k
) = a
1
and (b) = b for b ,= a
1
, ..., a
k
.
Let k be odd and a
1
, ...a
k1
, b
1
, ..., b
k
, ..., c
1
, ..., c
k+1
be dierent elements of 1, ..., n.
Show that
ord ((a
1
, ...a
k1
)(b
1
, ..., b
k
)(c
1
, ..., c
k+1
)) =
(k 1)k(k + 1)
2
.
7.2.3 Let G be a group with a xed element a. We consider a graph with the vertex set G and
for each x G we put an edge between x and ax. Show that this graph is a union of
cycles of size n = ord a.
7.2.4 Let G be the subgroup of GL
2
(R) generated by A and B, where
A =
_
2 0
0 1
_
, B =
_
1 1
0 1
_
.
30
Let H consist of all matrices
_
a
11
a
12
a
21
a
22
_
in G for which a
11
= a
22
= 1.
a) Show that H is an abelian subgroup of G.
b) Show that H is not nitely generated.
7.2.5 Suppose that in a not necessarily commutative ring R the square of any element is 0.
Prove that abc + abc = 0 for any three elements a, b, c.
7.2.6 Let a
1
, a
2
, .., a
51
be non-zero elements of a eld. We simultaneously replace each element
with the sum of the 50 remainings ones. In this way we get a sequence b
1
, ..., b
51
. If the
new sequence is a permutation of the original one, what can the characteristic of the eld
be?
7.3. Polynomials over C.
7.3.1 Let P
0
, P
1
, ..., P
n1
be the vertices of a regular n-gon inscribed in the unit circle. Prove
that [P
1
P
0
[[P
2
P
0
[...[P
n1
P
0
[ = n.
7.3.2 Let all roots of an nth degree polynomial P(z) with complex coecients lie on the unit
circle in the complex plane. Prove that all roots of the polynomial 2zP
## (z) nP(z) lie
on the same circle.
7.3.3 Let P(z) be an algebraic polynomial of degree n having only real zeros and real coe-
cients. (a) Prove that (n 1) (P
(x))
2
nP(x)P
## (x) for every real x. (b) Examine the
case of equality.
7.3.4 Consider the following set of polynomials:
T =
_
f : f =
3
k=0
a
k
x
k
, a
k
R, [f(1)[ 1, [f(1/2)[ 1
_
.
Evaluate sup
fP
max
1x1
[f
## (x)[ and nd all polynomials f T for which the above
supremum is attainded.
7.3.5 Let p(x) = x
5
+x and q(x) = x
5
+x
2
nd all pairs (w, z) of complex numbers with w ,= z
for which p(w) = p(z) and q(w) = q(z).
7.3.6 Let p(z) be a polynomial of degree n 1 with complex coecients. Prove that there
exist at least n + 1 complex numbers z for which p(z) is 0 or 1.
7.4. Linear algebra.
7.4.1 Find the maximum of x
3
3x on the set x: x
4
+ 36 13x
2
.
7.4.2 Let S be a set of real numbers which is closed under multiplication, i.e. a, b S implies
ab S. Let T and U be disjoint subsets of S whose union is S. Given that the product
of any three (not necessarily distinct) elements of T is in T and that the product of any
three elements of U is in U, show that at least one of the two subsets T, U is closed under
multiplication.
7.4.3 Let V be a real vector space, and let f, f
1
, f
2
. . . f
k
be linear maps from V to R. Suppose
that f(x) = 0 whenever f
1
(x) = f
2
(x) = . . . = f
k
(x) = 0. Prove that f is a linear
combination of f
1
, f
2
, . . . , f
k
.
7.4.4 Consider the eld Q of rational numbers (i.e. fractions of integers). We consider R as a
vector space over Q.
(a) Find a 2-dimensional subspace of R.
(b) Show that the equation f(x + y) = f(x) + f(y) has a solution not of the form
f(x) = cx on this subspace.
7.4.5 Let A: R
3
R
3
be linear. Suppose that Av and v are orthogonal for every v V .
(a) Show that A
T
= A.
(b) Show that there exists u R
3
such that Av = u v.
31
7.4.6 Recall that a function A is an involution if A
2
is the identity. Let V be a nite dimensional
real vector space.
(a) Let A: V V be an involution. Show that there exists a basis of V consisting of
Eigenvectors of V .
(b) Find the largest number of pairwise commutative involutions on V .
7.4.7 Let A and B be complex matrices which satisfy the equation AB + A + B = 0, where 0
is the additive neutral element. Show that AB = BA.
7.4.8 Let R 0. Suppose that F and G are linear maps (operators) from R
n
into R
n
satisfying F GG F = F.
a) Show that F
k
GG F
k
= kF
k
for all k N.
b) Show that F
k
= 0 for some k.
7.4.9 Let A be an n n diagonal matrix with characteristic polynomial
(x c
1
)
d
1
(x c
2
)
d
2
(x c
k
)
d
k
,
where c
1
, c
2
, . . . , c
k
are distinct (which means that c
1
appears d
1
times on the diagonal,
c
2
appears d
2
times on the diagonal, etc., and d
1
+d
2
+. . . +d
k
= n). Let V be the space
of all n n matrices B such that AB = BA. Prove that the dimension of V is
d
2
1
+ d
2
2
+ . . . + d
2
k
.
7.4.10 For n 1 let M be an n n complex matrix with distinct eigenvalues
1
,
2
, . . . ,
k
,
with multiplicities m
1
, m
2
, . . . , m
k
, respectively. Consider the linear operator L
M
dened
by L
M
(X) = MX + XM
T
, for any complex n n matrix X. Find its eigenvalues
and their multiplicities. (M
T
denotes the transpose of M; that is, if M = (m
k,l
), then
M
T
= (m
l,k
).)
7.4.11 Let A be an n n matrix with complex entries and suppose that n > 1. Prove that
AA = I
n
S GL
n
(C) such that A = SS
1
.
(If A = [a
ij
] then A = [a
ij
], where a
ij
is the complex conjugate of a
ij
; GL
n
(C) denotes the
set of all n n invertible matrices with complex entries, and I
n
is the identity matrix.)
7.5. Matrix calculus.
7.5.1 Compute the determinant of the n n matrix A = [a
ij
], where
a
ij
=
_
(1)
|ij|
if i ,= j
2 if i = j
7.5.2 Let A be a real 4 2 matrix and B be a real 2 4 matrix such that
AB =
_
_
1 0 1 0
0 1 0 1
1 0 1 0
0 1 0 1
_
_
Find BA.
7.5.3 Let M be an invertible 2n 2n matrix, represented in block form as
M =
_
A B
C D
_
and M
1
=
_
E F
G H
_
Show that det M det H = det A.
7.5.4 Let X be a non-singular matrix with columns (v
1
, v
2
, . . . , v
n
). Let Y be the matrix with
columns (v
2
, v
3
, . . . , v
n
, 0). Show that the matrixes A = Y X
1
and B = X
1
Y have rank
n 1 and have only 0s for eigenvalues.
32
7.5.5 a) Let the mapping f : M
n
R from the space of all real n n matrices to the reals
be linear (ie. f(A + B) = f(A) + f(B) and f(cA) = cf(A)). Prove that there exists a
unique matrix C M
n
such that f(A) = Trace(AC).
b) If in addition f(AB) = f(BA) for any A, B M
n
, prove that there exists R such
that f(A) = Trace(A).
7.5.6 For a nn real matrix A, e
A
is dened as
n=0
1
n!
A
n
. Prove or disprove that for all real
polynomials p and square matrices A and B, p(e
AB
) is nilpotent if and only if p(e
BA
) is
nilpotent. (The matrix A is nilpotent if A
k
= 0 for some k N.)
7.6. Sequences and series.
7.6.1 Calculate lim
n
1
n
+ 2
n
+ ... + n
n
n
n
.
7.6.2 Let x
1
= 2005, x
n+1
=
1
43x
n
for n 1. Find lim
n
x
n
.
7.6.3 Let a
0
=
2, b
0
= 2,
a
n+1
=
_
2
_
4 a
2
n
, b
n+1
=
2b
n
2 +
_
4 + b
2
n
.
a) Prove that the sequences a
n
and b
n
are decreasing and converge to 0.
b) Prove that the sequence 2
n
a
n
is increasing, the sequence 2
n
b
n
is decreasing and
those two sequences converge to the same limit.
c) Prove that there is a positive constant c such that for all n the following inequality
holds 0 < b
n
a
n
<
c
8
n
.
7.6.4 Suppose
n=1
a
n
< . Do the following sums have to converge as well?
a) a
1
+ a
2
+ a
4
+ a
3
+ a
8
+ a
7
+ a
6
+ a
5
+ a
16
+ a
15
+ ... + a
9
+ a
32
+ ...,
b) a
1
+a
2
+a
3
+a
4
+a
5
+a
7
+a
6
+a
8
+a
9
+a
11
+a
13
+a
15
+a
10
+a
12
+a
14
+a
16
+....
7.6.5 Suppose that a
n
> 0,
n=1
a
n
= and s
n
= a
1
+ ... + a
n
. Prove that
a)
n=1
a
n
a
n
+1
= ,
b)
n=1
a
n
s
n
= ,
c)
n=1
a
n
s
2
n
< .
7.6.6 Let
n
n=1
be a sequence of positive real numbers such that lim
n
n
= 0. Find
lim
n
1
n
n
k=1
ln
_
k
n
+
n
_
.
7.7. Calculus.
7.7.1 Let f : R
2
R be given by f(x, y) = (X
2
y
2
)e
x
2
y
2
.
a) Prove that f attains its minimum and its maximum.
b) Determine all points (x, y) such that
f
x
(x, y) =
f
y
(x, y) = 0 and determine for which
of them f has global or local minimum or maximum.
7.7.2 Find lim
t1
(1 t)
n=1
t
n
1 + t
n
, where t 1 means that t approaches 1 from below.
7.7.3 Let f be a continuous function on [0, 1] such that for every x [0, 1] we have
_
1
x
f(t) dt
1 x
2
2
.
33
Show that
_
1
0
f(t)
2
dt
1
3
.
7.7.4 Suppose n is a natural number. Evaluate
_
sin nx
(1 + 2
x
) sin x
dx
.
7.7.5 Let F : (1, ) R be the function dened by
F(x) :=
_
x
2
x
dt
ln t
.
Show that F is one-to-one (i.e. injective) and nd the range (i.e. set of values) of F.
7.7.6 Prove that
_
1
0
_
1
0
dx dy
x
1
+[ ln y[ 1
1.
34
8. Hints
8.1. Basics.
8.1.1 Write down occurences for rst few k.
8.1.2 How many elements can be larger than 1/k?
8.1.3 Both parts can be solved by looking at only two types subdivision operations, such as
one cube is divided into 2
d
cubes.
8.1.4 Plot the function. How many xed-points can f have?
8.1.5 There exist integers u, v such that ru + sv = 1.
8.1.6 It is easier to construct such a sequence if you already have a sequence of lenght k 1. . .
8.2. Abstract algebra.
8.2.1 Youre on your own here, sorry. . .
8.2.2 Let be the permutation in question.
i
(a
1
) = a
1
if and only if i is a multiple of k 1.
Similarly for b
1
and c
1
. If
j
xes these three elements, then it xes everything.
8.2.3 In the graph you move from x to ax to a
2
x to a
3
x and so on.
8.2.4 H is isomorphic to (has the same structure as) a subgroup of R. For part b recall that
the generators in particular are elements of H.
8.2.5 Look at squares like (a + b)
2
, (ab + c
2
), etc.
8.2.6 What is
b
i
a
i
? Recall that the characteristic is always a prime.
8.3. Polynomials over C.
8.3.1 Use complex numbers.
8.3.2 Find the product of the roots of Q(z) = 2zP
## (z) nP(z). Then try to prove that Q has
no roots outside the unit circle; the formula for P
## /P from the lecture notes could be
useful.
8.3.3 It is enough to prove the inequality for x = 0.
8.3.4 Try interpolation, for example.
8.3.5 It is not very dicult now, just write down the system and be patient in doing calcula-
tions.
8.3.6 If a is a root of p of multiplicity k, then a is a root of p
of multiplicity k 1.
8.4. Linear algebra.
8.4.1 This is really a second degree problem.
8.4.2 Use four elements, two in each of T and U.
8.4.3 Assume that f
1
, . . . , f
k
are linearly independent, and determine what the coecient of f
would have to be.
8.4.4
2 , Q.
8.4.5 Check what A does to basis vectors.
8.4.6 A can be diagonalized (see Section 4.2). What are the Eigenvalues of A?
8.4.7 A matrix A always commutes with its. . .
8.4.8 Use a telescoping sum. For (b), consider eigenvalues of a suitable operator (not of F or
G).
8.4.9 Block matrices are useful here.
8.4.10 Construct the eigenvectors of L
M
(X) out of the eigenvectors of M and their transposes.
8.4.11 Construct S as a linear combination of A and I
n
.
35
| 24,929
| 70,869
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-39
|
latest
|
en
| 0.840318
|
https://www.urionlinejudge.com.br/judge/en/profile/88963?sort=Ranks.language_id&direction=asc
| 1,623,776,955,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-25/segments/1623487621450.29/warc/CC-MAIN-20210615145601-20210615175601-00067.warc.gz
| 982,987,550
| 6,729
|
# PROFILE
Check out all the problems this user has already solved.
Problem Problem Name Ranking Submission Language Runtime Submission Date
1035 Selection Test 1 04379º 3823523 C 0.000 3/13/16, 1:28:55 AM
1015 Distance Between Two Points 05717º 3790480 C 0.000 3/9/16, 2:15:38 AM
1016 Distance 05257º 3788830 C 0.000 3/8/16, 10:35:36 PM
1017 Fuel Spent 05566º 3788977 C 0.000 3/8/16, 10:54:32 PM
1018 Banknotes 04439º 3766357 C 0.000 3/5/16, 7:32:40 PM
1019 Time Conversion 04919º 3789732 C 0.000 3/9/16, 12:40:15 AM
1020 Age in Days 05206º 3789914 C 0.000 3/9/16, 1:03:24 AM
1036 Bhaskara's Formula 04148º 3823736 C 0.000 3/13/16, 2:07:31 AM
1037 Interval 04151º 3877033 C 0.000 3/18/16, 4:56:32 PM
1049 Animal 01800º 4098571 C 0.000 4/8/16, 8:30:36 PM
1038 Snack 04674º 3940957 C 0.000 3/25/16, 11:24:18 PM
1040 Average 3 03308º 3941323 C 0.000 3/26/16, 12:10:07 AM
1041 Coordinates of a Point 04084º 3941471 C 0.000 3/26/16, 12:39:38 AM
1042 Simple Sort 03536º 3941652 C 0.000 3/26/16, 1:15:14 AM
1043 Triangle 03768º 3945964 C 0.000 3/26/16, 6:56:23 PM
1044 Multiples 04030º 3946234 C 0.000 3/26/16, 7:22:19 PM
1050 DDD 03466º 3963414 C 0.000 3/29/16, 12:59:39 AM
1045 Triangle Types 02428º 3947014 C 0.000 3/26/16, 9:28:20 PM
1046 Game Time 03278º 4081253 C 0.000 4/10/16, 8:48:06 PM
1047 Game Time with Minutes 01940º 3947974 C 0.000 3/27/16, 12:20:36 AM
1048 Salary Increase 02806º 3963192 C 0.000 3/29/16, 12:48:46 AM
1051 Taxes 02335º 4074297 C 0.000 4/9/16, 9:17:39 PM
1052 Month 03044º 4058694 C 0.000 4/8/16, 12:54:07 AM
1059 Even Numbers 03693º 4058749 C 0.000 4/8/16, 12:59:08 AM
1060 Positive Numbers 03105º 4058814 C 0.000 4/8/16, 1:06:39 AM
1064 Positives and Average 02815º 4059054 C 0.000 4/8/16, 1:26:18 AM
1065 Even Between five Numbers 02904º 4059272 C 0.000 4/8/16, 1:58:39 AM
1066 Even, Odd, Positive and... 02543º 4059313 C 0.000 4/8/16, 2:05:37 AM
1067 Odd Numbers 03001º 4059077 C 0.000 4/8/16, 1:32:15 AM
1014 Consumption 06041º 3811521 C 0.000 3/11/16, 5:56:47 PM
1 of 4
| 1,005
| 2,001
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2021-25
|
latest
|
en
| 0.320287
|
https://www.swolekreatine.com/2018/06/22/amazon-com-neverland-42-x-33-cm-16-5-x-13-in-decorative-pillow-pet-cushion-pokemon-pikachu-plush-doll-baby-marvelous-amazon-pillow-pet-4-829922.html
| 1,547,673,696,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-04/segments/1547583657867.24/warc/CC-MAIN-20190116195543-20190116221543-00256.warc.gz
| 954,599,234
| 18,236
|
» » » Amazon.com : Neverland 42 X 33 Cm/ 16.5 X 13 In Decorative Pillow Pet Cushion Pokemon Pikachu Plush Doll : Baby (marvelous Amazon Pillow Pet #4)
# Amazon.com : Neverland 42 X 33 Cm/ 16.5 X 13 In Decorative Pillow Pet Cushion Pokemon Pikachu Plush Doll : Baby (marvelous Amazon Pillow Pet #4)
Friday, June 22nd, 2018 - Category: Pillow
### X
Roman numerals,
• the numerals in the ancient Roman system of notation, still used for certain limited purposes, as in some pagination, dates on buildings, etc. The common basic symbols are I (=1), V (=5), X (=10), L (=50), C (=100), D (=500), and M (=1000). The Roman numerals for one to nine are: I, II, III, IV, V, VI, VII, VIII, IX. A bar over a letter multiplies it by 1000;
thus, X̄ equals 10,000. Integers are written according to these two rules: If a letter is immediately followed by one of equal or lesser value, the two values are added;
thus, XX equals 20, XV equals 15, VI equals 6. If a letter is immediately followed by one of greater value, the first is subtracted from the second;
thus, IV equals 4, XL equals 40, CM equals 900. Examples: XLVII(=47), CXVI(=116), MCXX(=1120), MCMXIV(=1914). Roman numerals may be written in lowercase letters, though they appear more commonly in capitals.
• ### X
Roman numerals,
• the numerals in the ancient Roman system of notation, still used for certain limited purposes, as in some pagination, dates on buildings, etc. The common basic symbols are I (=1), V (=5), X (=10), L (=50), C (=100), D (=500), and M (=1000). The Roman numerals for one to nine are: I, II, III, IV, V, VI, VII, VIII, IX. A bar over a letter multiplies it by 1000;
thus, X̄ equals 10,000. Integers are written according to these two rules: If a letter is immediately followed by one of equal or lesser value, the two values are added;
thus, XX equals 20, XV equals 15, VI equals 6. If a letter is immediately followed by one of greater value, the first is subtracted from the second;
thus, IV equals 4, XL equals 40, CM equals 900. Examples: XLVII(=47), CXVI(=116), MCXX(=1120), MCMXIV(=1914). Roman numerals may be written in lowercase letters, though they appear more commonly in capitals.
• ### In
prep.
1. (used to indicate inclusion within space, a place, or limits): walking in the park.
2. (used to indicate inclusion within something abstract or immaterial): in politics; in the autumn.
3. (used to indicate inclusion within or occurrence during a period or limit of time): in ancient times; a task done in ten minutes.
4. (used to indicate limitation or qualification, as of situation, condition, relation, manner, action, etc.): to speak in a whisper; to be similar in appearance.
5. (used to indicate means): sketched in ink; spoken in French.
6. (used to indicate motion or direction from outside to a point within) into: Let's go in the house.
7. (used to indicate transition from one state to another): to break in half.
8. (used to indicate object or purpose): speaking in honor of the event.
9. in that, because;
inasmuch as: In that you won't have time for supper, let me give you something now.
1. in or into some place, position, state, relation, etc.: Please come in.
2. on the inside;
within.
3. in one's house or office.
4. in office or power.
5. in possession or occupancy.
6. having the turn to play, as in a game.
7. [Baseball.](of an infielder or outfielder) in a position closer to home plate than usual;
short: The third baseman played in, expecting a bunt.
8. on good terms;
in favor: He's in with his boss, but he doubts it will last.
9. in vogue;
in style: He says straw hats will be in this year.
10. in season: Watermelons will soon be in.
11. be in for, to be bound to undergo something, esp. a disagreeable experience: We are in for a long speech.
12. in for it, [Slang.]about to suffer chastisement or unpleasant consequences, esp. of one's own actions or omissions: I forgot our anniversary again, and I'll be in for it now.Also,[Brit.,] for it.
13. in with, on friendly terms with;
familiar or associating with: They are in with all the important people.
1. located or situated within;
inner;
internal: the in part of a mechanism.
2. [Informal.]
• in favor with advanced or sophisticated people;
fashionable;
stylish: the in place to dine; Her new novel is the in book to read this summer.
• comprehensible only to a special or ultrasophisticated group: an in joke.
3. well-liked;
included in a favored group.
4. inward;
incoming;
inbound: an in train.
5. plentiful;
available.
6. being in power, authority, control, etc.: a member of the in party.
7. playing the last nine holes of an eighteen-hole golf course (opposed to out): His in score on the second round was 34.
n.
1. Usually, ins. persons in office or political power (distinguished from outs).
2. a member of the political party in power: The election made him an in.
3. pull or influence;
a social advantage or connection: He's got an in with the senator.
4. (in tennis, squash, handball, etc.) a return or service that lands within the in-bounds limits of a court or section of a court (opposed to out).
v.t. Brit. [Dial.]
1. to enclose.
### Decorative
dec•o•ra•tive (dekər ə tiv, dekrə-, dekə rā′-),USA pronunciation adj.
1. serving or tending to decorate.
2. serving only to decorate, in contrast to providing a meaningful experience.
deco•ra•tive•ness, n.
### Pillow
pil•low (pilō),USA pronunciation n.
1. a bag or case made of cloth that is filled with feathers, down, or other soft material, and is used to cushion the head during sleep or rest.
2. anything used to cushion the head;
3. Also called lace pillow. a hard cushion or pad that supports the pattern and threads in the making of bobbin lace.
4. a supporting piece or part, as the block on which the inner end of a bowsprit rests.
v.t.
1. to rest on or as on a pillow.
2. to support with pillows.
3. to serve as a pillow for: She pillowed the child with her body.
v.i.
1. to rest as on a pillow.
### Pet
pet1 (pet),USA pronunciation n., adj., v., pet•ted, pet•ting.
n.
1. any domesticated or tamed animal that is kept as a companion and cared for affectionately.
2. a person especially cherished or indulged;
favorite: He was the teacher's pet.
3. a thing particularly cherished.
1. kept or treated as a pet: a pet lamb.
2. especially cherished or indulged, as a child or other person.
3. favorite;
most preferred: a pet theory.
4. showing fondness or affection: to address someone with pet words.
v.t.
1. to fondle or caress: to pet a dog.
2. to treat as a pet;
indulge.
v.i.
1. to engage in amorous fondling and caressing.
### Cushion
cush•ion (kŏŏshən),USA pronunciation n.
1. a soft bag of cloth, leather, or rubber, filled with feathers, air, foam rubber, etc., on which to sit, kneel, or lie.
2. anything similar in form, used to dampen shocks or to prevent excessive pressure or chafing.
3. something to absorb or counteract a shock, jar, or jolt, as a body of air or steam.
4. something that lessens the effects of hardship, distress, or the like: His inheritance was a cushion against unemployment.
5. any part or structure resembling a cushion.
6. the resilient raised rim encircling the top of a billiard table.
7. a pad worn under the hair by women.
8. a portion of a radio or television script that can be adjusted in length or cut out altogether in order to end the program on time.
9. [Ice Hockey, Canadian.]the iced surface of a rink.
10. a pillow used in lacemaking.
11. a leather pad on which gold leaf is placed preparatory to gilding.
v.t.
1. to place on or support by a cushion.
2. to furnish with a cushion or cushions.
3. to cover or conceal with, or as if with, a cushion.
4. to lessen or soften the effects of: to cushion the blow to his pride.
5. to suppress (complaints, lamentations, etc.) by quietly ignoring.
6. to check the motion of (a piston or the like) by a cushion, as of steam.
7. to form (steam or the like) into a cushion.
### Plush
plush (plush),USA pronunciation n., adj., -er, -est.
n.
1. a fabric, as of silk, cotton, or wool, whose pile is more than &fracnumer;
1&fracdenom;
8&fracend;
inch (0.3 cm) high.
1. expensively or showily luxurious: the plushest hotel in town
2. abundantly rich;
lush;
luxuriant: plush, rolling lawns.
plushness, n.
### Doll
doll (dol),USA pronunciation n.
1. a small figure representing a baby or other human being, esp. for use as a child's toy.
• a pretty but expressionless or unintelligent woman.
• a girl or woman, esp. one who is considered attractive.
• a boy or man who is considered attractive.
• (sometimes cap.) an affectionate or familiar term of address (sometimes offensive when used to strangers, casual acquaintances, subordinates, etc., esp. by a male to a female).
2. a generous or helpful person: You're a doll for lending me your car.
v.t., v.i.
1. doll up, [Informal.]to dress in an elegant or ostentatiously stylish manner: She got all dolled up for a trip to the opera.
dollish•ness, n.
### Baby
ba•by (bābē),USA pronunciation n., pl. -bies, adj., v., -bied, -by•ing.
n.
1. an infant or very young child.
2. a newborn or very young animal.
3. the youngest member of a family, group, etc.
4. an immature or childish person.
5. a human fetus.
• [Sometimes Disparaging and Offensive.]a girl or woman, esp. an attractive one.
• a person of whom one is deeply fond;
sweetheart.
• (sometimes cap.) an affectionate or familiar address (sometimes offensive when used to strangers, casual acquaintances, subordinates, etc., esp. by a male to a female).
• a man or boy;
chap;
fellow: He's a tough baby to have to deal with.
• an invention, creation, project, or the like that requires one's special attention or expertise or of which one is especially proud.
• an object;
thing: Is that car there your baby?
1. of or suitable for a baby: baby clothes.
2. of or like a baby;
infantile: baby skin.
3. small;
comparatively little: a baby car.
4. treating babies: a baby doctor.
v.t.
1. to treat like a young child;
pamper.
2. to handle or use with special care;
treat gently.
baby•hood′, n.
baby•ish•ness, n.
Hello , this post is about Amazon.com : Neverland 42 X 33 Cm/ 16.5 X 13 In Decorative Pillow Pet Cushion Pokemon Pikachu Plush Doll : Baby (marvelous Amazon Pillow Pet #4). This attachment is a image/jpeg and the resolution of this photo is 830 x 830. It's file size is only 63 KB. If You want to save This image to Your laptop, you might Click here. You could too see more photos by clicking the image below or see more at this article: Amazon Pillow Pet.
Naturally, while in the Amazon.com : Neverland 42 X 33 Cm/ 16.5 X 13 In Decorative Pillow Pet Cushion Pokemon Pikachu Plush Doll : Baby (marvelous Amazon Pillow Pet #4) may play with an important function. Because of the sculpture, in addition to stunning, the garden also appears exotic more inspired, and persona. Thus, to be able to carve the sculpture deft such concerns, the terms of everything you are thinking about? It is truly important to note. As such, the sculpture not just sitting within the yard. Here are some items you have to consider to put Amazon Pillow Pet such as for example.
Note the stance sculpture with the concept / strategy Areas. With positioning, the sculpture appears more tuned towards the playground. Not different having a garden from oneanother. If your garden with notion that is minimalist, utilize the same type sculpture. Illustration barrel-designed statue nominal carvings or trinkets. Or, work with a pitcher statue digging nan small variance. Another instance, in case your garden in style that is traditional, position the sculpture can be a normal style. As an example Javanese puppet figurines. The exotic gardens also should Balinese sculpture Balinese style.
Notice the Exact Distance Between The place with statue. The best, a specific mileage is involving the sculpture of the area where the statue lookedfor instance deck. Hence, the sculpture is seen in the area easily. If the statue using the room's range too close or remote, the freedom of view is certainly challenging to obtain. Simply for representation, the space between your space together with the statue ought to be significant enough.
## Chewbacca Pillow
Category: Pillow - Date published: May 7th, 2018
Tags: Chewbacca Pillow, ,
## 21 X 27 Pillow Insert
Category: Pillow - Date published: April 17th, 2018
Tags: 21 X 27 Pillow Insert, , , , ,
## Good Night Pillow
Category: Pillow - Date published: August 2nd, 2018
Tags: Good Night Pillow, , ,
## Lion Pillows
Category: Pillow - Date published: May 7th, 2018
Tags: Lion Pillows, ,
## Lower Back Pillow For Sleeping
Category: Pillow - Date published: December 8th, 2017
Tags: Lower Back Pillow For Sleeping, , , , ,
## Flat Pillows For Neck Pain
Category: Pillow - Date published: September 18th, 2018
Tags: Flat Pillows For Neck Pain, , , , ,
## Amazon Pillow Pet
Category: Pillow - Date published: June 22nd, 2018
Tags: Amazon Pillow Pet, , ,
## Mash Pillows
Category: Pillow - Date published: February 5th, 2018
Tags: Mash Pillows, ,
## Clevamama Clevafoam Baby Pillow
Category: Pillow - Date published: February 6th, 2018
## Amazon.com Pillows
Category: Pillow - Date published: January 9th, 2018
Tags: Amazon.com Pillows, ,
## Lake House Throw Pillows
Category: Pillow - Date published: August 2nd, 2018
Tags: Lake House Throw Pillows, , , ,
## How To Use Tummy Time Pillow
Category: Pillow - Date published: April 5th, 2018
Tags: How To Use Tummy Time Pillow, , , , , ,
| 3,594
| 13,505
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.1875
| 3
|
CC-MAIN-2019-04
|
longest
|
en
| 0.775579
|
https://pedagogue.app/teaching-students-about-the-power-of-10-2/
| 1,721,134,248,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514745.49/warc/CC-MAIN-20240716111515-20240716141515-00593.warc.gz
| 398,477,072
| 29,315
|
# Teaching Students About the Power of 10
Teaching students about the power of 10 can be an interesting and engaging way to introduce them to the concept of large numbers and their relationship to each other. The power of 10 is a mathematical concept that refers to the exponential notation of a number, which is expressed as a product of a base number and a certain number of zeros. For example, 10^3 (ten to the power of three) is equal to 1,000, and 10^-3 (ten to the power of negative three) is equal to 0.001.
To teach students about the power of 10, it is important to begin with some basic ideas about place value and the relationship between digits and their place in a number. This can involve introducing students to the idea of a number line, with numbers increasing in magnitude as they move to the right of zero. This can be used to illustrate how each digit in a number has a specific place value, which is determined by its position in the number.
From there, students can be introduced to the concept of the power of 10, which involves multiplying a base number (such as 10) by itself a certain number of times (the exponent). This can be demonstrated using visual aids or manipulatives, such as blocks or cards, to show the relationship between the base number (10) and the exponent.
Once students have a basic understanding of the power of 10, they can begin to explore the application of this concept in the real world. This might involve discussing the use of scientific notation for very large or small numbers, such as in the fields of astronomy or physics. Students can also explore how the power of 10 can be used to solve problems in everyday life, such as calculating the distance between two cities or converting units of measurement.
With practice and repetition, students can develop a fluency in using the power of 10 to solve problems and understand the relationships between numbers. This can help them develop important skills in critical thinking, problem-solving, and mathematical literacy, which will serve them well throughout their academic and professional careers. By teaching students about the power of 10, educators can help them develop a deeper understanding of the world around them and lay the foundation for a lifetime of learning and exploration.
Choose your Reaction!
| 471
| 2,323
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.984375
| 4
|
CC-MAIN-2024-30
|
latest
|
en
| 0.955579
|
https://essaychimp.com/2017/10/16/use-the-following-normal-form-game-to-answer-the-questions-b-32/
| 1,600,838,000,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-40/segments/1600400209999.57/warc/CC-MAIN-20200923050545-20200923080545-00789.warc.gz
| 385,030,422
| 13,263
|
# Use the following normal-form game to answer the questions b
Use the following normal-form game to answer the questions below. Player 2 Player 2 Strategy … Show more Use the following normal-form game to answer the questions below. Player 2 Player 2 Strategy C D Player 1 A 20, 20 50, 5 Player 1 B 5, 50 35, 35 a. Identify the one-shot Nash equilibrium. (Click to select) (A,C) (B,D) (B,C) (A,D) b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one-shot Nash equilibrium? (Click to select) Yes No c. Suppose this game is infinitely repeated and the interest rate is 5 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? (Click to select) No Yes d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is ?. If ? is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium? (Click to select) Yes No • Show less
# Our Service Charter
1. ### Excellent Quality / 100% Plagiarism-Free
We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions
We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure
We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee
If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.
We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.
Excellent Quality
Zero Plagiarism
Expert Writers
or
| 903
| 4,168
|
{"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}
| 2.78125
| 3
|
CC-MAIN-2020-40
|
longest
|
en
| 0.930725
|
https://www.allinterview.com/showanswers/136146/to-varied-frequency-in-transmission-line-and-i-kept-it-as-a-constant-one.html
| 1,722,827,443,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640427760.16/warc/CC-MAIN-20240805021234-20240805051234-00811.warc.gz
| 511,176,730
| 7,407
|
how to varied the frequency in transmission line and how i
kept it as a constant one?
Answers were Sorted based on User's Feedback
how to varied the frequency in transmission line and how i kept it as a constant one?..
by varying the voltage
as per V/f ratio
Is This Answer Correct ? 7 Yes 4 No
how to varied the frequency in transmission line and how i kept it as a constant one?..
frequeny of a transmission line is varied by changing the synchronous speed of the generator.....which is affected by the equation syn.speed=(120f)/p...so the frequency of the transmission line is varied by changing the poles of the generator...........
however the frequency cannot be maintained as a constant one throughout....it has a slight variation of +/- ...but if there is huge variation the power station tries to decrease/increase the load there by maintaining the frequency as a constant one
Is This Answer Correct ? 3 Yes 3 No
More Electrical Engineering Interview Questions
Can a generator runs after getting 1st stator earth fault.
How to calculate Battery back up time for a 400 AH Battery bank having a load of 20 Amps and charging time required to fully charge this battery bank?
please send me jindal previous aptitude and technical question and answer.my email id is deep_raj@live.com
why C T secondary are rating 5A generaly .
Find the octal equivalent for the binary number 101101110
what does hapen if suddently frequency doubled
what about the input current fan when regulator regulates to speed low?
what is the difference in operation of 3 phase motor when am forward delta connection and reverse delta connection?
if we use contactor & MCCB both in a feeder.in this feeder rating of contactor is higher or lower or same of MCCB rating & why?
whytransformers rating in KVA?
explain why reduced voltage starters are required for large tree phase inudction motor
How many straight through joint is permissible in single core 33kv XLPE cable for a length of 985 mtr.
Categories
• Civil Engineering (5085)
• Mechanical Engineering (4451)
• Electrical Engineering (16632)
• Electronics Communications (3918)
• Chemical Engineering (1095)
• Aeronautical Engineering (239)
• Bio Engineering (96)
• Metallurgy (361)
• Industrial Engineering (259)
• Instrumentation (3014)
• Automobile Engineering (332)
• Mechatronics Engineering (97)
• Marine Engineering (124)
• Power Plant Engineering (172)
• Textile Engineering (575)
• Production Engineering (25)
• Satellite Systems Engineering (106)
• Engineering AllOther (1379)
| 554
| 2,542
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.625
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.927949
|
https://rdrr.io/rforge/waveslim/src/R/hilbert.R
| 1,579,471,806,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-05/segments/1579250595282.35/warc/CC-MAIN-20200119205448-20200119233448-00208.warc.gz
| 641,725,795
| 21,830
|
# R/hilbert.R In waveslim: Basic Wavelet Routines for One-, Two- and Three-dimensional Signal Processing
```########################################################################
dwt.hilbert <- function(x, wf, n.levels=4, boundary="periodic", ...) {
switch(boundary,
"reflection" = x <- c(x, rev(x)),
"periodic" = invisible(),
stop("Invalid boundary rule in dwt.hilbert"))
N <- length(x)
J <- n.levels
if(N/2^J != trunc(N/2^J))
stop("Sample size is not divisible by 2^J")
if(2^J > N)
stop("Wavelet transform exceeds sample size in dwt")
dict <- hilbert.filter(wf)
L <- dict\$length; storage.mode(L) <- "integer"
h0 <- dict\$lpf[[1]]; storage.mode(h0) <- "double"
g0 <- dict\$lpf[[2]]; storage.mode(g0) <- "double"
h1 <- dict\$hpf[[1]]; storage.mode(h1) <- "double"
g1 <- dict\$hpf[[2]]; storage.mode(g1) <- "double"
y <- vector("list", J+1)
names(y) <- c(paste("d", 1:J, sep=""), paste("s", J, sep=""))
x.h <- x.g <- x
for(j in 1:J) {
W <- V <- numeric(N/2^j)
out.h <- .C("dwt", as.double(x.h), as.integer(N/2^(j-1)), L, h1, h0,
W = W, V = V, PACKAGE = "waveslim")[6:7]
out.g <- .C("dwt", as.double(x.g), as.integer(N/2^(j-1)), L, g1, g0,
W = W, V = V, PACKAGE = "waveslim")[6:7]
y[[j]] <- complex(real = out.h\$W, imaginary = out.g\$W)
x.h <- out.h\$V
x.g <- out.g\$V
}
y[[J+1]] <- complex(real = x.h, imaginary = x.g)
attr(y, "wavelet") <- wf
attr(y, "levels") <- n.levels
attr(y, "boundary") <- boundary
return(y)
}
########################################################################
M <- length(x)
N <- 2^(ceiling(log(M, 2)))
xx <- c(x, rep(0, N - M))
y <- dwt.hilbert(xx, ...)
J <- length(y) - 1
for(j in 1:J) {
y[[j]] <- y[[j]][1:trunc(M/2^j)]
}
return(y)
}
########################################################################
idwt.hilbert <- function(y) {
switch(attributes(y)\$boundary,
"reflection" = x <- c(x, rev(x)),
"periodic" = invisible(),
stop("Invalid boundary rule in dwt.dbp"))
J <- attributes(y)\$levels
dict <- hilbert.filter(attributes(y)\$wavelet)
L <- dict\$length; storage.mode(L) <- "integer"
h <- dict\$hpf; storage.mode(h) <- "double"
g <- dict\$lpf; storage.mode(g) <- "double"
jj <- paste("s", J, sep="")
X <- y[[jj]]
for(j in J:1) {
jj <- paste("d", j, sep="")
XX <- numeric(2 * length(y[[jj]]))
X <- .C("idwt", y[[jj]], as.double(X), as.integer(length(X)),
L, h, g, XX=XX, PACKAGE="waveslim")\$XX
}
return(X)
}
########################################################################
modwt.hilbert <- function(x, wf, n.levels=4, boundary="periodic", ...) {
switch(boundary,
"reflection" = x <- c(x, rev(x)),
"periodic" = invisible(),
stop("Invalid boundary rule in modwt"))
N <- length(x)
storage.mode(N) <- "integer"
J <- n.levels
if(2^J > N) stop("wavelet transform exceeds sample size in modwt")
dict <- hilbert.filter(wf)
L <- dict\$length; storage.mode(L) <- "integer"
h0 <- dict\$lpf[[1]] / sqrt(2); storage.mode(h0) <- "double"
g0 <- dict\$lpf[[2]] / sqrt(2); storage.mode(g0) <- "double"
h1 <- dict\$hpf[[1]] / sqrt(2); storage.mode(h1) <- "double"
g1 <- dict\$hpf[[2]] / sqrt(2); storage.mode(g1) <- "double"
y <- vector("list", J+1)
names(y) <- c(paste("d", 1:J, sep=""), paste("s", J, sep=""))
W <- V <- numeric(N)
x.h <- x.g <- x
for(j in 1:J) {
out.h <- .C("modwt", as.double(x.h), N, as.integer(j), L, h1, h0,
W = W, V = V, PACKAGE="waveslim")[7:8]
out.g <- .C("modwt", as.double(x.g), N, as.integer(j), L, g1, g0,
W = W, V = V, PACKAGE="waveslim")[7:8]
y[[j]] <- complex(real = out.h\$W, imaginary = out.g\$W)
x.h <- out.h\$V
x.g <- out.g\$V
}
y[[J+1]] <- complex(real = x.h, imaginary = x.g)
attr(y, "wavelet") <- wf
attr(y, "boundary") <- boundary
attr(y, "levels") <- n.levels
return(y)
}
########################################################################
imodwt.hilbert <- function(y) {
if(attributes(y)\$boundary != "periodic")
stop("Invalid boundary rule in imodwt")
J <- length(y) - 1
dict <- hilbert.filter(attributes(y)\$wavelet)
L <- dict\$length
ht <- dict\$hpf / sqrt(2)
gt <- dict\$lpf / sqrt(2)
jj <- paste("s", J, sep="")
X <- y[[jj]]; N <- length(X)
XX <- numeric(N)
for(j in J:1) {
jj <- paste("d", j, sep="")
X <- .C("imodwt", y[[jj]], X, as.integer(N), as.integer(j),
as.integer(L), ht, gt, XX, PACKAGE="waveslim")[[8]]
}
return(X)
}
########################################################################
hilbert.filter <- function(name) {
select.K3L3 <- function() {
L <- 12
h0 <- c(1.1594353e-04, -2.2229002e-03, -2.2046914e-03, 4.3427642e-02,
-3.3189896e-02, -1.5642755e-01, 2.8678636e-01, 7.9972652e-01,
4.9827824e-01, 2.4829160e-02, -4.2679177e-02, -2.2260892e-03)
h1 <- qmf(h0)
g0 <- c(1.6563361e-05, -5.2543406e-05, -6.1909121e-03, 1.9701141e-02,
3.2369691e-02, -1.2705043e-01, -1.5506397e-02, 6.1333712e-01,
7.4585008e-01, 2.1675412e-01, -4.9432248e-02, -1.5582624e-02)
g1 <- qmf(g0)
return(list(length = L, hpf = list(h1, g1), lpf = list(h0, g0)))
}
select.K3L5 <- function() {
L <- 12
h0 <- c(5.4258791e-06, -2.1310518e-04, -2.6140914e-03, 1.0212881e-02,
3.5747880e-02, -4.5576766e-02, 3.9810341e-03, 5.3402475e-01,
7.8757164e-01, 2.6537457e-01, -1.3008915e-01, -5.9573795e-02,
1.2733976e-02, 2.8641011e-03, -2.2992683e-04, -5.8541759e-06)
h1 <- qmf(h0)
g0 <- c(4.9326174e-07, 3.5727140e-07, -1.1664703e-03, -8.4003116e-04,
2.8601474e-02, 9.2509748e-03, -7.4562251e-02, 2.2929480e-01,
7.6509138e-01, 5.8328559e-01, -4.6218010e-03, -1.2336841e-01,
-6.2826896e-03, 9.5478911e-03, 4.6642226e-05, -6.4395935e-05)
g1 <- qmf(g0)
return(list(length = L, hpf = list(h1, g1), lpf = list(h0, g0)))
}
select.K4L2 <- function() {
L <- 12
h0 <- c(-1.7853301e-03, 1.3358873e-02, 3.6090743e-02, -3.4722190e-02,
4.1525062e-02, 5.6035837e-01, 7.7458617e-01, 2.2752075e-01,
-1.6040927e-01, -6.1694251e-02, 1.7099408e-02, 2.2852293e-03)
h1 <- qmf(h0)
g0 <- c(-3.5706603e-04, -1.8475351e-04, 3.2591486e-02, 1.3449902e-02,
-5.8466725e-02, 2.7464308e-01, 7.7956622e-01, 5.4097379e-01,
-4.0315008e-02, -1.3320138e-01, -5.9121296e-03, 1.1426146e-02)
g1 <- qmf(g0)
return(list(length = L, hpf = list(h1, g1), lpf = list(h0, g0)))
}
select.K4L4 <- function() {
L <- 16
h0 <- c(2.5734665593981519e-05, -6.6909066441298817e-04,
-5.5482443985275260e-03, 1.3203474646343588e-02,
3.8605327384848696e-02, -5.0687259299773510e-02,
8.1364447220208733e-03, 5.3021727476690994e-01,
7.8330912249663232e-01, 2.7909546754271131e-01,
-1.3372674246928601e-01, -6.9759509629953295e-02,
1.6979390952358446e-02, 5.7323570134311854e-03,
-6.7425216644469892e-04, -2.5933188060087743e-05)
h1 <- qmf(h0)
g0 <- c(2.8594072882201687e-06, 1.9074538622058143e-06,
-2.9903835439216066e-03, -1.9808995184875909e-03,
3.3554663884350758e-02, 7.7023844121478988e-03,
-7.7084571412435535e-02, 2.3298110528093252e-01,
7.5749376288995063e-01, 5.8834703992067783e-01,
5.1708789323078770e-03, -1.3520099946241465e-01,
-9.1961246067629732e-03, 1.5489641793018745e-02,
1.5569563641876791e-04, -2.3339869254078969e-04)
g1 <- qmf(g0)
return(list(length = L, hpf = list(h1, g1), lpf = list(h0, g0)))
}
select.K5L7 <- function() {
L <- 24
h0 <- c(-2.5841959496364648e-10, 6.0231243121018760e-10,
2.1451486802217960e-06, -4.9989222844980982e-06,
-2.2613489535132104e-04, 5.1967501391358343e-04,
3.4011963595840899e-03, -7.1996997688061597e-03,
-1.7721433874932836e-02, 3.5491112173858148e-02,
3.0580617312936355e-02, -1.3452365188777773e-01,
2.1741748603083836e-03, 5.8046856094922639e-01,
7.4964083145768690e-01, 2.6775497264154541e-01,
-7.9593287728224230e-02, -4.3942149960221458e-02,
1.9574969406037097e-02, 8.8554643330725387e-03,
-7.2770446614145033e-04, -3.1310992841759443e-04,
1.4045333283124608e-06, 6.0260907100656169e-07)
h1 <- qmf(h0)
g0 <- c(-3.8762939244546978e-09, 2.9846463282743695e-07,
5.6276030758515370e-06, -7.7697066311187957e-05,
-2.1442686434841905e-04, 2.1948612668324223e-03,
9.5408758453423542e-04, -1.7149735951945008e-02,
1.5212479104581677e-03, 5.6600564413983846e-02,
-4.8900162376504831e-02, -1.3993440493611778e-01,
2.7793346796113222e-01, 7.6735603850281364e-01,
5.4681951651005178e-01, 3.6275855872448776e-02,
-8.8224410289407154e-02, 3.2821708368951431e-05,
1.7994969189524142e-02, 1.8662128501760204e-03,
-7.8622878632753014e-04, -5.8077443328549205e-05,
3.0932895975646042e-06, 4.0173938067104100e-08)
g1 <- qmf(g0)
return(list(length = L, hpf = list(h1, g1), lpf = list(h0, g0)))
}
select.K6L6 <- function() {
L <- 24
h0 <- c(1.4491207137947255e-09 -3.4673992369566253e-09,
-6.7544152844875963e-06, 1.6157040144070828e-05,
4.0416340595645441e-04, -9.4536696039781878e-04,
-4.2924086033924620e-03, 9.0688042722858742e-03,
1.8690864167884680e-02, -3.7883945370993717e-02,
-2.7337592282061701e-02, 1.3185812419468312e-01,
-2.1034481553730465e-02, -5.9035515013747486e-01,
-7.4361804647499452e-01, -2.5752016951708306e-01,
9.2725410672739983e-02, 4.9100676534870831e-02,
-2.4411085480175867e-02, -1.1190458223944993e-02,
1.7793885751382626e-03, 7.4715940333597059e-04,
-6.2392430013359510e-06, -2.6075498267775052e-06)
h1 <- qmf(h0)
g0 <- c(1.8838569279331431e-08, -1.1000360697229965e-06,
-1.4600820117782769e-05, 1.6936567299204319e-04,
2.6967189953984829e-04, -3.1633669438102655e-03,
-7.2081460313487946e-04, 1.9638595542490079e-02,
-3.0968325940269846e-03, -5.6722348677476261e-02,
5.2260784738219289e-02, 1.2763836788794369e-01,
-2.9566169882112192e-01, -7.6771793937333599e-01,
-5.3818432160802543e-01, -2.4023872575927138e-02,
9.9019132161496132e-02, -1.2059411664071501e-03,
-2.2693488886969308e-02, -1.8724943382560243e-03,
1.7270823778712107e-03, 1.5415480681200776e-04,
-1.1712464100067407e-05, -2.0058075590596196e-07)
g1 <- qmf(g0)
return(list(length = L, hpf = list(-h1, -g1), lpf = list(-h0, -g0)))
}
switch(name,
"k3l3" = select.K3L3(),
"k3l5" = select.K3L5(),
"k4l2" = select.K4L2(),
"k4l4" = select.K4L4(),
"k5l7" = select.K5L7(),
"k6l6" = select.K6L6(),
stop("Invalid selection for hilbert.filter"))
}
########################################################################
phase.shift.hilbert <- function(x, wf) {
coe <- function(g)
sum(0:(length(g)-1) * g^2) / sum(g^2)
J <- length(x) - 1
h0 <- hilbert.filter(wf)\$lpf[[1]]
h1 <- hilbert.filter(wf)\$hpf[[1]]
for(j in 1:J) {
ph <- round(2^(j-1) * (coe(h0) + coe(h1)) - coe(h0), 0)
Nj <- length(x[[j]])
x[[j]] <- c(x[[j]][(ph+1):Nj], x[[j]][1:ph])
}
ph <- round((2^J-1) * coe(h0), 0)
J <- J + 1
x[[J]] <- c(x[[J]][(ph+1):Nj], x[[J]][1:ph])
return(x)
}
########################################################################
modwpt.hilbert <- function(x, wf, n.levels=4, boundary="periodic") {
N <- length(x)
storage.mode(N) <- "integer"
J <- n.levels
if(2^J > N) stop("wavelet transform exceeds sample size in modwpt")
dict <- hilbert.filter(wf)
L <- dict\$length; storage.mode(L) <- "integer"
h0 <- dict\$lpf[[1]] / sqrt(2); storage.mode(h0) <- "double"
g0 <- dict\$lpf[[2]] / sqrt(2); storage.mode(g0) <- "double"
h1 <- dict\$hpf[[1]] / sqrt(2); storage.mode(h1) <- "double"
g1 <- dict\$hpf[[2]] / sqrt(2); storage.mode(g1) <- "double"
y <- vector("list", sum(2^(1:J)))
yn <- length(y)
crystals1 <- rep(1:J, 2^(1:J))
crystals2 <- unlist(apply(as.matrix(2^(1:J) - 1), 1, seq, from=0))
names(y) <- paste("w", crystals1, ".", crystals2, sep="")
W <- V <- numeric(N)
storage.mode(W) <- storage.mode(V) <- "double"
for(j in 1:J) {
## cat(paste("j =", j, fill=T))
index <- 0
jj <- min((1:yn)[crystals1 == j])
for(n in 0:(2^j / 2 - 1)) {
index <- index + 1
if(j > 1)
x <- y[[(1:yn)[crystals1 == j-1][index]]]
else
x <- complex(real=x, imaginary=x)
if(n %% 2 == 0) {
zr <- .C("modwt", as.double(Re(x)), N, as.integer(j), L, h1, h0,
W = W, V = V, PACKAGE="waveslim")[7:8]
zc <- .C("modwt", as.double(Im(x)), N, as.integer(j), L, g1, g0,
W = W, V = V, PACKAGE="waveslim")[7:8]
y[[jj + 2*n + 1]] <- complex(real=zr\$W, imaginary=zc\$W)
y[[jj + 2*n]] <- complex(real=zr\$V, imaginary=zc\$V)
}
else {
zr <- .C("modwt", as.double(Re(x)), N, as.integer(j), L, h1, h0,
W = W, V = V, PACKAGE="waveslim")[7:8]
zc <- .C("modwt", as.double(Im(x)), N, as.integer(j), L, g1, g0,
W = W, V = V, PACKAGE="waveslim")[7:8]
y[[jj + 2*n]] <- complex(real=zr\$W, imaginary=zc\$W)
y[[jj + 2*n + 1 ]] <- complex(real=zr\$V, imaginary=zc\$V)
}
}
}
attr(y, "wavelet") <- wf
return(y)
}
########################################################################
phase.shift.hilbert.packet <- function(x, wf) {
coe <- function(g)
sum(0:(length(g)-1) * g^2) / sum(g^2)
dict <- hilbert.filter(wf)
h0 <- dict\$lpf[[1]]; h1 <- dict\$hpf[[1]]
g0 <- dict\$lpf[[2]]; g1 <- dict\$hpf[[2]]
xn <- length(x)
N <- length(x[[1]])
J <- trunc(log(xn,2))
jbit <- vector("list", xn)
jbit[[1]] <- FALSE; jbit[[2]] <- TRUE
crystals1 <- rep(1:J, 2^(1:J))
for(j in 1:J) {
jj <- min((1:xn)[crystals1 == j])
for(n in 0:(2^j - 1)) {
if(j > 1) {
jp <- min((1:xn)[crystals1 == j-1])
if(n %% 4 == 0 | n %% 4 == 3)
jbit[[jj + n]] <- c(jbit[[jp + floor(n/2)]], FALSE)
else
jbit[[jj + n]] <- c(jbit[[jp + floor(n/2)]], TRUE)
}
Sjn0 <- sum((1 - jbit[[jj + n]]) * 2^(0:(j-1)))
Sjn1 <- sum(jbit[[jj + n]] * 2^(0:(j-1)))
ph <- round(Sjn0 * coe(h0) + Sjn1 * coe(h1), 0)
x[[jj + n]] <- c(x[[jj + n]][(ph+1):N], x[[jj + n]][1:ph])
}
}
return(x)
}
########################################################################
modhwt.coh <- function(x, y, f.length = 0) {
filt <- rep(1, f.length + 1)
filt <- filt / length(filt)
J <- length(x) - 1
coh <- vector("list", J)
for(j in 1:J) {
co.spec <- filter(Re(x[[j]] * Conj(y[[j]])), filt)
quad.spec <- filter(-Im(x[[j]] * Conj(y[[j]])), filt)
x.spec <- filter(Mod(x[[j]])^2, filt)
y.spec <- filter(Mod(y[[j]])^2, filt)
coh[[j]] <- (co.spec^2 + quad.spec^2) / x.spec / y.spec
}
coh
}
########################################################################
modhwt.phase <- function(x, y, f.length = 0) {
filt <- rep(1, f.length + 1)
filt <- filt / length(filt)
J <- length(x) - 1
phase <- vector("list", J)
for(j in 1:J) {
co.spec <- filter(Re(x[[j]] * Conj(y[[j]])), filt)
quad.spec <- filter(-Im(x[[j]] * Conj(y[[j]])), filt)
phase[[j]] <- Arg(co.spec - 1i * quad.spec)
}
phase
}
########################################################################
modhwt.coh.seasonal <- function(x, y, S=10, season=365) {
J <- length(x) - 1
coh <- shat <- vector("list", J)
for(j in 1:J) {
xj <- x[[j]]
yj <- y[[j]]
## Cospectrum
co <- matrix(Re(xj * Conj(yj)), ncol=season, byrow=TRUE)
co.spec <- c(apply(co, 2, mean, na.rm=TRUE))
gamma.c <- my.acf(as.vector(co))
omega.c <- sum(gamma.c[c(1, rep(seq(season+1, S*season, by=season),
each=2))])
quad <- matrix(-Im(xj * Conj(yj)), ncol=season, byrow=TRUE)
omega.q <- sum(gamma.q[c(1, rep(seq(season+1, S*season, by=season),
each=2))])
omega.cq <- sum(gamma.cq[S*season + seq(-S*season+1, S*season, by=season)])
## Autospectrum(X)
autoX <- matrix(Mod(xj)^2, ncol=season, byrow=TRUE)
x.spec <- c(apply(autoX, 2, mean, na.rm=TRUE))
## Autospectrum(Y)
autoY <- matrix(Mod(yj)^2, ncol=season, byrow=TRUE)
y.spec <- c(apply(autoY, 2, mean, na.rm=TRUE))
shat[[j]] <- 4 * (co.spec*omega.c + quad.spec * omega.q +
coh[[j]] <- (co.spec^2 + quad.spec^2) / x.spec / y.spec
}
list(coh = coh, var = shat)
}
########################################################################
modhwt.phase.seasonal <- function(x, y, season=365) {
J <- length(x) - 1
phase <- vector("list", J)
for(j in 1:J) {
co.spec <- Re(x[[j]] * Conj(y[[j]]))
co.spec <- c(apply(matrix(co.spec, ncol=season, byrow=TRUE), 2,
mean, na.rm=TRUE))
| 6,373
| 15,313
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-05
|
latest
|
en
| 0.361385
|
https://www.shaalaa.com/question-bank-solutions/heights-distances-ngers-could-catch-c_4845
| 1,513,409,199,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-51/segments/1512948585297.58/warc/CC-MAIN-20171216065121-20171216091121-00250.warc.gz
| 811,619,799
| 10,353
|
# Solution - Heights and Distances
Account
Register
Share
Books Shortlist
ConceptHeights and Distances
#### Question
A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane
What value is depicted in this question?
#### Solution
You need to to view the solution
Is there an error in this question or solution?
#### Reference Material
Solution for concept: Heights and Distances. For the course CBSE
S
| 170
| 778
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-51
|
latest
|
en
| 0.93976
|
https://medium.com/@mmsbrggr?source=post_internal_links---------2----------------------------
| 1,620,584,158,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-21/segments/1620243989006.71/warc/CC-MAIN-20210509153220-20210509183220-00256.warc.gz
| 410,070,868
| 31,056
|
I am a Ph.D. researcher, enjoying explaining complex things in simple terms || marcelmoos.com || Follow for more: marcelmoos.com/newsletter
# Five Paradoxes With Probabilities That Will Puzzle You
## Or can you outsmart them?
In our daily life, we constantly deal with uncertain situations. So — at least subconsciously — we are confronted with probabilities all the time. Moreover, it seems we have a good intuitive feeling for probabilities. Or do we really?
We know that flipping a coin 100 times will result in about 50 heads and 50 tails. Also, it’s clear to us that the probability of bumping into a friend on holidays abroad is very low, though not zero. However, there are situations when correct predictions following from probability theory are completely counter-intuitive.
Let’s dive into five paradoxes in probability theory…
# Flip a Coin on a Real Quantum Computer in Python
## Generate true randomness with a fun do-it-yourself beginner experiment.
Quantum computers can generate truly random numbers. That’s something a traditional computer cannot do without relying on external sources. Traditional computers can only generate numbers that appear to be random but in reality, are computed according to fixed rules. These numbers are called pseudo-random. If we generate enough of these pseudo-random numbers we will notice that they eventually repeat.
# What Really IS a Matrix Determinant?
## The geometric intuition behind determinants could change how you think about them.
Thinking back to my high-school years, linear algebra was a topic I was particularly fascinated with. It gave me the skill to solve large systems of linear equations and a geometric perspective on the problem making the whole process intuitive.
However, regarding matrix determinants, I was taught that they are numbers for matrices, how to compute them, and not much more. It took until my university courses that I learned the beauty behind determinants.
As soon as I learned about determinants’ geometric meaning, I was wondering why this wasn’t already taught in high school as it is very easy to…
# Run Your Python Code as Fast as C
## How you can supercharge the performance of your python code without changing a thing.
As a PhD researcher, it is crucial for my job to quickly code up an idea to see if it works or not. Python is an excellent tool enabling just that. It allows for focusing on the idea itself and not be bothered with boilerplate code and other tedious things.
However, Python comes with a major drawback: It is much slower than compiled languages like C or C++. So, what do we do after we tested an idea by building a Python prototype and now we want to turn it into a fast and performant tool? Most often than not…
# Monads Are Just Fancy Semicolons
## Monads can be scary — treating them like fancy semicolons makes them fun!
Monads are programmable semicolons. That’s it. For a programmer, a monad provides functions that allow for sequencing actions. Moreover, between every two following actions, a specific code snippet is executed.
So, a monad is a semicolon — but one whose exact behavior you can configure.
# Let’s Take a Step Back and Start Slow
In imperative languages like C or Java, semicolons are used to express a sequence of operations. The code in front of the semicolon is executed before the code after the semicolon. …
# The One-Sentence Proof in Multiple Sentences
Fermat’s theorem on sums of two squares had famously been proven in just one single sentence.
Can prime numbers be written as the sum of two squares? For 13 this is possible (2²+3²), but for example, 3 cannot be written in this way. Pierre de Fermat came up with a theorem on this topic, for which Don Zagier, an American mathematician gave a proof, which astonishingly is just one sentence long.
Numberphile [1] [2] made a great video on the one-sentence proof of Zagier but left out some details. …
# Why knowing the future would crash the economy
## A thought experiment using game theory explains why we mustn’t know our future.
Game theory is a branch of mathematics with a lot of applications. Especially in economics, game theory plays a very important role. That’s the reason why a lot of mathematicians are presented with the Nobel prize in economics. A widely known example is John Forbes Nash, who’s life is illustrated in the movie “A beautiful mind”.
As the name “game theory” suggests, there are some kinds of games involved. In fact “game” is very broadly defined. It means a scenario where two (or more) perfectly rational “players” have to make some kind of decision. The decisions they make determine whether…
Get the Medium app
| 984
| 4,684
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.640625
| 4
|
CC-MAIN-2021-21
|
latest
|
en
| 0.951814
|
https://www.jiskha.com/display.cgi?id=1152049543
| 1,511,389,703,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934806676.57/warc/CC-MAIN-20171122213945-20171122233945-00531.warc.gz
| 833,089,518
| 4,476
|
# graphing!
posted by .
can someone help me?
okay so I am given this :
(a) y= x-4
(b) y=2-x
I have to graph this manually and find the intersection.
okay so I know how to graphi it right with this formula: y=mx+b
okay but is the slope how can you tell and what number is the y intercept
i belive it goes as follows:
(a) m(slope)= 1/1
and b(y intercept)= -4
for b)
m= slope:-1/1
b yintercept: 2
for some reason I think I ma doing something wrong is this right cuz i don't know how to greaph whne they only give me one number????
you appear to be on the right track, I'm not sure what your question is asking.
For (a) y = x - 4 | m = 1 and b = -4 , as you have.
For (b) you might want to rearrange it as
y = -x + 2 | m = -1 and b = 2
Now just graph each line and see where they intersect. The intercept is where the line intersects the y axis and the slope is the change in y over the change in x.
Find the slope and y-intercept.
## Similar Questions
1. ### calculus/graphing calculator help
We were given a worksheet on modifying functions with the equation y=Af(Bx+C)+D. The first function we're given is y1=f(x)= x + x^2 and we're supposed to graph it. Then we're told to graph y2=2f(x), and we're given instructions on …
2. ### Vectors
I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3). a) Find their point of intersection. b) Find a vector equation for the line perpendicular to both of the given lines that passes …
3. ### calculus
a.) Given y=square root of (x) and y= (x) Find the area between two curves from x=0 to x=1 by integrating with respect to x (top-bottom) I'm more concerned about this one though: b.) Now integrate with respect to y given between y=0 …
4. ### Algebra
Questions on piecewise function graphing Obviously I can't get help with the actual graphing here but I am hoping someone can push me in the right direction Problem: f(x) {4, if 0<=x<2} {5, if 2<=x<4} {6, if 4<=x<6} …
5. ### algebra
Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x ≥ 10. 1.describe the meaning of the number 12 in the formula, in terms of its meaning in relation …
6. ### Algebra 2...
On isometric dot paper, graph the system of equations at right. What shape is their intersection?
7. ### General Chem
So for Chem we have to answer a question asking why graphing is a more accurate method for measuring density than manually calculating the density. I originally thought that manually calculating was better, but my teacher told me that …
8. ### Chemistry Graphing
So for Chem we have to answer a question asking why graphing is a more accurate method for measuring density than manually calculating the density. I originally thought that manually calculating was better, but my teacher told me that …
9. ### graphing
I am having tuble with this problem: Graph the line given by the formula y=2x+3. Using the graph, find: The value of y corresponding to the value of x equal to −1; 2; 3; 5 I don't really know how to find the answer can you guys …
10. ### graph linear equations
I have tried going through the TI-84 plus manual that came with my calculator, so that I can graph this linear equation: 3x+4y=-16. I have not been able to graph linear equations. Can someone please tell me how to enter this equation …
More Similar Questions
| 910
| 3,400
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.03125
| 4
|
CC-MAIN-2017-47
|
latest
|
en
| 0.92881
|
http://www.jiskha.com/health/physical_fitness/?page=4
| 1,441,285,398,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2015-35/segments/1440645315227.83/warc/CC-MAIN-20150827031515-00126-ip-10-171-96-226.ec2.internal.warc.gz
| 521,996,478
| 14,980
|
Thursday
September 3, 2015
# Homework Help: Health: Physical Fitness
## Recent Homework Questions About Physical Fitness
How Conceps Develops
Jimmy's mom puts a large-sized serving of peas on Jimmy's plate and a medium-sized serving of peas on her own plate. Jimmy points to his mother's plate and comments that she gave Jimmy more peas than she gave herself. Jimmy is demonstrating _______ knowledge. A. ...
Wednesday, January 14, 2015 by Daniea
Currently doing Math,life science,geography and ph
I am thinking of changing physical science and do business with math,life science,business and geography what career can i pursue?
Monday, January 12, 2015 by Tumi
Currently doing Math,life science,geography and ph
I am thinking of changing physical science and do business with math,life science,business and geography what career can i pursue?
Sunday, January 11, 2015 by Tumi
U.S History
1. Which of these was a precedent that George Washington set? (5 points) a)constitutional amendment process b)formal presidential dinners c)singing of the national anthem d)use of a presidential cabinet 2. "The time for the new election of a citizen to be president of the...
Friday, January 9, 2015 by ~Eun Woo~
Physical Science
An 80.00 kg man playing hockey catches a puck moving at 20 m/s. The man is initially at rest. The man and puck move together after the collision. The puck's mass is 0.16 kg. What is the final velocity? A. 13.6 m/s B. 0.04 m/s C. 1.36 m/s D. 4.0 m/s
Wednesday, January 7, 2015 by jenell
Living a Healthy Life
In a child care setting, physical hazards include A. plant allergens, microorganisms, and arthropods. B. radiation, temperature extremes, and noise. C. climbing stairs, lifting, and jumping in place. D. carbon monoxide, lead, and radon.
Wednesday, January 7, 2015 by Amanda
To run a four-minute mile, excellent physical condition is important. Phrase fragment Dangling modifier (******) Run-on sentence Misplaced modifier Next ones is underlined words so I put * around them *The dog ate the shoe* that was lying on the closet floor. Noun clause ...
Wednesday, January 7, 2015 by bam
Physical Science HELP
What and how do I balance this if it needs to be done? Help please Balance the equation, if necessary, for the reaction between zinc and iodine. Zn + I2 „_ 2ZnI2
Wednesday, January 7, 2015 by tracey
Physical science
a mass of 10g of sodium nitrate is dissolved in 10ml of water at 80 degrees celsius, at what temperature will it start to precipitate?
Tuesday, January 6, 2015 by Abraham
Criminology
Social control theories focus on: A. static aspects of the personality. B. physical features of the social environment. C. the process through which social integration develops. D. causative factors in criminal behavior. I think it's B, but not sure.
Sunday, December 21, 2014 by Pat
physical science
For questions #14 – 16, write an equation for the reaction of magnesium oxide with sodium chloride to produce magnesium chloride and sodium oxide. 14. Show the formulas of the reactants. 15. Show the formulas of the products. 16. Write the balanced the equation for this ...
Saturday, December 20, 2014 by Maria
Physical Science
Balancing Decay Reactions. Fill in the blank with the correct piece to balance the decay equation. 1. (184/74) W (4/2) He + _____ 2. (210/82) Pb______+ (206/80) Hg 3. (35/16) S (0/-1) e + _______ 4. ________ (0/-1) e + (60/28) Ni My work: 5. (...
Friday, December 19, 2014 by DFD
P.E
1. One of your friends plays video games for at least six hours each day and gets upset when he has to eat dinner with his family. This is a sign of? a. An anxiety disorder. b. A phobia c. Bipolar disorder d. An impulse-control disorder 2. A phobia is an example of a(n) a. An ...
Thursday, December 18, 2014 by 65789
Physical Education
Wednesday, December 17, 2014 by lol
History
What Physical Feature of the New World's Coastline greatly attracted European Colonits A.Offshore islands B.Fertile soil along high moutain cliffs C.Natural harbors along the Atlantic Coast D.Large lakes along the coastline D?
Tuesday, December 16, 2014 by M
History
What physical feature especially attracted European colonists? A.Many offshore islands B.Fertile soil along high mountain cliffs C.Natural harbors along Atlantic Ocean D.Large lakes located along the coastline
Tuesday, December 16, 2014 by M
P.E
1. One of your friends plays video games for at least six hours each day and gets upset when he has to eat dinner with his family. This is a sign of? a. An anxiety disorder. b. A phobia c. Bipolar disorder d. An impulse-control disorder 2. A phobia is an example of a(n) a. An...
Tuesday, December 16, 2014 by 36595
chemistry
If your car gets 21.4 mpg, how many L of CO2, will you release into the atmosphere, if you drove the 1280miles from Towson University to Key West Florida for a much needed break after taking Chemistry 121? Assume 1.05atm and 17.0C. What would your carbon load be in lbs (lbs of...
Monday, December 15, 2014 by jessica
chemistry
If your car gets 21.4 mpg, how many L of CO2, will you release into the atmosphere, if you drove the 1280miles from Towson University to key West Florida for a much needed break after taking Chemistry 121? Assume 1.05atm and 17.0C. What would your carbon load be in lbs (lbs of...
Monday, December 15, 2014 by Nancy
chemistry
If your car gets 21.4 mpg, how many L of CO2, will you release into the atmosphere, if you drove the 1280miles from Towson University to key West Florida for a much needed break after taking Chemistry 121? Assume 1.05atm and 17.0C. What would your carbon load be in lbs (lbs of...
Monday, December 15, 2014 by Anonymous
Physical science
What is the formula of magnesium sulfate and ammonia? My work:MgSO4 + 2NH4OH --> (NH4)2SO4 + Mg(OH)2 Correct/Balance the equation below. MgSO4 + NH4OH → (NH4)2SO4 + Mg(OH)2
Monday, December 15, 2014 by DFD
Chemistry
Which of the following is an example of quantization? A. The amount of time spent in a classroom B. The number of students in a classroom C. Learning happening in a classroom D. The temperature range in a classroom I know I asked this question but I would this paragraph. Is it...
Sunday, December 14, 2014 by Morgan
physical
A ball of mass m=8.5, at one end of a string of length L=3.6, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball at the bottom of the circle is:
Friday, December 12, 2014 by Anonymous
physical
The potential energy of a 2.0-kg particle moving along the x axis is given by U(x) = 5.0 x^2. When the particle is at x = 1.0 m it is traveling in the positive x direction with a speed of 1.5 m/s. It next stops momentarily to turn around at x =
Friday, December 12, 2014 by Anonymous
Science
Pure gold can be fashioned into elaborate masks and thin plates that can be incorporated into clothing.what physical trait of metal doea this demosnstrate
Friday, December 12, 2014 by Luz
Literature
I need some help with some literature questions based on this passage: From the winter of 1821, . . . I had what might truly be called an object in life; to be a reformer of the world. My conception of my own happiness was entirely identified with this object. The personal ...
Thursday, December 11, 2014 by Lilly G.
health
Which of the following statements is CORRECT regarding deciding whether an alcohol sale is legal? A. IF a person looks over 21, they likely are. B. Few minors have physical characteristics of an adult. C. if a person looks like a minor, they likely are a minor. D. signs of ...
Thursday, December 11, 2014 by jay
Physical Science
Fill in the blanks using the correct term from the list below. Active Combustion free heating systems passive heat pump thermal energy stroke 1. A house with large windows on its south side and few windows on its other sides probably uses a(n) Blank solar heating system. 2....
Wednesday, December 10, 2014 by Lindsey
Introductory to Physical Science
A student drops a stopper into 50.0mL of water and the level rises to to 56.1mL. If she submerges the same stopper into a cylinder of thick syrup, what will happen to the syrup? a.) it will rise 6.1mL b.) it will rise less than 6.1mL c.) it will rise greater than 6.1mL d.) it...
Tuesday, December 9, 2014 by Anthony
Physical Science
What is the temperature of oxygen that boils at negative 183 Celsius?
Tuesday, December 9, 2014 by Kristina
Geography
I have an essay that says.. "It has been said that Eastern Europe is a political region more than a physical region. Would you agree or disagree with this statement? You must provide a solid argument for your position." since it asks me for my opinion how do I write ...
Monday, December 8, 2014 by Elena
physical
Baseball of 0.15 kg is thrown upward at an initial velocity of 35 m/s. tow second later a 20 g bullet is fired at 250 m/s into the rising baseball . how high will the combined bullet and baseball rise.
Saturday, December 6, 2014 by mohamed
Psychology
Sexual dimorphism's are a) observable physical differences within single gender (e.g. tall men vs short men.) b) observable physical differences between the genders (e.g differences in mens and women's brains) c) assumed differences in the capacities of the genders (e....
Thursday, December 4, 2014 by Macy
some animals, but not humans have an organ called a gizzard located near the top of their digestive tract. this organ is small and can contain small rocks. it also has thick muscular walls. based on this physical description which of the following is most likely to be the ...
Thursday, December 4, 2014 by ashley
physical chemistry
A solution is prepared by adding 1g of sugar mannitol (MW 182.2g/g-mole) in 100g of water at 20◦C. (a) Assuming that mannitol and water form an ideal solution, what is the equilibrium vapor pressure of solution? The vapor pressure of pure water is 17.54mmHg at 20◦C
Wednesday, December 3, 2014 by JP
ENGLISH
Love is a surgeon. Love can cut into your flesh like a scalpel Love can operate upon your heart Love can circumcise you Perhaps you don't believe it But i know. Love operates Upon your skin, your hair, your gait For Love there is no remedy Except the surgeon's scalpel...
Wednesday, December 3, 2014 by Yeng
Corrections
Prisoners who petition that their civil rights have been violated most frequently cite all of the following concerns except a. due process. b. inadequate medical treatment. c. physical security. d. ineffective assistance of counsel. im confused between B and D
Monday, December 1, 2014 by Amy
Differential equations in Calculus...plsssss help?
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 by Bridget
Physical Science
Complete and balance the equation for the following single-replacement reactions. (Use the lowest possible coefficients. Omit states-of-matter from your answer.) Ni + Cu(NO3)2(aq)-->
Sunday, November 30, 2014 by Darrel
Calculus with Diffrential Equations: Pleease help?
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 by Bridget
Calculus
Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does ...
Sunday, November 30, 2014 by Bridget
Physical Education
What traditions have grown around baseball?
Sunday, November 30, 2014 by Just Wondering
Chemistry
please help! I don't understand any of this. Using the Solubility Rules, write the balanced molecular, total ionic, and net ionic equations (including physical states) for the following: Hints: There is no such thing as an Na3+. Na is in group 1A, so you know it can only ...
Wednesday, November 26, 2014 by Kate
Chemistry
1. Write a balanced molecular equation for the reaction of solid AgNO3 with aqueous NaCl. Be sure to include the correct number of coefficients and the state of the species (aq, s, l or g). 2. Write the total ionic equation for this reaction, including all physical states. 3. ...
Wednesday, November 26, 2014 by Jess
Health And Physical Ed
true or false the main process for digestion takes place in the stomach true false*** regular excersise stimulates_____which keeps the skeletal muscles moving to assist in digestion and excretion. peristalis ures digestion*** villi the main process of excretion takes place in ...
Sunday, November 23, 2014 by health/ pe CHECK ANSWERS
Health And Physical Ed
1. during the exchange of air in your lungs, oxygen is being taken into your bloodstream while this substance is being released microorganisms carbon dioxide*** plasma mucus 2. the gas exchange of oxygen to the bloodstream takes place in what part of respiratory system? ...
Sunday, November 23, 2014 by health/ pe CHECK ANSWERS
physical chemistry
Please prepare 0.5L of 1.2M HCl in 50% (v/v) aqueous methanol. The details of HCl are as follows: Hydrochloric acid: Purity : 36%-38% Density : 1.18g/mL Physical state : liquid Molecular weight : 36.42 g/mol Describe the procedures and apparatus you need to use for the ...
Saturday, November 22, 2014 by elvy
Living a Healthy Life
Some child psychologists have concluded that _______ is the strongest predictor of both scholastic and career achievement. A. respect for authority B. inherited intelligence C. emotional well-being D. physical illness C.
Friday, November 21, 2014 by Amanda
Living a Healthy Life
A child who has to struggle to climb into a chair is confronting a(n) _______ hazard. A. environmental B. biological C. physical D. ergonomic C.
Friday, November 21, 2014 by Amanda
Foundation of a Healthy Lifestyle
One reason early childhood education centers have become increasingly important providers of health education is that A. younger, healthier teachers and classroom aides have emerged. B. schools are more sanitary than 70 percent of home environments. C. working parents are ...
Thursday, November 20, 2014 by Amanda
Foundation of a Healthy Lifestyle
A strategy for health promotion among infants, toddlers, and young children focuses on educational programs, physical fitness, activities, and A. tobacco, alcohol, and drug use. B. family planning. C. nutrition. D. mental health and mental disorders. C.
Thursday, November 20, 2014 by Amanda
Foundation of a Healthy Lifestyle
Neuron development and elaboration, which occurs between birth and age 10, is prompted by A. intake of foods rich in vitamins and minerals. B. physical movement on the part of the child. C. aural prompts from the family, school, and environment. D. exposures to different ...
Thursday, November 20, 2014 by Amanda
Foundation of a Healthy Lifestyle
which of the following are the three major types of knowledge identified by Piaget? A. Linguistic, physiological, and arithmetical B. Physical, logicalmathematical, and social C. Micro, meso, and exo D. Subjective, objective, and hyperconscious B.
Thursday, November 20, 2014 by Amanda
Foundation of a Healthy Lifestyle
What are the three main factors in a readiness model? A. Maturation, learning, and motivation B. Psychological, social, and physical C. Age, intelligence, and agility D. Height, weight, and age A.
Thursday, November 20, 2014 by Amanda
English HELP!
The Americans with Disabilities Act claims that "The continuing existence of unfair and unnecessary discrimination and prejudice denies people with disabilities the opportunity to compete on an equal basis." Why do the authors include Part 4 in this section? How is ...
Wednesday, November 19, 2014 by school lover
child developement
compare 3 children 4 years, 18 months, 10 years to physical or cognitive growth
Wednesday, November 19, 2014 by Anonymous
physical science
A 3Kg bar of aluminum has to be heated form 25 degreesC to 75 degreesC . how many calories are needed to achieve this temperature increase?
Tuesday, November 18, 2014 by kimberly
Physical Education
Your body can get antibodies from? A. Immunizations. B. Being exposed to the virus or antibody and having your immune system make it. C. None of the above D. All of the above D? I don't know though becuase All of the above is under none of the above. Im really confused.
Tuesday, November 18, 2014 by Callie
physical
What is the value of the normal force if the coefficient of kinetic friction is 0.22 and the kinetic frictional force is 40 newtons?
Monday, November 17, 2014 by Anonymous
Will someone please check my answers as I need lots of help in science. 1. Which of the following is an example of matter? A. leaves B. shadow C. light from the sun* D. sound 2. Which of the following is an example of a chemical property of matter? A. ability to melt B. ...
Monday, November 17, 2014 by Haley
physical education
A 1kg ball is tossed straight up with a kinetic energy of 196J. How high does it go.
Sunday, November 16, 2014 by melina
statistics
A Coach found the correlation between physical fitness and athletic ability to be r=.65. the mean and standard deviation of the physical fitness test was 330, 50. the mean and standard deviation of the athletic ability test was 9, 2. If you have a physical fitness score of 350...
Sunday, November 16, 2014 by Nicole
Physical science
A car accelerates at 1.6m.sec along a straight road for 10s then moves at a constant speed for 20s calculate speed after the first 10s
Saturday, November 15, 2014 by Jeniffer
Physical science
A-b is 50m and b-c is 120 determine the displacement from a-c
Saturday, November 15, 2014 by Refiloe
Physical science
A-b is 50m and b-c is 120 calculate how long it will take to ride fro A to C as he rides at 5m per sec?
Saturday, November 15, 2014 by Happy
Physical science
A-b is 50m and b-c is 120 calculate the total distance
Saturday, November 15, 2014 by Lesedi
physical
help the positions of two particles A and B are P1 (3,4) in meters and P2 ( -3, -4 ) meters respectively. Meters the position A with respect to B is:
Friday, November 14, 2014 by David
Science Help!
Johhny left a glass of milk on his bedside table for a week, and it spoiled. At the end of the week, the glass contained a yellow liquid with white chunks, and there was a terrible odor. What can be concluded? A. The milk has undergone a physical change. B. The mass of the ...
Friday, November 14, 2014 by Callie
Health And Physical Ed
The best thing to put on severe sunburn to help relieve the pain is>
Friday, November 14, 2014 by Branden
Physical science
consider a flat square coil with 10 turns. The coil is 1m wide on each side and has a magnetic field of 1,0T passing through it. The plane of the coil is perpendicular to the magnetic field: the field points out of the page. Use faraday's law to calculate the induced emf, ...
Thursday, November 13, 2014 by Promise
Biochem
Thursday, November 13, 2014 by Pop
Early Childhood
When a teacher does NOT allow a girl to participate in a physical education class because she is dressed in a skirt, the teacher is contributing to: a. cultural difference b. gender inequity c. differential treatment d. sexism Think it may be (b) because of the unequal ...
Tuesday, November 11, 2014 by Anonymous
Physical Science
The sun's energy melts part of a glacier of ice at 0 degrees Celsius. The sun supplies 880 kilocalories to a big glacier of ice at 0 degrees Celsius. How many kilograms of ice will melt into liquid water at 0 degrees Celsius?
Tuesday, November 11, 2014 by Anonymous
Psychology
1. Which of the following is NOT an empirical question? A. Are women more talkative than men? B. Is dieting an effective weight loss strategy? C. Should we prohibit cell phone use while driving? D. Does cognitive psychotherapy help depressed people? 2. The tendency to notice ...
Physical Science
You supply 400 kilocalories of heat energy to a block of ice, with a mass of 14 kg. What will be the outcome?
Monday, November 10, 2014 by Bonni
Physical Science
The sun's energy melts part of a glacier of ice at 0 degrees Celsius. The sun supplies 880 kilocalories to a big glacier of ice at 0 degrees Celsius. How many kilograms of ice will melt into liquid water at 0 degrees Celsius?
Monday, November 10, 2014 by Bonni
creative writing
1. Poetry that is short in length and focuses on feelings and thoughts of the speaker or narrator is called:(Points : 3) narrative lyric a ballad a haiku 2. What is the rhyme scheme of most limericks?(Points : 3) AABBA ABBBA ABCABC AAAAB 3. Which is true about most narrative ...
Sunday, November 9, 2014 by 2phoneeeeee
physical science
Sophia exerts a steady 40-N horizontal force on a 8-kg box resting on a lab bench. The box slides against a horizontal friction force of 24 N. Show that the box accelerates at 2 m/s2.
Sunday, November 9, 2014 by alex
physical science
John is using a pulley to lift the sail on his sailboat. The sail weighs 150 N, and he must lift it 4.0 m. A. How much work must be done on the sail? B. If the pulley is 50% efficient, how much work must John do on the rope to lift the sail?
Thursday, November 6, 2014 by Aurora Simmons
physical science
A river does 6,500 j of work on a water wheel every second. The wheel efficiency is 12%. A. How much work in joules can the axle of the wheel do? B. What is the power output of the wheel in 1 s?
Thursday, November 6, 2014 by Aurora Simmons
physical science
A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4.25 m/s. But 3.2 s later, at the bottom of the slope it's speed is 22.75 m/s what is its average acceleration
Thursday, November 6, 2014 by Gracie
physical science
Calculate the kinetic or potential energy in joules for each of the following situations: A. A 2.5 kg book is held 2.0 m above the ground. B. A 15 g snowball is moving through the air at 3.5 m/s. C. A 35 kg child is sitting at the top of a slide that is 3.5 m above the ground...
Thursday, November 6, 2014 by Aurora Simmons
physical science
What is the kinetic energy of a 0.02 kg bullet that is traveling 300 m/s? Express your answer in joules.
Thursday, November 6, 2014 by Aurora Simmons
Science HELP
Sodium is a metal and chlorine is a poisonous gas. Neither is safe to eat. However, when sodium and chlorine combine, it produces edible table salt. What can be concluded? A. Table salt has similar physical properties of both reactants. B. Table salt is a metalloid with ...
Thursday, November 6, 2014 by Callie
Health and Physical Education 8 - It's urgent!
Please check my answers because I need to do good at this. 1. When consuming fats the healthiest choice is foods high in? A. saturated fats B. unsaturated fats * C. trans fat D. cholesterol 2. The body's main energy source should come from what essential nutrient? A. ...
Thursday, November 6, 2014 by Dominique
The family was poor. It was "poor but proud." The confused boy grew up thinking one should be proud of being poor. One of the in-laws slipped around occasionally and made liquor. He had plenty of cash, did not read books, and was tolerated but not admired. A cousin ...
Thursday, November 6, 2014 by 2phoneeeeee
Physical Education 8A
Will someone please check my answers? I starred my answers. 1. A person who does not recognize the signs of mental illness may not know he needs help. A. True* B. False 2. Which of the following is not a sign of psychotherapy? A. insight B. cognitive* C. medications D. group 3...
stats
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Between what times ...
Tuesday, November 4, 2014 by elenore
physical eduaction
Which of the following does NOT describe the concept of Growth? (Points : 1) a. measured quantitatively b. physical change c.influenced by children’s abilities d. increase in bone size
Monday, November 3, 2014 by ashley
physical science check asap
1. Tommy performed an experiment to test the solubility of sodium chloride in water. After he completed his experiment, he discovered that he had a few unused grams of NaCl leftover in a beaker. What should he do with the excess NaCl? A. Pour the excess back into the original ...
Monday, November 3, 2014 by Anonymous
physical science
1. Tommy performed an experiment to test the solubility of sodium chloride in water. After he completed his experiment, he discovered that he had a few unused grams of NaCl leftover in a beaker. What should he do with the excess NaCl? A. Pour the excess back into the original...
Monday, November 3, 2014 by Anonymous
essay edit
Can someone look over this? I've been working on wordiness, sentence structure, and repetition. Tangled and its Hidden Critique of Rapunzel Peeking at the mere surface of the film Tangled (2010) directed by Nathan Greno and Brian Howard, most would presume that it is ...
Sunday, November 2, 2014 by christine
essay excerpt edit
can someone edit this? To contrast, in the film Tangled (2010) the mother of Rapunzel, who is exhibited as a Queen, also falls ill, although it is due to legitimate medical ailments, as opposed to a sense of helplessness. She is then limited to a bedridden state while pregnant...
Sunday, November 2, 2014 by christine
physical eduaction
what can potentially have the most impact on physical education outcomes other than class size? a .type of equipment used b. amount of equipment available c. attitude of the classroom teacher d. lack of funding for equipment
Saturday, November 1, 2014 by ashley
physical science
A gold bar has a mass of 250 grams and is heated from 25 degrees Celsius to 55 degrees Celsius. How much heat did the gold bar absorb? The specific heat of gold is 0.13J/g*degrees C.
Saturday, November 1, 2014 by staci
statistics
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 37 and a standard deviation of 3. Using the empirical rule (as presented...
Friday, October 31, 2014 by Huong Nguyen
Physical sciences
The meaning of the term SPECIFIC HEAT CAPACITY for a substance
Friday, October 31, 2014 by Masilo malatji
Health
What is physical stress? A. A physical reaction to the heart to various triggers B. A physical reaction of the body to various triggers C. A physical reaction of the soul to various triggers D. A physical reaction of the mind to various triggers B
Thursday, October 30, 2014 by Night
The practice of working with school age children
Which of the following sets standards for physical environments to be accessible and appropriate for children with special needs? A. SACERS B. SRTS C. ADA D. WIA C.
Wednesday, October 29, 2014 by Amanda
The practice of working with school age children
When planning outdoor games, a caregiver should develop a wide selection of choices because A. the children have already played the most popular games at school. B. some games go out of date and can't be used. C. a caregiver should be in good physical condition before ...
Wednesday, October 29, 2014 by Amanda
Members
| 6,992
| 27,782
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.515625
| 3
|
CC-MAIN-2015-35
|
longest
|
en
| 0.939327
|
https://slidetodoc.com/chapter-26-electricity-and-magnetism-electric-field-continuous/
| 1,624,415,312,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-25/segments/1623488528979.69/warc/CC-MAIN-20210623011557-20210623041557-00524.warc.gz
| 463,698,348
| 10,414
|
# Chapter 26 Electricity and Magnetism Electric Field Continuous
• Slides: 34
Download presentation
Chapter 26 Electricity and Magnetism Electric Field: Continuous Charge Distribution 1
Find electric field at point P. Continuous Charge Distribution P 2
Electric Field: Continuous Charge Distribution Electric field In this situation, the system of charges can be modeled as continuous The system of closely spaced charges is equivalent to a total charge that is continuously distributed along some line, over some surface, or throughout some volume 3
Electric Field: Continuous Charge Distribution The total electric charge is Q. What is the electric field at point P ? P P linear volume Q P Q surface Q 4
Continuous Charge Distribution: Charge Density The total electric charge is Q. Volume V Linear, length L Amount of charge in a small volume dl: Q Linear charge density Q Amount of charge in a small volume d. V: Volume charge density Surface, area A Q Amount of charge in a small volume d. A: Surface charge density 5
Electric Field: Continuous Charge Distribution Procedure: – Divide the charge distribution into small elements, each of which contains Δq – Calculate the electric field due to one of these elements at point P – Evaluate the total field by summing the contributions of all the charge elements Symmetry: take advantage of any symmetry to simplify calculations For the individual charge elements Because the charge distribution is continuous 6
Electric Field: Symmetry no symmetry 7
Electric Field: Symmetry Electric field The symmetry gives us the direction of resultant electric field 8
Electric Field: Continuous Charge Distribution What is the electric field at point P ? - linear charge density 9
What is the electric field at point P ? - linear charge density 1. Symmetry determines the direction of the electric field. 10
What is the electric field at point P ? - linear charge density 2. Divide the charge distribution into small elements, each of which contains Δq 11
What is the electric field at point P ? - linear charge density 3. Evaluate the total field by summing the contributions of all the charge elements Δq Replace Sum by Integral 12
What is the electric field at point P ? - linear charge density 4. Evaluate the integral 13
14
What is the electric field at point P ? - linear charge density From symmetry Replace the Sum by Integral 15
What is the electric field at point P ? - surface charge density 1. Symmetry determines the direction of the electric field. 16
What is the electric field at point P ? - surface charge density 2. Divide the charge distribution into small elements, each of which contains Δq 3. Evaluate the total field by summing the contributions of all the charge elements Δq Approach A: straightforward at point (x, y) 17
Approach A What is the electric field at point P ? - surface charge density Replace the Sum by Integral at point 18
Approach A What is the electric field at point P ? - surface charge density Evaluate the Integral at point 19
Approach B What is the electric field at point P ? - surface charge density Linear density of the ring Charge of the ring Ring of width Length of the ring 20
21
22
Electric Field: Symmetry no symmetry 23
24
no symmetry, but we know and 25
26
no symmetry Ø We do not know the direction of electric field at point P Ø We need to find x and y component of electric field Then 27
no symmetry Ø We do not know the direction of electric field at point P Ø We need to find x and y component of electric field the symmetry tells us that one of the component is 0, so we do not need 28 to calculate it.
Important Example Find electric field 29
Important Example Find electric field 30
Important Example 31
Motion of Charged Particle 32
Motion of Charged Particle • When a charged particle is placed in an electric field, it experiences an electrical force • If this is the only force on the particle, it must be the net force • The net force will cause the particle to accelerate according to Newton’s second law - Coulomb’s law - Newton’s second law 33
Motion of Charged Particle What is the final velocity? - Coulomb’s law - Newton’s second law Motion in x – with constant velocity Motion in x – with constant acceleration - travel time After time t the velocity in y direction becomes then 34
| 919
| 4,334
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.875
| 4
|
CC-MAIN-2021-25
|
latest
|
en
| 0.881201
|
https://catalog.dmacc.edu/preview_course_nopop.php?catoid=12&coid=12634
| 1,563,735,333,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-30/segments/1563195527089.77/warc/CC-MAIN-20190721164644-20190721190644-00058.warc.gz
| 343,958,714
| 9,929
|
Jul 21, 2019
2018-2019 Course Catalog
2019-2020 Course Catalog 2018-2019 Student Handbook 2018-2019 Course Catalog [ARCHIVED CATALOG] 2017-2018 Course Catalog [ARCHIVED CATALOG] 2016-2017 Course Catalog [ARCHIVED CATALOG] 2015-2016 Course Catalog [ARCHIVED CATALOG] 2014-2015 Course Catalog [ARCHIVED CATALOG] 2013-2014 Course Catalog [ARCHIVED CATALOG] 2017-2018 Student Handbook [ARCHIVED CATALOG]
HELP 2018-2019 Course Catalog [ARCHIVED CATALOG] Print-Friendly Page [Add to Portfolio]
# MAT 114 - Elementary Educators Math I
Credits: 3
Lecture Hours: 2
Lab Hours: 2
Practicum Hours: 0
Work Experience: 0
Course Type: Core
This is the first of two courses focusing on math concepts taught in K-6. Topics will be covered from both a practical and theoretical standpoint, with an emphasis on practical understanding using concrete examples. Course content includes problem-solving, systems of whole numbers, numeration, algorithms for computation, topics from number theory, and topics from geometry including measurement, polygons, polyhedra, congruence and transformations. This course is for students in education fields and is not appropriate for students majoring in other areas. This is not a methods course.
Prerequisite: Minimum ALEKS scores of 46% or MAT 073 with a C- or better
Competencies
1. Apply integrated mathematical problem-solving strategies such as Polya’s method to solve problems from within and outside of mathematics
1. Solve problems including but not limited to inductive reasoning, deductive reasoning, and basic set operations by applying and adapting a variety of appropriate strategies
2. Model problem situations with objects
3. Use representations such as graphs, tables, and equations to draw conclusions
4. Build new mathematical knowledge through problem solving
5. Reflect on the process of mathematical problem solving
6. Analyze the mathematical thinking and strategies of others
7. Use the language of mathematics to express mathematical ideas precisely
8. Analyze the structure of numeration systems
9. Understand ways of representing numbers
10. Use multiple models to develop understanding of place value
11. Analyze non-decimal numeration systems
2. Comprehend the processes used by children to compute fluently and make reasonable estimates with whole numbers and extend them to non-decimal systems
1. Develop the meanings of operations and how they relate to one another
2. Illustrate general principles and properties of whole numbers such as commutatively using models and mathematical notation
3. apply standard and student developed algorithms for additions, subtraction, multiplication, and division
4. Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tool
3. Develop number theory concepts
1. Investigate prime and composite numbers
2. Investigate divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10.
3. Discover patterns in Pascal’s triangle
4. Apply geometric properties and relationships in real-word and mathematical problem solving
1. Describe geometric terms including point, line, plane, space, ray, line segment, angle, parallel lines, perpendicular lines, skew lines, and transversals
2. Analyze characteristics and properties of 2-dimensional geometric shapes developing mathematical arguments about geometric relationships using models where appropriate
3. Measure lengths using non-standard units, the metric system, and the customary system
4. Convert from one unit of measurement to another within the same system
5. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations
6. Represent translations, reflections, rotations, and dilations of objects in a plane by using sketches
7. Draw tessellations
8. Draw geometric objects
9. Build geometric objects including polyhedra
| 865
| 3,972
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.03125
| 3
|
CC-MAIN-2019-30
|
latest
|
en
| 0.830688
|
https://www.nycitylib.com/pdf/418181/honors-pre-calculus-midterm-exam-review-name:-january-2014-
| 1,563,676,540,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-30/segments/1563195526818.17/warc/CC-MAIN-20190721020230-20190721042230-00279.warc.gz
| 772,223,328
| 14,967
|
# Honors Pre-Calculus Midterm Exam Review Name: January 2014
0%
Honors Pre-Calculus Midterm Exam Review Name: January 2014 Chapter 1: Functions and Their Graphs 1.Evaluate the function at each specified value of the independent variable and simplify.
### Other related documents
Honors Pre-Calculus Midterm Exam Review Name: January 2014 ...
Honors Pre-Calculus Midterm Exam Review Name: January 2014 Chapter 1: Functions and Their Graphs 1.Evaluate the function at each specified value of the independent variable and simplify.
AP Calculus BC MIDTERM EXAM REVIEW #2 NO GRAPHING ...
ap calculus bc midterm exam review #2 multiple choice – no graphing calculator – show work and fill in scantron. 1. 2. 3. 4.
Name: Honors Modern World History MIDTERM EXAM REVIEW
Name: _____ Honors Modern World History MIDTERM EXAM REVIEW Directions: Complete all parts of this review guide in order to review information for your midterm exam on _____. Test Format: • Multiple Choice Section: 80 Questions for 1 point each
Geometry Honors Midterm Exam 2010-2011 (REVIEW) - Quia
____ 51. State whether 'ABC and 'AED are congruent. Justify your answer. a. yes, by SSS only b. yes, by either SSS or SAS c. yes, by SAS only d. No; there is not enough information to conclude that the triangles are congruent.
Honors Biology Midterm Exam Study Guide 2018 Midterm Exam ...
Honors Biology Midterm Exam Study Guide 2018 Midterm Exam Date = _____ An entire semester is just about done. So, what did you learn? What did you struggle with? No one has unlimited time, so knowing the answer to these questions is necessary to study efficiently and be successful.
MMW 14 Chang Track Fall 2014 Midterm Exam Review Guide ...
MMW 14 Chang Track Fall 2014 Midterm Exam Review Guide (This is meant to be a review guide, not the exam itself. Ultimately, you are accountable for all the key materials in the readings and lectures.) REVIEW SESSION: Tuesday, Nov. 11 from 8:00 to 9:00 pm in Asante 123 A/D Exam will be designed for 1 hour 20 minutes (PLEASE REMEMBER TO BRING AN ...
Vector Calculus (MATH 20E) Fall 2014 Midterm 1 Solutions ...
Vector Calculus (MATH 20E) Fall 2014 Midterm 1 Solutions (Version A) 1. (10 points) Let f(x;y) = exy. (a) Find the tangent plane to the surface given by the graph of the function z = f(x;y) at the
AP CALCULUS AB MIDTERM EXAM STUDY GUIDE
AP CALCULUS AB - MIDTERM EXAM STUDY GUIDE Below are topics and corresponding problems that you will be responsible for knowing on your midterm exam. It is important to understand that this is not an exhaustive list and you should also review your notes and homework problems.
Honors Biology – Midterm Exam 2015-2016
Honors Biology – Midterm Exam 2015-2016 Midterm Review Questions Disclaimer: This is by no means a comprehensive review and SHOULD NOT be used as a standalone review guide. Students should reference their notebook (notes, labs, homework assignments, quizzes) as well as their textbook for a more thorough review.
AP Calculus BC MidTerm Review - Yola
If the base b of a triangle is Increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 Inches per minute which of the following must be tme about the area A of ... AP Calculus BC MidTerm Review.jnt Author:
Honors Chemistry Midterm: Review Packet
10. Write the names of the following ionic and molecular compounds Name Formula Pb 3 (PO 4) 2 KMnO 4 O 2 F 5 ZnSO 4 MgO PSe 2 11. a) The molar mass of Ba(NO
GEOMETRY HONORS MIDTERM REVIEW - Mathorama
GEOMETRY HONORS MIDTERM REVIEW 1. In ∆ABC, BA BC.áCBD is an exterior angle of ∆ABC.What do you know about the other angles. 2. Find the length of NP. MQ = 70, MN = 10, MN=NO, and OP = PQ.
AP Calculus AB Midterm Review Questions – Answer Key
AP Calculus AB Midterm Review Questions – Answer Key 1. a) x 1 fx'() changes from negative to positive at b) x 5 changes from positive to negative at c) ( 7, 3) (2,3) (3,5) 1: (- these are the intervals where the slope of is negative d) x 7 An absolute minimum must occur at either a critical number or
Regents & Honors Chemistry Midterm Review Worksheet
Regents & Honors Chemistry Name_____ Midterm Review Worksheet Bring calculator, pencils, and this completed worksheet to the midterm exam. 1 For problems involving an equation, carry out the following steps: 1.
Name Date Per Honors Biology Midterm Review Chemistry
What does “CHONPS” stand for? How does this acronym relate to macromolecules and organic/biochemistry? 5. What does it mean to say that water is a polar molecule? Draw a diagram of water to illustrate the polar nature. While you’re at it, label the polar covalent and
Math 405 Midterm Exam 1 | Mar. 5, 2014
Math 405, Fall 2014 Midterm Exam 1 | Mar. 5, 2014 Page 1 of 5 1.Determine whether the following statements are true or false. Justify your answer (i.e., prove the claim, derive a contradiction or give a counter-example). (a)(10 points) If A ˆB, and B is countable, then A is countable.
MAT 111 Exam Review Questions Midterm Exam (#1
Find a cofunction with the same value as the given expression. 8) cos 11 ° Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 9) cot 0.1433 Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round your answer to the nearest whole number. 10 ...
AST 1002 Fall 2014 Midterm Exam Version 1 MULTIPLE CHOICE ...
23)In essence, the nebular theory holds that _____. A)the planets each formed from the collapse of its own separate nebula B)nebulae are clouds of gas and dust in space C)The nebular theory is a discarded idea that imagined planets forming as a result of a near-collision between our Sun and another star.
Review for Midterm Exam Trigonometry!
Review for Midterm Exam – Trigonometry! 1. What is 600q converted to radians in terms of S? (a) 11 6 S (b) 10 3 S (c) 5 3 S (d) 10 6 S 2. In a circle, a central angle whose measure is 2 S radians intercepts an arc whose length is 3 2 S centimeters. How many centimeters are in the radius of the circle? (a) 1 cm (b) 2 cm (c) 4 cm (d) 3 cm 3.
Review for Algebra 1 Midterm Exam
Review for Algebra 1 Midterm Exam Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Use the vertical line test to determine which of the following relations is a function. a. c. b. d. ____ 2. Evaluate f x = − 2x − 5 for x = 3.
MMW 13 Chang Track Spring 2014 Second Midterm Review Guide ...
MMW 13 Chang Track Spring 2014 Second Midterm Review Guide (This is meant to be a review guide, not the exam itself. Ultimately, you are accountable for all the key materials in the readings and lectures.) Exam will consist of multiple choice questions. You will have 50 minutes to complete the exam, BUT…
AP Biology: Midterm Exam Review Questions
SUGGESTED ANSWERS to AP Biology: Midterm Exam Review Questions (pp. 10-12) Evolution 1. Antibiotic resistance according to Darwin (Theory of Natural Selection): the bacteria in a group that are already naturally resistant to the antibiotic will survive and pass on the ability to be antibiotic resistant so OVER TIME there will be more
Midterm Exam Review Guide ans - bcsoh.org
Physical)Science)MidtermReview)))))Name_____Class:) 9. What)is)the)systemcalled)that)scientists)have)as)a)set)of)measuring)units?))
Algebra 2 – Midterm Exam Review by Topic
Algebra 2 – Midterm Exam Review by Topic Solving Linear Equations and Inequalities o Solving Equations o Absolute value – get the absolute value part by itself first (no distributing! Can’t touch the absolute value!) (#2) Set 2 equations – one is regular, the second one has a NEGATIVE
Midterm Exam Review English 2 Mrs. McCoid BAD BOY
1 Midterm Exam Review English 2 Mrs. McCoid BAD BOY These questions will be a combination of multiple choice and short answer. You will not have to write complete sentence answers.
BIOLOGY MIDTERM EXAM REVIEW PACKET
BIOLOGY MIDTERM EXAM REVIEW PACKET Name:_____ 1. What are the steps of the scientific method? List and describe each step in order. 2. Define the following: experiment, controlled experiment hypothesis, analysis, conclusion, variable, independent variable, dependent variable, control, constants. 3.
APWH Presentations: Midterm exam Review
APWH Presentations: Midterm exam Review ... Choose pictures, maps, graphs, memes, clipart, cartoons, etc. that illuminate the topic or point you are making. You may have a note card with some talking points in front of you but you should NOT read a script. ready to go.
AP STATISTICS MIDTERM EXAM REVIEW CHAPTER 6
“Insert tab A into slot B” is something you might read in the assembly instructions for pre-fabricated bookshelves. Suppose that tab A varies in size according to a Normal distribution with a mean of 30 mm. and a standard deviation of
Chapter 4 Midterm Exam Review - Ms. Astete
Chapter 4 Midterm Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 ____ 1. Name a line that contains point A. a. DC ... Four points are always coplanar. s: A decagon has 12 sides.
AP STATISTICS MIDTERM EXAM REVIEW CHAPTER 1
AP STATISTICS MIDTERM EXAM REVIEW CHAPTER 1 1. An office supply catalog gives a description of bookshelves that includes the following variables. ... These data probably understate the link between high blood pressure and death from cardiovascular disease, because ... Based on the boxplot, which of the following statements is true? A) The ...
Sociology 4111 (Uggen): Deviant Behavior 2014 Midterm Review
Sociology 4111 (Uggen): Deviant Behavior 2014 Midterm Review . PART I: BASIC CONCEPTS -- DEVIANCE, CONTROL, AND CAREERS . I. Social Facts and Social Constructions. II. Defining Deviance a. Basic Definitions of Deviance (Statistical, Absolutist, Reactivist, Normative) b. Adlers’ definition’s i. Deviance as violation of social norms ...
2015-2016 AP CHEMISTRY MIDTERM EXAM Review
2015-2016 AP CHEMISTRY MIDTERM EXAM Review The midterm exam follows the format of the AP Chemistry exam. The actual AP Chemistry exam consists of 2 sections: Section 1 is 60 multiple choice in a time of 90 minutes (50% of grade) Section 2 is 3 long free-response and 4 short free-response in 90 minutes (50% of grade) Due to the shortened time, the midterm is modified for a total time of 2 hours:
Midterm Exam 2 Review — Chapters 5–8 - stat.ucla.edu
Introduction to Statistical Methods for Business and Economics Midterm Exam 2 Review — Chapters 5–8 1. A basketball player has made about 70% of his free throws over several years. Suppose that his free throws are independent trials with probability 0.7 of a success on each trial. (a) What is the probability that he makes all in 6 attempts?
French I Midterm Exam Review - jeannette.uticak12.org
French I Midterm Exam Review A.Numbers. Write out the following numbers in French words. Be able to say and recognize all numbers from 1-100.
Finance 436 Review Notes for Midterm Exam II Chapter 5
Review Notes for Midterm Exam II Chapter 5 1. Investment assets vs. consumption assets 2. ... and that the dividend yield on a stock index is 4% per annum. The index is standing at ... (0 10 0 04) 4 12 u The actual futures price is only 405. This shows that the index futures price is too low relative to the index. The correct arbitrage strategy ...
General Biology Midterm Exam Review Guide
General Biology Midterm Exam Review Guide Part I: Important Vocabulary Term Definition 1 Polymer Large molecule composed of many repeated subunits (monomers) 2 Monomer A molecule that when combined with other monomers, forms large macromolecules or polymers 3 Catalyst
AP Calculus AB Name Mock AP Exam #3 Review
Page 1 of 36 AP Calculus AB Name_____ Mock AP Exam #3 Review The Mock AP Exam Thursday- Multiple Choice There will be 5 Calculator Multiplice Choice Questions and 15 Non-Calculator Multiple Choice Questions.
Pre-Calculus Semester I Exam REVIEW
15) Find the six trigonometric function values of the specified angle: - 76 6-7 6 csc: 16) .Given that θ is an acute angle in a right triangle, find the csc of θ when cos θ = 5
Calculus AB - AP Exam Review Packet
AP Calculus AB Name: Exam Review Sheet A - Session 2 1) Consider the curve given by x y xy224 7 3 a) Show that 32 83 dy y x dx y x b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. c) Find the value of 2 2
CHEMISTRY I HONORS FINAL EXAM REVIEW
CHEMISTRY I HONORS – FINAL EXAM REVIEW STRATEGY: Start by reading through your notes to refresh your memory on these topics.Then, use this review sheet as a starting point to identify the areas on which you need to spend more study time. For those areas, go back to homework assignments, quizzes,
Honors Chemistry Semester 1 Exam Review
• What is simple harmonic motion? • What factors affect simple harmonic motion of a pendulum and a mass-spring system? • What is a mechanical wave? • What distinguishes one mechanical wave from another? • How do the different characteristics used to measure waves relate to each other?
American History Final Exam Review 2013-2014 Ch 29 Review ...
American History Final Exam Review 2013-2014 Ch 29 Review--Vietnam ... 25.____What country controlled Vietnam during World W ar II? ____ 26. Who were the Communist forces that took control of Cambodia in 1975? ... How did the Bay of Pigs invasion affect U.S.-Cuban relations?
Review Questions Midterm Exam SOCI 270 Drugs, Society and ...
Review Questions – Midterm Exam SOCI 270 – Drugs, Society and Behavior Text Chapters 1-5, 8 | High Price: Chapters 1-7 Prof K. Reymers, Spring 2018 Chapter 4: The Nervous System 17. What is a “neuron” and what parts make it up? 18. What is a “glial cell” and what are its functions? 19.
Spanish 3 Midterm Exam REVIEW - Loudoun County Public ...
1 Spanish 3 Midterm Exam REVIEW The exam is made up of 4 parts: A. Reading (25%) B. Listening (25%) C. Speaking (25%) D. Writing (25%) You can practice and prepare for the speaking and writing, but you will not receive the
Midterm Exam Review - 7th Grade Math - Maclay School
Midterm Exam Review - 7th Grade Math Practice Questions. This is not an all inclusive list of questions. These questions are a representation of the type of questions you will encounter on your exam. Please use past quizzes and tests as well as class notes to study for this exam. 1) Identify a possible pattern.
Honors Chemistry Final Exam Review Fall
Honors Chemistry Final Exam Review Fall 1 ... review will help you to see what multiple choice chemistry questions are like. ... An answer key with worked out answers is on my website. Material covered: Chapter 1 Measurement and Chemical Math (not temp.) Chapter 1 Matter ...
Name: Period: CHEMISTRY I HONORS SEMESTER 2 EXAM REVIEW
Chemistry Semester 2 Exam Review Last Name_____ Per___ 2 7. Nitrogen gas reacts with hydrogen gas to produce ammonia: ___N 2 + ___H 2 ___NH 3 If 100.0 g of nitrogen gas reacts with 20.0 g of hydrogen gas what mass of ammonia will be produced?
Honors Physics Semester 2 Final Exam Review
Honors Physics Semester 2 Final Exam Review Page 4 Pictured below is a new roller coaster. A physics student riding and the coaster car have a combined mass of 200 kg.
Physical Science Semester 1 Midterm Exam REVIEW! GOOD LUCK :)
____ 32. Grinding quartz crystals down to produce sand is an example of a a. change of state. c. chemical reaction. b. chemical change. d. physical change.
Final Exam Review AP Calculus AB Find the slope of the ...
Final Exam Review AP Calculus AB Find the slope of the curve at the given point P and an equation of the tangent line at P. 1) y = x 2 + 11x - 15, P(1, - 3) Use the graph to evaluate the limit. 2) lim ... A man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 20 ft high. At what rate is the length of his
Honors Biology Semester 2 Final Exam Review Guide
Honors Biology Semester 2 Final Exam Review Guide As the final exam approaches, so should your preparation for the test. You should review all old exams given this semester: Cell Cycle, DNA, Genetics, Evolution. Also, you should review topics related to the Human Body. This guide is only the start, it should not be the end all, be all review guide!
Honors PreCalculus Final Exam Review Name MULTIPLE CHOICE ...
Honors PreCalculus Final Exam Review Name_____ Mr. Serianni MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1) 295°6'24'' A)295.11° B)295.07° C)295.12° D)295.17°
Chemistry I Honors – Semester Exam Review – Fall 2000
CHEMISTRY I HONORS – 1st SEMESTER EXAM REVIEW STRATEGY: Start by reading through your notes to refresh your memory on these topics.Then, use this review sheet as a starting point to identify the areas on which you need to spend more study time. For those areas, go back to homework assignments, quizzes,
Honors Chemistry Final Exam Review Spring 2017 Here are ...
41. The concentration of iodide ions in a 0.193 M solution of barium iodide is _____. c. 47 K d. 57 K a. 0.193 M b. 0.386 M c. 0.0965 M d. 0.579 M e. 0.0643 M 42. Silver ions can be precipitated from aqueous solutions by the addition of aqueous chloride: Ag (aq) Cl (aq) AgCl (s) Silver chloride is virtually insoluble in
Honors Chemistry Final Exam Study Guide and Review Packet
Honors Chemistry Final Exam Study Guide and Review Packet Final Exam Preparation There are many benefits to preparing for and taking a final exam. Keep in mind that you are trying to ... Review your chemistry journal (class notes & reading notes). Organize and review your worksheets, labs, problem sets.
Algebra II Honors Final Exam Review - Lemon Bay High School
Algebra II Honors Final Exam Review Short Answer 1. Evaluate the series 5n n= 3 8 ∑. 2. Evaluate the series (n+4)
Wiley CPAexcel Exam Review 2016 Study Guide January ...
questions along with those from cpareviewforfree.com. The questions had a similar feel to the Ninja ... Wiley CPAexcel Exam Review 2015 Study Guide (January): Regulation (Wiley Cpa Exam Review) Wiley CPAexcel Exam Review 2016 Study Guide January: Auditing and Attestation (Wiley Cpa
[Type here] Biology 2014 Midterm Review [Type here]
68. Using resources in way that does not cause long-term environmental harm is called 69. The 1930s Dust Bowl in the Great Plains was caused by 70. An example of sustainable resource use is the use of predators and parasites to 71. One property that makes DDT hazardous over the long run is that DDT is 72.
SPRING 2014 HONORS COURSE OFFERINGS ALL-HONORS COURSES
SOC 3200 01 2397 W,Th,F 11:30 – 12:30 Avri Beard Communications and Performing Arts History of American Musical Theatre (Flexible Core- Group B: U.S. Experience in its Diversity)
Exam 2 Review Oct 13, 2014 Dr. Koen 3D Rigid Body, Trusses
a ball-and-socket joint and by two cables BDC and CE. Cable BDC is continuous and passes over a pulley at D. Calculate the tension in the cables and the x,y,z components of reaction at A if a crate has a weight of 80 lb. Thought process… 3d Rigid Body Equilibrium Problem Draw FBD to identify unknowns Ball & Socket at A Two cables (always pull)
We use cookies, just to track visits to our website, we store no personal details.
| 4,903
| 19,334
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-30
|
latest
|
en
| 0.856496
|
https://theacademicessays.com/obtain-the-file-duct-m-from-the-course-website-this-pseudocode-solves-the-2d-incompressible-navier-stokes-equations-for-flow-in-a-duct-using-a-fractional-step-pressure-correction-method-you-will-hav/
| 1,590,969,638,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347413786.46/warc/CC-MAIN-20200531213917-20200601003917-00094.warc.gz
| 588,950,824
| 12,931
|
# Obtain the file duct.m from the course website. This pseudocode solves the 2D incompressible Navier-Stokes equations for flow in a duct using a fractional step pressure correction method. You will have to
AMME5202 Assignment 2: Navier-Stokes equations
Due: 5pm Friday, Week 11 (25/05/2018) Submit online via Turnitin.
This assignment should take a typical student 12 hours to complete.
Obtain the file duct.m from the course website. This pseudocode solves the 2D incompressible Navier-Stokes equations for flow in a duct using a fractional step pressure correction method. You will have to add in variable initialisation etc. to get it running.
• (4 marks) Run the code to obtain the steady state solution for a duct of length 0.0 ≥ x ≥ 4.0, height 0.0 ≥ y ≥ 0.1, inlet velocity Uin = 1.0, density ρ = 1.0 and viscosity ν = 0. Determine a suitable grid-size and verify that it provides the correct solution for fully developed laminar duct flow. Hand in plots of velocity profiles and details of how you determined the grid size and verified the solution accuracy.
• (1 marks) Write out the physical specification for this problem, that is the equations in continuous form, the domain size, the boundary and initial conditions, etc.
• (1 marks) Provide details for the discretisation scheme used. Comment on the stability and accuracy of the schemes.
• (4 marks) This code is very inefficient. Determine and implement modifications to improve the performance of the code. Document the improved performance. To obtain full marks for this component requires a significant improvement in performance, a factor greater than 2 should be possible.
• (4 marks) Modify the code to include a mixing length turbulence model, set appropriate inlet conditions and domain size to obtain fully developed turbulent duct flow. Compare your results to the 1/7 power law profile and comment. Include full details of your implementation of the model.
• (2 marks) An approximation is available for the wall shear stress in pipe flow.
τ0 = 0.03325ρu˜7/4ν1/4R−1/4,
where ˜u is the cross-stream average of the pipe velocity and R is the pipe radius. Calculate the wall shear stress
,
obtained from your turbulent simulations using the mixing length model, then compare to the approximation given above and comment.
• (2 marks) Place useful comments in the code and hand in commented code, including performance modifications and mixing length turbulence model.
• (2 marks) Presentation and report formatting.
This essay is written by:
Prof. SirMojo Verified writer
Finished papers: 435
Proficient in:
English, History, Business and Entrepreneurship, Nursing, Psychology, Management
You can get writing help to write an essay on these topics
100% plagiarism-free
Hire This Writer
| 621
| 2,775
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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
| 0.853801
|
http://www.britannica.com/topic/spherical-triangle
| 1,455,080,392,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-07/segments/1454701158609.98/warc/CC-MAIN-20160205193918-00210-ip-10-236-182-209.ec2.internal.warc.gz
| 320,006,488
| 10,979
|
# Spherical triangle
Mathematics
Thank you for helping us expand this topic!
Once you are finished and click submit, your modifications will be sent to our editors for review.
Britannica does not currently have an article on this topic. Below are links to selected articles in which the topic is discussed.
• ## definition by Menelaus
Menelaus of Alexandria
Greek mathematician and astronomer who first conceived and defined a spherical triangle (a triangle formed by three arcs of great circles on the surface of a sphere).
trigonometry: Passage to Europe
Until the 16th century it was chiefly spherical trigonometry that interested scholars—a consequence of the predominance of astronomy among the natural sciences. The first definition of a spherical triangle is contained in Book 1 of the Sphaerica, a three-book treatise by Menelaus of Alexandria (c. ad 100) in which Menelaus developed the spherical equivalents of...
• ## place in spherical trigonometry
trigonometry: Spherical trigonometry
Spherical trigonometry involves the study of spherical triangles, which are formed by the intersection of three great circle arcs on the surface of a sphere. Spherical triangles were subject to intense study from antiquity because of their usefulness in navigation, cartography, and astronomy. (See the section Passage to Europe.)
MLA style:
"spherical triangle". Encyclopædia Britannica. Encyclopædia Britannica Online.
Encyclopædia Britannica Inc., 2016. Web. 09 Feb. 2016
<http://www.britannica.com/topic/spherical-triangle>.
APA style:
Harvard style:
spherical triangle. 2016. Encyclopædia Britannica Online. Retrieved 09 February, 2016, from http://www.britannica.com/topic/spherical-triangle
Chicago Manual of Style:
Encyclopædia Britannica Online, s. v. "spherical triangle", accessed February 09, 2016, http://www.britannica.com/topic/spherical-triangle.
While every effort has been made to follow citation style rules, there may be some discrepancies.
Please refer to the appropriate style manual or other sources if you have any questions.
Click anywhere inside the article to add text or insert superscripts, subscripts, and special characters.
You can also highlight a section and use the tools in this bar to modify existing content:
Editing Tools:
We welcome suggested improvements to any of our articles.
You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind:
1. Encyclopaedia Britannica articles are written in a neutral, objective tone for a general audience.
2. You may find it helpful to search within the site to see how similar or related subjects are covered.
3. Any text you add should be original, not copied from other sources.
4. At the bottom of the article, feel free to list any sources that support your changes, so that we can fully understand their context. (Internet URLs are best.)
Your contribution may be further edited by our staff, and its publication is subject to our final approval. Unfortunately, our editorial approach may not be able to accommodate all contributions.
MEDIA FOR:
spherical triangle
Citation
• MLA
• APA
• Harvard
• Chicago
Email
You have successfully emailed this.
Error when sending the email. Try again later.
| 715
| 3,236
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.59375
| 3
|
CC-MAIN-2016-07
|
latest
|
en
| 0.874305
|
http://cache1.abcteach.com/search.php?category=0&q=expanded&search_type=1&match_words=2&limit_search=1&_form_action=&search_form1_form_visited=1
| 1,596,718,824,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-34/segments/1596439736962.52/warc/CC-MAIN-20200806121241-20200806151241-00452.warc.gz
| 20,728,631
| 26,626
|
You are an abcteach Member, but you are logged in to the Free Site. To access all member features, log into the Member Site.
# SEARCH RESULTS: expanded
Clip Art:
= Preview Document = Member Site Document
There are 24 documents matching your search.
• 10 pages of practice in writing numbers in expanded notation from tens to hundred thousands (place value increases per page). Created with our abctools Math Worksheet Generator.
• This Tens (primary/elem) Worksheet is perfect to practice math skills. Your elementary grade students will love this Tens (primary/elem) Worksheet. 3 tens = 30; 1 ten + 3 tens = X tens; 2 worksheets. Common Core: 1.NBT.1, 2.NBT.2
• This Ones and Tens (primary/elem) Worksheets is perfect to practice math skills. Your elementary grade students will love this Ones and Tens (primary/elem) Worksheets. 4 pages: 3 tens =; 4 ___ = 40, etc. This set is a good introduction to place value. Common Core: 1.NBT.1, 2.NBT.2
• Cut out the tags and then put them together on a ring for an original expandable autograph book.
• This Place Value Charts and Expanded Notation Math is perfect to practice place value skills. Your elementary grade students will love this Place Value Charts and Expanded Notation Math. Two advanced place value worksheets and one expanded notation with answers. (created with abctools®) Common Core: 1.NBT.1, 2.NBT.2
• Roll dice to make a number for practice with the following skills: place value, rounding, addition, subtraction, and writing in standard form, word form, expanded form, and expanded notation. Includes pages for numbers in the thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, and billions.
• Roll dice to make a number for skill practice. Includes pages for Decimal, Fraction, Improper Fraction, and Mixed Number. Decimal skills include: place value, rounding, addition, subtraction, money, doubling, number line, and writing in standard form, word form, expanded form, and expanded notation. Fraction skills include: numberator, denominator, word form, equivalents, decomposing, conversation, addition, subtraction, and drawing the fraction as part of a whole, set, strip diagram, and on a number line.
• This Place Value (ones, tens, hundreds) Set 1 is perfect to practice place value skills. Your elementary grade students will love this Place Value (ones, tens, hundreds) Set 1. using expanded notation Common Core: 1.NBT.1, 2.NBT.2
• This Place Value (ones, tens, hundreds) Set 2 is perfect to practice place value skills. Your elementary grade students will love this Place Value (ones, tens, hundreds) Set 2. using expanded notation Common Core: 1.NBT.1, 2.NBT.2
• This lesson (including lesson plan and worksheet) explains food chains, and then offers students a variety of activities to illustrate and expand their knowledge.
• Use this 'Book: Hatchet (upper elem/middle)' printable worksheet in the classroom or at home. Your students will love this 'Book: Hatchet (upper elem/middle)'. The Newbery-winning novel Hatchet (by Gary Paulsen) is a popular book, even among reluctant readers. Expand your reading with a chapter summary sheet, vocabulary expansion exercises, comprehension review, and MUCH more.
• Use these detailed maps to help review (or expand) students' geographical knowledge of continents, countries, oceans, and seas, as well as to practice map labeling.
• Eight pages of sentence practice to strengthen writing skills, including: combining multiple short sentences into complex sentences; creative "cause and effect" sentence practice; contrast sentences; and expanded sentences.
• PowerPoint with Audio. Part of the Living on Planet Earth series. This presentation includes colorful images and illustrations to explain how plants grow by describing their basic structure having roots, stems and leaves. Describes how glucose is converted into celulose to develop starch for food reserves. Part 2 of 2 units.
• This KWHL chart expands upon the traditional KWL chart, while having students learn about their school. This chart addresses informational reading core curriculum. CC: ELA: RI.1-3.1
• This KWHLAQ chart expands upon the traditional KWL, while having students learn about their school. This chart addresses the common core standards. CC: ELA: RI.4-5.1
• Eight colorful math mats and cards for practice in place value including ones, tens and hundreds. Printable manipulatives are included or you can use real items. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math pages for practice in place value including ones, tens and hundreds. May be used for student practice or to model use of corresponding printables. CC: Math: 2.NBT.A.1-4, B.5-8
• This Numbers and Operations in Base Ten - Spring Theme (grade 2) Math Mats is perfect to practice number and operation skills. Your elementary grade students will love this Numbers and Operations in Base Ten - Spring Theme (grade 2) Math Mats. Eight colorful math mats and cards for practice in place value including ones, tens and hundreds. Printable manipulatives are included or you can use real items. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math mats and cards for practice in place value including ones, tens and hundreds. Printable manipulatives are included or you can use real items. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math pages for practice in place value including ones, tens, and hundreds. May be used for student practice or to model use of corresponding printable math mats. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math mats and cards for practice in place value including ones, tens and hundreds. Printable manipulatives are included or you can use real items. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math pages for practice in place value including ones, tens, and hundreds. May be used for student practice or to model use of corresponding printable math mats. CC: Math: 2.NBT.A.1-4, B.5-8
• Eight colorful math pages for practice in measuring, telling time, counting coins, and displaying data in graphs. May be used for student practice or to model use of corresponding printable math mats. CC: Math: 2.MD.1-10
| 1,430
| 6,159
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-34
|
latest
|
en
| 0.866621
|
http://gray.23.33.ilmusicante.net/rules-integers-math-worksheet/
| 1,611,430,666,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-04/segments/1610703538431.77/warc/CC-MAIN-20210123191721-20210123221721-00511.warc.gz
| 47,141,559
| 28,553
|
Rules Integers Math Worksheet
In Free Printable Worksheets249 views
4.22 / 5 ( 195votes )
Top Suggestions Rules Integers Math Worksheet :
Rules Integers Math Worksheet Boost your learner s knowledge of integers with this number sense worksheet in this sixth grade math worksheet compare and order integers part 1 students will plot positive and negative numbers on In this math each of the integers that make up an eight digit number once they have filled in all the numbers they enter it into a calculator to find the answer to a riddle designed for fifth One letter variables integer math only etc gw basic qbasic etc were as capable as pascal and c freebasic qb64 are capable of building modern applications deal with it.
Rules Integers Math Worksheet Mathematical rules are based on the defining limits we place on the particular as one might guess this is not the kind of math you want to use when balancing a checkbook or calculating current Storing the results in 16 bit integers will therefore waste 6 bits for each value which is more than one third using bitfields will let us use a single 32 bit integer and split it up in three 10 When ronayne complained about the absence of any reading instruction school staff referred her to a class website with some generic exercises a worksheet introducing write or do math of those.
Rules Integers Math Worksheet The mind your decisions youtube channel offers up a thorny math problem designed for 9 year olds our solution involves narrowing down the possibilities using the logic of puzzle solving the If you do the quick math on that it means that you ll phaseout completely your first stimulus check may have already been offset the rules were different for the first round of payments under Aside from math and it s only a more extreme version of what goes on when schools are physically open the parents i spoke with said their kids didn t want to do those worksheets.
No rules rules netflix and the culture of reinvention a workbook is a spreadsheet that is composed of one or more worksheets by default a new workbook opens with a single worksheet.
People interested in Rules Integers Math Worksheet also searched for :
Rules Integers Math Worksheet. The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use.
You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now!
Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Rules Integers Math Worksheet.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
Rules Integers Math Worksheet. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice.
Author: Larysa Usyk
Have faith. But just because it's possible, doesn't mean it will be easy. Know that whatever life you want, the grades you want, the job you want, the reputation you want, friends you want, that it's possible.
Top
| 1,386
| 6,969
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.796875
| 3
|
CC-MAIN-2021-04
|
latest
|
en
| 0.930237
|
http://www.jiskha.com/display.cgi?id=1254707130
| 1,498,388,494,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-26/segments/1498128320489.26/warc/CC-MAIN-20170625101427-20170625121427-00328.warc.gz
| 567,216,213
| 3,720
|
posted by .
Find The Product. Estimate to check.
0.12 X 0.9 = 10.8 or is it .108?
estimate is 12 X 10 =120
Is this correct?
Thank you
nine-tenths of twelve hundredths?
.108
estimate? .1x 1.0= .1
| 72
| 201
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.828125
| 3
|
CC-MAIN-2017-26
|
latest
|
en
| 0.824951
|
https://community.fabric.microsoft.com/t5/Desktop/Weighted-Average/m-p/1937387/highlight/true
| 1,723,729,648,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641291968.96/warc/CC-MAIN-20240815110654-20240815140654-00266.warc.gz
| 138,809,721
| 52,283
|
cancel
Showing results for
Did you mean:
Find everything you need to get certified on Fabric—skills challenges, live sessions, exam prep, role guidance, and more. Get started
Anonymous
Not applicable
## Weighted Average
Hello,
I need to compute a weighted average for the consumer price.
Currently, CP YTD is computed as Average(DB(consumer price). However, if I use this formula I receive an arithmetic average.
I need to weigh the consumer price for NES YTD (Sales).
the formula needs to be something like: (CP YTD*NES YTD)/sum(NES YTD). however, I need to do that for each level.
for example:
for liv6 [(NES Ytd 541... * CP YTD 541... )/ sum (NES YTD 541... + NES YTD 541... and so on) ]
the denominator needs to be dynamically adjusted depending on the level that is analysed.
How can I do that in DAX?
Thanks for the help
1 ACCEPTED SOLUTION
Community Support
Try to use the sumx function.
``````WA =
VAR total_ =
CALCULATE(
[NES YTD],
ALL(xxxxx)
)
VAR _Table =
SUMMARIZE(
Sales,
xxx[Row1],xxx[Row2]
),
"nes", [NES YTD],
"cp", [CP YTD]
)
RETURN
SUMX(
_Table ,
[cp] * [nes]/total_
)``````
3 REPLIES 3
Anonymous
Not applicable
I have just some further questions?
1. What do you mean with xxx?
In Var total_ do I need to insert the name of the table?
2. in Var _Table is sales a new or existing table?
3. What do Row1 and Row2 refer to?
Community Support
It refers to the column name of row labels. If the problem still exists, Please provide some sample data, preferably a pbix after removing sensitive data.
Community Support
Try to use the sumx function.
``````WA =
VAR total_ =
CALCULATE(
[NES YTD],
ALL(xxxxx)
)
VAR _Table =
SUMMARIZE(
Sales,
xxx[Row1],xxx[Row2]
),
"nes", [NES YTD],
"cp", [CP YTD]
)
RETURN
SUMX(
_Table ,
[cp] * [nes]/total_
)``````
| 501
| 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}
| 3.140625
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.858333
|
publishbookmark.com
| 1,643,338,540,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320305341.76/warc/CC-MAIN-20220128013529-20220128043529-00384.warc.gz
| 528,855,219
| 38,882
|
# Importance of Probability in Real Life
Probability theory is a crucial subject that we can study at various mathematical levels. Probability is the basis of Statistical theory and its applications. Probability is used to define random or chances of events to occur. Every day we are challenged with probability statements involving the words. Mathematically, probability is the possibility that something might occur. It is used in many applications of our daily existence, including weather forecasts, player statistics, sports strategies, insurance claims, games and recreational activities, executing business, etc. Another vital application of probability theory in daily life is reliability. Chance and the ability to understand and determine the likelihood of any diverse combination of outcomes versus one another is significant in real life.
Probability and statistics are closely connected because statistical data are generally analyzed to comprehend whether conclusions can be drawn legitimately about a distinct phenomenon and make forecasts about future events. Thus, early election results are analyzed to understand if they conform to predictions from polls which are conducted before the election and predict the election’s outcome. This is one of the most commonly observed situations in the day-to-day. However, we have different distributions, such as binomial distribution, to analyze and interpret the data. Besides, we can apply several formulas and techniques of probability to get the desired results while dealing with real-life scenarios. For example, permutation and combination rules and procedures are beneficial for answering probability problems.
In the twenty-first century, probability is used to control traffic flow through a telephone interchange, a highway system, or a computer. Also, we can estimate the spread of rumours and predict the rate of return in high-risk investments with the help of probability techniques. For example, when we get anything insured, we investigate which insurance policy would be appropriate depending on our usage, the chances of loss, and feasible recovery.
As we know, we can apply probability while deciding medical-related issues. For example, when patients are advised to undergo surgery, they generally want to identify the operation’s success rate. This rate is nothing but a probability rate. This rate can be calculated using the Bayes theorem. Based on the same, the patient decides whether or not to go ahead with the same. Besides, weather forecasting is one of the essential applications of probability. This can be observed in our daily existence whenever we plan to go for a tour, an outing, or picnic. In this case, we generally tend to know the weather forecast to decide whether to proceed or cancel the program. For example, assume it asserts that there is a chance of raining on that particular day is eighty percent. To estimate these weather forecasts in terms of percentage, Meteorologists use a unique tool and technique. First, they study the historical databases of some days, which have a similar temperature, pressure, humidity, pressure, and other relevant factors. Then, finally, they conclude that on eighty out of a hundred similar days in the earlier period, it had rained.
Apart from the above specified scenarios, we can observe that the applications of probability include games such as flipping a coin, throwing dice, drawing cards, selection of objects from the specified sample space, etc. Thus, whenever we examine the chances for the occurrence of an event, we are applying the concept of probability knowingly or unknowingly.
Latest articles
### Just how much does expert termite therapy price in Australia?
Specialist Termite Treatment Adelaide Even if it is obligatory and you understand that it is an unpreventable expense, you will certainly have an interest in...
### Why Corporate Photography is Important for Your Company
In today's media stressed world picture is greatly vital. Just exactly how a product, service or organisation looks is as virtually vital as what...
### Shield Sail Standard Installation
When checking out exterior amusement park, recreational locations, restaurants, and business structures, you will certainly commonly see installations of textile extended across an area...
### Exactly How Online Betting Solutions Boost Your Success Price
There are currently many on the online sports betting Singapore sites online which are riding on the ever-growing popularity of spread betting as well...
Related articles
| 811
| 4,569
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.84375
| 4
|
CC-MAIN-2022-05
|
longest
|
en
| 0.943465
|
https://topnursingassignments.com/a-container-and-a-jug-had-a-total-of-2-15-quarts-of-oil-in-them-when-0-18-quart-of-oil/
| 1,685,622,570,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-23/segments/1685224647810.28/warc/CC-MAIN-20230601110845-20230601140845-00265.warc.gz
| 644,699,281
| 11,077
|
# a container and a jug had a total of 2.15 quarts of oil in them. When 0.18 quart of oil…
a container and a jug had a total of 2.15 quarts of oil in them. When 0.18 quart of oil was poured from the container into the jug, the container had 4 times as much oil as the jug. how many quarts of oil were in the container at first?
| 94
| 328
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-23
|
longest
|
en
| 0.991686
|
http://antive-rtl.famithemes.com/download/a-concise-introduction-to-the-theory-of-integration-second-edition
| 1,553,575,042,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-13/segments/1552912204790.78/warc/CC-MAIN-20190326034712-20190326060712-00161.warc.gz
| 11,092,499
| 17,325
|
# A concise introduction to the theory of integration, second by Daniel W. Stroock PDF
By Daniel W. Stroock
ISBN-10: 0817637591
ISBN-13: 9780817637590
ISBN-10: 3764337591
ISBN-13: 9783764337599
This version develops the fundamental idea of Fourier rework. Stroock's procedure is the single taken initially by means of Norbert Wiener and the Parseval's formulation, in addition to the Fourier inversion formulation through Hermite services. New routines and ideas were further for this variation.
Best introduction books
Get A Practical Guide to Swing Trading PDF
This is Your probability To Get the one functional guide For starting And skilled Swing investors ,That offers Them the full easy process to begin Being A revenue Taker In Any industry situation. .. "A sensible consultant to Swing Trading", that might express you the most secure method to constant, convinced profit-taking in any inventory industry.
Get Constrained Extrema Introduction to the Differentiable Case PDF
Those notes are the results of an interrupted series of seminars on optimiza tion thought with monetary functions beginning in 1964-1965. this is often pointed out in terms of explaining the asymmetric sort that pervades them. in recent times i've been utilizing the notes for a semester direction at the topic for graduate scholars in economics.
Additional resources for A concise introduction to the theory of integration, second edition
Sample text
13) X CX) CX) m =l n = m E rn for infinitely many n E z+ } n ---+ CX) n ---+ CX) with equality holding when {rn} 1 is monotone. One says that the limit limn ---+ CX) rn exists if equality holds in (2. 1. 13) , in which case lim n ---+ CX) rn limn ---+ CX) rn. Let (E, B, Jt) be a measure space and {rn} 1 C B. Prove each of the follow Ing. ( i) and ( ii ) In particular, under the condition in ( ii ) , conclude that ( iii ) nlim ---+ CX) rn ) if nlim ---+ CX) rn exists. ---+ CX) Jt ( rn ) == Jl (nlim Finally, show that ( iv ) Jl (nlim ---+ CX) rn ) == o if CX) L Jt (rn) < 1 oo .
V In n E z + } { : is a non-decreasing sequence of measurable functions. Hence, by the preceding, lim ( 11 V V In ) sup == In n ---+ CX) n> 1 is measurable; and a similar argument shows that infn > 1 In is measurable. Noting that infn > m In does not decrease as m increases, we also see that · · · inf In In == mlim n CX) m > ---+ nlim ---+ CX) is measurable; and, of course, the same sort of reasoning leads to the measur ability of limn ---+ CX) In . Finally, since ( cf. Exercise 3. 1 . 16) � { x E E : nlim---+ CX) ln (x) exists } == { n�limCX) In == n�limCX) In } , it is an element of B; and from this it is clear that the function I described in the last part of the statement is measurable.
6 applied to r and rC, we can find A E �a and B E <5 6 such that rc c AC, r c B, I B\r l == 0, and l r \ A I == l AC \ rC I == 0, from which I B \ A I == 0 is immediate. On the other hand, if there exist A E Fa and B E <56 such that A C r C B and I B \ A I == 0, then r == A U (r \ A ) is measurable because 1 r \ A l e < I B \ A I == 0. Hence, it remains only to check (2. 1 . 13) . We first prove (2. 1 . 13) under the additional assumption that each of the rn ' s is bounded. Given E > 0, choose open sets Gn so that rnC c Gn and I Gn \ rn C I < 2- n E .
| 934
| 3,293
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2019-13
|
longest
|
en
| 0.804946
|
https://sports.answers.com/team-sports/How_many_bases_do_you_receive_if_a_fielder_catches_a_ball_in_his_cap
| 1,726,421,624,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700651632.84/warc/CC-MAIN-20240915152239-20240915182239-00047.warc.gz
| 508,771,803
| 50,115
|
0
# How many bases do you receive if a fielder catches a ball in his cap?
Updated: 9/28/2023
Wiki User
14y ago
If it is a batted ball, the batter and all runners are awarded 3 bases.
If it is a thrown ball, the batter and all runners are awarded 2 bases from whatever base they had occupied when the ball was thrown.
Wiki User
14y ago
Wiki User
12y ago
4
Earn +20 pts
Q: How many bases do you receive if a fielder catches a ball in his cap?
Submit
Still have questions?
Related questions
### Is a caught fly ball a force out?
No it is not it is the end of the game
### What is the ruling if a fielder throws his mitt up into the air and the ball falls into the mitt and he catches the mitt with the ball in it?
It is scored as a triple Really, no he caught the ball so obviously he got him out First answer is correct, batter is awarded three bases.
### Is it an out if the defensive player catches the ball then drops his glove but the ball remains in the glove?
No, the glove is considered an extension of the fielder's hand so if the glove comes off the fielder is deemed to have dropped the ball.
### What if a fielder catches a ball but loses his glove and the ball stays in the glove?
If the glove or mitt falls off in the process of catching the ball, it is not a legal catch. The fielder must have control of the ball in the glove and then remove it himself.
### If a player catches a fly ball and in attempting to throw it to hold a runner but drops the ball is this an error on the player and is the hitter awarded a hit?
If the fielder catches the ball and, during the motion of reaching into the glove to grab the ball to throw, the ball drops to the ground the batter is called out. As long as the fielder has complete control of the ball before attempting to throw, the umpire will call the batter out.
### What are two ways that the batter can be out in baseball?
three strikes and fielder or outfielder catches ball without dropping it.
### If a batted ball hits a runner and pops up in the air and a fielder catches the ball is the batter out also?
No...as soon as the batted ball touches the runner, the ball is dead.
### What is catching in the sport of cricket?
It is where a batsmen hits the ball into the air and without a bounce a fielder catches it meaning the batsmen is out.
### When tagging up does the runner have to wait for fielder to have possession or first touch?
The fielder has to have the ball in his possession but if he drops it he doesn't have to tag up. Actually, the fielder doe NOT have to have possession of the ball for a base runner to tag up and advance. Once the runner is on the base ("tagging up") he may advance as soon as the fielder touches the ball, whether he has possession or not. In other words, the base runner may advance even if the fielder is bobbling the ball and then catches it, i. e. has possession.
### Is a batsman given run- out when the fielder catches the ball in one hand and hits the wicket with other hand?
No, it is the ball that must come into contact with the bails to be considered a run-out.
### If a ball is a pop fly and the opponent catches it is the hitter out?
Yes, the hitter is out and if the fielder who caught the ball can get it to a base before the runner gets back the runner is out making it a double play
### If a cricket ball hits an umpirte is the ball live?
Yes it is. Law 32 section 3 paragraph e states that a fair catch is made when "a fielder catches the ball after it has touched an umpire, another fielder or the other batsman" (2000 MCC laws of cricket 3rd edition 2008)
| 857
| 3,608
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.609375
| 3
|
CC-MAIN-2024-38
|
latest
|
en
| 0.968316
|
https://secondsminutes.com/470-5-seconds-in-minutes-and-seconds
| 1,669,960,973,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00245.warc.gz
| 526,088,106
| 5,478
|
# 470.5 seconds in minutes and seconds
## Result
470.5 seconds equals 7 minutes and 50.5 seconds
You can also convert 470.5 seconds to minutes.
## Converter
Four hundred seventy point five seconds is equal to seven minutes and fifty point five seconds.
| 62
| 257
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-49
|
latest
|
en
| 0.814565
|
https://en.oxforddictionaries.com/definition/quartic
| 1,544,852,652,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-51/segments/1544376826715.45/warc/CC-MAIN-20181215035757-20181215061757-00204.warc.gz
| 577,899,123
| 25,088
|
# Definition of quartic in English:
## quartic
Mathematics
• Involving the fourth and no higher power of an unknown quantity or variable.
• ‘Based on Tartaglia's formula, Cardan and Ferrari, his assistant, made remarkable progress finding proofs of all cases of the cubic and, even more impressively, solving the quartic equation.’
• ‘Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.’
• ‘Assessing the higher-degree models (unconstrained cubic model and quartic model) proved difficult computationally, with many replicates failing to converge to a likelihood maximum.’
• ‘MacMahon then worked on invariants of binary quartic forms, following Cayley and Sylvester.’
• ‘Orthogonal contrasts were used to test linear, quadratic, cubic, and quartic effects of proportions of SFGS in diet substrates on rate of fermentation.’
### noun
Mathematics
• A quartic equation, function, curve, or surface.
• ‘Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic.’
• ‘Ferrari had solved the quartic by radicals in 1540 and so 250 years had passed without anyone being able to solve the quintic by radicals despite the attempts of many mathematicians.’
• ‘After subsequent work failed to solve equations of higher degree, Lagrange undertook an analysis in 1770 to explain why the methods for cubics and quartics are successful.’
• ‘Cardan published both the solution to the cubic and Ferrari's solution to the quartic in Ars Magna convinced that he could break his oath since Tartaglia was not the first to solve the cubic.’
• ‘Pacioli does not discuss cubic equations but does discuss quartics.’
### Origin
Mid 19th century: from Latin quartus ‘fourth’ + -ic.
/ˈkwɔːtɪk/
| 440
| 1,876
|
{"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}
| 2.796875
| 3
|
CC-MAIN-2018-51
|
latest
|
en
| 0.957765
|
https://www.ilmkidunya.com/online-test/fsc-part-2-physics-chapter-4-test-preparation
| 1,716,834,737,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971059045.25/warc/CC-MAIN-20240527175049-20240527205049-00758.warc.gz
| 704,617,730
| 67,122
|
×
15th Chapter
### 12th Class Physics Chapter 15 Test
Here you can prepare 12th Class Physics Chapter 15 Electromagnetic Induction Test. Click the button for 100% free full practice test.
## Second Year Physics Chapter 15 Online MCQ Test for 2nd Year Physics Chapter 15 Electromagnetic Induction Preparation
This online test contains MCQs about following topics:.
- Induced EMF and Induced Current - Motional EMF - Faraday's Law and Induced EMF - Lenz's Law and Direction of Induced EMF - Mutual Induction - Self Induction - Energy Stored in an Inductor - Alternating Current Generator - D.C. Generator - Back Motor Effect in Generator - D.C. Motor - Back EMF Effect in Motors - Transformer
FSC Part 2 Physics Ch 15 Test
### Second Year Physics Chapter 15 Online MCQ Test for 2nd Year Physics Chapter 15 Electromagnetic Induction Preparation
1 The device in which induced emf is statically induced emf is:
• A. Transforms
• B. AC generator
• C. Alevator
• D. Dynamo
2 split rings are used in
• A. A.C. generator
• B. A.C. motor
• C. Transformer
• D. D.C. motor
3 Output of D.C. motor is
• A. A.C. energy
• B. Mechanical energy
• C. Chemical energy
• D. D.C. energy
4 The working principle of transformer is.
• A. Self induction
• C. Mutual induction
• D. Electromagnetic induction
5 When a motor is over loaded then the magnitude of back emf.
• A. Increases
• B. Decreases
• C. Remain constant
• D. Zero
6 Energy stored in inductor is.
• A. 1/2 L I<sup>2</sup>
• B. 1/2 LI
• C. 1/2 L2I
• D. 1/2 L2I2
7 The application of mutual induction is a.
• A. D.C. motor
• C. Television
• D. Transformer
8 A 50 mH coil carries a current of 2.0 a , then energy stored in tis magnetic field is.
• A. 0.1 J
• B. 10 J
• C. 100 J
• D. 1000 J
9 1 Henry =
• A. VSA<sup>-1</sup>
• B. VS<sup>-1</sup>A<sup>-1</sup>
• C. V<sup>-1</sup>SA
• D. VSA<sup>-2</sup>
10 The direction of induced current is always so as to oppose the change which causes the current, this is the statement of
• A. Lenz's law
• C. Ampere's law
• D. Coulomb's law
### Top Scorers of Physics Fsc Part 2 Chapter 4 Online Test
#### Numaira Mubarak
Lahore22 - Apr - 2024
17/17
21 Sec
M
Lahore02 - Mar - 2024
17/17
35 Sec
R
#### Ramis Shahid
Lahore28 - Mar - 2024
17/17
01 Mins 10 Sec
R
#### Ramis Shahid
Lahore28 - Mar - 2024
17/17
01 Mins 59 Sec
R
#### Ramis Shahid
Lahore28 - Mar - 2024
17/17
02 Mins 38 Sec
H
#### Hassan Khan
Lahore21 - Apr - 2024
17/17
03 Mins 11 Sec
#### Numaira Mubarak
Lahore22 - Apr - 2024
16/17
21 Sec
M
Lahore02 - Mar - 2024
16/17
35 Sec
M
Lahore02 - Mar - 2024
16/17
35 Sec
R
#### Ramis Shahid
Lahore28 - Mar - 2024
16/17
01 Mins 10 Sec
S
#### Shahida Parveen
Lahore23 - Apr - 2024
16/17
01 Mins 13 Sec
K
#### Kiran Kainat
Lahore28 - Mar - 2024
16/17
01 Mins 24 Sec
R
#### Riaz Ahmed
Lahore10 - Apr - 2024
16/17
01 Mins 54 Sec
A
#### Areej Fatima
Lahore25 - Mar - 2024
16/17
02 Mins 05 Sec
M
Lahore21 - Apr - 2024
16/17
02 Mins 14 Sec
Sort By:
• #### Sania Saeed
16 Nov 2017
ye log poore number nai dete jan bhooj kar
Like (1)
• A
#### Ayesha
11 May 2017
2 mcqs k ans ghalat hain irrespective k wo book ki statements hain
Like (2)
X
to continue to ilmkidunya.com
Fill the form. Our admission consultants will call you with admission options.
X
to continue to ilmkidunya.com
X
to continue to ilmkidunya.com
X
| 1,176
| 3,348
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.796875
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.754658
|
https://docgo.net/philosophy-of-money.html?utm_source=errata-Czo7c1j
| 1,518,992,648,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-09/segments/1518891812259.30/warc/CC-MAIN-20180218212626-20180218232626-00750.warc.gz
| 630,108,167
| 16,481
|
# Errata
Description
List of Errata for Principles of Signal Detection and Parameter Estimation
Categories
Published
View again
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
List of Errata for Principles of Signal Detection andParameter EstimationChapter 1 1. On page 1, lines 12 and 13, the hyphenated word the-ses should be replaced by these(no s, no hyphenation).2. On page 4, line 3, replace give by given.3. On page 4, line 9, a period is missing after observations. Chapter 2 1. On page 18, line 11, replace Y 1 by Y 1 .2. On page 29, line 1 just below Fig. 2.1, replace South-West by South-East.3. On page 35, equation (2.67) should be P D = ... . The change replaces P F by P D .4. On page 53, the summation on the last line of equation (2.130) should be M − 1 i =0 (sumwith respect to i instead of j ). Chapter 3 1. On page 81, 5 lines from the bottom, a closing parenthesis is missing in min( I 0 ( γ ) ,I 1 ( γ )).2. On page 93, equation (3.77) should be δ B n ( y 1 ,..., y n ) = 1 for L n ( y 1 ,..., y n ) ≥ B 0 for L n ( y 1 ,..., y n ) ≤ A, i.e., exchange A and B on the right hand side of the equation. Chapter 4 1. On page 119, line 2 should be: C ( x , ˆ x ) = || x − ˆ x || 1 , i.e., a hat is missing on top of the second x on the right hand side of the equation.1 2. On page 119, equation (4.25), integrations should be over dx i , not d y .3. On page 120, in the equation 8 lines from the bottom, the second equality should be ··· = m X + K XY K − 1 Y ( Y − m Y )The change is that the minus sign after m X should be replaced by a plus sign.4. In the equation appearing on the second line of p. 129, replace ( Y − m y ) T by ( Y − m Y ) T , i.e. the Y subscript of m should be in capital bold font instead of lower casebold font.5. Equation (4.77) on p. 131 should be G = K LLS H T R − 1 , i.e., R should be replaced by R − 1 .6. On page 135, Case 3, a closing parenthesis is missing on the right hand side of thefirst line of the first equation, which should be L ( y ,m,v ) △ = ln( f Y ( y | m,v ))7. On page 137, 5 lines from the bottom, the equation should be b ( S , x ) = exp( x T S − t ( x ))The change is that v ( x ) should be replaced by t ( x ) to maintain consistency with theexponential canonical form (4.80).8. On line 6 of page 139, replace ”where O T ...” by ”where 0 T ...” The change consists of replacing a bold face capital O by a bold face capital zero.9. On page 143, in the equation 10 lines from the bottom, a hat is missing on top of θ ML , which should be replaced by ˆ θ ML .10. On the last line of page 150, replace ”... at the most ...” by ”... at most ...” i.e., delete”the”. Chapter 5 1. On page 177, on the right hand side of equation (5.21), replace A by A , i.e. the A should be capital italic, not capital calligraphic.2. On page 187, in the equations on line 3 and on line 7, the product should be from k = 1 to N − 2 (instead of N − 1).3. On page 192, the right hand side of the first line of equation (5.56) should be P [ R ≥ η | A ] and on the second line , the integral should be ∞ η , i.e. the limits of integrationshould be η and ∞ .2 Chapter 7 1. On page 304, equation (7.76), the element in the third row and second column of matrix C ( t ) should be K ( t + 1 ,t ) (a ”1” is missing).2. On page 318, on the fourth line of Problem 7.4, replace ”... and since X (0) = − X ( T ),...” by ”... and since K (0) = − K ( T ),...” Chapter 9 1. On page 411, equation (9.204) should be: h ( t,ω 0 ) = ℜ{ ˜ s ∗ ( T − t )exp( j ( ω c + ω 0 ) t ) } = c ( T − t )cos(( ω c + ω 0 ) t − ψ ( T − t )) . The changes consist of inserting a closing bracket } at the end of the first line, andreplacing c ( t − t ) by c ( T − t ) after the equality sign on the second line.2 On page 413, the first line of equation (9.208) should be < ˜ s 1 , ˜ s 2 > = ∞−∞ ˜ s ( t − d 1 )˜ s ∗ ( t − d 2 )exp( j ( ω 1 − ω 2 ) t ) dt The change consists of inserting dt at the end of the equation.3. On page 424, the first sentence of Problem 9.5 should be:Consider the CT version of Problem 5.9.4. On page 424, 10th line of Problem 9.5, replace ”intefering” by ”interfering” (an ’r’ ismissing). Chapter 11 1. On page 503, the first line of equation (11.84) should be: Q ( θ , θ k ) = − 12tr Q − 1 Φ k − AΨ k − Ψ T k A T + AΘ k A T The change consists of replacing Ω k by Θ k in the last term of this equation.2. On page 505, replace lines 15 and 16 by:Then by taking the conditional expectation with respect to Y on both sides of (11.93)and using the repeated conditioning identity (11.90), ...The change consists of inserting ”conditional” in front of expectation on line 15, andreplacing (11.89) by (11.90) on line 16.3 3. On page 508, the first subequation of equation (11.108) should beˆ X k ( t ) = a sk ( t ) ˆ X k ( t + 1) + P ck ( t ) ˆ X fk ( t ) /P fk ( t )The change consists of exchanging P ck ( t ) and P fk ( t ) in the last term of the equation.4. On page 509, line 8, ψ k is defined as ψ k = T t =1 ˆ X k ( t ) ˆ X k ( t − 1) + P k ( t,t − 1)A subscript k was omitted in ˆ X ( t − 1).5. On page 512, the left hand side of equation (11.115) should be2ln L G ( Y ) = ··· The Latex source code for this equation contained a minor error.6. On page 516, line 3 of Problem 11.1 should be: H 1 : Y ( t ) = Z ( t ) + V ( t )In other words, replace H 0 by H 1 .7. On page 518, the equation on the second line from the bottom should be q = (1 − a 2 ) P . 8. In the first line of page 521, replace 1 < ℓ < N/ 2 by 1 ≤ ℓ < N/ 2.9. On page 521, the equation appearing on the 6th line from the bottom should be m kℓ = P kℓ v [ˆ Y 1 ( e jω ℓ ) + A k e jω ℓ D k ˆ Y 2 ( e jω ℓ )]Compared to the srcinal equation, this requires replacing the opening parenthesis (on the right hand side of the equation by a square bracket [, inserting a hat on top of Y 2 , and inserting a closing bracket ]. Chapter 12 1. The left hand side of equation (12.174) on page 577 should be L k =0 h k D ( t − k ) = ··· Instead of starting from k = 1, the summation should start from k = 0.4
Jul 23, 2017
#### Honk(hiporosmolar non ketotik)
Jul 23, 2017
Search
Similar documents
View more...
Tags
## Physics & Mathematics
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.
Thanks to everyone for your continued support.
No, Thanks
| 2,402
| 6,756
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-09
|
longest
|
en
| 0.730013
|
https://www.numbersaplenty.com/15688
| 1,669,854,812,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446710777.20/warc/CC-MAIN-20221130225142-20221201015142-00622.warc.gz
| 982,909,423
| 3,587
|
Cookie Consent by FreePrivacyPolicy.com
Search a number
15688 = 233753
BaseRepresentation
bin11110101001000
3210112001
43311020
51000223
6200344
763511
oct36510
923461
1015688
1110872
1290b4
1371aa
145a08
1549ad
hex3d48
15688 has 16 divisors (see below), whose sum is σ = 30780. Its totient is φ = 7488.
The previous prime is 15683. The next prime is 15727. The reversal of 15688 is 88651.
It is a happy number.
15688 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.
It can be written as a sum of positive squares in 2 ways, for example, as 13924 + 1764 = 118^2 + 42^2 .
It is a super-2 number, since 2×156882 = 492226688, which contains 22 as substring.
It is an Ulam number.
Its product of digits (1920) is a multiple of the sum of its prime factors (96).
It is a plaindrome in base 10 and base 15.
It is not an unprimeable number, because it can be changed into a prime (15683) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (7) of ones.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 270 + ... + 322.
15688 is a Friedman number, since it can be written as 8*8+5^6-1, using all its digits and the basic arithmetic operations.
215688 is an apocalyptic number.
It is an amenable number.
15688 is a deficient number, since it is larger than the sum of its proper divisors (15092).
15688 is a wasteful number, since it uses less digits than its factorization.
15688 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 96 (or 92 counting only the distinct ones).
The product of its digits is 1920, while the sum is 28.
The square root of 15688 is about 125.2517464948. The cubic root of 15688 is about 25.0335549425.
It can be divided in two parts, 1568 and 8, that multiplied together give a square (12544 = 1122).
The spelling of 15688 in words is "fifteen thousand, six hundred eighty-eight".
| 592
| 2,046
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.46875
| 3
|
CC-MAIN-2022-49
|
latest
|
en
| 0.912817
|
https://niedrogadroga.pl/pulverisation/Sep_870/
| 1,656,971,599,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-27/segments/1656104496688.78/warc/CC-MAIN-20220704202455-20220704232455-00254.warc.gz
| 469,794,562
| 9,593
|
low consumption ball mill calculation
Welcome to the broken dawn
# low consumption ball mill calculation
## Ball Mill Design/Power Calculation
Jun 19, 2015 · If P is less than 80% passing 70 microns, power consumption will be; Ball Mill Power Calculation Example #1. A wet grinding ball mill in closed circuit is to
## Ball Mill Parameter Selection & Calculation - Power ...
Aug 30, 2019 · 1 Calculation of ball mill capacity. The production capacity of the ball mill is determined by the amount of material required to be ground, and it must have a certain margin when designing and selecting. There are many factors affecting the production capacity of the ball mill, in addition to the nature of the material (grain size, hardness, density, temperature and humidity), the degree of ...
## How to Size a Ball Mill -Design Calculator & Formula
May 15, 2015 · A) Total Apparent Volumetric Charge Filling – including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls – expressed as a percentage of the net internal mill volume (inside liners). B) Overflow Discharge Mills operating at low ball fillings – slurry may accumulate on top of the ball charge; causing, the Total Charge Filling Level to be ...
## AMIT 135: Lesson 7 Ball Mills & Circuits – Mining Mill ...
For overflow ball mills, the charge should not exceed 45% of the mill volume . For grate discharge mills, the charge should occupy about 50% of the mill volume . Bond developed a relationship that can be used to determine the percent charge by volume as a function of the vertical height above the charge, He, and the radius of the mill, R, i.e.,
## Ball mill media optimization - Metcom Tech
torque mill test is the mill energy input divided by the solids load. The energy specific cumulative grinding rate at each screen size is calculated from a torque-mill test as in the example that follows. Torque mill solids load during test: 11.25 kg (24.8 lb) of ball mill feed sample from plant survey. Sample is reconstituted with water to be
## Using Abrasion Index for calculating Steel Balls and mill ...
b. When feed size was 16mm ball consumption was high. When we used 12mm feed it reduced drastically. c. Wt% solids in ball mill : At high wt% solids consumption was high. But at normal wt%solids it was low. Similarly consumption depends on operating parameters which need to experienced by an operator, or do lab R&D tests.
## Optimization of mill performance by using
Optimization of mill performance by using online ball and pulp measurements by B. Clermont* and B. de Haas* Synopsis Ball mills are usually the largest consumers of energy within a mineral concentrator. Comminution is responsible for 50% of the total mineral processing cost. In today’s global markets, expanding mining groups are trying
## Ball Mills - an overview | ScienceDirect Topics
8.3.2.2 Ball mills. The ball mill is a tumbling mill that uses steel balls as the grinding media. The length of the cylindrical shell is usually 1–1.5 times the shell diameter ( Figure 8.11). The feed can be dry, with less than 3% moisture to minimize ball coating, or slurry containing 20–40% water by weight.
## TECHNICAL NOTES 8 GRINDING R. P. King
mill is the energy consumption. The power supplied to the mill is used primarily to lift the load (medium and charge). Additional power is required to keep the mill rotating. 8.1.3 Power drawn by ball, semi-autogenous and autogenous mills A simplified picture of the mill load is shown in Figure 8.3 Ad this can be used to establish the essential ...
## CALCULATION OF THE POWER DRAW OF DRY
of the Bond ball mill grindability test. For all model based methods, a reliable method to calculate mill power draw for a given mill is required for the calculation of power draw. Morrell (1996) proposed a mathematical model for autogenous, semi-autogenous and ball mills which is based on the motion of grinding charge inside the mill.
## reducingreducing power consumption in ball mill project
Ball Mill Design/Power Calculation. Jun 19, 2015 · If P is less than 80% passing 70 microns, power consumption will be; Ball Mill Power Calculation Example #1. A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15
## Ball Mill Motor/Power Sizing Calculation
Sep 15, 2015 · Ball Mill Motor/Power Sizing Calculation. A) Total Apparent Volumetric Charge Filling – including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls – expressed as a percentage of the net internal mill volume (inside liners). B) Overflow Discharge Mills operating at low ball fillings ...
## Orway Mineral Consultants Canada Ltd. Mississauga, ON ...
The Bond equation is used to calculate ball mill specific energy from T 80 to the final product P 80 size. The total circuit specific energy is the sum of the SAG mill and ball mill specific energies. W ... (very low circulating loads) the transfer size is a function of mill performance, .)).) ...
## calculation of specific power consumption of ball mill ...
calculation of specific power consumption of ball mill with. 250tph river stone crushing line in Chile. ... low production cost and simple maintenance method, which can satisfy the requirements about high efficiency and coarse crushing. Output size : 140-250mm Production capacity : 2015-8895T/H ... 20TPH vertical mill for limestone ...
## Ball mill media optimization - Metcom Tech
torque mill test is the mill energy input divided by the solids load. The energy specific cumulative grinding rate at each screen size is calculated from a torque-mill test as in the example that follows. Torque mill solids load during test: 11.25 kg (24.8 lb) of ball mill feed sample from plant survey. Sample is reconstituted with water to be
## (PDF) DESIGN AND FABRICATION OF MINI BALL MILL
May 30, 2016 · Ta chometer or manual calculation is used to . ... Charge behaviour and power consumption in ball mills: ... we need to fabricate a low cost mini ball mill. To fabricate this ball mill
## CALCULATION OF THE POWER DRAW OF DRY
of the Bond ball mill grindability test. For all model based methods, a reliable method to calculate mill power draw for a given mill is required for the calculation of power draw. Morrell (1996) proposed a mathematical model for autogenous, semi-autogenous and ball mills which is based on the motion of grinding charge inside the mill.
## low consumption energy mineral ball mill for or
Low Mineral Consumption Big Ball Mill Grinding Ball Mill. Low Mineral Consumption Big Ball Mill Grinding Ball Mill. Ball Mills Industry Grinder For Mineral Jxsc Machine JXSC ball mill manufacturer has industrial ball mill and small ball mill for sale power range 185800KW During the production process the ball grinding machine may be called cement mill limestone ball mill sand mill coal mill ...
## Modelling and simulation of ball mill wear - ScienceDirect
Feb 01, 1993 · Ball mill specifications [22] Length Inside diameter Operating speed Lifters No. of lifters Lifter profile area Ball size Ball density Ball charge volume Ball hardness Material density (pyrochlore ore) Input tonnage Ball mill liner life span Charge and liner wear rate Operating condition 4.27 m 3.06 m (with lifters) 16.9 rpm Shiplap (see Fig ...
## MILLING CONTROL & OPTIMISATION - Mintek
• Mill feed cuts were prevented, resulting in a stable mill loading. • No huge power dips occurred, since any sign of the mill overloading was detected and rectified timeously. • The standard deviation of the mill load, flotation feed flow and density was considerably less
## (PDF) 📄 Addition of pebbles to a ball-mill to improve ...
of pebbles in the mill charge was low (up to 30%), the larger pebbles wore away significantly faster than ... analogous to the ball-mill calculation. A. ... a 25% saving in steel ball consumption ...
## Low Consumption Small Ball Mill Price - Buy Cement Mill ...
Low Consumption Small Ball Mill Price , Find Complete Details about Low Consumption Small Ball Mill Price,Cement Mill,Silica Sand Ball Mill,Used Ball Mill Sale from Grinding Equipment Supplier or Manufacturer-Henan Winnermac Heavy Industrial Machinery Co., Ltd.
## hot selling low consumption ball mill in czechrepublic
High capacity low consumption alumina ball mill priceOKCHEM Please note that all emails sent by OKCHEM are from servicemail or notifications Please be alert of other emails sent to you in the name of OKCHEM. paint ball mill paint ball mill Suppliers and.
## Ball mill - SlideShare
Apr 24, 2015 · The ball mill is used for grinding materials such as coal,pigments,and fedspar for pottery. Grinding can be carried out in either wet or dry but the former is carried out at low speeds. The advantages of wet grinding are less power consumption,increased capacity,no dust formation etc
## reducingreducing power consumption in ball mill project
Ball Mill Design/Power Calculation. Jun 19, 2015 · If P is less than 80% passing 70 microns, power consumption will be; Ball Mill Power Calculation Example #1. A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15
## Ball charges calculators - thecementgrindingoffice
- Ball top size (bond formula): calculation of the top size grinding media (balls or cylpebs):-Modification of the Ball Charge: This calculator analyses the granulometry of the material inside the mill and proposes a modification of the ball charge in order to improve the mill efficiency:
## calculation of power consumption for ball mills and grinding
Ball Mill Power Calculation Pdf . the power consumption calculation of a ball drum mill The Power Consumption Calculation of a Ball Drum Mill . ball mill design calculation pdf, Chat Online In Grinding, selecting (calculate) the correct or optimum ball size that allows for the best and optimum/ideal or target grind size to be achieved by your
## 5 Ways to Improve the Ball Mill Efficiency - Fote ...
Jan 11, 2020 · In this way, the ball mill efficiency is improved with an appropriate crushing and energy consumption. Ball mills of different length and diameter. The theoretical ratio of length to diameter is between 1.09 and 1.5. While according to different requirements, customers get customized ball mills with different ratios of length to diameter.
## Calculation Of Specific Power Consumption Of Ball
Power Consumption Calculation For Closed Circuit Ball. How to calculate power consumption in ball mill.Technical notes 8 grinding r p king mineral technologies , ball mill power calculation ,figure 85 effect of mill filling on power draft for ball mills the data , a simple equation for calculating net power draft is , austins formula gives slightly higher values than morrells for mills that ...
## MODELING THE SPECIFIC GRINDING ENERGY AND BALL
Ball mill power draw predicted from the Denver slide rule, kW 0 200 400 600 Calculated ball-mill power draw from the m odel derived, kW Data compared Line y=x Fig. 2. Comparison of the ball mill power draw from the Denver slide rule and the proposed model. Dashed line corresponds to y=x.
## 33 Things You Didn't Know About Ball Mill
Aug 24, 2021 · 33. Reasons for high ball consumption of ball mill. If the ball consumption of the ball mill is too high, the causes shall be found and solved in time, so as to save the steel consumption cost and improve the grinding efficiency. The reasons for the high steel consumption are as follows: 1) Steel ball quality. The quality of steel ball has a ...
## low consumption ball mill for copper ore
Low Power Consumption Factory 1830*3000 Steel Ball Mill . Low Power Consumption Factory 1830*3000 Steel Ball Mill For Grinding Copper Ore Coal Mill Size Hot In Kazakhstan And Uzbekistan , Find Complete Details about Low Power Consumption Factory 1830*3000 Steel Ball Mill For Grinding Copper Ore Coal Mill Size Hot In Kazakhstan And Uzbekistan,Ball Mill For Grinding Copper Ore,Steel Ball
## PROCESS CONTROL FOR CEMENT GRINDING IN VERTICAL
The power ingesting of a grinding process is 50-60% in the cement production power consumption. The Vertical Roller Mill (VRM) reduces the power consumption for cement grinding approximately 30-40% associated with other grinding mills. The process variables in cement grinding process using VRM are strongly nonlinear and having large time
## Choosing Cutting Parameters/Calculating Cutting Speed and ...
4. Calculate the Table Feed V f (m/min) Use the formula: V f = N * f n * K f. K f is the feed rate multiplier coefficient taking into consideration that chip load is less than theoretical value. Take the value of K f from Table 5 or Table 6. 3. Calculate Spindle Speed Use the formula: N = SFM x 3.82 (÷Dw) Table 3 - Working Diameter For Ball ...
## Ball Mill For Limestone Grinding Power Calculation- EXODUS ...
Calculation of cement ball mill capacity calculation ball mill pdf free download calculation of the power draw of dry multicompartment ball mills description calculation of a power is a pivotal equipment for regrinding it is widely used for a cement oline chat. More Details Calculation Of Power Consumption For Ball Mills And Grinding.
## PROCESS DIAGNOSTIC STUDIES FOR CEMENT MILL
Ball mills are predominantly used machines for grinding in the cement industry. Although ball mills ... • Empty heights of both the chambers measured to calculate the ball charge, % filling and estimate the power consumption at mill shaft. Based on the empty height measurements, charging of grinding media in ... consumption of mill section.
## china high efficient low consumption paint ball mill machine
high efficient ore grinding mill with low price in china. high efficient ore grinding mill with low price in china. Ftm good prices nonmetallic ores and rocks ball mill features low energy consumption ball mill production line adopted high advanced energysaving technology and classification technique as a result, our production line can save over energy for producing same quantity materialsget ...
## low consumption wet raw ball mill flotation cell
Jul 29 Ball mill A ball mill is a type of grinder used to grind and blend materials for use in mineral dressing The grinding media is the balls which may be made of steel chrome steel . Get Price. Get Price; iron power making plant ball mill with low consumption. Ball Mill Power Calculation Example #1.
| 3,147
| 14,483
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.875
| 3
|
CC-MAIN-2022-27
|
latest
|
en
| 0.872457
|
https://www.slideserve.com/paul2/continuous-probability-distributions
| 1,511,354,962,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934806586.6/warc/CC-MAIN-20171122122605-20171122142605-00597.warc.gz
| 885,630,059
| 17,599
|
1 / 55
# Continuous Probability Distributions - PowerPoint PPT Presentation
Exponential. f ( x ). Uniform. f ( x ). Normal. f ( x ). x. x. x. Continuous Probability Distributions. Uniform Probability Distribution Normal Probability Distribution Exponential Probability Distribution. Continuous Probability Distributions.
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
## PowerPoint Slideshow about 'Continuous Probability Distributions' - paul2
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
f (x)
Uniform
f (x)
Normal
f (x)
x
x
x
Continuous Probability Distributions
• Uniform Probability Distribution
• Normal Probability Distribution
• Exponential Probability Distribution
• A continuous random variable can assume any value in an interval on the real line or in a collection of intervals.
• It is not possible to talk about the probability of the random variable assuming a particular value.
• Instead, we talk about the probability of the random variable assuming a value within a given interval.
f (x)
Uniform
f (x)
Normal
f (x)
x
x1
x2
x1
x2
x
x1
x2
x
x1
x2
Continuous Probability Distributions
• The probability of the random variable assuming a value within some given interval from x1 to x2 is defined to be the area under the graph of the probability density function between x1and x2.
• A random variable is uniformly distributed whenever the probability is proportional to the interval’s length.
• The uniform probability density function is:
f (x) = 1/(b – a) for a<x<b
= 0 elsewhere
where: a = smallest value the variable can assume
b = largest value the variable can assume
• Expected Value of x
• Variance of x
E(x) = (a + b)/2
Var(x) = (b - a)2/12
• Uniform Probability Distribution
Slater customers are charged
for the amount of salad they take.
Sampling suggests that the
uniformly distributed
between 5 ounces and 15 ounces.
• Uniform Probability Density Function
f(x) = 1/10 for 5 <x< 15
= 0 elsewhere
where:
x = salad plate filling weight
• Expected Value of x
• Variance of x
E(x) = (a + b)/2
= (5 + 15)/2
= 10
Var(x) = (b - a)2/12
= (15 – 5)2/12
= 8.33
10
15
Example: Slater's Buffet
• Uniform Probability Distribution
f(x)
1/10
x
10
12
15
Example: Slater's Buffet
What is the probability that a customer
will take between 12 and 15 ounces of salad?
f(x)
P(12 <x< 15) = 1/10(3) = .3
1/10
x
• The normal probability distribution is the most important distribution for describing a continuous random variable.
• It is widely used in statistical inference.
• It has been used in a wide variety of applications:
Heights
of people
Scientific
measurements
• It has been used in a wide variety of applications:
Test
scores
• Amounts
• of rainfall
= mean
= standard deviation
= 3.14159
e = 2.71828
Normal Probability Distribution
• Normal Probability Density Function
where:
• Characteristics
The distribution is symmetric, and is bell-shaped.
x
• Characteristics
The entire family of normal probability
distributions is defined by itsmeanm and its
standard deviations .
Standard Deviation s
x
Mean m
• Characteristics
The highest point on the normal curve is at the
mean, which is also the median and mode.
x
• Characteristics
The mean can be any numerical value: negative,
zero, or positive.
x
-10
0
20
• Characteristics
The standard deviation determines the width of the
curve: larger values result in wider, flatter curves.
s = 15
s = 25
x
• Characteristics
Probabilities for the normal random variable are
given by areas under the curve. The total area
under the curve is 1 (.5 to the left of the mean and
.5 to the right).
.5
.5
x
are within of its mean.
68.26%
+/- 1 standard deviation
of values of a normal random variable
are within of its mean.
95.44%
+/- 2 standard deviations
of values of a normal random variable
are within of its mean.
99.72%
+/- 3 standard deviations
Normal Probability Distribution
• Characteristics
95.44%
68.26%
Normal Probability Distribution
• Characteristics
x
m
m + 3s
m – 3s
m – 1s
m + 1s
m – 2s
m + 2s
A random variable having a normal distribution
with a mean of 0 and a standard deviation of 1 is
said to have a standard normal probability
distribution.
The letter z is used to designate the standard
normal random variable.
s = 1
z
0
• Converting to the Standard Normal Distribution
We can think of z as a measure of the number of
standard deviations x is from .
is used to compute the cumulative
probability given a z value.
NORMSDIST
is used to compute the z value
given a cumulative probability.
NORMSINV
Using Excel to ComputeStandard Normal Probabilities
• Excel has two functions for computing probabilities and z values for a standard normal distribution:
NORM S DIST
NORM S INV
(The “S” in the function names reminds
us that they relate to the standard
normal probability distribution.)
Using Excel to Compute cumulativeStandard Normal Probabilities
• Formula Worksheet
Using Excel to Compute cumulativeStandard Normal Probabilities
• Value Worksheet
Using Excel to Compute cumulativeStandard Normal Probabilities
• Formula Worksheet
Using Excel to Compute cumulativeStandard Normal Probabilities
• Value Worksheet
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Standard Normal Probability Distribution
Pep Zone sells auto parts and supplies
oil. When the stock of this oil drops to
20 gallons, a replenishment order is
placed.
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Standard Normal Probability Distribution
The store manager is concerned that sales are being lost due to stockouts while waiting for an order. It has been determined that demand during replenishment leadtime is normally distributed with a mean of 15 gallons and a standard deviation of 6 gallons.
The manager would like to know the probability of a stockout, P(x > 20).
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Stockout Probability
Step 1: Convert x to the standard normal distribution.
z = (x - )/
= (20 - 15)/6
= .83
Step 2: Find the area under the standard normal
curve between the mean and z = .83.
see next slide
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Probability Table for the
Standard Normal Distribution
P(0 <z< .83)
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Stockout Probability
Step 3: Compute the area under the standard normal
curve to the right of z = .83.
P(z > .83) = .5 – P(0 <z< .83)
= 1- .2967
= .2033
Probability
of a stockout
P(x > 20)
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Stockout Probability
Area = .5 - .2967
= .2033
Area = .2967
z
0
.83
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Standard Normal Probability Distribution
If the manager of Pep Zone wants the probability of a stockout to be no more than .05, what should the reorder point be?
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Reorder Point
Area = .4500
Area = .0500
z
0
z.05
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Reorder Point
Step 1: Find the z-value that cuts off an area of .05
in the right tail of the standard normal
distribution.
We look up the area
(.5 - .05 = .45)
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Reorder Point
Step 2: Convert z.05 to the corresponding value of x.
x = + z.05
= 15 + 1.645(6)
= 24.87 or 25
A reorder point of 25 gallons will place the probability
of a stockout during leadtime at (slightly less than) .05.
Pep cumulative
Zone
5w-20
Motor Oil
Example: Pep Zone
• Solving for the Reorder Point
By raising the reorder point from 20 gallons to
25 gallons on hand, the probability of a stockout
decreases from about .20 to .05.
This is a significant decrease in the chance that Pep
Zone will be out of stock and unable to meet a
customer’s desire to make a purchase.
Using Excel to Compute cumulativeNormal Probabilities
• Excel has two functions for computing cumulative probabilities and x values for any normal distribution:
NORMDIST is used to compute the cumulative
probability given an x value.
NORMINV is used to compute the x value given
a cumulative probability.
Pep cumulative
Zone
5w-20
Motor Oil
Using Excel to ComputeNormal Probabilities
• Formula Worksheet
Pep cumulative
Zone
5w-20
Motor Oil
Using Excel to ComputeNormal Probabilities
• Value Worksheet
Note: P(x> 20) = .2023 here using Excel, while our
previous manual approach using the z table yielded
.2033 due to our rounding of the z value.
SLOW cumulative
Exponential Probability Distribution
• The exponential probability distribution is useful in describing the time it takes to complete a task.
• The exponential random variables can be used to describe:
Time between
vehicle arrivals
at a toll booth
Time required
to complete
a questionnaire
Distance between
major defects
in a highway
for cumulativex> 0, > 0
Exponential Probability Distribution
• Density Function
where: = mean
e = 2.71828
Exponential Probability Distribution cumulative
• Cumulative Probabilities
where:
x0 = some specific value of x
Using Excel to Compute cumulativeExponential Probabilities
The EXPONDIST function can be used to compute
exponential probabilities.
The EXPONDIST function has three arguments:
1stThe value of the random variable x
2nd1/m
the inverse of the mean
number of occurrences
in an interval
3rd“TRUE” or “FALSE”
we will always enter
“TRUE” because we’re seeking a cumulative probability
Using Excel to Compute cumulativeExponential Probabilities
• Formula Worksheet
Using Excel to Compute cumulativeExponential Probabilities
• Value Worksheet
Example: Al’s Full-Service Pump cumulative
• Exponential Probability Distribution
The time between arrivals of cars
at Al’s full-service gas pump follows
an exponential probability distribution
with a mean time between arrivals of
3 minutes. Al would like to know the
probability that the time between two successive
arrivals will be 2 minutes or less.
.4 cumulative
.3
.2
.1
Example: Al’s Full-Service Pump
• Exponential Probability Distribution
f(x)
P(x< 2) = 1 - 2.71828-2/3 = 1 - .5134 = .4866
x
1 2 3 4 5 6 7 8 9 10
Time Between Successive Arrivals (mins.)
Using Excel to Compute cumulativeExponential Probabilities
• Formula Worksheet
Using Excel to Compute cumulativeExponential Probabilities
• Value Worksheet
Relationship between the Poisson cumulativeand Exponential Distributions
The Poisson distribution
provides an appropriate description
of the number of occurrences
per interval
The exponential distribution
provides an appropriate description
of the length of the interval
between occurrences
| 2,870
| 11,427
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.84375
| 4
|
CC-MAIN-2017-47
|
latest
|
en
| 0.813591
|
http://wiki.stat.ucla.edu/socr/index.php?title=AP_Statistics_Curriculum_2007_Gamma&diff=11153&oldid=11146
| 1,521,796,529,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-13/segments/1521257648205.76/warc/CC-MAIN-20180323083246-20180323103246-00191.warc.gz
| 319,461,380
| 6,547
|
# AP Statistics Curriculum 2007 Gamma
(Difference between revisions)
Jump to: navigation, search
Revision as of 20:43, 11 July 2011 (view source)TracyTam (Talk | contribs) (→Gamma Distribution)← Older edit Revision as of 20:49, 11 July 2011 (view source)TracyTam (Talk | contribs) (→Example)Newer edit → Line 52: Line 52: Suppose you are fishing and you expect to get a fish once every 1/2 hour. Compute the probability that you will have to wait between 2 to 4 hours before you catch 4 fish. Suppose you are fishing and you expect to get a fish once every 1/2 hour. Compute the probability that you will have to wait between 2 to 4 hours before you catch 4 fish. - One fish every 1/2 hour means we would expect to get $\theta=1/0.5=2$ fish every hour on average. Using $\theta=2$ and $k=4$, we can compute this as follows: + One fish every 1/2 hour means we would expect to get $\theta=1/0.5=2 fish every hour on average. Using [itex]\theta=2 and [itex]k=4, we can compute this as follows: :[itex]P(2\le X\le 4)=\sum_{x=2}^4\frac{x^{4-1}e^{-x/2}}{\Gamma(4)2^4}=0.12388$ :$P(2\le X\le 4)=\sum_{x=2}^4\frac{x^{4-1}e^{-x/2}}{\Gamma(4)2^4}=0.12388$
## Revision as of 20:49, 11 July 2011
### Gamma Distribution
Definition: Gamma distribution is a distribution that arises naturally in processes for which the waiting times between events are relevant. It can be thought of as a waiting time between Poisson distributed events.
Probability density function: The waiting time until the hth Poisson event with a rate of change λ is
$P(x)=\frac{\lambda(\lambda x)^{h-1}}{(h-1)!}{e^{-\lambda x}}$
For $X\sim Gamma(k,\theta)\!$, where k = h and θ = 1 / λ, the gamma probability density function is given by
$\frac{x^{k-1}e^{-x/\theta}}{\Gamma(k)\theta^k}$
where
• e is the natural number (e = 2.71828…)
• k is the number of occurrences of an event
• if k is a positive integer, then Γ(k) = (k − 1)! is the gamma function
• θ = 1 / λ is the mean number of events per time unit, where λ is the mean time between events. For example, if the mean time between phone calls is 2 hours, then you would use a gamma distribution with θ=1/2=0.5. If we want to find the mean number of calls in 5 hours, it would be 5 $\times$ 1/2=2.5.
• x is a random variable
Cumulative density function: The gamma cumulative distribution function is given by
$\frac{\gamma(k,x/\theta)}{\Gamma(k)}$
where
• if k is a positive integer, then Γ(k) = (k − 1)! is the gamma function
• $\textstyle\gamma(k,x/\theta)=\int_0^{x/\theta}t^{k-1}e^{-t}dt$
Moment generating function: The gamma moment-generating function is
$M(t)=(1-\theta t)^{-k}\!$
Expectation: The expected value of a gamma distributed random variable x is
$E(X)=k\theta\!$
Variance: The gamma variance is
$Var(X)=k\theta^2\!$
### Applications
The gamma distribution can be used a range of disciplines including queuing models, climatology, and financial services. Examples of events that may be modeled by gamma distribution include:
• The amount of rainfall accumulated in a reservoir
• The size of loan defaults or aggregate insurance claims
• The flow of items through manufacturing and distribution processes
• The load on web servers
• The many and varied forms of telecom exchange
The gamma distribution is also used to model errors in a multi-level Poisson regression model because the combination of a Poisson distribution and a gamma distribution is a negative binomial distribution.
### Example
Suppose you are fishing and you expect to get a fish once every 1/2 hour. Compute the probability that you will have to wait between 2 to 4 hours before you catch 4 fish.
One fish every 1/2 hour means we would expect to get θ = 1 / 0.5 = 2 fish every hour on average. Using θ = 2 and k = 4, we can compute this as follows:
$P(2\le X\le 4)=\sum_{x=2}^4\frac{x^{4-1}e^{-x/2}}{\Gamma(4)2^4}=0.12388$
The figure below shows this result using SOCR distributions
| 1,143
| 3,913
|
{"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": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.75
| 5
|
CC-MAIN-2018-13
|
longest
|
en
| 0.924558
|
http://geniusbrainteasers.com/month/2014/05/
| 1,701,955,787,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00274.warc.gz
| 21,420,144
| 11,842
|
BRAIN TEASERS
# Monthly Archive - May 2014
brain teasers, puzzles, riddles, mathematical problems, mastermind, cinemania... These are the tasks listed 1 to 10.
Register with your Google Account and start collecting points.
Check your ranking on list.
## Determine the value of the number ABCD
Determine the value of the number ABCD
The first user who solved this task is Djordje Timotijevic.
#brainteasers #math
## CINEMANIA: From which movie is this scene?
CINEMANIA: From which movie is this scene?
The first user who solved this task is Sanja Šabović.
#brainteasers #movie #film #cinemania #riddles
## CINEMANIA: Guess the movie title
A skilled extractor is offered a chance to regain his old life as payment for a task considered to be impossible. Film was made in 2010.
The first user who solved this task is Djordje Timotijevic.
#brainteasers #movie #film #cinemania
### Kyle Kinane: Always a Miracle
Im in my 30s; everybodys having kids or miracles. Oh, its a miracle. Its always a miracle. Im like, You had sex, right? Yeah? Then no, thats exactly whats supposed to happen from that. I spend all my time preventing miracles; that is whats happening. I call it a miracle when the girl doesnt get pregnant. Thats when I start getting spiritual.
Jokes of the day - Daily updated jokes. New jokes every day.
## Find a word that connects all 4 photos
Find a word that connects all 4 photos
The first user who solved this task is Eric Newton.
#brainteasers #wordpuzzles
## What a winning combination?
The computer chose a secret code (sequence of 4 digits from 1 to 6). Your goal is to find that code. Black circles indicate the number of hits on the right spot. White circles indicate the number of hits on the wrong spot.
The first user who solved this task is Sanja Šabović.
#brainteasers #mastermind
## Calculate the number 477
NUMBERMANIA: Calculate the number 477 using numbers [8, 6, 9, 7, 14, 425] and basic arithmetic operations (+, -, *, /). Each of the numbers can be used only once.
The first user who solved this task is Sanja Šabović.
#brainteasers #math #numbermania
## Find the right combination
The computer chose a secret code (sequence of 4 digits from 1 to 6). Your goal is to find that code. Black circles indicate the number of hits on the right spot. White circles indicate the number of hits on the wrong spot.
The first user who solved this task is Darko Nesovic.
#brainteasers #mastermind
## CINEMANIA: From which movie is this scene?
CINEMANIA: From which movie is this scene?
The first user who solved this task is Eric Newton.
#brainteasers #movie #film #cinemania #riddles
## Calculate the number 594
NUMBERMANIA: Calculate the number 594 using numbers [7, 1, 4, 9, 34, 554] and basic arithmetic operations (+, -, *, /). Each of the numbers can be used only once.
The first user who solved this task is Sanja Šabović.
#brainteasers #math #numbermania
## Find values A, B and C and multiply them
Find values A, B and C and multiply them
The first user who solved this task is Slobodan Strelac.
| 798
| 3,048
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.375
| 3
|
CC-MAIN-2023-50
|
latest
|
en
| 0.882213
|
https://discuss.bbchallenge.org/t/decider-unilateral-bouncers/63/4
| 1,680,348,778,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296949958.54/warc/CC-MAIN-20230401094611-20230401124611-00148.warc.gz
| 252,179,647
| 8,340
|
# [Decider] Unilateral Bouncers
Unilateral Bouncers: principle
This attempts to decide [Family] Unilateral bouncers.
The principle is inspired by the former description of unilateral bouncers as “[…] each successive bounce can be inductively described from the previous ones.”
To decide a machine we have an observer follow along with a run of it and try to extract the tape segments and states that we need to inductively proof that the machine never halts.
E.g. If s, i, h are tape segments and X, Y states and we find the rules:
(i) Xh turns into iYh
(ii) iYh turns into Yi
(iii) sY turns into sX
(iv) Xi turns into iX
then starting from sXh we get sXh → siYh → sYih → sXih → siXh → … → siiXh → … → siiiXh → … and can proof by induction that we get all s(i^n)Xh and thus never halt.
To show that the rules always work the machine isn’t allowed to leave the segment that it is currently transforming, i.e. Xi has to be converted into iX without leaving the i part of the tape.
To detect crablike traversing of the increment segment we allow for a buffer b in the detection:
sbXh → siYbh → sYbih → sbXih → sibXh → … → siibXh → … → siiibXh → …
now the rules work as long as e.g. bXi is converted into ibX without leaving the i or b part or the tape.
And the buffer and increment can be different for the left and right movement:
sbXh → siYph → sYpjh → sbXjh → sibXh → … → siibXh → … → siiibXh → …
Once s,h,i,j,b,p,X,Y are defined and the conversions observed (without leaving the relevant tape segment) the decider has found a unilateral bouncer. If an attempt to define the tape segments and states doesn’t lead to the correct conversions we continue the run and try again with new definitions.
Growth direction
The observer only looks for unilateral bouncers that grow to the right. A second observer could be written to find those that grow to the left, but that means any changes have to be made in two places. Mashing them together seems unwise as it would complicate the proof and be prone to errors.
We can find the left-growers by inverting the machines from the seed database before simulating them, i.e. switch all L transitions to R transitions and vice versa. For left-growers that gives us a symmetric machine that grows to the right and can be detected.
Decider examples and counterexamples
Decider code
https://github.com/Iijil1/stuff/blob/main/main.go
Decider tests
https://github.com/Iijil1/stuff/blob/main/main_test.go
Results
110570 Unilateral Bouncers that grow to the left
110781 Unilateral Bouncers that grow to the right
Total: 221351 decided
Database subset of application
11/06/22: I have run the decider on all undecided machines remaining in the seed database, that means 1538612 machines were tested. This was done in two runs, one looking for unilateral bouncers that grow to the right, the other looking for those growing to the left.
Decider correctness
It should be relatively straightforward to proof this decider correct. See this outline for the form the proof could take.
1 Like
Thank you for your work, it is very interesting! I find your idea very elegant and nice to reason about. I have not dived into the code yet as I want to be sure I understand the idea fully first.
`sX.iiih -> siiX.ih -> siiiX.h -> siii.Y(i^k)h -> si.Yii(i^k)h -> s.Yiii(i^k)h -> s(i^p)X.iii(i^k)h`
• I put a ‘.’ to indicate if the machine is looking at the first symbol of the block to the right of the state or to the left, `sX.iiih` means that the machine is in state X currently looking at the left most symbol of the first `i`
• I generalised a bit saying that `X.h` can turn into `.Y(i^k)h` with `k` a constant of the machine (you have k=1). Same in the other direction with p where you have p = 0 in your case.
I would believe that this generalisation, with `p` >= 1 gives some bilateral bouncers.
My points are:
1. I believe that a limitation of your technique is that it assumes that the increment is the same going left and going right? For instance, this bilateral bouncer uses different increments in both directions: https://bbchallenge.org/9821166 but I don’t know if unilateral bouncers can do the same.
2. In the general case wouldn’t you need a buffer `b'` for what comes after `X` as well as what comes before `X`?
3. It seems to me that implementing the above with p>=0 and k>=1 should give us many unilateral and bilateral bouncers. I expect that the machines that we will miss are those that:
• Do not use the same increment in both directions (with a potential offset in how both directions parse the increment)
• Are of “higher order” in the sence that s,i,h,X,Y are not unique but alternate once over two for instance (I believe it is the case of https://bbchallenge.org/2188111)
(Here’s a funny machine which seems to need a buffer for `s`: https://bbchallenge.org/8163699, look in explore mode)
What do you think?
Yeah, the X always reads to the right and the Y always reads to the left. I omitted the direction in the short notation because it reminded me of formal grammar rules.
That X.h turns into .Y(i^k)h seems to me like the result we want to proof? So the rule we need to detect is the base case and that each bounce adds 1 additional iteration. Stuff with k>1 is then handled by the proof later using the segments and rules the decider chose and verified.
(If you think k should be >1 for a single bounce, then i should be longer instead)
Explicitly describing the growth rule in the program would be useful if we want to accelerate the simulation. But it seems unnecessary for classifying and deciding the infinite.
1. In the first simplified description the increment is the same in both direction, just to not throw all the different letters at the reader at once. In the 3rd example sequence there is i for the increment in one direction and j in the other. That is what the decider actually looks for.
2. On the non-buffer side of the state there is the segment we are currently converting into something else. Once whatever segment after that is entered we count that as entering the phase where we convert that new segment. Note that even if we haven’t really finished converting the old segment into its final form, it will now be part of the new buffer and we really only need to be finished with the conversion once the buffer of whatever segment conversion is going on doesn’t cover it any more.
In practice we can choose very long buffers and turn around segments to give enough space for full conversions. Those will then be mostly just repetitions of i/j, but while that would be inconvenient for a manual proof the program handles that sort of thing just fine.
3. The proof technique can be adapted to find bilateral bouncers, I have a version that does that. Some care needs to be taken with the borders of the segments and phase transitions, and how the growth of the tape goes into that. I find it safer to keep them separate for now.
• As mentioned above, different increment in the two directions is not a problem.
• The “higher order” bouncers are indeed not detected. One could write a version to detect those by going through everything twice, detecting and verifying two versions of each segment. But that gets messy and I don’t know if that is worth it with something like CTL on the horizon.
(buffer for s would not really be necessary, just choose a longer s. Though when going through the detection we still need to attach the same buffer to the state, in case it is needed to finish transforming any of the increment segments)
1 Like
I am now convinced that your decider does indeed recognise unilateral bouncers and am also confident that a formal of correctness is within reach.
I propose that we vote on whether your decider should officially be applied on bbchallenge now. Let’s give this vote 2 full weeks, starting now.
Here are my pros and cons:
Pros:
1. The technique is elegant and yields a compact and concise code, amenable to being formally proved correct (@Iijil gave a draft of the proof).
2. The technique seems to allow to decide all unilateral bouncers. (I still personally need to do a bit of work on my side to get 100% convinced but I trust @Iijil confidence on the matter).
Cons:
1. A decider for bilateral bouncers will probably also recognise unilateral bouncers.
2. Unilateral bouncers seem to “only” correspond to ~15% of the currently 1.5M undecided machines. This poses the question of whether even simpler techniques that this one could end up deciding more machines (such as your [Decider] Halting Segment).
My personal vote is in favor of applying the decider: deciding 15% of the currently undecided machines is still a significant contribution and the technique can be proved correct without too many efforts (it seems). I also like the fact that the decider seems to exactly recognise the class of unilateral bouncers. Finally, I would like to acknowledge the significant effort realised by @Iijil to put this decider outhere while achieving all the standards that we care for the code of deciders. Thank you!
I vote we use it. I still need to reconstruct it at some point, haven’t exactly had the most energy to do that recently, but lijil has given quite a lot of evidence that it works, and I’m keen for this project to move along.
1 Like
| 2,194
| 9,306
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.0625
| 3
|
CC-MAIN-2023-14
|
longest
|
en
| 0.923747
|
http://openstudy.com/updates/504d235de4b0f79a4d9255cf
| 1,448,839,674,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2015-48/segments/1448398460263.61/warc/CC-MAIN-20151124205420-00080-ip-10-71-132-137.ec2.internal.warc.gz
| 172,422,189
| 9,507
|
jewjewbri 3 years ago What is the slope of the line that passes through the points (-3, 5) and (1, 7)?
$slope=m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }$ if (-3, 5) is (x1, y1) and (1,7) is (x2, y2), plug in the values.
| 96
| 219
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.1875
| 3
|
CC-MAIN-2015-48
|
longest
|
en
| 0.796086
|
https://forum.ansys.com/forums/topic/transient-structural-connect-solution-of-one-transient-result-to-the-next/
| 1,685,386,348,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-23/segments/1685224644907.31/warc/CC-MAIN-20230529173312-20230529203312-00390.warc.gz
| 297,447,255
| 31,421
|
## General Mechanical
#### Transient Structural: connect solution of one transient result to the next
• Mimi Chen
Subscriber
Hello,
I want to simulate a "human" doing a series of actions, for example:
1. stand up
2. walk 2 meters
3. climb the stairs
I would like to have the three actions in three different transient structural blocks, because then I do not have to recalculate the whole thing again from step 1 if I just want to change something in the step 2 or step 3. So for example, I want to change some parameters at step 3, which means I want to start the simulation when the "human" is 2m away from the original point.
Here's the simulation of the "human" standing up from a chair:
Then, I dragged another transient structural block and connected the "solution" to the "setup":
Then, opened the setup, it shows this, everything from the previous step 1 simulation is gone:
How do I solve this problem?
• peteroznewman
Subscriber
Use Rigid Dynamics instead of Transient Structural, it will take much less time to solve.
• Mimi Chen
Subscriber
True, but I can also make all the parts rigid in Transient Structural, so it works the same as Rigid Dynamics. But that's not the original problem in my post.
• Erik Kostson
Ansys Employee
Hi
Rigid body dynamics system and solver is a completely different solver to transient Structural solver (see help manual for more info).
Rigid dynamics is aimed for rigid body dynamics (say how a mechanism moves), while transient can be used for impact (flexible bodies), earthquake analysis in time domain, shock loads, etc, but not so much for rigid body dynamics (there we use the other system or in 2023 R1 Ansys motion which is also aimed for rigid body dynamics).
As for the original question, what you do when you connect them to each other as you show, is to transfer over data (loads or displacements on cut boundaries) in order to do a submodel analysis. See what that means (sub-modelling) and how it is done (static or transient system is the same with regards to submodel).
All the best
Erik
• Mimi Chen
Subscriber
Hi Erik,
I understand that the transient structural and the rigid body dynamics use completely different solver, and that transient strcutural can simulate impact, shock loads, etc., while rigid body dynamics cannot. But for my use case, I can use both transient structural and rigid body dynamics right? And the results should be the same using the two?
I tried to do a simpler simulation of 4-bar-linkage using both transient structural and rigid body dynamics, shown in the screenshot below for results comparison:
As shown in the comparison, I used the same settings for everything, but the results using two different solvers are completely different: Max stress 151.99 Pa for rigid body dynamics and 15693 Pa for transient structural, I don't understand why this happens? Do you have a clue?
Moreover, coming back to the topic of my original question, I checked the submodeling video, and find it not so relevant to what I asked about. As I understood, submodeling is something like running a "coarse" parent analysis first on a large assembly, then run a "finer" analysis in a specific part. However, what I wanted to ask is to solve step 1: sit to stand, then use the result from step 1 directly to solve step 2, so whenever I want to change a parameter in step 2, I don't have to re-run step 1 again. These two steps are basically using the same mesh and not a finer mesh, just two differen actions. I hope this explanation is clearer. Is this possible?
Thank you and best regards,
Mimi
| 805
| 3,594
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-23
|
latest
|
en
| 0.899789
|
http://oeis.org/A007963
| 1,542,264,300,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-47/segments/1542039742567.46/warc/CC-MAIN-20181115054518-20181115080518-00200.warc.gz
| 235,673,973
| 5,328
|
This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007963 Number of (unordered) ways of writing 2n+1 as a sum of 3 odd primes. 12
0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 6, 8, 7, 9, 10, 10, 10, 11, 12, 12, 14, 16, 14, 16, 16, 16, 18, 20, 20, 20, 21, 21, 21, 27, 24, 25, 28, 27, 28, 33, 29, 32, 35, 34, 30, 37, 36, 34, 42, 38, 36, 46, 42, 42, 50, 46, 47, 53, 50, 45, 56, 54, 46, 62, 53, 48, 64, 59, 55, 68, 61, 59, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,7 COMMENTS Ways of writing 2n+1 as p+q+r where p,q,r are odd primes with p <= q <= r. The two papers of Helfgott appear to provide a proof of the Odd Goldbach Conjecture that every odd number greater than five is the sum of three primes. (The paper is still being reviewed.) - Peter Luschny, May 18 2013; N. J. A. Sloane, May 19 2013 REFERENCES George E. Andrews, Number Theory (NY, Dover, 1994), page 111. Ivars Peterson, The Mathematical Tourist (NY, W. H. Freeman, 1998, pages 35-37. Paulo Ribenboim, "VI, Goldbach's famous conjecture," The New Book of Prime Number Records, 3rd ed. (NY, Springer, 1996), pages 291-299. LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 H. A. Helfgott, Minor arcs for Goldbach's problem, arXiv:1205.5252 [math.NT], 2012. H. A. Helfgott, Major arcs for Goldbach's theorem, arXiv:1305.2897 [math.NT], 2013. H. A. Helfgott, The ternary Goldbach conjecture is true, arxiv:1312.7748 [math.NT], 2013. H. A. Helfgott, The ternary Goldbach problem, arXiv:1404.2224 [math.NT], 2014. F. Smarandache, Only Problems, Not Solutions!. EXAMPLE a(10) = 4 because 21 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7. MAPLE A007963 := proc(n) local a, i, j, k, p, q, r ; a := 0 ; for i from 2 do p := ithprime(i) ; for j from i do q := ithprime(j) ; for k from j do r := ithprime(k) ; if p+q+r = 2*n+1 then a := a+1 ; elif p+q+r > 2*n+1 then break; end if; end do: if p+2*q > 2*n+1 then break; end if; end do: if 3*p > 2*n+1 then break; end if; end do: return a; end proc: seq(A007963(n), n=0..30) ; # R. J. Mathar, Sep 06 2014 MATHEMATICA nn = 75; ps = Prime[Range[2, nn + 1]]; c = Flatten[Table[If[i >= j >= k, i + j + k, 0], {i, ps}, {j, ps}, {k, ps}]]; Join[{0, 0, 0, 0}, Transpose[Take[Rest[Sort[Tally[c]]], nn+2]][[2]]] (* T. D. Noe, Apr 08 2014 *) PROG (Sage) def A007963(n): c = 0 for p in Partitions(n, length = 3): b = True for t in p: b = is_prime(t) and t > 2 if not b: break if b : c = c + 1 return c [A007963(2*n+1) for n in (0..77)] # Peter Luschny, May 18 2013 (Perl) use ntheory ":all"; sub a007963 { my(\$n, \$c)=(shift, 0); forpart { \$c++ if vecall { is_prime(\$_) } @_; } \$n, {n=>3, amin=>3}; \$c; } say "\$_ ", a007963(2*\$_+1) for 0..100; # Dana Jacobsen, Mar 19 2017 (PARI) a(n)=my(k=2*n+1, s, t); forprime(p=(k+2)\3, k-6, t=k-p; forprime(q=t\2, min(t-3, p), if(isprime(t-q), s++))); s \\ Charles R Greathouse IV, Mar 20 2017 CROSSREFS Cf. A068307, A087916, A294294 (lower bound of scatterplot), A294357, A294358 (records). Sequence in context: A248868 A320614 A030566 * A137222 A077641 A194210 Adjacent sequences: A007960 A007961 A007962 * A007964 A007965 A007966 KEYWORD nonn AUTHOR R. Muller EXTENSIONS Corrected and extended by David W. Wilson 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified November 15 01:39 EST 2018. Contains 317224 sequences. (Running on oeis4.)
| 1,558
| 3,931
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-47
|
latest
|
en
| 0.71645
|
https://uscollegeresearch.com/academic-help-online-1905/
| 1,685,815,034,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-23/segments/1685224649302.35/warc/CC-MAIN-20230603165228-20230603195228-00102.warc.gz
| 660,145,505
| 9,627
|
# Academic help online
1. A company currently sells 60,000 units a month at \$10 per unit. The marginal cost per unit is \$6. The company is considering raising the price by 10% to \$11. If the price elasticity of demand is _______________ in that price range, then profit would increase if the company decided to raise the price by 10%.a. Equal to –3b. Greater than +1c. Less than –3.5d. Greater than –22. The price elasticity of demand for bread is –0.5. If the price falls by 5%, the quantity demanded will change by:a. –2 .5%b. +2.5%c. –1.0%d. +10%3. Actions a firm can take to change a product’s demand curve include:a. Reducing the price of a substitute product the firm also produces.b. Reducing the price of a complementary product the firm also produces.c. Differentiating its product from competitors by offering an extended warrantee.d. All of the above will change a product’s demand curve.4. A product can be classified as a normal good if an increase in the income of buyers causes:a. A decrease in quantity demanded.b. A decrease in demand.c. An increase in demand.d. An increase in quantity demanded.5. Assume that beer and pretzels are complements in consumption; if the price of beer increases, we would expect to see:a. An increase in the demand for pretzels.b. A decrease in the demand for pretzels.c. An increase in the quantity of pretzels demanded.d. A decrease in the quantity of potatoes demanded.
| 348
| 1,423
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.65625
| 3
|
CC-MAIN-2023-23
|
longest
|
en
| 0.905082
|
http://math.stackexchange.com/questions/270780/listing-all-the-subfield-and-corresponding-subgroup
| 1,469,399,512,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-30/segments/1469257824185.14/warc/CC-MAIN-20160723071024-00294-ip-10-185-27-174.ec2.internal.warc.gz
| 165,299,409
| 18,569
|
Listing all the subfield and corresponding subgroup
Here is an exercise in the book of Dummit Foote :
Find the Galois group of the splitting field of $(x^2-2)(x^2-3)(x^2-5)$ over $\mathbb{Q}$. Then list all the subgroups and the corresponding subfield
Here is my argument :
It is not hard to see that $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})=K$ is the splitting field for the above polynomial. Since the degree of the extension $K/\mathbb{Q}$ is 8, so the order of the Galois group is 8. The automorphism in $Gal(K/\mathbb{Q})$ are :
\begin{cases} \sqrt{2}\mapsto \sqrt{2}\\ \sqrt{3}\mapsto \sqrt{3}\\ \sqrt{5}\mapsto -\sqrt{5}\\ \end{cases} \begin{cases} \sqrt{2}\mapsto \sqrt{2}\\ \sqrt{3}\mapsto -\sqrt{3}\\ \sqrt{5}\mapsto -\sqrt{5}\\ \end{cases} \begin{cases} \sqrt{3}\mapsto \sqrt{3}\\ \sqrt{5}\mapsto \sqrt{5}\\ \sqrt{2}\mapsto -\sqrt{2}\\ \end{cases} \begin{cases} \sqrt{3}\mapsto \sqrt{3}\\ \sqrt{2}\mapsto -\sqrt{2}\\ \sqrt{5}\mapsto -\sqrt{5}\\ \end{cases} \begin{cases} \sqrt{5}\mapsto \sqrt{5}\\ \sqrt{2}\mapsto -\sqrt{2}\\ \sqrt{3}\mapsto -\sqrt{3}\\ \end{cases} \begin{cases} \sqrt{5}\mapsto \sqrt{5}\\ \sqrt{3}\mapsto -\sqrt{3}\\ \sqrt{2}\mapsto -\sqrt{2}\\ \end{cases} \begin{cases} \sqrt{5}\mapsto -\sqrt{5}\\ \sqrt{2}\mapsto -\sqrt{2}\\ \sqrt{3}\mapsto -\sqrt{3}\\ \end{cases} \begin{cases} \sqrt{5}\mapsto \sqrt{5}\\ \sqrt{2}\mapsto \sqrt{2}\\ \sqrt{3}\mapsto \sqrt{3}\\ \end{cases}
From there, we see that except the identity map(the last map) are of order 2. But I do not know any group of order 8 having that property.
My first question is : what is the Galois group in this case ?
Here is the other argument :
Any element of $K$ can be represented in the form : $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}+e\sqrt{5}+m\sqrt{10}+n\sqrt{15}+p\sqrt{30}$ Under the map : \begin{cases} \sqrt{2}\mapsto -\sqrt{2}\\ \sqrt{3}\mapsto -\sqrt{3}\\ \sqrt{5}\mapsto -\sqrt{5}\\ \end{cases} this element turns to : $a-b\sqrt{2}-c\sqrt{3}+d\sqrt{6}-e\sqrt{5}+m\sqrt{10}+n\sqrt{15}-p\sqrt{30}$.
This element is fixed under that map iff $b=c=e=p=0$ or it must has the form : $a+b\sqrt{6}+c\sqrt{10}+d\sqrt{15}$.
But from that I can not deduce the corresponding subfield with the subgroup generated by the above map. My second question is : What is that corresponding subfield ?
-
wait I'm not seeing how $\sqrt{5}$ is in the splitting field... did you make a typo? – dinoboy Jan 5 '13 at 8:20
+1 for the formatting effort. – user1551 Jan 5 '13 at 8:25
Thanks @dinoboy for [pointing it out. I have edited it. – knot Jan 5 '13 at 8:29
For the first question, consider $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$. Note this relationship for "independent" automorphisms.
Alright, since I don't know how to do the larger tables in latex here (usually I use xymatrix!) lets (diagrammatically) look at the example at the beginning of 14.2 in Dummit and Foote. The Galois group of $\mathbb{Q}(\sqrt{2},\sqrt{3})/\mathbb{Q}$ gives the table
$$\begin{array}{cccccccc} & \{1\} & \\ \nearrow & \uparrow & \nwarrow \\ \{1,\tau\} & \{1,\sigma\tau\} & \{1,\sigma\} \\ \nwarrow & \uparrow & \nearrow \\ & \{1,\sigma,\tau,\sigma\tau\} \end{array}$$ In particular, when both $\sqrt{2}$ and $\sqrt{3}$ are permuted, the fixed field is $\mathbb{Q}(\sqrt{6})$.
Now, in our larger example, if $\sqrt{6}$ is fixed, the automorphism $\sigma_2\sigma_3$ is being applied (where $\sigma_n:\sqrt{n}\mapsto -\sqrt{n}$). Similarly, when $\sqrt{10}$ and $\sqrt{15}$ are fixed, the respective automrophisms are $\sigma_2\sigma_5$ and $\sigma_3\sigma_5$. Here's where a complete description of the Galois group is useful: $$\operatorname{Gal}(\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})/\mathbb{Q}) \simeq \{1,\sigma_2,\sigma_3,\sigma_5,\sigma_2\sigma_3,\sigma_2\sigma_5,\sigma_3\sigma_5,\sigma_2\sigma_3\sigma_5\}$$
The subgroup you're interested in is then $\{1,\sigma_2\sigma_3,\sigma_2\sigma_5,\sigma_3\sigma_5\}$.
-
Ok, I get your idea, but could you please show me what was wrong in my second argument? (the argument of the subfield) – knot Jan 5 '13 at 8:39
So, what is the fixed field for the group generated by that map ($\sqrt{2}\mapsto-\sqrt{2},$\sqrt{3}\mapsto-\sqrt{3}, $\sqrt{5}\mapsto-\sqrt{5})$ ? – knot Jan 5 '13 at 9:01
@knot, alright....... hopefully I'm not making any sleep deprived mistakes this time! I completely misinterpreted something from my initial reading of the question (my fault, not yours!) but I hope it's OK now. – Alex Jan 5 '13 at 9:30
| 1,613
| 4,488
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.65625
| 4
|
CC-MAIN-2016-30
|
latest
|
en
| 0.447166
|
https://www.coursehero.com/file/6845438/Lecture-15-Thermochemistry-Part-2/
| 1,521,472,207,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-13/segments/1521257646952.38/warc/CC-MAIN-20180319140246-20180319160246-00605.warc.gz
| 780,012,101
| 444,747
|
{[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
Lecture 15 - Thermochemistry Part 2
# Lecture 15 - Thermochemistry Part 2 - Oct 5 2011 Lecture 15...
This preview shows pages 1–7. Sign up to view the full content.
1 Lecture 15 Thermochemistry, part 2 Internal energy changes The internal energy of a system is the sum of all the KE and PE of all of the components of the system. Changes are defined as final minus initial ' E = E final - E initial Oct 5, 2011
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2 First Law of Thermodynamics The first law of thermodynamics states that the energy gained or lost by a system must equal the energy lost or gained by (cal) is the amount of heat necessary to raise the temperature of 1 g of ' E = q + w ' E = change in system’s internal energy (energy gain is positive) q = heat (heat absorbed is positive) w = work (work done by system is negative) Work done by the system Work is force times distance many types of work, including “PV” work Change in Internal Energy 2-1 2-2 2-3
3 Energy flow: heat and work Enthalpy (H) = E + PV Change in Enthalpy ( ' H) = ' E + P ' V At constant pressure q P = ' E + P ' V, therefore q P = ' H ' H = change in enthalpy: an energy flow as heat (at constant pressure) ' H > 0, Endothermic; ' H < 0, Exothermic Enthalpy and Change in Enthalpy
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
4 Enthalpy for heating Heat Capacities Molar heat capacity (c p ) is the heat required to raise the temperature of 1 mole of a substance by 1 o C at constant pressure. q = nc p ' T ) is the heat required to of a ) is the quantity of heat needed to raise the temperature of some 4-1
5 Heat capacities can vary Substance c p (J/mol·°C) Water (s) 37.1 Water (l) 75.3 Ethanol (l) 113.1 Graphite C(s) 8.54 Al, Cu, Fe (s) 24.4, 24.5, 25.1 Specific Heat Capacity: Example A 1.0 gram block of Al (c s = 0.9 J/°Cg) at 100°C and a 1.0 gram block of Fe (c s = 0.4 J/°Cg) at 0 °C are added to 10 mL of water (c s = 4.2 J/°Cg) at 50°C. What will be the final temperature of the water? A) < 50 °C B) 50 °C C) > 50 °C
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
6 Specific Heat Capacity of Al and Fe Consider the following arguments for each answer and vote: A. The specific heat capacity of Fe(s) is smaller than that of Al(s), so heat from both the Al(s) and the water will be required to warm the Fe(s).
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### Page1 / 16
Lecture 15 - Thermochemistry Part 2 - Oct 5 2011 Lecture 15...
This preview shows document pages 1 - 7. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online
| 815
| 2,860
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-13
|
latest
|
en
| 0.865479
|
https://quant.stackexchange.com/questions/36665/is-there-uniform-stochastic-process/36666
| 1,716,330,270,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-22/segments/1715971058522.2/warc/CC-MAIN-20240521214515-20240522004515-00361.warc.gz
| 407,886,898
| 37,726
|
# Is there uniform stochastic process?
Shall I construct a stochastic process $X(t)$ such that $X(s+t)-X(s)\sim U(-t,t)$ ? Or is there already any similar formula?
Let $U$ be uniform in $[-1,1]$ and let $X_t=Ut$, which is uniform in $[-t,t]$. Then $$X_{t+s}-X_s=U(t+s)-Us=Ut$$ so this works. So it's not so much a stochastic process as just a random variable giving the slope of a line.
| 118
| 388
|
{"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}
| 2.765625
| 3
|
CC-MAIN-2024-22
|
latest
|
en
| 0.88669
|
https://www.thenational.academy/teachers/lessons/solving-a-simultaneous-equation-algebraically-6gukjd
| 1,719,301,172,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-26/segments/1718198865694.2/warc/CC-MAIN-20240625072502-20240625102502-00017.warc.gz
| 895,698,634
| 36,169
|
# Solving a simultaneous equation algebraically
## Switch to our new maths teaching resources
Slide decks, worksheets, quizzes and lesson planning guidance designed for your classroom.
## Lesson details
### Key learning points
1. In this lesson, we will learn to solve simultaneous equations algebraically. We will interpret pictorial representations of equations and write them as simultaneous algebraic equations.
### Licence
This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
## Video
Share with pupils
## Worksheet
Share with pupils
## Starter quiz
Share with pupils
### 5 Questions
Q1.
If x=2 and y=3, what is the value of 2x+3y?
12
4x+9y
5
Q2.
Is x=3 the solution to 2x+7=13?
no
Q3.
Use substitution to decide which of the following are solutions to x+y=3.
Correct answer: x=2 and y=1
x=3 and y=0
y=1 and x=1
Q4.
Use substitution to decide which of the following is the solution to x+y=3 and 3x+4y=10.
x=1 and y = 2
Correct answer: x=2 and y = 1
x=3 and y=4
x=4 and y=-0.5
Q5.
Use substitution to decide which of the following is the solution to x+y=3 and 5y+3x=15.
Correct answer: x=0 and y = 3
x=1 and y=2
x=1.5 and y = 1.5
x=2 and y=1
## Exit quiz
Share with pupils
### 5 Questions
Q1.
If x=3 and 2x+5y=41, what is the value of y?
3
5
7.8
Q2.
7x+2y=24 AND 4x+2y=18. Find the value of 3x
2
5
7
Q3.
7x+2y=24 AND 4x + 2y = 18. Find the value of y
2
6
7
Q4.
9x +6y=168 AND 9x +4y=160. Solve
Others
x=15 and y = 18
Correct answer: x=16 and y=4
x=9 and y=6
y=16 and x=4
Q5.
4x +8y=116 AND 4x +4y=68. Solve
x=12 and y=5
x=4 and y = 8
Correct answer: x=5 and y=12
x=8 and y = 4
| 606
| 1,717
|
{"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}
| 4.71875
| 5
|
CC-MAIN-2024-26
|
latest
|
en
| 0.848181
|
https://edspi31415.blogspot.com/2018/08/hp-12c-platinum-and-dm-41l-rounding.html
| 1,603,507,191,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-45/segments/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00510.warc.gz
| 306,490,164
| 20,824
|
## Monday, August 27, 2018
### HP 12C Platinum and DM 41L: Rounding Numbers
HP 12C Platinum and DM 41L: Rounding Numbers
Introduction
The following programs will round any positive number to any number of decimal places, regardless of your fix/float settings. The formula for rounding x to n decimal places:
int(10^n * x + 0.5) / 10^n
HP 12C Platinum Program (also for HP 12C): Rounding a positive number
Step Key Code Key 001 1 1 002 0 0 003 34 x<>y 004 21 y^x 005 20 * 006 43, 40 LST x For HP 12C regular: the code is 43, 36 007 34 x<>y 008 48 . 009 5 5 010 40 + 011 43, 25 ITNG 012 34 x<>y 013 10 ÷ 014 43, 33, 000 GTO 000
DM 41L (also for HP 41C) Program ROUND: Rounding a positive number
01 LBL ROUND
02 10^X
03 *
04 LASTx
05 x<>y
06 .5
07 +
08 INT
09 x<>y
10 /
11 RTN
Examples
Instructions: Enter x, press [ENTER], enter n, execute the program
x n Result 0.83 1 0.8 8.21365 4 8.2137 170561.7737 0 170562 π 4 3.1416
Source:
Keith Oldham, Jan Myland, and Jerome Spanier An Atlas of Functions Second Edition, Springer. 2009 ISBN 978-0-387-48806-6
Eddie
All original content copyright, © 2011-2018. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.
#### 1 comment:
1. I've got to give your 12C and 15C programs a try. I recently unpacked my calculators from my move.
### HP 42S/DM42: Height of a Fire, Time to Clear a Corridor
HP 42S/DM42: Height of a Fire, Time to Clear a Corridor HP 42S/DM42/Free42 Program: FIREHGT The program FHGT approximates the height of a...
| 584
| 1,783
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-45
|
longest
|
en
| 0.642536
|
http://www.velocityreviews.com/forums/printthread.php?t=25940
| 1,386,675,425,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-48/segments/1386164017049/warc/CC-MAIN-20131204133337-00092-ip-10-33-133-15.ec2.internal.warc.gz
| 613,967,832
| 3,206
|
Velocity Reviews (http://www.velocityreviews.com/forums/index.php)
- VHDL (http://www.velocityreviews.com/forums/f18-vhdl.html)
- - Info on packing regular tree-like structures into rectangles? (http://www.velocityreviews.com/forums/t25940-info-on-packing-regular-tree-like-structures-into-rectangles.html)
Info on packing regular tree-like structures into rectangles?
Hi,
I got thinking about recursive design of circuits in VHDL I created a
recursive circuit and got it
to simulate correctly but then had the thought that the RTL is a binary
tree of similar interconnect with each leaf being the same.
When this gets synthesized and layed out I guess that the regularity is
lost unless layed out by hand.
If I were to lay this out by hand, are their any existing papers on
packing such regular structures into rectangular spaces?
Are there any layout and routing tools designed for such tasks?
Ralf Hildebrandt 12-06-2005 03:56 PM
Re: Info on packing regular tree-like structures into rectangles?
f'up to comp.lang.vhdl
> I got thinking about recursive design of circuits in VHDL I created a
> recursive circuit
Hmm .. what do you mean with "recursive circuit"? Eighter the
transistors / cells / macroblocks are implemented or not.
You may design a component, that is used by a controller (like a FSM),
that realizes a recursive algorithm, but then not the circuit is
recursive - only the algorithm is.
> When this gets synthesized and layed out I guess that the regularity is
> lost unless layed out by hand.
Why do you care about regularity of the layout of a digital circuit?
Except for signal delays there is no reason to think about the layout -
AFAIK.
A HDL is such a wounderful thing, that seperates layout problems from
functional behavoir.
Ralf
Re: Info on packing regular tree-like structures into rectangles?
Hi Ralf,
You can instantiate a component inside itself, and instantiation can be
controlled with "if" conditional statements.
Use changing generic values, e.g. count down a generic parameter for
successive instantiations, and use the generic to control what is
instantiated at each recursive instantiation level and also ensure that
the recursive instantiation stops.
What you design by this method can be very large and very regular from
little code. Other large regular structures (memories are the most
obvious example), have customized layouts.
If your RTL instantiates a large rectangular array of similar
structures with similar interconnectivity you might want to be able to
tile similar blocks and inter-block signals in the layout.
I am producing a binary tree of similar tiles and was thinking about
laying it out efficiently.
| 585
| 2,684
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-48
|
longest
|
en
| 0.9039
|
http://www.mathcaptain.com/calculus/integration-by-substitution.html
| 1,571,265,235,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570986670928.29/warc/CC-MAIN-20191016213112-20191017000612-00060.warc.gz
| 298,067,258
| 11,325
|
The term "Integration" is used to find the function whose derivative is given, which is called the anti derivative of a function. For instance, if we know the acceleration of an object at any instant, then there exists a question, whether we can find the velocity or the position of the object at any instant. There are several such practical situations where the process of integration is involved.
The development of integral calculus arises out of the efforts of solving the problems of the following types.
1. The problem of finding the function when its derivative is given.
2. The problem of finding the area bounded by the graph of a function under certain conditions.
These two types lead to two forms of integrals, indefinite and definite integrals which together constitute Integral Calculus. In this section we shall discuss about the method of integration by substitution.
## Integration by Substitution Formula
By the method of substitution we change the given integral of one variable into another integral of another variable.
Let the integral be I = $\int$ f(x) dx
Substituting x = g(t),
$\frac{dx}{dt}$ = g'(t)
=> dx = g'(t) . dt
Substituting this in the given integral we get,
I = $\int$ f(x) . dx
= $\int$ f (g (t)) . g' (t) . dt
The change of variable formula is one of the important tools available to us in the name of integration by substitution.
Let us discuss with some of the Formulae to integrate by substitution.
1. $\int$ f (ax + b) dx = $\frac{1}{a}$ f (ax + b)
2. $\int$ sin (ax + b) dx = - $\frac{1}{a}$ cos (ax + b) + C
3. $\int$ cos (ax + b) dx = $\frac{1}{a}$ sin (ax + b) + C
4. $\int$ csc2(ax + b) dx = - $\frac{1}{a}$ cot (ax + b) + C
5. $\int$ sec2(ax + b) dx = - $\frac{1}{a}$ tan (ax + b) + C
6. $\int$ sec (ax + b) . tan (ax + b) dx = $\frac{1}{a}$ sec (ax + b) + C
7. $\int$ csc (ax + b) . cot (ax + b) dx = - $\frac{1}{a}$ csc (ax + b) + C
8. $\int$ tan (ax + b) dx = - $\frac{1}{a}$ ln | cos (ax + b) | + C
9. $\int$ cot (ax + b) dx = - $\frac{1}{a}$ ln | sin (ax + b) | + C
10. $\int$ sec (ax + b) dx = - $\frac{1}{a}$ ln | sec (ax + b) + tan (ax + b) | + C
11. $\int$ csc (ax + b) dx = - $\frac{1}{a}$ ln | csc (ax + b) - cot (ax + b) | + C
12. $\int$ $\frac{1}{ax+b}$ dx = $\frac{1}{a}$ ln | ax + b | + C
13. $\int$ eax+b dx = $\frac{1}{a}$ eax+b + C
14. $\int$ abx+c dx = $\frac{1}{b}$ $\frac{a^{bx+c}}{ln|a|}$ + C
## Integration by Substitution Examples
### Solved Examples
Question 1: Evaluate $\int$ x $\sqrt{(x^{2}\;-\;5)}$
Solution:
We have, I = $\int$ x $\sqrt{(x^{2}\;-\;5)}$
Substituting, u = x2 - 5
we get $\frac{du}{dx}$ = 2x
=> du = 2 x . dx
=> $\frac{du}{2}$ = x dx
Substituting in the given integral I, we get,
I = $\int$ $\sqrt{x^{2}-5}$ x dx
= $\int$ $\sqrt{u}$ $\frac{du}{2}$
= $\frac{1}{2}$ $\int$ $\sqrt{u}$ du
= $\frac{1}{2}$ . $\frac{u^{(\frac{1}{2}+1)}}{\frac{1}{2}+1}$ + C
= $\frac{1}{2}$ . $\frac{u^{3/2}}{\frac{1}{2}}$ + C
$\int$ x $\sqrt{x^{2}\;-\;5}$
= $\frac{1}{2}$ . $\frac{(x^{2}\;-\;5)^{\frac{3}{2}}}{\frac{1}{2}}$ + C
Question 2: Evaluate $\int$ x ( 1 + x ) 5 . dx
Solution:
We have I = $\int$ x ( 1 + x ) 5 . dx
Substituting, u = 1 + x
we get $\frac{du}{dx}$ = 1
=> du = dx
and 1 + x = u
=> x = u - 1
Therefore, the given integral will become,
I = $\int$ ( u - 1 ) u5 . du
= $\int$ ( u6 - u5 ) . du
= $\frac{u^{7}}{7}$ - $\frac{u^{6}}{6}$ + C
$\int$ x ( 1 + x ) 5 . dx = $\frac{(1\;+\;x)^{7}}{7}$ - $\frac{(1\;+\;x)^{6}}{6}$ + C
Question 3: Evaluate $\int$ $\frac{ln\;|\;x\;|\;}{x}$ dx
Solution:
We have I = $\int$ $\frac{ln|x|}{x}$ dx
Substituting, u = ln|x|
we get, $\frac{du}{dx}$ = $\frac{1}{x}$
Therefore, du = $\frac{dx}{x}$
Substituting in the given integral we get,
I = $\int$ $\frac{ln|x|}{x}$ dx
= $\int$ u du
= $\frac{u^{2}}{2}$ + C
$\int$ $\frac{ln\;|\;x\;|\;}{x}$ dx = $\frac{(ln\;|\;x\;|\;)^{2}}{2}$ + C
Question 4: $\int$ $\frac{sinx}{2\;+\;3cosx}$ dx
Solution:
We have I = $\int$ $\frac{sinx}{2+3cosx}$ dx
Substituting, u = 2 + 3 cos x
we get, $\frac{du}{dx}$ = - 3 sin x
Therefore, we have d u = - 3 sin x. dx
=> $\frac{du}{-3}$ = sin x. dx
Substituting in the given integral, we get,
I = $\int$ $\frac{sinx}{2+3cosx}$ dx
= $\int$ $\frac{1}{u}$ . $\frac{du}{-3}$
= $\frac{1}{-3}$ $\int$ $\frac{du}{u}$
= - $\frac{1}{3}$ . ln | u | + C
$\int$ $\frac{sinx}{2\;+\;3cosx}$ dx = - $\frac{1}{3}$ . ln | (2 + 3 cos x ) | + C
Question 5: $\int$ $\frac{3x^{2}}{1\;+\;x^{6}}$ dx
Solution:
We have, I = $\int$ $\frac{3x^{2}}{1+x^{6}}$ dx
Substituting, u = x3
We get, $\frac{du}{dx}$ = 3 x2 .
=> du = 3 x2 . dx
Since u = x3
we have u2 = ( x3 )2 = x6
Substituting, in the given integral we get,
I = $\int$ $\frac{3x^{2}}{1\;+\;x^{6}}$ dx
= $\int$ $\frac{du}{1\;+\;u^{2}}$
= arc tan u + C
= arc tan ( 1 + x3 ) + C
therefore, we get,
$\int$ $\frac{3x^{2}}{1\;+\;x^{6}}$ dx = arc tan ( 1 + x3 ) + C
Question 6: $\int$ sec4 x . dx
Solution:
We have I = $\int$ sec4 x . dx
= $\int$ sec2 x . sec2 x . dx
= $\int$ ( 1 + tan2 x ) . sec2 x . dx
Substituting u = tan x
$\frac{du}{dx}$ = sec2 x
=> du = sec2 x . dx
Substituting in the given integral, we get,
I = $\int$ sec4 x . dx
= $\int$ ( 1 + tan2 x ) . sec2 x . dx
= $\int$ ( 1 + u2 ) du
= u + $\frac{u^{3}}{3}$ + C
$\int$ sec4 x . dx = tan x + $\frac{tan^{3}x}{3}$ + C
## Integration by Substitution Practice
### Practice Problems
Question 1: $\int$ (4 - 9 x)5 . dx
Question 2: $\int$ sin5 x dx
Question 3: $\int$ $\frac{x^{3}}{x^{2}+1}$ dx
Question 4: $\int$ $\frac{(x-1)}{\sqrt{x-4}}$ dx
Question 5: $\int$ $\frac{2x+5}{x^{2}+5x+9}$ dx
Question 6: $\int$ $\frac{secx}{ln|secx\;+\;tanx|}$ . dx
Question 7: $\int$ $\frac{1\;+\;cosx}{1\;-\;cosx}$ . dx
Question 8: $\int$ $\frac{(x+1)}{x^{2}+2x-3}$
Question 9: $\int$ etan x . sec2 x. dx
Question 10: $\int$ $\frac{1}{e^{x}\;+\;e^{-x}}$ . dx
| 2,348
| 5,858
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.875
| 5
|
CC-MAIN-2019-43
|
latest
|
en
| 0.79357
|
https://www.pveducation.org/zh-hans/list-of-equations?page=2
| 1,611,288,357,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-04/segments/1610703529080.43/warc/CC-MAIN-20210122020254-20210122050254-00307.warc.gz
| 949,673,756
| 12,864
|
# List of Equations
The equations below are formatted with MathML. They are rendered in MathJax so should work across all browsers, mobile phones etc.
### Copying an equation.
• Right click on the equation
• From the popup menu chose: Show Math As, MathML Code.
• A new window will open. Select and copy the MathML code.
### To convert to other formats such as GIF
Paste the mathml code into http://www.mathmlcentral.com/Tools/FromMathML.jsp
### Paste into Microsoft word
In most word versions a shortcut is to right-click within the word document and select "Keep Text Only (T)"
• Insert, equation
• Paste the MathML code
• It should magically turn into a word equation that you can also edit
• If you still see MathML code, click on the drop down menu in word and change it to "Keep Text Only (T)"
$I={I}_{L}-{I}_{0}\left[\mathrm{exp}\left(\frac{qV}{nkT}\right)-1\right]$
$I={I}_{L}-{I}_{0}\left[\mathrm{exp}\left(\frac{qV}{nkT}\right)\right]$
${V}_{OC}=\frac{kT}{q}\mathrm{ln}\left[\frac{\left({N}_{A}+\Delta n\right)\Delta n}{{n}_{i}^{2}}\right]$
${I}_{D}=1.353×{0.7}^{\left(A{M}^{0.678}\right)}$
$Pb+S{{O}_{4}}^{2-}\underset{charge}{\overset{discharge}{⇔}}PbS{O}_{4}+2{e}^{-}$
$Pb{O}_{2}+Pb+2{H}_{2}S{O}_{4}\underset{charge}{\overset{discharge}{⇔}}2PbS{O}_{4}+2{H}_{2}O$
$Pb{O}_{2}+S{{O}_{4}}^{2-}+4{H}^{+}+2{e}^{-}\underset{charge}{\overset{discharge}{⇔}}PbS{O}_{4}+2{H}_{2}O$
$Li\to L{i}^{+}+{e}^{-}$
$L{i}^{+}+{e}^{-}\to Li$
$E={E}^{0}-\frac{RT}{nF}×\mathrm{ln}\left(Q\right)$
${n}_{0}{p}_{0}={n}_{i}^{2}$
$\frac{dE}{dx}=\frac{\rho }{\epsilon }=\frac{q}{\epsilon }\left(p\left(x\right)-n\left(x\right)-{N}_{A}^{-}+{N}_{D}^{+}\right)$
$\frac{d\mathbf{E}}{dx}=\frac{\rho }{\epsilon }$
| 657
| 1,711
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 18, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.578125
| 3
|
CC-MAIN-2021-04
|
longest
|
en
| 0.497143
|
https://quiz.jagranjosh.com/josh/quiz/index.php?attempt_id=3061537&page=3
| 1,590,478,218,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-24/segments/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00544.warc.gz
| 461,270,284
| 13,011
|
# Percentage
Are you preparing for campus placements,Banking,SSC, IAS, Insurance,Defence and other competitive exams? Then, make sure to take some time in practicing the Percentage questions and answer in Quantitative Aptitude. Moreover, only those questions are included that are relevant and likely to be asked in any competitive exam. So, take these questions and answer, brush up your skills and practice to stay fully prepared for any your exam.
• Q22.There are some coins and plates of either silver or gold in a box. 40% of the objects are coins, 60% of the plates are of silver and 30% of the coins are of gold. What is the percentage of silver articles?
Show Solution Report Error
Please wait...
• Q23.In an examination, a student got 30% marks and failed by 25 marks. In the same examination, another got 40% and pass by 50 marks. Find the passing mark in the examination?
Show Solution Report Error
Please wait...
• Q24.X sells a laptop at Rs. 48,000. He gave discount of 7% on the initial amount of Rs. 30,000 and 5% on the remaining amount. His competitor Y sells the same laptop, at Rs. 48,000. If he wants to be competitive, how much % of discount he should offer on the marked price of the laptop?
Show Solution Report Error
Please wait...
• Q25.In a class, 40% students failed in paper I, 50% in paper II, and 10% passed both the papers. If each student of the class appeared for at least one of the two papers, then what percentage of students passed in only paper I?
Show Solution Report Error
Please wait...
• Q26.In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.
Show Solution Report Error
Please wait...
• Q27.If the length and breadth of a rectangle are changed by +20% and –10% respectively. What is the % change in area of rectangle?
Show Solution Report Error
Please wait...
• Q28.In an election between two candidates one got 72% of total valid votes. 25% of the total votes are invalid. If the total votes are 8200, what is the number of valid votes the other candidate got?
Show Solution Report Error
Please wait...
| 522
| 2,213
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.765625
| 4
|
CC-MAIN-2020-24
|
latest
|
en
| 0.941037
|
https://www.jiskha.com/questions/561987/there-are-three-seating-categories-at-a-stadium-for-a-softball-game-class-a-seats-cost
| 1,596,876,183,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-34/segments/1596439737319.74/warc/CC-MAIN-20200808080642-20200808110642-00314.warc.gz
| 713,994,262
| 6,581
|
# CIS 115
There are three seating categories at a stadium. For a softball game, Class A
# seats cost \$15, Class B cost \$12. and Class C seats cost \$9. Design a modular
# program that asks how many tickets for each class of seats were sold, and then
# displays the amount of income generated from ticket sales.
1. 👍 0
2. 👎 0
3. 👁 1,351
1. Assistance needed.
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
1. 👍 0
2. 👎 0
Input: number of tickets sold in each category.
Output: total revenue generated
Data:
Class A seats cost \$15=A,
Class B cost \$12.=B
Class C seats cost \$9.=C
Start:
a <- Enter # of seats sold for class A
b <- ....
c <- ...
Calculate
total<- A*a+B*b+C*c
output total
1. 👍 0
2. 👎 0
## Similar Questions
1. ### Math
An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there all together? a. write 2
asked by Emily on October 29, 2010
2. ### mathematics
A stadium in circular shape has area 91000 Sq.ft. How to find center of the stadium?
asked by Anna on July 18, 2020
3. ### Math (arithmetic)
The total seating capacity of an auditorium is 1,065. The first row has 21 seats arithmetic series and each row has one seat more than the row in front of it. How many rows of seats are there in the auditorium?
asked by Roxane on June 25, 2015
4. ### arithmetic
PLEASE I REALLY NEED HELP WITH THIS The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the
asked by soka on August 6, 2011
1. ### physics
A human wave. During sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (Fig. below). As the wave reaches a group of spectators, they stand with a cheer and then sit.
asked by chirayu on April 30, 2009
2. ### math help!
a hockey arena has a total seating capacity of 15690.the first row of seats around the rink has 262 seats. the number of seats in each subsequent row increases by 18. how many rows of seats are in the arena?
asked by Riana on January 27, 2013
3. ### Math
A small aeroplane has 14 seats for passengers. The seats are arranged in 4 rows of 3 seats and a back row of 2 seats . 12 passengers board the aeroplane. (i) How many possible seating arrangements are there for the 12 passengers?
asked by Raj on August 22, 2019
4. ### MAth
The front row of a stadium has 25 seats. Each of the other rows has two more seats than the row in front of it. how many seats are there altogether in the first 20 rows? i know how to do this in the "long" way but how do you do
asked by Sarah on January 9, 2013
1. ### precalculus
The first row of seating in section A of an arena has 7 seats. There are 25 rows in section A, each row containing two more seats than the row preceeding it. How many seats are in section A? How do you use geometric sequence to
asked by Anonymous on May 10, 2018
2. ### Math
A softball player bats twice in a game. Each at-bat results in an out, getting on base, or hitting a home run. What is the number of possible outcomes in the sample space? A) 3 B) 6 C) 9 D) 12
asked by pyramid on December 18, 2019
3. ### Maths
A car showroom had 10y cars, 20y motorcycles and 18 vans. In a particular month, 4y cars , 3y motorcycles and 15 vans were sold. a.) Find the total number of wheels on the remaining vehicles in terms of x. b.) If y=21, how many
asked by Alexander on November 7, 2012
4. ### statistics
A new restaurant with 123 seats is being planned. Studies show that 63% of the customers demand a smoke free area. How many seats sould be in the non-smoking area in order to be very sure (mean+3StandardDeviation) of having enough
asked by Judy on November 13, 2011
| 1,105
| 4,018
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.34375
| 3
|
CC-MAIN-2020-34
|
latest
|
en
| 0.956657
|
https://blenderartists.org/forum/showthread.php?272679-Addon-WIP-Sverchok-parametric-nodes-for-architects/page51&s=4c3d6ac73ad33a028843808816c97986
| 1,506,061,399,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-39/segments/1505818688671.43/warc/CC-MAIN-20170922055805-20170922075805-00236.warc.gz
| 638,322,595
| 17,285
|
Thread: [Addon][WIP] Sverchok, parametric nodes for architects.
1. Vector and points are represented in the same way in in Sverchok, but how they can be interpreted is very different.
As side note even the .co is not needed. Two different ways.
Code:
```>>> bpy.context.scene.cursor_location
Vector((0.030590057373046875, -0.3238258361816406, -0.31893348693847656))
>>> bpy.context.scene.cursor_location.to_tuple()
(0.030590057373046875, -0.3238258361816406, -0.31893348693847656)
>>> bpy.context.scene.cursor_location[:]
(0.030590057373046875, -0.3238258361816406, -0.31893348693847656)```
The last two can be used for output in script node.
2. Originally Posted by Linusy
Vector and points are represented in the same way in in Sverchok, but how they can be interpreted is very different.
choices, choices! definitely worth reading the mathutils api carefully:
http://www.blender.org/documentation...dule-mathutils
3. Originally Posted by zeffii
and btw to convert a vector to a format suitable for Verts use
Code:
```some_vector.to_tuple()
# instead of stuff like
(some_vector[0], some_vector[1], some_vector[2])```
I just want to make sure you want to say that it was necessary to do so:
Code:
``` clv= bpy.context.scene.cursor_location
Verts= clv.to_tuple()
out_sockets = [
['v', 'Cursor Location', [Verts]]
]```
?
4. yep Ko! should be identical result. with less typing :]
that or the slice notion linusy suggested: some_vector[:]
5. normal-reflect.png
Normals and reflections for plane.
When we make per face color possible sometime in the future you could make your own mesh shader. (Which would be a stupid way to do it I think)
reflections.png
Made an updated version with both plane and light angle animated. 'Dancing flowers?'
File: http://www.pasteall.org/blend/29155
reflect3.png
File v2: http://www.pasteall.org/blend/29169
6. parametric circle
I think math node needs
2pi
+1
-1
*2
/2
pow2
7. Feel free to extend it, it is all dynamic, just keep enum numbers stable in mode_items.
8. hey zeffii, nice one! i also made a parametric circle some time ago this is the most optimized version i could come up with : Bildschirmfoto 2014-05-14 um 16.23.52.png
9. para-cirle.png
2 pi is good. Found a really old bug in constants in scalar math node also.
Perhaps a number field with safe defaults for all values would be nice also.
10. Speaking about weaknesses of the "Viewer text" node:
111111.png
Data socket not working properly in such setup. The strangest thing is if I use > data socket works fine, but if I use < it works only through "socket convert" node (and only vertices output). When i click on "UPDATE" button crawls error report.
11. Viewer text needs a big overhaul. Use text out for now, more raw data but usable.
12. I'm not going to be programming for a week or 2, except perhaps bug-fixing catastrophic stuff. Nice noodles guys, endless combinations.
13. @Zeffii
Zeff, before you are away, let's make the Grease Pencil thing happening and I want to make Alien Language using Sverchok.
Like this below Probably a LOT easier in Sverchok.
14. @Linusy
Awesome examples on Normal stuff!! I seriously need your brain, man
15. I was doing this multiple thread connections between two meshes thing. And I was kind of stuck when I wanted to do VECTORIZED INPUT random.
My writing is here: (not a plug, I need solution)
http://blendersushi.blogspot.com.au/...f-threads.html
Maybe Linusy or Nikita or Liero or Zeffii can help where I am wrong or if I could simplify things.
At the beginning, it is simple.
A SINGLE THREAD between 2 points:
O x x x x x x x x x x O
It gets confusing when I started to add random move. The first and last point should never move.
Multiple thread works if the Vector Random is the same:
O randx randx randx randx randx randx O
O randx randx randx randx randx randx O
O randx randx randx randx randx randx O
O randx randx randx randx randx randx O
However, now I wanted to really use all kind random value. But then I might mess up the pattern.
Any better idea?
Thanks.
16. Just tried to animate a script that changes the active material index of the active object- wild overheating.
The first time I really understood the danger of frequent updates.
17. Как вам, нравится?
download this exemple
http://www.pasteall.org/blend/29194
18. Круто! ......
19. PrtScr capture_5.png
I am thinking of deleting "Faces" from mesh, based on "Displace Modifier". I am wondering if this is possible using Sverchok?
I could List Mask the Points, by monitoring if the vertex.co.positionZ > 0, and that seems to be showing alright using Viewer Draw. However, Sverchok does not really bake Points and the point index seems to be changing if I do this.
How would this work with BMesh Viewer? Or whether this is a good idea at the moment?
20. I am getting R6034 Runtime Error with blender-2.70a-windows64 each time I start Blender with Sverchok enabled.
The reason for the error is
Code:
`import uuid`
call in the util.py
However the error doesn't prevent uuid Python module and Sverchok from normal operation. It's simply annoying to see the window with the error.
There is already a bug ticket for the error.
Page 51 of 106 First ... 41495051525361101 ... Last
Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•
| 1,405
| 5,383
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.625
| 3
|
CC-MAIN-2017-39
|
longest
|
en
| 0.781828
|
https://practicaldev-herokuapp-com.global.ssl.fastly.net/irby/cryptography-a-gentle-overview-j8i?comments_sort=oldest
| 1,680,395,439,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296950363.89/warc/CC-MAIN-20230401221921-20230402011921-00125.warc.gz
| 514,781,514
| 23,552
|
## DEV Community
Matt Irby
Posted on • Updated on
# Cryptography – A Gentle Overview (Part 1: Intro)
## Introduction
I recently gave a lunch-and-learn discussing cryptography, and I figured I could convert the talk into a series of blog posts. While cryptography is a topic I enjoy learning, it is certainly not a field I am an expert in by any means. However, I feel that discussing it (verbally or written) helps me reinforce the knowledge.
At depth, cryptography can be a complicated subject matter because it can get into the weeds of mathematics and understanding abstract concepts. So, these posts will be a gentle introduction to the topic that will discuss some concepts in cryptography at a high-level.
This post will start off with a definition of cryptography, introduce some vocabulary, and wrap up with a little note about encryption. The next post will take what has been discussed here and flesh it out more.
Let's get started!
## What is Cryptography, Anyway?
Cryptography is the process of protecting information and communication by obscuring its contents so it can only be read by an intended party. If the contents are to be read, there should be a guarantee about who originated the information. The mechanisms by which the information is obscured should use strong, mathematically intensive functions.
In the open internet, we can't blindly trust that our communication is safe. There is always the chance that our communication could be intercepted or forged by a malicious actor. When information is stored, it should be protected by an unwanted person from reading its contents. Cryptography can help ensure information is protected when sent between parties (in-transit) or stored (at rest).
Information security aims to address three pillars: confidentiality, integrity, and availability. These make up the CIA triad of security. In cryptography, while confidentiality and integrity are relevant, availability is not a concern. However, we do care about verifying where information came from.
• Confidentiality: Information cannot be read by unauthorized parties.
• Integrity: Data is not tampered with during transmission. It is complete.
• Authenticity: Only the sender could have sent the message.
## Introducing Some Vocabulary
Before diving in, let's introduce some vocabulary and provide some definitions.
• Plaintext: Ordinary, readable text before encryption and after decryption
• Ciphertext: Unreadable text that is output of encryption and input to decryption
• Hashing: One-way conversion of a plaintext to a ciphertext. This should not be able to convert back to plaintext.
## Cryptographic Cast of Characters
If you come across literature concerning cryptography, sometimes example scenarios are provided to explain a concept. These examples probably involve characters named Alice, Bob, Eve, Mallory, etc. Alice and Bob are innocent actors while Eve and Mallory are typically malicious actors. For more information on these characters, feel free to check out this Wikipedia article on Alice and Bob.
## Encryption
Encryption is the act of converting something readable into an unreadable form. Decryption is the act of converting something unreadable into a readable form. Information is encrypted using a key and decrypted using a key. The keys do not need to be the same.
The main types of encryption include:
• Symmetric Encryption: The same key is used to encrypt and decrypt a message (secret key)
• Asymmetric Encryption: A public key is used to encrypt a message and a private key is used to decrypt a message. Also known as public key encryption
• Hybrid Encryption: A blend of symmetric and asymmetric encryption.
### Initialization Vectors
So far, we've discussed a key and plaintext as input to encryption. If a plaintext is encrypted twice with the same key, is the resulting ciphertext the same? From what we have, the resulting ciphertext would be the same. This can be a bad thing. If an attacker knows the encryption of plaintext A produces ciphertext B, any time they see B they can infer that A was input. This would violate confidentiality.
Another component is needed to maintain confidentiality of encryption – an initialization vector (IV). The IV should be unpredictable / random and generated prior to any message encryption. Even if the plaintext and key are the same, a unique random IV will guarantee each resulting ciphertext will be different. The IV is usually appended at the start of the ciphertext and is used as input to decryption. It does not need to be secret.
Randomness is one of the most crucial parts of cryptography, especially for IVs. It is also near impossible to produce a truly random value – how do you produce a truly random number? I won't go into detail for this post about randomness (this post goes into good detail). IVs should be seeded using a secure random number generator.
### Bits and Bytes
Nearly everything in cryptography is expressed in bits and bytes. Some encryption schemes (ciphers) work from fixed-length groups of bits called blocks. As you come across different algorithms, keys/blocks may require different bit sizes (256-bit / 512-bits).
While key length does not imply security, some encryption algorithms have been proven to be weak when key size is small (see here). A larger key size can decrease performance. When choosing an encryption algorithm, always research its implementation, what key sizes are recommended, and whether it's still considered secure. As computers get faster, encryption with smaller key sizes can be "broken" more quickly.
## Summary & Up Next
A lot of material has been covered so far!
The next post in this series will take a look at symmetric and asymmetric encryption, understand what they are, how they could be applied, and what their limitations are. It will also dive into hashing and explain its usage. The post will conclude with how encryption and hashing could be used to fulfill the CIA triad of cryptography.
Thank you!
## Part 2
Part 2 of this post is now available! Link to the next article: here
| 1,194
| 6,091
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.65625
| 3
|
CC-MAIN-2023-14
|
latest
|
en
| 0.940917
|
https://www.termpaperwarehouse.com/essay-on/Math/342705
| 1,620,499,226,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-21/segments/1620243988923.22/warc/CC-MAIN-20210508181551-20210508211551-00356.warc.gz
| 1,033,645,354
| 17,469
|
Free Essay
# Math
In: Science
Submitted By dalizi1
Words 1069
Pages 5
Contents 0. Preface 1. Functions and Models 1.1. Basic concepts of functions 1.2. Classification of functions 1.3. New functions from old functions 1 2 2 5 8
0. Preface Instructor: Jonathan WYLIE, mawylie@cityu.edu.hk Tutors: Radu Gogu, rgogu2@student.cityu.edu.hk. Texts: Single Variable Calculus, by James Stewart, 6E. In this semester, we will cover the majority of Chap 1-4, 7, 12. Upon completion of this course, you should be able to understand limit, derivatives, and its applications in mathematical modeling and infinite series.
1
2
1. Functions and Models In this chapter, we will briefly recall functions and its properties covered by high school. 1.1. Basic concepts of functions. Text Sec1.1: 5, 7, 39, 57, 67. Definition 1.1. A function f is a rule that assigns to each element x in a set D exactly one element, called f (x), in a set E. Usually, we write a function f : x → f (x) where (1) x ∈ D, i.e. x belongs to a set D , called the Domain; (2) f (x) ∈ E, i.e. f (x) belongs to a set E, called the Range; (3) x is independent variable, (4) f (x) is dependent variable.
3
For a function f , its graph is the set of points {(x, f (x)) : x ∈ D} in xy-plane. One can also use a table to represent a function. Example 1.1. Sketch the graph of following two piecewise defined functions. (1) f (x) = |x|. i.e. Absolute value of x. (2) f (x) = [x]. i.e. largest integer not greater than x.
The graph of a function is a curve. But the question is: which curves are graphs of functions? Proposition 1.2 (Vertical Line Test). A curve in the xyplane is the graph of a function if and only if no vertical line intersects the curve more than once. VLT is equivalent to following statements: for any given input x, the output f (x) is determined uniquely. Otherwise, f is not well-defined function.
4
Symmetry of a function is an important topic. (1) A function f is even if f (−x) = f (x), ∀x ∈ D. (2) A function f is odd if f (−x) = −f (x), ∀x ∈ D.
Monotonicity of a function is another important topic. (1) A function f is increasing on an interval I, if f (x1) < f (x2), ∀x1 < x2 in I. (2) A function f is decreasing on an interval I, if f (x1) > f (x2), ∀x1 < x2 in I
5
1.2. Classification of functions. Text Sec1.2: 13, 17 A mathematical model is a mathematical description of a realworld phenomenon, and usually represented by a function. ex. We will later study some math models for population, demand of product, speed of an object, ... Some typical functions used for models are (1) Polynomial function P (x) = anxn + an−1xn−1 + · · · + a1x + a0 where ai are coefficients. If an = 0, then the degree of P (x) is n. (a) Linear model f (x) = mx + b where m is slope, b is y-intercept. ex. The relationship between Fahrenheit (F) and Celsius (C) is F = 9 C + 32. 5 (b) Quadratic model f (x) = ax2 + bx + c. (c) Cubic model A polynomial with degree 3.
(2) Power function f (x) = xa where a is constant. Ex. Sketch the graph of power function if a is (1) positive integer; (2) reciprocal of positive integer; (3) -1;
6
(3) Rational function P (x) Q(x) where P, Q are polynomials. ex. find domain of f (x) = 2−3x . x2 −4 f (x) =
(4) Algebraic function It is a function constructed by poly√ nomials using algebraic operations (such as +, −, ×, ÷, n ).
ex. find domain and symmetry of f (x) =
x2 +1 x3
(5) Trigonometric functions The common trigonometric functions are sin, cos, tan, cot. See more details on Reference Page 2 of the Text.
(6) Exponential functions f (x) = ax where the base a = 1 is a positive constant. ex. Sketch the graph of y = ax when a is a constant satisfying (1) a < 1 (2) a > 1.
7
(7) Logarithmic functions f (x) = loga x where a = 1 is a positive constant. ex. Sketch the graph of y = loga x when a is a constant satisfying (1) a < 1 (2) a > 1.
(8) Transcendental functions It is a non-algebraic function, including the trig; inverse of trig; exp.; log; and ... ex. Can you find a Transcendental function not mentioned in the above?
Example 1.2. Classify following functions as one of the types we discussed: poly, power, rational, algebraic, Trig, exp, log, transc., (1) f (x) = 5x, (2) g(x) = x5 1+x (3) h(x) = 1−√x (4) u(x) =
1+x 1−x1.5
+ x 2.
8
1.3. New functions from old functions. Text Sec1.3: 23, 35, 57, 63, 65 We will discuss two ways of obtaining a new function from old functions: (1) Shifting, stretching, or reflecting a given function; (2) Combination/Composition of two given functions Let a > 0 and b > 1. Given a function y = f (x), we can obtain a new function using following transformations (1) y = f (x) + a, by shifting y = f (x) a units upward; i.e. ↑a (2) y = f (x) − a, by ↓a (3) y = f (x − a), by →a (4) y = f (x + a), by ←a (5) y = bf (x) by stretching y = f (x) vertically by a factor of b, i.e. b (6) y = 1 f (x), by compressing y = f (x) vertically by a factor b of b, 1/b (7) y = f (bx), by compressing horizontally, ↔1/b. (8) y = f (x/b), by stretching horizontally, ↔b (9) y = −f (x), by reflect y = f (x) about x-axis, i.e. Rx. (10) y = f (−x), by reflect y = f (x) about y-axis, i.e. Ry . Example 1.3. Using transformation, graph √ √ f (x) = 2 −x − 1, and g(x) = |2 −x − 1|.
9
Given Two functions of f and g, we may have following combinations: using definition of +, −, ×, ÷ f + g, f − g, f g, f /g Also, composition f ◦ g is defined by (f ◦ g)(x) = f (g(x)). Example 1.4. Given F (x) = cos2(x+9), find function f, g, h s.t. F = f ◦ g ◦ h.
Remark 1.3. f ◦ g = g ◦ f in general.
### Similar Documents
Free Essay
#### Math
...and solve problems in everyday life”. In my everyday life I have to keep the balance in my check book, pay bills, take care of kids, run my house, cook, clean etc. With cooking I am using math, measuring how much food to make for four people (I still haven’t mastered that one). With bills I am using math, how much each company gets, to how much money I have to spare (which these days is not much). In my everyday life I do use some form of a math. It might not be how I was taught, but I have learned to adapt to my surroundings and do math how I know it be used, the basic ways, none of that fancy stuff. For my weakest ability I would say I fall into “Confidence with Mathematics”. Math has never been one of my favorite subjects to learn. It is like my brain knows I have to learn it, but it puts up a wall and doesn’t allow the information to stay in there. The handout “The Case for Quantitative Literacy” states I should be at ease with applying quantitative methods, and comfortable with quantitative ideas. To be honest this class scares the crap out of me, and I am worried I won’t do well in this class. The handout also says confidence is the opposite of “Math Anxiety”, well I can assure you I have plenty of anxiety right now with this class. I have never been a confident person with math, I guess I doubt my abilities, because once I get over my fears and anxiety I do fine. I just have to mentally get myself there and usually it’s towards the end of the class. There are......
Words: 418 - Pages: 2
#### Math
...solutions. If you have a graphing calculator, this method is the quickest. If you don't have a calculator, it can be difficult to graph the equation. Completing the square: This is probably the most difficult method. I find it hardest to remember how to apply this method. Since the quadratic formula was derived from this method, I don't think there is a good reason to use completing the square when you have the formula Factoring: this is probably the easiest method for solving an equation with integer solutions. If you can see how to split up the original equation into its factor pair, this is the quickest and allows you to solve the problem in one step. Week 9 capstone part 1 Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts...
Words: 662 - Pages: 3
#### Math
...This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1] Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become......
Words: 634 - Pages: 3
Free Essay
#### Math
...Sample Exam 2 - MATH 321 Problem 1. Change the order of integration and evaluate. (a) (b) 2 0 1 0 1 (x y/2 + y)2 dxdy. + y 3 x) dxdy. 1 0 0 x 0 y 1 (x2 y 1/2 Problem 2. (a) Sketch the region for the integral f (x, y, z) dzdydx. (b) Write the integral with the integration order dxdydz. THE FUNCTION f IS NOT GIVEN, SO THAT NO EVALUATION IS REQUIRED. Problem 3. Evaluate e−x −y dxdy, where B consists of points B (x, y) satisfying x2 + y 2 ≤ 1 and y ≤ 0. − Problem 4. (a) Compute the integral of f along the path → if c − f (x, y, z) = x + y + yz and →(t) = (sin t, cos t, t), 0 ≤ t ≤ 2π. c → − → − → − (b) Find the work done by the force F (x, y) = (x2 − y 2 ) i + 2xy j in moving a particle counterclockwise around the square with corners (0, 0), (a, 0), (a, a), (0, a), a > 0. Problem 5. (a) Compute the integral of z 2 over the surface of the unit sphere. → → − − → − → − − F · d S , where F (x, y, z) = (x, y, −y) and S is → (b) Calculate S the cylindrical surface defined by x2 + y 2 = 1, 0 ≤ z ≤ 1, with normal pointing out of the cylinder. → − Problem 6. Let S be an oriented surface and C a closed curve → − bounding S . Verify the equality → − → − → → − − ( × F ) · dS = F ·ds − → → − if F is a gradient field. S C 2 2 1...
Words: 254 - Pages: 2
Free Essay
#### Math
...STAT2011 Statistical Models sydney.edu.au/science/maths/stat2011 Semester 1, 2014 Computer Exercise Weeks 1 Due by the end of your week 2 session Last compiled: March 11, 2014 Username: mac 1. Below appears the code to generate a single sample of size 4000 from the population {1, 2, 3, 4, 5, 6}. form it into a 1000-by-4 matrix and then find the minimum of each row: > rolls1 table(rolls1) rolls1 1 2 3 4 5 6 703 625 679 662 672 659 2. Next we form this 4000-long vector into a 1000-by-4 matrix: > four.rolls=matrix(rolls1,ncol=4,nrow=1000) 3. Next we find the minimum of each row: > min.roll=apply(four.rolls,1,min) 4. Finally we count how many times the minimum of the 4 rolls was a 1: > sum(min.roll==1) [1] 549 5. (a) First simulate 48,000 rolls: > rolls2=sample(x=c(1,2,3,4,5,6),size=48000,replace=TRUE) > table(rolls2) rolls2 1 2 3 4 5 6 8166 8027 8068 7868 7912 7959 (b) Next we form this into a 2-column matrix (thus with 24,000 rows): > two.rolls=matrix(rolls2,nrow=24000,ncol=2) (c) Here we compute the sum of each (2-roll) row: > sum.rolls=apply(two.rolls,1,sum) > table(sum.rolls) sum.rolls 2 3 4 5 6 7 8 9 10 11 742 1339 2006 2570 3409 4013 3423 2651 1913 1291 1 12 643 Note table() gives us the frequency table for the 24,000 row sums. (d) Next we form the vector of sums into a 24-row matrix (thus with 1,000 columns): > twodozen=matrix(sum.rolls,nrow=24,ncol=1000,byrow=TRUE) (e) To find the 1,000 column minima use > min.pair=apply(twodozen,2,min) (f) Finally compute......
Words: 597 - Pages: 3
#### Math
...Diana Garza 1-16-12 Reflection The ideas Stein presents on problem saving and just math in general are that everyone has a different way of saving their own math problems. For explains when you’re doing a math problem you submit all kinds of different numbers into a data or formula till something works or maybe it’s impossible to come up with a solution. For math in general he talks about how math is so big and its due in large measure to the wide variety of situations how it can sit for a long time without being unexamined. Waiting for someone comes along to find a totally unexpected use for it. Just like has work he couldn’t figure it out and someone else found a use for it and now everyone uses it for their banking account. For myself this made me think about how math isn’t always going to have a solution. To any math problem I come across have to come with a clear mind and ready to understand it carefully. If I don’t understand or having hard time taking a small break will help a lot. The guidelines for problem solving will help me a lot to take it step by step instead of trying to do it all at once. Just like the introduction said the impossible takes forever. The things that surprised me are that I didn’t realize how much math can be used in music and how someone who was trying to find something else came to the discovery that he find toe. What may people were trying to find before...
Words: 270 - Pages: 2
#### Math
...say whether I was able to learn how to be a better teacher and what the teacher did that I could possibly use in the future. While analyzing and going through the process of this assignment it is helping realize how to become a better teacher as well. I would also like to get more comfortable and experience on using this template of the paper. Memories Of A Teacher My teacher, Mr. G, used many different instructional techniques and approaches to his lessons. Mr. G had taught me math for three years in a row, so I think that I have a good grasp on his approaches to the lessons that he would teach. He would assign many homework assignments, as well as in-class assignments, which helped me and other students understand and get practice with the lesson that we were learning. I think that with math having a lot of homework is a good thing. In my mind, the only way to learn how to do math is plenty of practice. The more you practice, the easier it will be. Mr. G would also have the students do some math problems on the chalk board or smart board to show the class and go over the corrections with the whole class so that everyone would understand the problem. Playing “racing” games also helped and added fun to the class. With the “racing” games, the students would get into groups and have to take...
Words: 1027 - Pages: 5
#### Math
...Jasmine Petersen Dr. Abdeljabbar MAT 1111 April 23, 2014 Algebra is one of the most important subjects someone can learn. It is a subject that transfers into daily life. A lot of people do not realize that they are using algebra. Algebra can be anything from calculating the amount of money you’ve spent on your grocery shopping, designing structural plans for a building, and keeping track of the calories you have in your diet. Our professor told us that in every subject, we use math. My major is chemistry and mathematics is used widely in chemistry as well as all other sciences. Mathematical calculations are absolutely necessary to explore important concepts in chemistry. You’ll need to convert things from one unit to another. For example, you need to convert 12 inches to feet. Also, we use simple arithmetic to balance equations. A lot of things I’ve had learned from this course and one of them was that we use Math for everyday life. I’ve also learned many ways how to solve equations such as linear, quadratic, exponential, and logarithmic equations. All the material that we did learn was all easy to learn and understand. I believe that the instructor did a good job explaining on how to solve problems. If my friend was asking me how to determine the differences between the equation of the ellipse and the equation of the hyperbola, I would first give he or she the definition of the two words ellipse and hyperbola. An ellipse is a set of all points in a plane such that the......
Words: 623 - Pages: 3
Free Essay
#### Math
...A | Course Title & Number | Calculus II: MTH104 | B | Pre/Co-requisite(s) | Pre-requisite: MTH103 (Calculus I) | C | Number of credits | 3 | D | Faculty Name | Dr. Ghada Alobaidi | E | Term/ Year | Fall 2014 | F | Sections | Course | Days | Time | Location | MTH104.02 MTH104.04MTH104.06 | UTR UTRMW | 9:00-9:50 10:00-10:50 8:00-9:15 | PHY 113NAB 007NAB010 | | | | | | G | Instructor Information | Instructor | Office | Telephone | Email | Ghada Alobaidi | NAB 249 | 06 515 2754 | galobaidi@aus.edu | Office Hours: UT: 11:00 – 12:30 , R: 11:00 – 12:00 or by appointment. | H | Course Description from Catalog | Covers techniques of integration, improper integrals, sequences, infinite series, power series, parameterized curves, polar coordinates, integration in polar coordinates and complex numbers. | I | Course Learning Outcomes | Upon completion of the course, students will be able to: * Read, analyze, and apply to problems, written material related to the study of calculus. * Use the appropriate technique(s) – including integration by parts, trigonometric substitutions, partial fractions, etc. to integrate algebraic, logarithmic, exponential, trigonometric, and composite functions. * Evaluate improper integrals and test them for convergence. * Compute arc length and surface area of revolution of graphs and parametric curves. * Graph polar curves and find enclosed area and arc length. * Apply theorems about limits......
Words: 1366 - Pages: 6
#### Math
...Math is used everyday – adding the cost of the groceries before checkout, totaling up the monthly bills, estimating the distance and time a car ride is to a place a person has not been. The problems worked this week have showed how math works in the real world. This paper will show how two math problems from chapter five real world applications numbers 35 and 37 worked out. Number 35 A person hired a firm to build a CB radio tower. The firm charges \$100 for labor for the first 10 feet. After that, the cost of labor for each succeeding 10 feet is \$25 more than the preceding 10 feet. That is, the nest 10 feet will cost \$125; the next 10 feet will cost \$150, etc. How much will it cost to build a 90-foot tower? Solving this problem involves the arithmetic sequence. The arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount (Bluman, 2011). n = number of terms altogether n = 9 d = the common differences d = 25 ª1 = first term ª1 = 100 ªn = last term ª2 = ª9 The formula used to solve this problem came from the book page 222. ªn = ª1 + (n -1)d ª9 = 100 + (9-1)25 ª9 = 100 + (8)25 ...
Words: 540 - Pages: 3
#### Math
...you come to geometry, your opinion may vary. This class introduces a lot of new topics, which can be challenging, and take lots of practice outside of school if you do not pay attention or do your math homework. I strongly advise you to do your math homework everyday, not for just a grade, but it also helps you when it comes time for quizzes and tests. She rarely checks homework, but when she does, she will not tell you. It is also a great review for tests and quizzes. Ms.Hull’s tests and quizzes are not the easiest things you will take. The quizzes take new concepts and apply to the quiz. Also, her tests are usually always hard. It is a good idea to practice new concepts and review old ones from previous units, so you can get a good grade on the tests. I also advise you to be organized throughout the year. Organization is the key to success especially in math class. Tool kits are an extremely helpful resource to use. There are going to be a lot of conjectures and theorems that will be new, and it would be hard to just memorize them. My overall geometry year was not exactly the way I hoped it would turn out. It was extremely had, and it moves at a very quick pace, so keeping up was hard for me personally. If I could have done something differently, it would have been practicing math more often. Each concept was hard, and I did not have anytime to review it, because I have a lot of honors classes which require a lot of work too. The key to being successful in this......
Words: 361 - Pages: 2
Free Essay
#### Math
...|7|SURVEY OF MATHEMATICS FALL 2015 | |8| | |8| | |8| | |8| | | | | | |Instructor | | |Gary F. Melendy | | | | | |Title | | |Instructor ...
Words: 1789 - Pages: 8
#### Math
...find the national average cost of food for an individual, as well as for a family of 4 for a given month. http://www.cnpp.usda.gov/sites/default/files/usda_food_plans_cost_of_food/CostofFoodJan2012.pdf 5. Find a website for your local city government. http://www.usa.gov/Agencies/Local.shtml 6. Find the website for your favorite sports team (state what that team is as well by the link). http://blackhawks.nhl.com/ (Chicago Blackhawks) 7. Many of us do not realize how often we use math in our daily lives. Many of us believe that math is learned in classes, and often forgotten, as we do not practice it in the real world. Truth is, we actually use math every day, all of the time. Math is used everywhere, in each of our lives. Math does not always need to be thought of as rocket science. Math is such a large part of our lives, we do not even notice we are computing problems in our lives! For example, if one were interested in baking, one must understand that math is involved. One may ask, “How is math involved with cooking?” Fractions are needed to bake an item. A real world problem for baking could be as such: Heena is baking a cake that requires two and one-half cups of flour. Heena poured four and one-sixth cups of flour into a bowl. How much flour should Heena take out of the bowl? In this scenario of a real world problem, we have fractions, and subtraction of fractions, since Heena has added four and one-sixth cups of flour, rather than the needed...
Words: 665 - Pages: 3
Free Essay
#### Math
...Math was always the class that could never quite keep my attention in school. I was a daydreamer and a poor student and applying myself to it was pretty much out of the question. When I would pay some attention I would still forget the steps it had taken me to find the solution. So, when the next time came around I was lost. This probably came about because as a kid I wasn’t real fond of structure. I was more into abstract thought and didn’t think that life required much more than that at the time. I was not interested in things I had to write down and figure out step by step on a piece of paper. I figured I could be Tom Sawyer until about the age of seventy two. My thoughts didn’t need a rhyme or reason and didn’t need laws to keep them within any certain limits. The furthest I ever made it in school was Algebra II and I barely passed that. The reason wasn’t that I couldn’t understand math. It was more that I didn’t apply myself to the concepts of it, or the practice and study it took to get there. I was always more interested in other concepts. Concepts that were gathered by free thinkers, philosophers, idealists. Now I knew that a lot of those figures I read about tried their hand in the sciences, physics, and mathematics in their day, but I was more interested in their philosophical views on everyday life. It was not until I started reading on the subject of quantum physics and standard physics that I became interested in math. The fact that the laws of standard......
Words: 473 - Pages: 2
Free Essay
#### Maths
...Click here to see Shortcut Keys or Alt codes for Greek Letters. Math Operators Math Symbols | Name | Alt + numbers | Codes, Alt + X | − | Minus Sign | Alt + 0150 | 2212 | × | Multiplication Sign | Alt + 0215 | 00D7 | ÷ | Division Sign | Alt + 0247 | 00F7 | ± | Plus-Minus Sign | Alt + 0177 | 00B1 | ∓ | Minus-Plus Sign | Alt + 8723 | 2213 | ∙ | Bullet Operator | Alt + 0183 | 2217 | ∽ | Reversed tilde | Alt + 8765 | 223D | ≈ | Almost equal to | Alt + 8776 | 2248 | ≌ | All equal to | Alt + 8780 | 224C | ≠ | Not equal to | Alt + 8800 | 2260 | ≡ | Identical to | Alt + 8801 | 2261 | ≢ | Not identical to | Alt + 8802 | 2262 | ≤ | Less than or equal to | Alt + 8804 | 2264 | ≥ | Greater than or equal to | Alt + 8805 | 2265 | Other Math Symbols Math Symbol | Name | Alt + numbers | Codes, Alt + X | ‰ | Per mille sign | Alt + 0137 | 2030 | ′ | Prime | | 2032 | ″ | Double prime | | 2033 | ‴ | Triple prime | | 2034 | ∆ | Increment (Delta) | Alt + 8710 | 2206 | | | Vertical Line | | 007C | ° | Degree Sign | Alt + 0176 | 00B0 | ² | Superscript Two | Alt + 0178 | 00B2 | ³ | Superscript Three | Alt + 0179 | 00B3 | √ | Square root | Alt + 8730 | 221A | ∛ | Cube root | Alt + 8731 | 221B | ∜ | Fourth root | Alt + 8732 | 221C | ∞ | Infinity | Alt + 8734 | 221E | ¼ | Quarter | Alt + 0188 | 00BC | ½ | Half | Alt + 0189 | 00BD | ¾ | Three Quarters | Alt + 0190 | 00BE | ∑ | Summation | Alt + 8721 | 2211 | µ | Micro Sign | Alt +......
Words: 494 - Pages: 2
| 7,127
| 25,583
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.46875
| 4
|
CC-MAIN-2021-21
|
latest
|
en
| 0.843862
|
https://mathoverflow.net/questions/179285/existence-of-finite-nonabelian-groups-satisfying-certain-identities
| 1,556,199,053,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-18/segments/1555578721441.77/warc/CC-MAIN-20190425114058-20190425140058-00490.warc.gz
| 480,197,578
| 31,026
|
# Existence of finite nonabelian groups satisfying certain identities
Is there a finite nonabelian group satisfying all of the following identities? $$(x^py^p)^2 = (y^px^p)^2, \quad p = 2,3,5,7,11,\ldots (\text{primes})$$
I thank you all in advance.
• What is the motivation? – Noah Schweber Aug 24 '14 at 18:49
• Yes: Extra-special $2$-groups have that property. – Geoff Robinson Aug 24 '14 at 19:02
Assuming you want that to hold for all $x,y \in G,$ any (non-Abelian) extra-special $2$-group $G$ will have that property. For there are only two squares in $G$: the identity, and the unique element of order $2$ in $Z(G).$ However, note that $(x^{p}y^{p})^{2}$ and $(y^{p}x^{p})^{2}$ are conjugate in $G$, so since they are both central, they are equal. By the way, it is easy to see that any finite group of odd order with the stated property is Abelian.
Later edit following YCor's comment: As remarked after that comment, it appears to me that the condition in the original question is equivalent to $(yx)^{2} = (xy)^{2}$ for all $x,y \in G.$ This is because we may choose a prime $q > |G|,$ and then $g \to g^{q}$ is a bijection from $G$ to itself. Hence, given $x,y \in G,$ there are unique elements $a$ and $b$ in $G$ such that $x = a^{q}$ and $y = b^{q}.$ Hence we have $(xy)^{2} = (yx)^{2}$ by hypothesis. (Late addition: Actually, it's easier than this: Just take a prime $p \equiv 1$ (mod $|G|$) ).
I will prove that a finite group $G$ with $(xy)^{2} = (yx)^{2}$ for all $x,y \in G$ has a normal Sylow $2$-subgroup $S$, and that $G/S$ is Abelian (of odd order). Note that the condition is inherited by homomorphic images. Hence, by induction, we may suppose that $O_{2}(G) = 1.$ The result is clear if $G$ has odd order, as noted above, so suppose that $G$ contains an involution $t.$ Then (by the Baer-Suzki theorem), there is a conjugate $u$ of $t$ such that $\langle t,u \rangle$ (which is a dihedral group) is not a $2$-group. Hence $t$ inverts a non-idetity element $g \in G$ of odd order. Then $v = tg$ is also an involution of $G.$ Also, $tv = g$ has odd order. Also, $vgv = vt$ has odd order as $v = v^{-1}.$ Since $(vt)^{2} = (tv)^{2}$ and both have the same odd order, we have $vt = tv$ ( for if that order is $n,$ we have $vt = ((vt)^{2})^{\frac{n+1}{2}} = ((tv)^{2})^{\frac{n+1}{2}} = tv).$ But this contradicts the fact that $tv = g$ is a non-identity element of odd order, as $t$ and $v$ are involutions.
Perhaps it is possible to say more about the structure of $G$ For example, $G = A_{4}$ does not have the property of the question: if $x,y$ are distinct elements of order $3$ in $A_{4}$ which are conjugate then $(xy)^{2} \neq (yx)^{2}.$
Even later edit: In fact, a finite group $G$ with the stated property is nilpotent with an Abelian Sylow $p$-subgroup for each odd prime $p.$ Given what is proved already, it suffices to prove that the elements of odd order are closed under multiplication. Otherwise, we have $x,y$ of odd order such that $z = xy$ has even order. Then $y = x^{-1}z$ has odd order, so as above, we obtain that $x^{-1}z = zx^{-1}$ since those two elements of odd order have equal squares. Hence $x$ and $xy$ commute, so that $x$ and $y$ commute, a contradiction.
Hence understanding the finite groups $G$ with that stated property reduces to understanding finite $2$-groups $G$ such that $x$ and $yxy$ commute for all $x,y \in G.$
• Note: actually they satisfy the identity for $p=1$, which implies the identity for all $p$. This holds for every group satisfying the identity $xy^2=y^2x$. – YCor Aug 24 '14 at 20:29
• @YCor: Yes, it is enough that squares are central. Also, I think that there is eventually a prime $q$ which does not divide $|G|$ means that the given condition is equivalent to $(xy)^{2} = (yx)^{2}$ since $g \to g^{q}$ is a bijection from $G$ to $G$ for such a prime. – Geoff Robinson Aug 25 '14 at 9:31
| 1,226
| 3,880
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.65625
| 4
|
CC-MAIN-2019-18
|
longest
|
en
| 0.919274
|
https://www.mathhomeworkanswers.org/13991/write-equation-point-slope-form-line-through-point-with-slope
| 1,544,976,812,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-51/segments/1544376827769.75/warc/CC-MAIN-20181216143418-20181216165418-00072.warc.gz
| 956,585,306
| 12,224
|
Write an equation in point-slope form of the line through point J(–5, 6) with slope –4.
y=mx+b
6= -4(-5)+b
6= 20+b
b=6 -20
b= -14
y= -4x - 14
answered Jan 10, 2012 by (220 points)
edited Jan 10, 2012 by cirej012
y-y1=m(x-x1)
y-6=-4(x-(-5))
y-6= -4x - 20
sorry!!! this is the answer because my first answer is being solve using slope-intercept form, i just remember :)
answered Jan 10, 2012 by (220 points)
| 160
| 417
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.625
| 4
|
CC-MAIN-2018-51
|
latest
|
en
| 0.905313
|
https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Fundamentals_of_General_Organic_and_Biological_Chemistry_(LibreTexts)/10%3A_Acids_and_Bases/10.11%3A_Titration
| 1,723,228,337,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640768597.52/warc/CC-MAIN-20240809173246-20240809203246-00269.warc.gz
| 122,486,935
| 31,015
|
Skip to main content
# 10.11: Titration
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
## Learning Objectives
• Describe a titration experiment.
• Explain what an indicator does.
• Perform a titration calculation correctly.
The reaction of an acid with a base to make a salt and water is a common reaction in the laboratory, partly because many compounds can act as acids or bases. Another reason that acid-base reactions are so prevalent is because they are often used to determine quantitative amounts of one or the other. Performing chemical reactions quantitatively to determine the exact amount of a reagent is called a titration. A titration can be performed with almost any chemical reaction for which the balanced chemical equation is known. Here, we will consider titrations that involve acid-base reactions.
In a titration, one reagent has a known concentration or amount, while the other reagent has an unknown concentration or amount. Typically, the known reagent (the titrant) is added to the unknown quantity and is dissolved in solution. The unknown amount of substance (the analyte) may or may not be dissolved in solution (but usually is). The titrant is added to the analyte using a precisely calibrated volumetric delivery tube called a burette (also spelled buret; see Figure $$\PageIndex{1}$$). The burette has markings to determine how much volume of solution has been added to the analyte. When the reaction is complete, it is said to be at the equivalence point; the number of moles of titrant can be calculated from the concentration and the volume, and the balanced chemical equation can be used to determine the number of moles (and then concentration or mass) of the unknown reactant.
For example, suppose 25.66 mL (or 0.02566 L) of 0.1078 M HCl was used to titrate an unknown sample of NaOH. What mass of NaOH was in the sample? We can calculate the number of moles of HCl reacted:
# mol HCl = (0.02566 L)(0.1078 M) = 0.002766 mol HCl
We also have the balanced chemical reaction between HCl and NaOH:
HCl + NaOH → NaCl + H2O
So we can construct a conversion factor to convert to number of moles of NaOH reacted:
$0.002766\cancel{mol\, HCl}\times \frac{1\, mol\, NaOH}{1\cancel{mol\, HCl}}=0.002766\, mol\, NaOH\nonumber$
Then we convert this amount to mass, using the molar mass of NaOH (40.00 g/mol):
$0.002766\cancel{mol\, HCl}\times \frac{40.00\, g\, NaOH}{1\cancel{mol\, HCl}}=0.1106\, g\, NaOH\nonumber$
This type of calculation is performed as part of a titration.
## Example $$\PageIndex{1}$$
What mass of Ca(OH)2 is present in a sample if it is titrated to its equivalence point with 44.02 mL of 0.0885 M HNO3? The balanced chemical equation is as follows:
2HNO3 + Ca(OH)2 → Ca(NO3)2 + 2H2O
### Solution
In liters, the volume is 0.04402 L. We calculate the number of moles of titrant:
# moles HNO3 = (0.04402 L)(0.0885 M) = 0.00390 mol HNO3
Using the balanced chemical equation, we can determine the number of moles of Ca(OH)2 present in the analyte:
$0.00390\cancel{mol\, HNO_{3}}\times \frac{1\, mol\, Ca(OH)_{2}}{2\cancel{mol\, HNO_{3}}}=0.00195\, mol\, Ca(OH)_{2}\nonumber$
Then we convert this to a mass using the molar mass of Ca(OH)2:
$0.00195\cancel{mol\, Ca(OH)_{2}}\times \frac{74.1\, g\, Ca(OH)_{2}}{\cancel{mol\, Ca(OH)_{2}}}=0.144\, g\, Ca(OH)_{2}\nonumber$
## Exercise $$\PageIndex{1}$$
What mass of H2C2O4 is present in a sample if it is titrated to its equivalence point with 18.09 mL of 0.2235 M NaOH? The balanced chemical reaction is as follows:
$\ce{H2C2O4 + 2NaOH → Na2C2O4 + 2H2O} \nonumber$
Answer
0.182 g
How does one know if a reaction is at its equivalence point? Usually, the person performing the titration adds a small amount of an indicator, a substance that changes color depending on the acidity or basicity of the solution. Because different indicators change colors at different levels of acidity, choosing the correct one is important in performing an accurate titration.
10.11: Titration is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by LibreTexts.
• Was this article helpful?
| 2,906
| 8,425
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.109375
| 3
|
CC-MAIN-2024-33
|
latest
|
en
| 0.197763
|
https://www.coursehero.com/file/8707817/Chapter-5-part2-student/
| 1,526,908,863,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-22/segments/1526794864186.38/warc/CC-MAIN-20180521122245-20180521142245-00292.warc.gz
| 712,495,261
| 416,471
|
{[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
Chapter 5_part2_student
# Chapter 5_part2_student - Discount,SalePrice,andSalesTax...
This preview shows pages 1–5. Sign up to view the full content.
Applications of Percent ` Discount Sale Price and Sales Tax Discount, Sale Price, and Sales Tax ` Simple Interest ` Buying on Credit ` Compound Interest The amount an item is reduced from the regular, or original, price is called the discount . D iscount …D D ISCOUNT = (O RIGINAL P RICE ) × (P ERCENT M ARKDOWN ) Th t kd i itt d i l The percent markdown is written as a decimal to calculate the discount. Example: Find the discount, given the original price d th t kd and the percent markdown. 1) Hardware 500 baht; 20% off 1) Hardware, 500 baht; 20% off Solution i (O i i l i ) ( kd ) Discount = (Original Price) × (Percent Markdown) = 500 × 0.20 100 = 100 The discount is 100 baht. ) h b h d 2) Shoes, 290 baht; 15% discount Solution Sometimes the markdown is given as a fraction !!!
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Example: Shampoo with a regular price of 129 BHT are on l k 1/3 ff Wh t i th di t? sale mark 1/3 off. What is the discount? Solution As consumers, we are usually concerned with the sale price rather than the amount of discount. The sale price can be found by subtracting the discount from the original price. …Complement… Two positive numbers less than 1 are called complements if th i i 1 if their sum is 1. Example: Find the complements Find the complements. 1) 0.7 1– 0.7 = 0.3; the complement of 0.7 is 0.3. 2) 0.15 3) 40% 4) ¼ The sale price can be found by multiplying the original Sale Price price by the complement of the markdown. …Sale Price… S ALE P RICE = (O RIGINAL P RICE ) × (C OMPLEMENT OF M ARKDOWN ) Example: Find the sale price. 1) Hardware, 500 baht; 20% off Solution l 2) Shoes, 290 BHT; 15% discount Solution …Discount Formula… Discount: d = pm When: d pm Sale Price: s = p – d or s = pc d = amount of discount m = percent markdown p = original price Original Price: p = s/c C l t / s = sale price c = complement of Complement: c = s/p percent markdown
Example: During a 20% off sale, an item is marked 384 BHT. What is the regular price? Solution Example: If the sale price of an item is 2,288 BHT and the regular price is 3,520 BHT, what is the percent markdown? Solution …Sales Tax Formula… S ALE s T AX = (O RIGINAL P RICE ) × (T AX R ATE ) Example: Find the Pennsylvania sales tax for building materials that cost \$84 65 [Pennsylvania sales tax rate: 6%] materials that cost \$84.65. Solution Sale Tax = (Original Price) × (Tax Rate) = 84.65(0.06) = 5.079 The sale tax is \$5.08. To find the total price, add the sale tax to the original price, this means that the price (including tax) is \$84.65 + \$5.08 = \$89.73 Total Price = (Original Price) + (Sales Tax) Total Price (Original Price) (Sales Tax) = (Original Price) + (Original Price) × (Tax rate) = (Original Price)(1 + Tax rate) Distributive property …Price (Including Tax)… T OTAL A MOUNT = (O RIGINAL P RICE )(1 + T AX R ATE )
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Example: In New Jersey, a truck tire at Sears costs \$159.98. What is the total cost of the tire (including tax) [New Jersey sales tax rate: 6%] Solution 8.2 Simple Interest Simple Interest “Interest” is money paid for the use of money.
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern
| 1,195
| 4,491
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.765625
| 4
|
CC-MAIN-2018-22
|
latest
|
en
| 0.83065
|
https://techcommunity.microsoft.com/t5/Excel/Assistance-needed-with-Index-Match-or-another-alternative/m-p/550729/highlight/true
| 1,571,578,870,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2019-43/segments/1570986710773.68/warc/CC-MAIN-20191020132840-20191020160340-00495.warc.gz
| 711,811,719
| 52,854
|
• 412K Members
• 3,413 Online
• 467K Conversations
SOLVED
New Contributor
# Assistance needed with Index/Match or another alternative
Could someone please assist with the following:
1. Sheet1 contains a number of different scales (Scale1, Scale2, Scale3...) that are numeric or alphanumeric.
2. The main scale has values 0 to 100. All scales are as rows.
3. Sheet 2 contains a drop down to show all the available scales from sheet 1
4. If a user selects a scale from the drop down (e.g., Scale2) and enters a value, then the corresponding value from the main scale should be displayed.
5. A value on Scale2 can correspond to multiple values on the main scale.
6. The formula should display the highest corresponding value from the main scale.
Example:
Scale 2 Values are: A1, A1, A1, A1, A2, A2... Main Scale Values 100, 99, 98, 97, 96, 95. So A1 can equal 100, 99, 98 or 97. Only 100 (the highest value) should be displayed.
Your help is greatly appreciated.
Thanks
4 Replies
# Re: Assistance needed with Index/Match or another alternative
Hi
Sounds like you could use MAXIFS to bring back the max value from Main Scale that corresponds to the selected Scale
e.g. = MAXIFS( MainScaleColumn, ScaleColumn, SelectedScale)
Solution
# Re: Assistance needed with Index/Match or another alternative
@Spicierboar , as variant, for such model
=AGGREGATE(14,6,1/(INDEX(A3:G4,MATCH(B6,A3:A4,0),2):INDEX(A3:G4,MATCH(B6,A3:A4,0),7)=B7)*\$B\$2:\$G\$2,1)
Highlighted
# Re: Assistance needed with Index/Match or another alternative
@Sergei Baklan This works. Thank you.
# Re: Assistance needed with Index/Match or another alternative
@Spicierboar , you are welcome
Related Conversations
flashing a white screen while open new tab
cntvertex in Discussions on
13 Replies
Stable version of Edge insider browser
HotCakeX in Discussions on
35 Replies
Tabs and Dark Mode
cjc2112 in Discussions on
22 Replies
How to Prevent Teams from Auto-Launch
chenrylee in Microsoft Teams on
28 Replies
Edge insider Dev bypasses IE mode website list
HotCakeX in Enterprise on
4 Replies
| 576
| 2,070
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-43
|
latest
|
en
| 0.709154
|
https://www.computing.net/answers/office/coutifs-excel-2010-3-conditions/15849.html
| 1,603,338,324,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-45/segments/1603107878879.33/warc/CC-MAIN-20201022024236-20201022054236-00635.warc.gz
| 667,017,132
| 8,990
|
# COUTIFS EXCEL 2010 3 Conditions
October 21, 2011 at 20:47:03
Specs: Windows XP, 4 gig
In Excel 2010 I have a 3 condition Countifs that says if State is AK count if the Beds are 0 and the Revenue is 0. One column has all the states. Another has all the hospitals, another has the number of beds and the last on has the gross patient revenue. I just want to get a count of the number of Hospitals in a particular State where the number of beds is 0 and the revenue is 0. I figured out how to count beds equal 0 (8) and revenue equal 0 (9) but the count should be 7 that meets both criteria. I think I need to use an AND logical but not sure how. Thanks
See More: COUTIFS EXCEL 2010 3 Conditions
#1
October 21, 2011 at 21:58:10
Since I can't see your spreadsheet from where I'm sitting, I can only offer an example of what might work for you.With this data set, the formula below will return 2 since there are 2 instances where the state is AK and there is a 0 in both column B and C.=COUNTIFS(A1:A12, "AK", B1:B12, 0, C1:C12, 0)``` A B C 1 AK 0 0 <--- 2 NY 2 1 3 NJ 0 0 4 MI 1 1 5 AK 0 0 <--- 6 NY 0 1 7 NJ 5 0 8 MI 0 1 9 AK 1 0 10 NY 0 1 11 NJ 1 0 12 MI 0 0 ```Click Here Before Posting Data or VBA Code ---> How To Post Data or Code.
Report •
#2
October 22, 2011 at 21:15:34
Thank you... I thought I had done that but it was returning 3 on mine. Treating is as an "OR" condition. The Hospital data actually exists on another tab of the sheet where I have all the hospitals in the USA and wanted to get a count by state as to how many hospitals met the condiiton of No Beds and No Revenue. I will retry with your logic.
Report •
Related Solutions
| 516
| 1,656
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.84375
| 3
|
CC-MAIN-2020-45
|
latest
|
en
| 0.946591
|
https://durrell2012.com/what-is-a-tabular-and-graphical-methods/
| 1,679,708,089,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00796.warc.gz
| 258,039,869
| 12,109
|
# What is a tabular and graphical methods?
## What is a tabular and graphical methods?
The most frequently used tabular format for data summarization is Frequency table and Cross-tabulation. Graphical Methods are a visual way of presenting data using charts and graphs. The visuals make the data intuitive and self-understandable.
What is the difference between tabular form and graphical form of data?
Table vs Chart. The main difference between table and chart is that table displays data in the form of row and columns whereas chart is the graphical representation of data in varied forms.
### What is graphical data?
Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate.
What is tabular representation of data?
Tabulation, i.e., tabular presentation of data is a method of presentation of data. ● It is a systematic and logical arrangement of data in the form of rows and columns with respect to the characteristics of data.
## What is graphical method in statistics?
Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.
How do you present data in a tabular form?
Organize tabular data into rows and columns. Each row represents a single record or data point, while columns contain information pertaining to that record. Each record or row in the data set should be uniquely identified by one or more columns in combination.
### What is the use of tabular and graphical forms in presenting and interpreting data in research why these forms are important in the presentation and interpretation of data?
Text, tables, and graphs are effective communication media that present and convey data and information. They aid readers in understanding the content of research, sustain their interest, and effectively present large quantities of complex information.
Why do we represent data graphically?
The aim of presenting scientific data graphically is to utilise the power of visual display to communicate information efficiently, while avoiding deception or confusion. This is important both in how we communicate our findings to others, and to our understanding and analysis of the data.
## What is tabular data example?
The characteristics of tabular data are: They consists of rows and columns. For instance, each song or email message or file is a row. Each of their characteristics—the song title, the message subject, the filename—is a column.
What is economics table?
A table is a systematic and orderly arrangement of information, facts, or data using rows and columns for presentation, which make it easier for better understanding.
### What is the difference between descriptive and tabular statistics?
Descriptive statistics makes use of graphical techniques and numerical descriptive measures to summarize and present the data. Tabular method of data presentation is wide spread in all spheres of human life. These methods are used to summarize data from a sample or population into table format.
What is tabular presentation of data?
Tabular method of data presentation is wide spread in all spheres of human life. These methods are used to summarize data from a sample or population into table format. Data is grouped into categories and the number (or frequency) of observations in each category is obtained.
## What is a table?
A rectangular arrangement of data in which the data are positioned in rows and columns. 2. Table 1. Activity 1 2 3 4 5 Total Name of Members 15 25 20 25 15 100 1.
What are tabular and frequency distribution methods in statistics?
These methods are used to summarize data from a sample or population into table format. Data is grouped into categories and the number (or frequency) of observations in each category is obtained. Frequency distribution is a type of tabular method.
| 770
| 4,050
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-14
|
longest
|
en
| 0.905488
|
https://www.h2xengineering.com/post/pipe-volume-calculator-free-spreadsheet
| 1,652,805,361,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662519037.11/warc/CC-MAIN-20220517162558-20220517192558-00451.warc.gz
| 944,739,452
| 143,923
|
• H2X Team
# Pipe Volume Calculator (FREE Spreadsheet)
Pipe volume is an important calculation that is commonly used by various members of a project team during the design of a construction project.
Some examples of where the pipe volume calculation and results are used are:
• The structural engineer will design their structure to handle the weight of pipes
• The plumbing engineer needs to be aware that long 'dead-legs' have lots of consequences. 'Dead-legs' are the cold water that is drawn off before heated water commences to discharge from the heated water outlet e.g. waiting for the cold water to turn warm before getting into the shower. The consequences of having long dead-legs are:
• The end-user will be unhappy waiting a long time for warm water, especially if they are in a building such as a luxury hotel
• The client will not want to cover expensive bills from the wasted water and energy
• Sustainability consultants often like to minimise the wasted water and energy to achieve a better rating for building's sustainability
Pipe Volume Formula
It is relatively easy to calculate the volume of water in a pipe by yourself, using a simple formula.
The volume of water in a pipe is calculated by multiplying the internal diameter of the pipe by its length. The calculation is dependent on two factors:
1. The internal diameter or the radius of a pipe
(as the diameter or the radius of a pipe increases, the pipe volume also increases)
2. The length of the pipe
(as the length of a pipe increases, the pipe volume also increases)
The volume of a pipe is measured in litres (L), metres cubed (m³), or gallons (gal).
The formula that you can use to measure the volume of a pipe is:
V = π⋅(D/2)²⋅L
In the pipe volume formula:
V is the pipe volume
D is the diameter of the pipe
L is the length of the pipe
π has a constant value of 22/7 (3.14)
Wait Time Formula
Once you know the pipe volume, you can also calculate how long you will need to wait for the water to come out of the outlet (e.g. the shower or sink).
The outlet flow rate is measured in litres per second (L/sec), metres cubed per second (m³/sec), or gallons per minute (gpm).
The formula that you can use to measure the wait time is:
T = V / Q
In the wait time formula:
T is the time
V is the pipe volume
Q is the outlet flow rate
Free Pipe Volume & Wait Time Spreadsheet
How to Use The Pipe Volume and Wait Time Spreadsheet
The pipe volume calculator comes with simple instructions. As shown below, you are required to enter information into certain cells and the results will be provided:
If you want to calculate the volume across multiple sections of pipes that differ in size, the pipe volume spreadsheet is set up to allow you to get those results too.
It is very important that you use the internal pipe diameter in the calculation, using the nominal or outside pipe diameter will produce the wrong results.
The spreadsheet also includes some generic pipe data but please do some research to ensure they are correct for your application before using them.
Create a Pipe Volume Chart
You can also create your own charts in the pipe volume spreadsheet.
Again, there are simple instructions that direct you to enter information into certain cells and the results will be provided:
Once you have created the chart, you can export it as a PDF to be referred to in the future.
How Can H2X Help With Pipe Volume Calculations?
When you use H2X, the pipe volume calculation is automatically undertaken as you draw your layout. The results are shown below:
You can also export a PDF of the project with the dead-leg results showing. You can share this with the project team to provide evidence that the plumbing system has been designed with the pipe volume and dead-legs in mind.
You can read this post about why 'length' should not be used as a measurement for dead-leg calculations.
###### FEATURES
Water Services Calculations
Gas Services Calculations
Fire Services Calculations
Sanitary Drainage Calculations
3D Revit Model
Cost & Bill of Materials Export
Design Warnings
| 870
| 4,104
|
{"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}
| 3.9375
| 4
|
CC-MAIN-2022-21
|
latest
|
en
| 0.93522
|
https://www.coursehero.com/file/211578/M251finalsp03/
| 1,516,483,791,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-05/segments/1516084889733.57/warc/CC-MAIN-20180120201828-20180120221828-00242.warc.gz
| 862,902,222
| 65,584
|
M251final(sp03)
# M251final(sp03) - MATH 251 Spring 2003 Final Exam May 8...
This preview shows pages 1–3. Sign up to view the full content.
MATH 251 Spring 2003 Final Exam May 8, 2003 NAME : ID : INSTRUCTOR : There are 15 questions on 5 pages. Please read each problem carefully before starting to solve it. For each multiple choice problem 4 answers are given, only one of which is correct. Mark only one choice. For partial credit questions, all work must be shown - credit will not be given for an answer unsupported by work. N O CALCULATORS ARE ALLOWED . P LEASE DO NOT WRITE IN THE BOX BELOW . 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: Total:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
MATH 251 Spring 2003 -Final Exam- 1. (6 points) Consider the undamped system of a 7 kg mass hanging from a spring. An external force of 3 sin(10 t ) newtons is applied to the system, which then enters reso- nance. What is the spring constant? (a) 7 (b) 10 (c) 100 (d) 700 2. (6 points) What is the inverse Laplace transform of F ( s ) = e - 3 s 1 s +2 ? (a) u 3 ( t ) + 1 2 δ ( t - 3) (b) u 3 ( t ) e 2 t +3 (c) u 3 ( t ) e - 2 t +6 (d) δ ( t - 3) e - 2 t 3. (6 points) What is the partial fraction expansion of 7 s - 2 s 2 ( s - 2) ? (a)
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### Page1 / 5
M251final(sp03) - MATH 251 Spring 2003 Final Exam May 8...
This preview shows document pages 1 - 3. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online
| 527
| 1,618
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-05
|
latest
|
en
| 0.809011
|
https://forum.unitronics.com/topic/552-help-needed-with-challenging-algorithm/
| 1,709,099,385,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474697.2/warc/CC-MAIN-20240228044414-20240228074414-00578.warc.gz
| 262,990,301
| 19,235
|
# Help needed with challenging algorithm
## Recommended Posts
• MVP 2023
I have an odd customer request that has me stumped as to how to program this efficiently - perhaps someone here can help.
I am using a v570 PLC to control 10 valves. I have 10 demand digital inputs (requests to open individual valves) and 10 digital outputs to open and close the valves. The pump that pushes chemical through these valves is not capable of handling more than a few open valves simultaneously, also some of the valves are more important than others. So, the customer would like an input on-screen to adjust the number of valves that can be open simultaneously and a priority selection for any or all of the valves. If there are more than the input value number of valves being requested to open simultaneously, then additional valves should be held off until an open valve closes. Valve opening should be in FIFO order with priority valves taking precedence.
The biggest problem I'm having is trying to deal with the FIFO (i.e. maintaining a continuous and current hierarchical list of valves waiting their turn to open) and for dealing with the conflict that allows the priority valves to move to the head of the line.
Can anyone suggest the basic framework of an algorithm that will accomplish this in VisiLogic?
##### Share on other sites
Hi Flex,
I want to give you some initial tips:
There is Functional block (FB) Events. There you define a vector of bits. In your case each bit wil represent output of a valve. One fo thhe functions of this FB will show you how many bits are active (how many valves are open). You can easilly compare this number with the limit, set from, let's say HMI and block new valves to be open.
If there is more requests during block, you can enter the pointer of the valve requested in a vector of MI.
In VisiLogic > help menu > Examples > Project examples > Ladder you can find a nice working example V570 Vector FIFO. I hope it will help you to manage the vector of waiting to open valves.
It seems now you have the basic elements to start programming. I guess few details are missing.
Let me know if these tips are useful and which further help you need.
##### Share on other sites
• MVP 2023
Thank you very much, Emil. I will spend a couple of days looking at this and get back to you.
## Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.
× Pasted as rich text. Paste as plain text instead
Only 75 emoji are allowed.
× Your previous content has been restored. Clear editor
× You cannot paste images directly. Upload or insert images from URL.
×
×
| 589
| 2,753
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10
|
longest
|
en
| 0.954572
|
https://pgoutcomes.net/distributive-property-practice-worksheet/
| 1,620,337,226,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-21/segments/1620243988763.83/warc/CC-MAIN-20210506205251-20210506235251-00508.warc.gz
| 484,603,466
| 8,715
|
# Distributive property practice worksheet ideas
» » Distributive property practice worksheet ideas
Your Distributive property practice worksheet images are ready in this website. Distributive property practice worksheet are a topic that is being searched for and liked by netizens now. You can Download the Distributive property practice worksheet files here. Find and Download all free images.
If you’re searching for distributive property practice worksheet images information related to the distributive property practice worksheet keyword, you have visit the right site. Our website always gives you hints for seeing the maximum quality video and picture content, please kindly surf and locate more informative video articles and graphics that match your interests.
Distributive Property Practice Worksheet. Multiplicands up to 30. 3 x 2 and -3 -4x - 2. However negative numbers are used throughout the questions. Showing top 8 worksheets in the category - Distributive Property Practice.
Using The Distributive Property No Exponents 2 Terms B Algebra Worksheets Distributive Property Math Practice Worksheets From pinterest.com
Multiplicands up to 30. 93y 10 11s 2 a. Using the distributive property printable worksheets multiplication addition. The distributive property makes multiplication with large numbers easier by breaking them into smaller addends. We got this image from the web that we feel would be probably the most representative pictures for Distributive Property Practice Worksheet. 124u t 7 b.
### 411b a 4 a.
Examples of questions included. 38 5p 2 b. Jun 13 2020 - Distributive Property Practice Worksheet Did you know that Distributive Property Practice Worksheet is one of the hottest topics in this category. Users can directly refer the answer key to verify the work with steps for the corresponding practice problems given in the 3OAB5 activities under common core state standards for 3rd grade. Rewrite Using the Distributive Property Worksheets How to Rewrite a Value Using the Distributive Property - The distributive property allows us to multiply the number by each addend of the sum. Distributive Property of Multiplication Printable Worksheets.
Source: pinterest.com
Once you find your worksheet click on pop-out icon or print icon to worksheet. 411b a 4 a. 511 10a 3 a. The generator includes only very simple problems with linear expressions. However negative numbers are used throughout the questions.
Source: pinterest.com
93y 10 11s 2 a. 4 View Profile Use this version or check out other variations created by teachers from the Wizer community. 4 7 2x 4 9x 2. The distributive property is a useful strategy for helping students to simplify larger multiplication problems especially when doing mental math. Students explicitly rewrite and answer multiplication equations using the distributive property.
Source: pinterest.com
The Distributive Property and Algebraic Expressions. We got this image from the web that we feel would be probably the most representative pictures for Distributive Property Practice Worksheet. 58a d 3 b. Distributive Property Other contents. 811s 5t 5 5 a.
Source: pinterest.com
Distributive Property of Multiplication Printable Worksheets. 511 10a 3 a. 46z k 6 b. 44t 3 6r 6 a. Rewrite Using the Distributive Property Worksheets How to Rewrite a Value Using the Distributive Property - The distributive property allows us to multiply the number by each addend of the sum.
Source: pinterest.com
Add to my workbooks 8 Download file pdf Embed in my website or blog Add to Google Classroom. The Distributive Property and Algebraic Expressions. Solving Equations with the Distributive Property 1 This 12 problem worksheet is designed to introduce you to solving equations that have contain the Distributive Property. 4 2x 7 8x 28. 811s 5t 5 5 a.
Source: pinterest.com
123y 11 5 b. Students explicitly rewrite and answer multiplication equations using the distributive property. It lets us solve the expression often written in the form of a b c. Users can directly refer the answer key to verify the work with steps for the corresponding practice problems given in the 3OAB5 activities under common core state standards for 3rd grade. Some of the worksheets displayed are Using the distributive property date period The distributive property Mcq The distributive property Classwork Sample work from 941246 the distributive property 3 Distributive property using area name.
Source: pinterest.com
4 7 2x 4 9x 2. Multiplicands up to 30. 108 11u 1 b. Free practice example worksheets with answer key in pdf for easy printing. Distributive Property worksheets and online activities.
Source: pinterest.com
122x 10w 9 7 a. 108 11u 1 b. Distributive Property Practice Worksheet October 14 2019 Impact. The numbers are small so that students do not get lost with a lot of multiplication. Solving Equations with the Distributive Property 1 This 12 problem worksheet is designed to introduce you to solving equations that have contain the Distributive Property.
Source: pinterest.com
3 x 2 and -3 -4x - 2. Distributive Property Other contents. Some of the worksheets displayed are Using the distributive property date period The distributive property Mcq The distributive property Classwork Sample work from 941246 the distributive property 3 Distributive property using area name. 122x 10w 9 7 a. Jun 13 2020 - Distributive Property Practice Worksheet Did you know that Distributive Property Practice Worksheet is one of the hottest topics in this category.
Source: pinterest.com
46z k 6 b. 511 10a 3 a. Distributive Property of Multiplication Printable Worksheets. The distributive property makes multiplication with large numbers easier by breaking them into smaller addends. 122x 10w 9 7 a.
Source: pinterest.com
The Distributive Property and Algebraic Expressions. Add to my workbooks 8 Download file pdf Embed in my website or blog Add to Google Classroom. The worksheets in this collection unpack and explore the distributive property with visuals and multiplication and addition equations. The distributive property is a useful strategy for helping students to simplify larger multiplication problems especially when doing mental math. 7 u2l0 y1T2 b oK fuAtDa7 SQohfKtIw Yavr YeQ 4LRL GCp0 m HAQl5lt nrJi OgNhFt 9sN zr 0eds reCr9vQeRdPW P qM taBdIea Uwoi 9t NhP pIqn jfTi cn MiQtaex sA Cl 3gbe ab drda K Z1 n7 Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Using the Distributive Property Date_____ Period____.
Source: pinterest.com
The Distributive Property and Algebraic Expressions. We got this image from the web that we feel would be probably the most representative pictures for Distributive Property Practice Worksheet. The distributive property is a useful strategy for helping students to simplify larger multiplication problems especially when doing mental math. 55g 12 2x 4 b. 122x 10w 9 7 a.
Source: pinterest.com
Using the distributive property printable worksheets multiplication addition. Use the distributive property to simplify the following expression. 3 x 2 and -3 -4x - 2. 46z k 6 b. 811s 5t 5 5 a.
Source: pinterest.com
3rd grade Distributive Property of Multiplication Printable Worksheets Third graders can learn to confidently tackle multiplication and the distributive property with these engaging worksheets. 38 5p 2 b. Only positive whole numbers are featured in the equations. Youll be asked to simplify different. 93y 10 11s 2 a.
Source: pinterest.com
Students explicitly rewrite and answer multiplication equations using the distributive property. Jun 13 2020 - Distributive Property Practice Worksheet Did you know that Distributive Property Practice Worksheet is one of the hottest topics in this category. Students explicitly rewrite and answer multiplication equations using the distributive property. The distributive property makes multiplication with large numbers easier by breaking them into smaller addends. Youll be asked to simplify different.
Source: pinterest.com
These worksheets are especially meant for pre-algebra and algebra 1 courses grades 6-9. Users can directly refer the answer key to verify the work with steps for the corresponding practice problems given in the 3OAB5 activities under common core state standards for 3rd grade. Some of the worksheets displayed are Using the distributive property date period The distributive property Mcq The distributive property Classwork Sample work from 941246 the distributive property 3 Distributive property using area name. 55g 12 2x 4 b. This is exactly why were showing this topic at the moment.
Source: pinterest.com
The distributive property makes multiplication with large numbers easier by breaking them into smaller addends. Algebra Worksheet – Using the Distributive Property Answers Do Not Include Exponents Author. 108 11u 1 b. Users can directly refer the answer key to verify the work with steps for the corresponding practice problems given in the 3OAB5 activities under common core state standards for 3rd grade. Use the distributive property to simplify the following expression.
Source: pinterest.com
4 7 2x 4 9x 2. The numbers are small so that students do not get lost with a lot of multiplication. With this worksheet generator you can make customizable worksheets for the distributive property and factoring. The Distributive Property and Algebraic Expressions. These worksheets are especially meant for pre-algebra and algebra 1 courses grades 6-9.
This site is an open community for users to submit their favorite wallpapers on the internet, all images or pictures in this website are for personal wallpaper use only, it is stricly prohibited to use this wallpaper for commercial purposes, if you are the author and find this image is shared without your permission, please kindly raise a DMCA report to Us.
If you find this site helpful, please support us by sharing this posts to your favorite social media accounts like Facebook, Instagram and so on or you can also bookmark this blog page with the title distributive property practice worksheet by using Ctrl + D for devices a laptop with a Windows operating system or Command + D for laptops with an Apple operating system. If you use a smartphone, you can also use the drawer menu of the browser you are using. Whether it’s a Windows, Mac, iOS or Android operating system, you will still be able to bookmark this website.
| 2,263
| 10,436
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.25
| 3
|
CC-MAIN-2021-21
|
latest
|
en
| 0.850167
|
http://brainden.com/forum/index.php/topic/437-hole-in-a-sphere/page-11
| 1,419,311,378,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-52/segments/1418815948154.77/warc/CC-MAIN-20141217113228-00173-ip-10-231-17-201.ec2.internal.warc.gz
| 41,234,865
| 21,185
|
## Welcome to BrainDen.com - Brain Teasers Forum
Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse
# Hole in a sphere
Best Answer bonanova, 23 August 2007 - 07:11 AM
The volume of the spherical caps is given by:
[list]
where
[list]
[*] h = the height of the cap (difference between r and the distance from the centre of the[/*:m:1cc31][list] sphere to the centre of the circular end of the hole)
Kudos to cpotting for the cap formula.
Spoiler for Here's the mathematical solution
Spoiler for Here's the logical solution
Go to the full post
166 replies to this topic
### #101 bonanova
bonanova
bonanova
• Moderator
• 5918 posts
• Gender:Male
• Location:New York
Posted 14 June 2008 - 08:23 AM
Does this hold for offset holes?
I'm neither a mathematician, nor much of a logician. But when I thought of this puzzle, I refused to think on so large of a scale. I imagined a 12" sphere with an offset hole. I imagined the shape that would be drilled out, and considered that 6" length, was that the longest length, the shortest, or the average. At that point I could no longer go on.
Sigh.
Tyg
Don't know what you mean by offset, but the hole is drilled though the center of the sphere.
Does that help?
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell
### #102 PickleLlama
PickleLlama
Newbie
• Members
• 1 posts
Posted 23 June 2008 - 07:41 PM
Spoiler for spoiler courtesy of bonanova
• 0
### #103 bonanova
bonanova
bonanova
• Moderator
• 5918 posts
• Gender:Male
• Location:New York
Posted 24 June 2008 - 07:54 AM
Spoiler for spoiler courtesy of bonanova..
Nice job.
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell
### #104 Interested
Interested
Newbie
• Members
• 1 posts
Posted 15 July 2008 - 05:51 PM
Apart from the degree of mathematical and logical aptitude, I praise you, bonanova, for your patience!
I agree 100%!!! It took me 46 posts to get it although if jason81 would have added his answer sooner I may have been much faster on the uptake. I am just proud that I got it at all as I was loosing hope.
Thank you again Bonanova for your patience. We need more teachers like you in our school system...
Not to bite off of Jkyle1980, but where do I send my tuition as well...?
• 0
### #105 Aiken38
Aiken38
Newbie
• Members
• 5 posts
Posted 15 July 2008 - 07:30 PM
36pi, nice.. i started working out the mathmatical solution and then it got me thinking and then i figured it out.. cool!
• 0
### #106 AliceJH
AliceJH
Junior Member
• Members
• 29 posts
Posted 01 August 2008 - 04:37 PM
The question does not state the diameter or length of the hole (a cyclinder with a curved top and bottom) in relation to diameter of the sphere. This information is essential. We only know that the diameter of the sphere must be greater than 6 inches. You can use the same size apple corer for different size apples.
Edited by AliceJH, 01 August 2008 - 04:39 PM.
• 0
### #107 bonanova
bonanova
bonanova
• Moderator
• 5918 posts
• Gender:Male
• Location:New York
Posted 01 August 2008 - 04:42 PM
I agree 100%!!! It took me 46 posts to get it although if jason81 would have added his answer sooner I may have been much faster on the uptake. I am just proud that I got it at all as I was loosing hope.
Thank you again Bonanova for your patience. We need more teachers like you in our school system...
Not to bite off of Jkyle1980, but where do I send my tuition as well...?
Hi interested,
Thanks for the kind words.
Hope you're enjoying Brain Den as much as I do.
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell
### #108 xucam
xucam
• Members
• 246 posts
Posted 11 November 2008 - 08:25 PM
The problem as originally stated is not solvable, as it could be reasonably interpreted as a 6-inch diameter hole all the way through an object.
I would argue that you cannot drill a 6 inch hole through a sphere with radius = 3 any more than you can through a sphere of r = 2. A hole with no volume is not a hole. It may be true that the r=3 case is a boundry which a solution approaches, and obviously the volume of such an intact sphere is 4/3 * 3 * 3 * 3 * pi cu. in.= 36 pi cubic inches.
There was also discussion of the 'caps' that would fit on top of the inscribed cylinder in the problem. Clearly, for the example of boring through the earth with a bit whose radius is almost as big as the radius of the earth, these caps would be massive (basically, you've just cut away 6-inch slice of the earth through the center). The volume of these caps is very obviously dependent on the radius of the sphere, and are thus not included in the 'answer'.
There was another purported 'solution' which seems to me to be flawed:
You're all making this too hard. You just need to know the area of each slice of the donut, which is simply the difference of two circles.
L = length of bore
x = radius of sphere cross-section at height z
A = area of donut cross-section at height z
Forming two simple right triangles:
r? = R? - L?/4
x? = R? - z?
The first equation stipulates that the radius of the cylinder equals the radius of the sphere minus (the length of the bore divided by 4), which means that
r = R - 1.5 which could be true for one such case, but is hardly a general solution - if the difference between the radii of the cylinder and sphere were 1.5 inches then the volume would be way more than 36 pi cubic inches.
Also, the stated 'solution' of 36pi isn't a volume at all, whereas 36 pi cubic inches is...
But still, great for you that you felt like a genius and thanks for sharing.
Maybe this has already been posted. A friend asked me this a while back, and I answered her in less than a minute. She said I was a genius. But I said there were two ways to arrive at the answer, and I simply chose the easier way.
A 6-inch [long] hole is drilled through a sphere.
What is the volume of the remaining portion of the sphere?
The hard way involves calculus. The easy way uses logic.
... combining 2 posts by the author ...
The easy way is to suppose the answer is the same for
any sphere [with diameter not less than 6 inches], and
calculate the answer for a 6-inch diameter sphere.
• 0
### #109 AfroAllianceRRR
AfroAllianceRRR
Newbie
• Members
• 5 posts
Posted 11 November 2008 - 11:33 PM
6(pi)rsquared.
Bssically just putting it down as an expresion of the voloume of the drilled hole equals the empty space of the the sphere, I think it might be unorthodox but it worth a shot
• 0
### #110 bonanova
bonanova
bonanova
• Moderator
• 5918 posts
• Gender:Male
• Location:New York
Posted 01 April 2009 - 05:38 PM
6(pi)rsquared.
Bssically just putting it down as an expresion of the voloume of the drilled hole equals the empty space of the the sphere, I think it might be unorthodox but it worth a shot
Not quite.
There are three volumes to consider.
• The cylindrical hole
• The spherical end caps on either end of the hole cylinder
• The remaining volume of the sphere.
It's the third item we seek.
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell
#### 0 user(s) are reading this topic
0 members, 0 guests, 0 anonymous users
| 2,093
| 8,085
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2014-52
|
latest
|
en
| 0.925432
|
https://exercism.io/tracks/clojure/exercises/anagram/solutions/1cc4fb14520bc92e32d5764c
| 1,603,667,287,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-45/segments/1603107890028.58/warc/CC-MAIN-20201025212948-20201026002948-00332.warc.gz
| 321,491,934
| 6,634
|
🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉
# bostonaholic's solution
## to Anagram in the Clojure Track
Published at Jul 13 2018 · 1 comment
Instructions
Test suite
Solution
Given a word and a list of possible anagrams, select the correct sublist.
Given `"listen"` and a list of candidates like `"enlists" "google" "inlets" "banana"` the program should return a list containing `"inlets"`.
## Source
Inspired by the Extreme Startup game https://github.com/rchatley/extreme_startup
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
### anagram_test.clj
``````(ns anagram-test
(:require [clojure.test :refer [deftest is]]
anagram))
(deftest no-matches
(is (= []
(anagram/anagrams-for "diaper" ["hello" "world" "zombies" "pants"]))))
(deftest detect-simple-anagram
(is (= ["tan"] (anagram/anagrams-for "ant" ["tan" "stand" "at"]))))
(deftest does-not-confuse-different-duplicates
(is (= [] (anagram/anagrams-for "galea" ["eagle"]))))
(deftest eliminate-anagram-subsets
(is (= [] (anagram/anagrams-for "good" ["dog" "goody"]))))
(deftest detect-anagram
(is (= ["inlets"]
(let [coll ["enlists" "google" "inlets" "banana"]]
(anagram/anagrams-for "listen" coll)))))
(deftest multiple-anagrams
(is (= ["gallery" "regally" "largely"]
(let [coll ["gallery" "ballerina" "regally"
"clergy" "largely" "leading"]]
(anagram/anagrams-for "allergy" coll)))))
(deftest case-insensitive-anagrams
(is (= ["Carthorse"]
(let [coll ["cashregister" "Carthorse" "radishes"]]
(anagram/anagrams-for "Orchestra" coll)))))
(deftest word-is-not-own-anagram
(is (= [] (anagram/anagrams-for "banana" ["banana"]))))
(deftest capital-word-is-not-own-anagram
(is (= [] (anagram/anagrams-for "BANANA" ["banana"]))))``````
``````(ns anagram)
(defn- normalize [word]
(sort word))
(defn anagrams-for
"returns a list of anagrams for a given word and list of possible anagrams"
[word possibles]
(let [normalized-word (normalize word)]
(filter #(= normalized-word (normalize %)) possibles)))``````
## Community comments
Find this solution interesting? Ask the author a question to learn more.
Good to go for me. However one hint: you could make the program more effective (nlogn vs n) by swapping sort for another core clojure function which you have used in one of your past assignments.
### What can you learn from this solution?
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.
• What compromises have been made?
• Are there new concepts here that you could read more about to improve your understanding?
| 752
| 2,851
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-45
|
latest
|
en
| 0.631619
|
https://dioptionuifd.web.app/show84950ri/the-adjusted-interest-rate-lo.html
| 1,642,563,812,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00592.warc.gz
| 260,523,727
| 6,343
|
### Category Show84950
An adjustable-rate mortgage (ARM) is a loan with an interest rate that changes. ARMs may start with lower monthly payments than fixed-rate mortgages, but If you have an Adjustable Rate Mortgage (ARM), you've probably heard of incorrect calculations by lenders when it comes to changing the loan's interest rate. Adjustable-rate mortgages are loans whose interest rates adjust with Libor, the fed funds rate, or Treasury bills. Types, pros and cons.
Interest Rates Chapter 5.1-5.3. Outline Interest Rate Quotes and Adjustments – The Effective Annual Rate (EAR) and the Annual Percentage Rate (APR) The. 6 Nov 2019 The Bank of Thailand's Monetary Policy Committee (MPC) on Wednesday voted to cut the policy interest rate to a record low of 1.25% in a bid Adjusted interest is one of the “tricky” calculation methods developed by lenders. Adjusted interest is based upon a specific rate of nominal interest. For example, we can calculate a 12% nominal interest rate by using one of the “tricks”, which we will explain by giving an example. If an investor simply takes a linear estimate by subtracting 3 percent from 23.3 percent, he arrives at an inflation-adjusted return of 20.3 percent, which in this example is 0.6 percent too high. Each month, the IRS provides various prescribed rates for federal income tax purposes. These rates, known as Applicable Federal Rates (or AFRs), are regularly published as revenue rulings. The list below presents the revenue rulings containing these AFRs in reverse chronological order, starting with January 2000.. Enter a term in the Find Box.
## 5 Oct 2014 This column exploits adjustable rate mortgages that originated before the Crisis and featured an automatic reset of the interest rate.
### Adjustable-Rate Mortgages (ARMs) begin with a fixed interest rate and then adjust up or down after the initial term. ARMs are a good option for buyers who don't
The interest rate adjustment period is how often your rate is adjusted on an adjustable rate mortgage (ARM), after the initial rate period is over. For example, a 5/1 5 Oct 2014 This column exploits adjustable rate mortgages that originated before the Crisis and featured an automatic reset of the interest rate. How will this decision change my repayments? NAB will automatically adjust your home loan interest rate to reflect the change on 13 March 2020
### Adjustable rate mortgages can provide attractive interest rates, but your payment is not fixed. This calculator helps you to determine what your adjustable
As the name implies, ARMs have interest rates that adjust over time. Typically, the starting rate remains fixed for a set number of years, such as three, five, or even Your interest rate and monthly payment may increase or decrease depending on the interest rates at that time. ARM loans are named depending on the length of
## How often the interest rate changes on an adjustable-rate mortgage depends on the specific terms of your adjustable-rate mortgage (ARM). So before you sign
Adjustable rates transfer part of the interest rate risk from the lender to the borrower. They can be used 2 Mar 2020 An adjustable-rate mortgage (ARM) is a type of mortgage in which the interest rate applied on the outstanding balance varies throughout the 3 Sep 2019 The initial interest rate on an adjustable-rate mortgage (ARM) is set below the market rate on a comparable fixed-rate loan, and then the rate ดอกเบี้ย (Interest) คือ เงินตอบแทนที่ได้เพิ่มขึ้นจากการออมหรือลงทุน เช่น ทั้งนี้ ใน สหรัฐอเมริกา นิยมเรียกสินเชื่อจำลองอัตราดอกเบี้ยแบบลอยตัวว่า Adjustable Rate Mortgage Adjusted Interest Rate means, with respect to the interest rate to be borne by an Adjustable Rate Bond during any Adjustment Period, the interest rate per annum 15 Nov 2019 For an adjustable-rate mortgage, the index is a benchmark interest rate that reflects general market conditions and the margin is a number set
Adjustable rates transfer part of the interest rate risk from the lender to the borrower. They can be used
| 886
| 4,041
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2022-05
|
latest
|
en
| 0.932204
|
https://www.studypool.com/discuss/304149/simple-interest-problem-help?free
| 1,505,829,211,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-39/segments/1505818685698.18/warc/CC-MAIN-20170919131102-20170919151102-00385.warc.gz
| 858,653,182
| 13,869
|
##### Simple Interest Problem Help
label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5
The simple interest formula is A=P(1+r)t squared where P represents the amount origionally deposited, r is the interest rate, and A is the account after t years.
Find r if A=2700, P=2300 and t=5
Express r as a pecentage to one decimal place (x.x%)
Dec 10th, 2014
A = P(1+r)t
A = P + Prt
2700 = 2300 + 2300 (r)(5)
2700 = 2300 + 11500r
400 = 11500 r
r = 0.03478 = or 0.035
Dec 10th, 2014
...
Dec 10th, 2014
...
Dec 10th, 2014
Sep 19th, 2017
check_circle
| 207
| 585
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.671875
| 4
|
CC-MAIN-2017-39
|
latest
|
en
| 0.843022
|
https://www.physicsforums.com/threads/pretty-simple-optimization-problem.313112/
| 1,713,095,707,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296816879.25/warc/CC-MAIN-20240414095752-20240414125752-00703.warc.gz
| 887,240,283
| 15,068
|
# Pretty simple optimization problem
• wapakalypse
In summary, the task is to determine the dimensions of a closed box with a square base that will minimize the cost of materials. The volume of the box is 252ft^3 and the materials used for the bottom, sides, and top cost 5$per ft.^2, 3$ft^2, and 2$ft^2 respectively. The next step is to find another formula, possibly using the volume equation v=lwh, to derive and solve for the dimensions. The hint given is to calculate the areas of the different sections, keeping in mind that there are only two free parameters since the bottom is a square. wapakalypse A closed box with a square base is to contain 252ft^3. The bottom costs 5$ per ft.^2, the top is 2$ft^2 and the sides cost 3$ft^2. Find the dimensions that will minimize the cost.
As for equations we have v=lwh and I'm not sure as to how to find the next relative equation.
I just need to find another formula so I can derive and solve. Any help is much appreciated.
Thankss
What are the areas of the different sections?
phsopher said:
What are the areas of the different sections?
It doesn't say, that's directly quoted from the text.
i want to say its something like
3(lw)=sides 5(lw)-bottom 2(lw)-top
That was meant to be a hint for your next equation. Calculate the areas and you can work out the cost from that. Note that there are only two free parameters since the bottom is a square.
## 1. What is an optimization problem?
An optimization problem is a mathematical problem that involves finding the best possible solution from a set of feasible options. This solution is typically the one that maximizes or minimizes a certain objective function.
## 2. How do you solve an optimization problem?
The most common method for solving optimization problems is using mathematical techniques such as calculus, linear algebra, and algorithms. These methods involve finding the optimal values of the decision variables that satisfy the given constraints and optimize the objective function.
## 3. What is the objective function in an optimization problem?
The objective function is a mathematical expression that defines the goal of the optimization problem. It represents the quantity that needs to be maximized or minimized in order to find the optimal solution.
## 4. What are the constraints in an optimization problem?
Constraints are conditions that must be satisfied in order to find a feasible solution to the optimization problem. These conditions can be mathematical equations or inequalities that limit the values of the decision variables.
## 5. What are some real-world applications of optimization problems?
Optimization problems have a wide range of applications in various fields such as engineering, economics, finance, and computer science. Some common examples include optimizing production processes, portfolio management, resource allocation, and route planning.
• Calculus and Beyond Homework Help
Replies
1
Views
1K
• Calculus and Beyond Homework Help
Replies
11
Views
3K
• Calculus and Beyond Homework Help
Replies
3
Views
6K
• Calculus
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
3K
• General Math
Replies
6
Views
1K
• Calculus and Beyond Homework Help
Replies
1
Views
2K
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
759
• Calculus and Beyond Homework Help
Replies
2
Views
3K
| 783
| 3,414
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.03125
| 4
|
CC-MAIN-2024-18
|
latest
|
en
| 0.927625
|
https://cs.stackexchange.com/questions/91047/choose-minimum-subset-of-edges-in-tree-that-connects-all-important-nodes
| 1,713,162,235,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-18/segments/1712296816942.33/warc/CC-MAIN-20240415045222-20240415075222-00731.warc.gz
| 170,058,454
| 39,239
|
Choose minimum subset of edges in tree that connects all important nodes
Let's say we have given weighted tree of size $n$ and list of important nodes in the tree $k$.
We want to choose subset of edges of the tree such that:
• For each two important nodes at least one edge of the path between them will be choosen
• The sum of the subset of edges will be minimized
Note that we only need to find the sum of the edges in the subset, not the edges in the subset.
For example if we have the tree with the edges $(1, 2) \text{ weight = 3}, (1,3) \text{ weight = 10}$ And our important nodes are: $2, 3$. We should chose only the edge $(1,2)$
| 167
| 643
|
{"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}
| 3.296875
| 3
|
CC-MAIN-2024-18
|
longest
|
en
| 0.892398
|
http://www.mathworks.com/matlabcentral/fileexchange/4266-grtheory-graph-theory-toolbox
| 1,469,400,967,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-30/segments/1469257824185.14/warc/CC-MAIN-20160723071024-00317-ip-10-185-27-174.ec2.internal.warc.gz
| 582,658,254
| 14,615
|
Code covered by the BSD License
### Highlights from grTheory - Graph Theory Toolbox
4.54286
4.5 | 35 ratings Rate this file 113 Downloads (last 30 days) File Size: 34.3 KB File ID: #4266 Version: 1.3
# grTheory - Graph Theory Toolbox
### Sergii Iglin (view profile)
16 Dec 2003 (Updated )
28 functions for different tasks of graph theory
File Information
Description
GrTheory - Graph Theory Toolbox.
Functions:
grBase - find all bases of digraph;
grCoBase - find all contrabases of digraph;
grCoCycleBasis - find all independent cut-sets for a connected graph;
grColEdge - solve the color problem for graph edges;
grColVer - solve the color problem for graph vertexes;
grComp - find all components of graph;
grCycleBasis - find all independent cycles for a connected graph;
grDecOrd - solve the problem about decomposition of the digraph to the sections with mutually accessed vertexes (strongly connected components);
grDistances - find the distances between any vertexes of graph;
grEccentricity - find the (weighted) eccentricity of all vertexes, radius, diameter, center vertexes and the periphery vertexes;
grIsEulerian - find the Eulerian cycle of graph;
grIsomorph - solve the problem about isomorphism for two graphs;
grMaxComSu - solve the maximal complete sugraph problem for the graph;
grMaxFlows - solve the maximal flow problem for the digraph;
grMaxMatch - solve the maximal matching problem for the graph;
grMaxStabSet - solve the maximal stable set problem for the graph;
grMinAbsEdgeSet - solve the minimal absorbant set problem for the graph edges;
grMinAbsVerSet - solve the minimal absorbant set problem for the graph vertexes;
grMinCutSet - solve the minimal cut-set problem for the digraph;
grMinEdgeCover - solve the minimal edge cover problem for the graph;
grMinSpanTree - solve the minimal spanning tree problem for the graph;
grMinVerCover - solve the minimal vertex cover problem for the graph;
grPERT - solve the project evaluation research task;
grPlot - draw the plot of the graph (digraph);
grShortPath - solve the shortest path problem for the digraph;
grShortVerPath - for digraph with weighted vertexes solve the problem about the path with minimal weight of verticies;
grTranClos - built the transitive closure for the digraph;
grTravSale - solve the nonsymmetrical traveling salesman problem;
grValidation - auxiliary function (the data validation);
grTheoryTest - test program for all functions.
Required Products Optimization Toolbox
MATLAB release MATLAB 7.0.1 (R14SP1)
Other requirements PC
26 Apr 2016 Han Li
### Han Li (view profile)
I'm trying to use grIsmorph, but is asking for function psimilar...
Where can I find this?
Comment only
27 Mar 2016 V L
### V L (view profile)
03 Mar 2016 komal
### komal (view profile)
kindly give detail about how to install n use grtheory tool box. given information is not complete. help me please
Comment only
17 Oct 2015 abishek ganesan
### abishek ganesan (view profile)
i have installed this grtheory toolbox
Can anyone tel me how to work with it please
good gooop
23 Mar 2015 sam esa
### sam esa (view profile)
dear sir, I would ask if matlab toolbox function have function or program on Binary Decision Diagram algorithm ... thank you
16 Oct 2014 Chenjie
### Chenjie (view profile)
20 Aug 2014 Liang
### Liang (view profile)
24 May 2014 Muhammad Abrar Akber
### Muhammad Abrar Akber (view profile)
MIQP is missing to use grTravSale, How and where to get it?
Comment only
10 Oct 2013 Rohini Sharma
### Rohini Sharma (view profile)
please tell me how to rin this in MATLAB.
Thanks
Comment only
31 Jul 2012 Yonggon
### Yonggon (view profile)
Sumantra, make sure your graph is connected. As long as your graph is connected, you should get correct result.
For this one, with arbitrary edges to make the graph connected without introducing any new cycle, I get
2-5-7-2, 2-5-8-11-7-2, and 2-5-8-14-15-11-7-2.
Comment only
26 Jul 2012 Sumantra Sarkar
### Sumantra Sarkar (view profile)
I think there is a bug in the grCycleBasis function. I have a large edge matrix, a part of which is:
2 5
2 7
5 8
5 7
7 11
8 11
8 14
11 15
14 15
Clearly, there are three cycles in this graph. viz. 2-5-7-2, 5-7-11-8-5 and 8-11-15-14-8. However, the function fails to recognize these three cycles individually and returns 2-5-8-7-11-2 and 2-5-8-14-15-11-7-2, completely ignoring the edges 5-7 and {5-7,8-11} respectively. It happens for several other subsets also. Please suggest a solution.
Thank you.
p.s. It calculates the number of cycles correctly though.
Comment only
12 Mar 2012 Martin
18 Jan 2012 kira
### kira (view profile)
Hi:
I'm also trying to use grIsmorph, but is asking for function psimilar...
Where can you find this?
Comment only
18 Nov 2011 Nina
### Nina (view profile)
Hi! I am trying to run grTheoryTest for isomorphism (case 12) but it's looking for the function or method psimilar. I googled for the file psimilar.m as well as search this site for it. Help? Please? Pretty please, I need this to work in a week :(
Also, do you know how to do subgraphs? Apart from doing a for while removing and adding various vertices?
Comment only
28 Mar 2011 kira
### kira (view profile)
Hi, I have a question using grplot...
For my purposes, I need to draw digraphs with 'vplotstyle'='ko'... and I also need that the arrows don't go to the center of the nodes, ie, not to the vertex position, but to the edge of the circles... I'm looking at the code, and I have identified the vector that generates the edges... but I still don't know how to modify them to do what I want... Could you give some clue...
Greetings...
Comment only
02 Oct 2010 Tianfan XUE
### Tianfan XUE (view profile)
Excellent Job! Thank you very much!
30 Jun 2010 Sergii Iglin
### Sergii Iglin (view profile)
The size of task is determined by the function BINTPROG.
Comment only
09 Jun 2010 Wang
### Wang (view profile)
There is something wrong with grMinVerCover.m and grMinEdgeCover.m when worked in large-scale complex networks(1000 nodes, 2500 edges). The result are both empty cell matrix. But it works well in small-scale networks.
So I want to konw whether there is limited to input data.
Thank you.
19 Apr 2010 Sergii Iglin
### Sergii Iglin (view profile)
>> E=[1 2;1 4;1 5;2 3;2 4;2 5;3 4;3 5;4 5]
E =
1 2
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
>> nMS=grMaxComSu(E)
nMS =
1
2
4
5
Comment only
30 Mar 2010 Tomaz
### Tomaz (view profile)
I think there is even more serious bug in grMaxComSu.m than Florian suggested.
For example, I forwarded the function following set:
E=[1 2;1 4;1 5;2 3;2 4;2 5;3 4;3 5;4 5]
function returned completely wrong result.
If I don't seriously misunderstand concept of max complete subgraph, the solution should be graph with nodes 1,2,4,5.
However, function suggests non-logical solution: 1,2.
Can somebody please re-test this and confirms the problem or explain to me, where does my logic go wrong?
If somebody already encountered this problem, I would appreciate if she/he would share with us the observation or even a solution.
Sergeii great overall work and it would be really nice to see this bug removed...
Does anybody know any other public file for solving the problem of searching max complete subgraph?
Comment only
02 Sep 2009 Florian
### Florian (view profile)
does exactly what I'm looking for!
A minor bug in grMaxComSu.m
If the graph itself is a clique e.g. [1 2; 1 3; 2 3] the function gives an error. E1 in the code is then empty. Possibly account for this cas in a future version. Great work!
19 Nov 2008 Andrew Jackson
### Andrew Jackson (view profile)
11 Sep 2008 Chao Wang
good job
26 Aug 2008 rose rose
very good!
19 Aug 2008 li pengfei
18 Aug 2008 Tim Davis
Comment to Swamy Korada: Finding all possible paths between 2 nodes is an NP-hard problem. Any such algorithm would either give an approximate solution, or take exponential time.
Comment only
10 Aug 2008 fan fanwen
Great work
Is there a script to find all possible paths between 2 nodes?
Comment only
07 May 2008 Andi Patombongi
06 May 2008 jason tharmaraj
can you send me complex networks analysis codes
Good package it sounds!
One additional question: Could the input be thousands of nodes in one graph?
19 Oct 2007 xue huiyan
thanks
19 Oct 2007 hiro mano
28 Sep 2007 gloria macapagal
it is very good toolbox
28 Jun 2007 li yifan china
22 Jul 2006 wael rashwan
20 Oct 2005 giu giu
There are some bugs
31 Aug 2005 Pablo Riera
Excellent
25 May 2005 sanith Wijesinghe
10 Apr 2005 Igor Yegorkin
Beautiful job!
02 Apr 2005 Vlastislav Weiner
Salesman problem doesn't work without miqp function. But where could I find it???
Comment only
29 Dec 2004 Zhenya Donchik
I`m very interesting by the theory of managment
13 Dec 2004 Alexandre Felt
Great job, works fine!
14 Jun 2004 Michael Waisberg
The plotgraph function only works well with small graphs. It produces awful graphs when using more than four vertex. The toolbox could come with some function to format the data. I used one called cedge.m which worked well. Also, to use this toolbox you will need to install at least arrow.m.
12 Mar 2004 ahmed kolsi
23 Feb 2004 Nick Valuy
12 Feb 2004 Alex Pesch
I think, the Optimization Toolbox is required. The function MaxFlows for example is not running here, because 'linprog' doesn't exist.
Comment only
21 Dec 2003 x s
A bug in grPlot is corrected.
24 Dec 2003
Draws the graph and solves the tasks: Maximal Flow, Maximal Matching, Minimal Vertex Cover, Minimal Spanning Tree, Shortest Path etc.
20 Jan 2004
Draws the graph and solves the tasks: Maximal Flow, Maximal Matching, Minimal Vertex Cover, Minimal Spanning Tree, Shortest Path etc.
09 Feb 2004
ShortPath had update for fast calculation
26 Aug 2004
14 Sep 2004
PlotGraph is updated
11 Oct 2004
CycleBasis is updated
28 Mar 2006
All functions are updated, new functions are added.
30 Mar 2006
Summary title is updated
26 Apr 2006
The function grMinAbsEdgeSet are included.
09 May 2006
two new functions are created.
16 May 2006
29 Jun 2006
Two new functions is added. One function with bugs is deleted.
05 Jul 2006
08 Aug 2006
The function grDecOrd has update.
11 Jul 2009 1.1
| 2,788
| 10,215
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.5625
| 3
|
CC-MAIN-2016-30
|
latest
|
en
| 0.758231
|
http://www.theblaze.com/stories/2012/08/08/watch-the-mind-boggling-ted-talk-thats-so-confusing-and-fascinating-we-had-to-watch-it-twice
| 1,511,508,486,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934807146.16/warc/CC-MAIN-20171124070019-20171124090019-00649.warc.gz
| 505,275,747
| 25,217
|
# Watch the Mind-Boggling TED Talk That’s so Confusing and Fascinating We Had to Watch It Twice
How big is infinity? Seems like a rhetorical question, right? Everyone knows infinity is infinite, but leave it to the folks at TED to tackle discussing the ins and outs of what this means.
Dennis Wildfogel, according to the presentation description, “[uses] the fundamentals of set theory [to] explore the mind-bending concept of the ‘infinity of infinities’ — and how it led mathematicians to conclude that math itself contains unanswerable questions.”
Wildfogel first discusses how matching a fundamental method of thinking about a quantity without really counting. He offers the example of a packed auditorium to illustrate this point — the number of people sitting matches the number of chairs set out.
“What we mean when we say two sets are the same size is that the elements of them can be matched up one by one in some way,” he said, getting to the point that there are as many even numbers as there are whole numbers.
Continuing, Wildfogel points out “what still bothers us is our distress over the fact that the even numbers only seem to be part of the whole numbers.” He then starts talking about making a list of all the fractions, shows how the fractions match up with the whole numbers, brings up rational and irrational numbers . . . and then we start getting lost in our after lunch food coma.
As Gizmodo puts it, this discussion will either “make you smarter” or “infinitely frustration.” Check it out to see which camp you fall into:
| 332
| 1,554
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 2.53125
| 3
|
CC-MAIN-2017-47
|
longest
|
en
| 0.930534
|
https://www.slideserve.com/lyn/announcements-3307051
| 1,511,510,249,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-47/segments/1510934807146.16/warc/CC-MAIN-20171124070019-20171124090019-00639.warc.gz
| 876,601,189
| 13,179
|
Announcements
1 / 16
# Announcements - PowerPoint PPT Presentation
Announcements. Scores from the fourth exam are available on WebCT. Final exam is Monday, May 9, at 7:30 am. Students with last names A-K go to 225 CB. Students with last names L-Z go to 300 CB. All students must bring their ID. Iowa Book and Supply will buy back textbooks and PRS units.
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
## PowerPoint Slideshow about 'Announcements' - lyn
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Announcements
• Scores from the fourth exam are available on WebCT.
• Final exam is Monday, May 9, at 7:30 am.
• Students with last names A-K go to 225 CB.
• Students with last names L-Z go to 300 CB.
• All students must bring their ID.
• Iowa Book and Supply will buy back textbooks and PRS units
Expansion of the Universe and Curved Spacetime
• Expansion of the Universe
• Geometry
• Non-Euclidean geometry
• Geometry of the Universe
Motion at constant velocity
distance = velocity time velocity = 0.5 cm/s
time = distance / velocity = 3 cm/(0.5 cm/s) = 6 s
Receding galaxy
Velocity =
= 500 km/s
= 0.508 Mpc/Gyr
When were galaxies in the same place?
time = distance / velocity = 7 Mpc/(0.508 Mpc/Gyr)
= 13.8 Gyr ago
Hubble expansion v = H0d
Time = distance/velocity
= d/H0d
= 1/H0
= 1/(71 km/s/Mpc)
= 13.8 Gyr
An observer at a distance of 3 billion light years from us looking in our general direction would see
• most of the galaxies approaching her.
• the same Hubble’s law that we see.
• about equal numbers of red and blue shifted galaxies.
• everything rushing away from a point near the Milky Way galaxy.
Two dimensional geometry
• Only two directions: up/down and left/right
: north/south and east/west
• All motion of particles, light confined to two dimensions
• Examples: black board, piece of paper, surface of sphere, surface of donut, surface of saddle
Geometry
• How are the diameter and circumference of a circle related?
• What is the sum of all of the angles in a triangle?
Geometry in flat space
• Circumference = 2 radius
= 3.1415926… 2 = 6.28…
• The sum of the angles in a triangle is 180º
Non-Euclidean Geometry
• How about in a curved space?
• Do demo 8C10.50
Geometry in positively curved space
• Circumference < 2 radius
• The sum of the angles in a triangle > 180º
Properties of positively curved space
• Finite
• Unbounded
• No center
How do the properties of positively curved space differ from flat space?
Geometry in negatively curved space
• Circumference > 2 radius
• The sum of the angles in a triangle < 180º
Review questions
• Suppose it was discovered that the Hubble constant is twice the value that it is currently thought to be, how would this change our estimate of the age of the Universe?
• Compare a flat universe with a positively curved universe as to whether they are finite, bounded, and have a center.
| 897
| 3,382
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.15625
| 3
|
CC-MAIN-2017-47
|
latest
|
en
| 0.893268
|
https://www.coursehero.com/file/6781647/note7/
| 1,521,508,117,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-13/segments/1521257647244.44/warc/CC-MAIN-20180319234034-20180320014034-00333.warc.gz
| 798,398,006
| 85,743
|
{[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
# note7 - Math021 week 7 Definition 7.1 When there is is a...
This preview shows pages 1–3. Sign up to view the full content.
Math021, week 7 Definition 7.1 When there is is a quantity changing over time and f ( t ) is that quantity at time t . f 0 ( t ) is called the rate of change of the given quantity at time t . Example 7.2 In a chemical reaction chamber, the concentration of a certain reactant A after t seconds is [ A ]( t ) = 1 k ( t + c ) M. Here k and c are two fixed positive numbers. Show that the rate of change of the concentration of A is proportional to the square of the concentration of A . solution: The rate of change of the concentration of A (rate of reaction) is d dt [ A ] = d dt 1 k ( t + c ) = - 1 k ( t + c ) 2 = - k [ A ] 2 . Thus, the assertion is proved. Example 7.3 Water is pumped into a inverted conical vessel with semi-vertical angle π/ 6 at a rate of R m 3 s - 1 . Evaluate the rate at which water level in the vessel is raising at the moment when the water level is at H meters. solution: Let V ( t ) be the volume of water in the vessel after t seconds. h ( t ) is the water level in the vessel after t seconds. Then, V ( t ) = 1 3 h ( t ) π ( h ( t ) tan π 6 ) 2 = π 9 h ( t ) 3 for all t. Taking derivatives on both sides of the equation yields V 0 ( t ) = π 3 h ( t ) 2 h 0 ( t ) . Suppose that after t 0 seconds, the water level in the vessel is H meters. That is, h ( t 0 ) = H . It is given that V 0 ( t ) = R for all t . In particular, V 0 ( t 0 ) = R . We evaluate the previous equation at t 0 and it yields R = π 3 H 2 h 0 ( t 0 ) 1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
or h 0 ( t 0 ) = 3 R πH 2 . The water level is raising at a rate of 3 R πH 2 ms - 1 at the moment when the water level is H meters. Example 7.4 One is keeping an eye on a car which is moving in a straight line. At the moment when the car is cloest to the guy, the car is D meters away from the guys and it is moving at a speed of V meters per second. Evaluate the rate at which the guy turns his head at that moment.
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### Page1 / 6
note7 - Math021 week 7 Definition 7.1 When there is is a...
This preview shows document pages 1 - 3. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online
| 716
| 2,475
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.03125
| 4
|
CC-MAIN-2018-13
|
latest
|
en
| 0.921113
|
https://www.scribd.com/presentation/225956139/MET-302-Mechanics-of-Materials-Chapter-2
| 1,534,619,195,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-34/segments/1534221213693.23/warc/CC-MAIN-20180818173743-20180818193743-00184.warc.gz
| 984,699,910
| 23,719
|
# Chapter Objectives
Understand the concept of normal and shear strain
Apply the concept to determine the strains for
various types of problems
1. Normal Strain
2. Shear Strain
3. Cartesian Strain Components
In-class Activities
NORMAL STRAIN
s
s s
avg
A
A ÷ A
=
'
c
( ) s s A + ~ A c 1 '
s
s s
n A B
A
A ÷ A
=
÷
'
lim
along
c
SHEAR STRAIN
' lim
2
along
along
u
t
¸
t A C
n A B
nt
÷
÷
÷ =
CARTESIAN STRAIN
• The approximate lengths of the sides
of the parallelepiped are
• The approximate angles between sides, again
originally defined by the sides Δ x, Δ y and Δ z are
• Notice that the normal strains cause a change in
volume of rectangular element, whereas the shear
strain cause a change in shape
( ) ( ) ( ) z y x
z y x
A + A + A + c c c 1 1 1
xz yz xy
¸
t
¸
t
¸
t
÷ ÷ ÷
2
2
2
1) The center portion of the rubber balloon has a
diameter of d = 100 mm. If the air pressure
within it causes the balloon’s diameter to
become d = 125mm, determine the average
normal strain in the rubber.
a) 0.2
b) 0.25 π
c) 0.25
d) 1.25
2) What is the unit of strain?
a) mm
b) mm/m
c) Micron
d) no unit
EXAMPLE 1
( ) | |dz z dz
2 / 1 3
10 40 1 '
÷
+ =
EXAMPLE 1 SOLUTION
Part (a)
• Since the normal strain is reported at each point along
the rod, it has a deformed length of
• The sum along the axis yields the deformed length of
the rod is
• The displacement of the end of the rod is therefore
( ) | |dz z dz
2 / 1 3
10 40 1 '
÷
+ =
( ) | | m 20239 . 0 10 40 1 '
2 . 0
0
2 / 1 3
= + =
}
÷
dz z z
(Ans) mm 39 . 2 m 00239 . 0 2 . 0 20239 . 0 + = = ÷ = A
B
EXAMPLE 1 Solutions (cont)
Part (b)
• Assumes the rod has an original length of 200
mm and a change in length of 2.39 mm. Hence,
(Ans) mm/mm 0119 . 0
200
39 . 2 '
= =
A
A ÷ A
=
s
s s
avg
c
EXAMPLE 2
dashed shape shown in Fig. 2–6a. Determine (a)
the average normal strain along the side AB, and
(b) the average shear strain in the plate at A
relative to the and y axes.
EXAMPLE 2 Solutions (cont)
Part (a)
• Line AB, coincident with the y axis, becomes line after
deformation, thus the length of this line is
• The average normal strain for AB is therefore
causes a contraction of AB.
( ) mm 018 . 248 3 2 250 '
2
2
= + ÷ = AB
( ) ( )
(Ans) mm/mm 10 -7.93 =
250
250 - 248.018
AB
AB ' AB 3 -
avg
AB
= =
-
ε
EXAMPLE 2 Solutions (cont)
CONCEPT QUIZ
1) The rectangular membrane has an unstretched
length L1 and width L2. If the sides are
increased by small amounts ΔL1 and ΔL2,
determine the normal strain along the diagonal
AB.
( )
( )
2
2
2
1
2
2
2
1
2 1
2 1
2
2
2
1
2
2
2
1
2
2
1
1
D) C)
B) A)
L L
L L
L L
L L
L L
L L
L
L
L
L
+
A + A
+
A + A
+
A + A A
+
A
L1
Δ L2
ΔL1
L2
CONCEPT QUIZ (cont)
2) The rectangular plate is subjected to the
deformation shown by the dashed line.
Determine the average shear strain γ
xy
of the
plate.
( )
2 2
200 150
3
200
150
200
3
150
3
+
D) C)
B) A)
Thank You
| 1,096
| 2,843
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.375
| 4
|
CC-MAIN-2018-34
|
latest
|
en
| 0.817932
|
https://www.doubtnut.com/question-answer/if-theta-is-the-angle-between-the-vectors-a2hati-2hatj-hatk-and-b6hati-3hatj-2hatk-then-644016468
| 1,643,109,810,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-05/segments/1642320304810.95/warc/CC-MAIN-20220125100035-20220125130035-00713.warc.gz
| 780,477,947
| 84,109
|
HomeEnglishClass 12MathsChapterProduct Of Vectors
If theta is the angle between ...
# If theta is the angle between the vectors a=2hati+2hatj-hatk and b=6hati-3hatj+2hatk, then
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 1-5-2021
Apne doubts clear karein ab Whatsapp par bhi. Try it now.
Get Answer to any question, just click a photo and upload the photo
and get the answer completely free,
Watch 1000+ concepts & tricky questions explained!
Text Solution
costheta=(4)/(21)costheta=(3)/(19)costheta=(2)/(19)costheta=(5)/(21)
A
Transcript
TimeTranscript
00:00 - 00:59good morning friends are next question is based on vector algebra is theta is the angle between the vector is equal to two ICAP + 2 J - K and b is equal to 6.2 find the value of cos theta so as we know that SB no cos theta is equal to a.bd Mod a w b i don't be which is 2i + 2 J minus k x b b is 6 - 3 J + 2 k
01:00 - 01:59/ 2 square square + -1 square into Tech square plus minus 3 square + to care now this is cos theta now cos theta is equal to 23-6 2006 minus x + 26 12 - 2 / route 9 into route
02:00 - 02:5949 will be equal to 12 - 8 is 4/3 into 7 is equal to 4 by 21 to the right answer of this question is 4521 and option A is correct
| 397
| 1,288
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.625
| 4
|
CC-MAIN-2022-05
|
longest
|
en
| 0.880747
|
http://elf.43.junowebmaillogin.com/finding-lines-of-symmetry-worksheet/
| 1,606,454,156,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-50/segments/1606141189141.23/warc/CC-MAIN-20201127044624-20201127074624-00049.warc.gz
| 30,327,718
| 17,925
|
# Finding Lines Of Symmetry Worksheet
## Finding Lines Of Symmetry Worksheet Teacher Made
Finding Lines Of Symmetry Worksheet This Worksheet Asks Children To Identify The 2d Shapes Shown Including Their Sides And Lines Of Symmetry
### Find The Lines Of Symmetry Worksheet
Id Language English School Subject Math Grade Level Grade 5 6 Age 9 12 Main Content Symmetry Other Contents Shapes Symmetry Lines Add To My Workbooks 28 Download File Embed In My Website Or Blog Add To Classroom
#### Symmetry Worksheets Math Worksheets 4 Kids
Symmetry Worksheets Consist Of A Variety Of Skills For Children In Grade 1 Through Grade 5 To Understand The Lines Of Symmetry In Different Shapes Printable Exercises To Identify And Draw The Lines Of Symmetry Complete The Shapes Count The Lines Of Symmetry In Each Shape To Identify Symmetrical Or Asymmetrical Shapes And To Determine The Perimeter Of Shapes Are Given Here For Practice Begin Your Practice With Our Free Symmetry Worksheets
##### Symmetry Worksheets Geometry Math Fun Worksheets
These Printable Worksheets Have Practice Pages To Identify The Line Of Symmetry Symmetrical And Asymmetrical Objects Counting The Number Of Lines Of Symmetry Drawing The Other Half Or The Mirror Image Of The Symmetrical Object Cut Paste Activity And Much More Download All And Practice To The Fullest
###### Finding The Line Of Symmetry Futurelearn
Activity One A 1 Find The Line Of Symmetry For Values Of B 4 To 4 Activity Two A 2 Find The Line Of Symmetry For Values Of B 8 To 8 Activity Three A 1 Find The Line Of Symmetry For Values Of B 4 To 4 Activity Four A 2 Find The Line Of Symmetry For Values Of B 8 To 8 Generalise Your Findings
Finding Lines Of Symmetry Lesson Plans Worksheets
In This Finding Lines Of Symmetry Worksheet 2nd Graders Look At Six Drawings And Mark Yes Or No To Answer The Question Is This A Line Of Symmetry Get Free Access See Review Lesson Planet Module 1 Transformations And Symmetry For Teachers 9th 12th Standards No Need To Change Anything About The Resource The First Of Eight Modules In The Mvp Geometry Unit Focuses On Transformations In
Lines Of Symmetry Worksheets Teaching Resources
Two Worksheets One Requires Pupils To Cut Out The Shapes And Fold Along The Lines To See If The Shape Has A Line Of Symmetry Second Requires The Pupils To Reflect The Shape So That It Has A Line Of Symmetry Free
Finding Lines Of Symmetry Worksheet. The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use.
You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now!
Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Finding Lines Of Symmetry Worksheet.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
Finding Lines Of Symmetry Worksheet. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice.
| 1,423
| 6,943
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.078125
| 3
|
CC-MAIN-2020-50
|
latest
|
en
| 0.545709
|
https://metric2011.wordpress.com/2011/01/31/notes-of-jean-lasserres-lecture-nr-1/
| 1,521,822,712,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-13/segments/1521257648404.94/warc/CC-MAIN-20180323161421-20180323181421-00749.warc.gz
| 629,298,139
| 21,382
|
## Notes of Jean Lasserre’s lecture nr 1
Moments, positive polynomials and optimization
Hierarchies will come only at the very end, as a tool that helps solving basic problems with many applications. The main theorems will have two facets: real algebraic geometry (positive polynomials), and functional analysis (moments). Implementability is an important feature, to keep in mind.
Let me advertise my recent book [L].
1. Semi-definite programming
${A_i}$, ${b}$ given real symmetric matrices. Unknown is a real vector ${x=(x_1 ,\ldots,x_n)}$. Problem: minimize a linear functional ${c\cdot x}$ subject to the constraint that ${\sum_{i=1}^n x_i A_i -b}$ is positive semidefinite.
The dual problem is to maximize Trace${(bY)}$ over matrices ${Y}$ subject to the constraints that ${Y}$ is positive semidefinite and Trace${(YA_i)\geq 0}$ for all ${i}$.
Softwares SeduMi, SDPT3 can handle thousands of variables. These are hand-made, since industry does not seem to need SDP software now. Pioneers: Nemirovsky, Nesterov, Shor, Yudin.
Guy Kindler: what about special sets of data ? Answer: Symmetries and sparsity allow larger sizes.
From now on, take SDP as a black box.
2. Global optimization
Want to minimize a function on a subset ${K}$ of ${{\mathbb R}^n}$,
• real semialgebraic set.
• discrete cube.
Usually, people are happy with local minima.
2.1. Primal point of view
Proposition 1 Let ${\mathcal{P}(K)}$ denote the set of probability measures on ${{\mathbb R}^n}$ supported on ${K}$.
$\displaystyle \begin{array}{rcl} f^* :=\min f =\inf_{\mu\in\mathcal{P}(K)}\int_{{\mathbb R}^n}f\,d\mu. \end{array}$
This is an LP in infinite dimensions.
2.2. Dual point of view
The dual problem of the above LP is simply
Proposition 2 Let ${\mathcal{P}(K)}$ denote the set of probability measures on ${{\mathbb R}^n}$ supported on ${K}$.
$\displaystyle \begin{array}{rcl} f^* :=\max\{\lambda\,;\, f(x)-\lambda\geq 0\,\forall x\in K\}. \end{array}$
We need practical criteria to express constraints, either the fact that a measure is supported by ${K}$, or that a function is nonnegative on ${K}$. These do not exist in full generality, but exist when ${K}$ is a compact basic semialgebraic set, and ${f}$ a polynomial (or more generally semialgebraic).
2.3. Basic semialgebraic sets
Definition 3 A subset ${K\subset{\mathbb R}^n}$ is basic semialgebraic if it can be defined by real algebraic equations and closed real algebraic inequations.
A powerful theorem from real algebraic geometry will provide us with a sequence of approximations to a semialgebraic global optimization problem, which are computationnally feasible.
The central tool is a set of necessary and sufficient condition for
• a finite Borel measure to be supported on ${K}$,
• a polynomial to be positive on ${K}$.
In both cases, these conditions translate into Linear Matrix Inequalities, or Linear Inequalities satisfied by the Moments
$\displaystyle \begin{array}{rcl} y_{\alpha}:=\int_{{\mathbb R}^n}X^{\alpha}\,d\mu. \end{array}$
of ${\mu}$ (and not ${\mu}$ itself), and on the coefficients of certain polynomials.
No convexity nor discreteness assumptions.
This sounds suspicious: the same tools used to solve convex continuous problems and boolean problems ? These are known to behave very differently. This must be kept in mind too.
3. The generalized problem of moments
Data: a subset ${K\subset{\mathbb R}^n}$, functions ${f_j}$. Unknown: a finite measure on ${K}$. Goal: minimize ${\int f_0 \,d\mu}$ subject to constraints ${\int f_j \,d\mu \geq b_j}$.
This problem was popular in the early XXth century, and solved in the ${1}$-dimensional case. It encompasses many problems in applied mathematics, see [M]. I give examples.
3.1. Convex envelope
Data: a set ${K\subset{\mathbb R}^n}$, a function ${f:K\rightarrow{\mathbb R}}$ (${f=+\infty}$ ouside ${K}$). Output: the largest convex function ${\hat{f}}$ on ${{\mathbb R}^n}$ such that ${\hat{f}\leq f}$.
3.2. Probability
Data: a set ${K\subset{\mathbb R}^n}$, a Borel subset ${S\subset K}$. Output: an estimate on ${\mathop{\mathbb P}(X\in S)}$, assuming certain moments of the random variable ${X}$ take prescribed values.
3.3. Volume of a basic semialgebraic set
There is a polytime approximation scheme (Kannan, Lovácz, Simonovitz, [KLS].
Here is an alternative method. Sample points uniformly in a box ${K}$. The corresponding moments ${\gamma_{\alpha}}$ are known. Write Lebesgue measure as ${\phi+\nu}$ where ${\phi}$ is supported on ${S}$ and ${\nu}$ on ${K\setminus S}$. Then
$\displaystyle \begin{array}{rcl} Volume(S)=\sup\{\int_{S}d\phi \,;\,\phi\textrm{ supported on }S,\,\int X^{\alpha}\,d\phi +\int X^{\alpha}\,d\nu=\gamma_{\alpha}\,\forall\alpha\in{\mathbb N}^{n}\}. \end{array}$
3.4. Measures given by marginals
Generalization of the Monge-Kantorovitch mass transportation problem. Express equality of marginals along certain coordinates by equality of all moments not involving these coordinates.
3.5. Pricing European call options
Want to set price for the following service: buy a given quantity at a fixed future date. There are two unknown measures, the occupation measure (how much time the asset visits an interval) and the exit measure (value of the asset at given horizon). The solution involves a moment problem.
The Black-Scholes model is a special case. See Lasserre, Prieto, Zervos 2006, [LPZ].
3.6. Optimal control
3.7. Multivariate integration of exponentials
Data: a function ${h}$ on ${[0,1]}$. Goal: compute ${\int_{0}^{1}\exp(h(x))\,dx}$.
Use infinitely many integrations by parts. This gives a collection of linear relations between moments of the measure ${\mu=\exp(h(x))\,dx}$. Minmaxing over unknown measure ${\mu}$ subject to these relations is a moment problem. This provides both upper and lower bounds on the integral, which converge as the number of contraints taken into account tends to infinity.
4. Positive polynomials
Hilbert’s 17th problem has a simple solution in one variable: a polynomial is ${\geq 0}$ on ${{\mathbb R}}$ iff it is a sum of squares of polynomials. However,
Theorem 4 (Artin) In several variables, a polynomial is ${\geq 0}$ on ${{\mathbb R}}$ iff it is a sum of squares of rational functions.
The differenced between nonnegative polynomials and sums of squares of polynomials, in several variables, can be quantitatively measured (Blekherman). With a fixed degree, the relative volume tends to zero as the number of variables tends to infinity.
4.1. Sums of squares
Checking wether a polynomial is a sum of square amounts to solve a set of linear matrix inequalities. Indeed, let ${v_d (X)}$ be the vector with entries all degree ${\leq d}$ monomials. Expand
$\displaystyle \begin{array}{rcl} v_d (X)v_d (X)^{\top}=\sum_{|\alpha|\leq 2d}B_{\alpha} X^{\alpha}. \end{array}$
Solve the system of linear matrix inequalities
$\displaystyle \begin{array}{rcl} \mathrm{Trace}(B_{\alpha}Q)=f_{\alpha}\,\quad Q\gg 0. \end{array}$
Then reconstruct ${P}$
Theorem 5 (Berg) Use ${\ell_1}$ norm of coefficients. Sums of squares are dense in polynomials nonnegative on ${[-1,1]^n}$.
Theorem 6 (Lasserre, Netzer) Let ${\Theta_r (X)=\sum_{i=1}^{n}X_{i}^{2r}}$. Let ${f}$ be nonnegative on ${[-1,1]^n}$. Then there exists ${r(\epsilon)}$ such that ${f+\epsilon \Theta_r}$ is a sum of squares.
Theorem 7 (Lasserre) Let ${\theta_r (X)=\sum_{k=0}^{r}\sum_{i=1}^{n}X_{i}^{2r}}$. Let ${f}$ be nonnegative on ${{\mathbb R}^n}$. Then there exists ${r(\epsilon)}$ such that ${f+\epsilon \theta_r}$ is a sum of squares.
Theorem 8 (Polyá) Let ${f}$ be nonnegative on ${(0,+\infty)^n}$. Then there exists ${r}$ such that ${f(x_1 +\cdots+x_n)^{2r}}$ has nonnegative coefficients.
This gives a certificate of nonnegativity of a polynomial on the orthant.
4.2. Theory
Theorem 9 (Krivine 1964, Stengle 1974) Let ${K}$ be a semi-algebraic set, defined by ${g_i \geq 0}$, ${h_j \not=0}$, ${f_k =0}$. Let ${P(g_1 ,\cdots, g_m)}$ be the set of polynomials in the ${g_i}$‘s with coefficients sums of squares. Let ${M(f_1 ,\cdots, f_m)}$ be monoid generated by the ${f_k}$‘s and ${I(h_1 ,\ldots,h_m)}$ the ideal generated by the ${h_j}$‘s.
Then ${K=\emptyset}$ iff there exists ${g\in P(g_1 ,\cdots, g_m)}$, ${f\in M(f_1 ,\cdots, f_m)}$ and ${h\in I(h_1 ,\cdots, h_m)}$ such that
$\displaystyle \begin{array}{rcl} g+f^2 +h=0. \end{array}$
Furthermore, there are theoretical bounds.
Note the problem is becomes an SDP. This can be used to provide a certificate that ${K}$ is empty.
4.3. The case of basic semialgebraic sets
Theorem 10 (Schmüdgen 1991) Let ${K}$ be a basic semi-algebraic set, defined by ${g_i \geq 0}$. Then a polynomial ${f}$ is positive on ${K}$ iff ${f\in P(g_1 ,\cdots, g_m)}$.
Definition 11 Let ${Q(g_1 ,\cdots, g_m)}$ be the set of linear combinations of ${g_i}$‘s with coefficient sums of squares.
Theorem 12 (Putinar, Jacobi, Prestel 1993) Let ${K}$ be a basic semi-algebraic set. Assume that there exists a constant ${M}$ such that ${M-|X|^2 \in Q(g_1 ,\cdots, g_m)}$. Then a polynomial ${f}$ is positive on ${K}$ iff ${f\in Q(g_1 ,\cdots, g_m)}$.
If one fixes an upper bound on the degree of the sum of squares, finding them is solving an SDP.
In practice, if one knows the radius of a ball that contains ${K}$ (this may happen), just add ${g_{m+1}=M-|X|^2}$ to the defining inequalities. Then the extra assumption in Theorem 12 is satisfied.
References
[KLS] Kannan, Ravi; Lovász, László; Simonovits, Miklós; Random walks and an O*(n5) volume algorithm for convex bodies. Random Structures Algorithms 11 (1997), no. 1, 1–50.
[L] Lasserre, Jean-Bernard; Moments, positive polynomials and their applications. Imperial College Press Optimization Series, 1. Imperial College Press, London, 2010.
[LPZ] Lasserre, J. B.; Prieto-Rumeau, T.; Zervos, M; Pricing a class of exotic options via moments and SDP relaxations. Math. Finance 16 (2006), no. 3, 469–494.
[M] Landau, Henry; Moments in mathematics. Papers from the American Mathematical Society annual meeting held in San Antonio, Tex., January 20?22, 1987. Edited by Henry J. Landau. Proceedings of Symposia in Applied Mathematics, 37. AMS Short Course Lecture Notes. American Mathematical Society, Providence, RI, 1987.
| 3,049
| 10,231
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 116, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-13
|
latest
|
en
| 0.820828
|
http://www.jiskha.com/members/profile/posts.cgi?name=William&page=8
| 1,386,767,413,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2013-48/segments/1386164036653/warc/CC-MAIN-20131204133356-00054-ip-10-33-133-15.ec2.internal.warc.gz
| 388,732,256
| 3,120
|
Wednesday
December 11, 2013
# Posts by William
Total # Posts: 227
Math
Find the length of VR, the direct distance across the river, to the nearest tenth.
religion
The Middle East is the spiritual homeland for all of the following world religions EXCEPT
7th gr. Algebra
what is the meaning of a relative frequency of 1?
Physics
A car moves with a speed v on a horizontal circular highway turn of radius is R = 100. Assume the height of the car’s center of mass above the ground is h = 1 m, and the separation between its inner and outer wheels (car's width) is w = 2 m. The car does not skid (sta...
algebra
Which of the following are liner? Explain a) y + -2/3x b) y=1/x c) y=x(to the second power)+8x+15
geometry
a block prism has a volume of 36 cubic units, what is the least and greatest surface area it could have
Math - Calculus
Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2].
Math - Calculus
Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? ...Other than simply using my TI-84, I have no idea how to accomplish this.
Math - Calculus
Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? ...Other than simply using my TI-84, I have no idea how to accomplish this.
Physics Craziness
A big olive (m = 0.40 kg) lies at the origin of an xy coordinate system, and a big Brazil nut (M = 1.2 kg) lies at the point (1.0,2.0) m. At t = 0, a force o = (2.0 + 3.0) N begins to act on the olive, and a force n = (-3.0 - 2.0) N begins to act on the nut. In unit-vector not...
Pages: <<Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | Next>>
Search
Members
| 558
| 1,848
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.328125
| 3
|
CC-MAIN-2013-48
|
latest
|
en
| 0.897213
|
https://math.stackexchange.com/questions/2048955/what-is-the-formula-for-the-decimal-representation-of-fracab-where-b-is
| 1,618,657,780,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618038119532.50/warc/CC-MAIN-20210417102129-20210417132129-00297.warc.gz
| 505,662,075
| 37,926
|
# What is the formula for the decimal representation of $\frac{a}{b}$ where $b$ is not coprime to 10?
If we want to turn a proper fraction $$\frac{a}{b}$$ into a decimal, then when $$b$$ is coprime to 10 we just need to rewrite $$\frac{a}{b}$$ in the form $$\frac{m}{10^{\phi(b)}-1}$$ where $$\phi$$ is Euler's totient function. And then the repeatend is $$m$$ and the period of repetition is $$\phi(b)$$. (This follows from Fermat's Little Theorem.)
But my question is, what do we do when $$b$$ is not coprime to 10? In that case we would need to rewrite $$\frac{a}{b}$$ in the form $$\frac{k + \frac{l}{m}}{10^n}$$ where $$k < 10^n$$, $$\frac{l}{m}$$ is a proper fraction, and $$m$$ is coprime to 10. Then $$k$$ would be the non-repeating part, $$n$$ would be the length of the nonrepeating part, and we can convert $$l/m$$ into a decimal using the procedure given in the beginning of my post.
But is there a formula for the four numbers $$k$$, $$l$$, $$m$$, and $$n$$ in terms of $$a$$ and $$b$$, short of doing long division to convert the fraction into a decimal?
• if $b$ is not co-prime to $10$, then you an break $\frac ab$ into a repeating and a finite decimal. – Doug M Dec 8 '16 at 2:02
• @DougM Yes I know, that's why I said I want to rewrite $\frac{a}{b}$ as $\frac{k + \frac{l}{m}}{10^n}$ where $m$ is coprime to 10. $\frac{k}{10^n}$ is the finite decimal and $\frac{l}{m}$ yields the repeating decimal (although shifted $n$ digits to the right). Now it's just a matter of finding formulas for $k$, $l$, $m$, and $n$. – Keshav Srinivasan Dec 8 '16 at 2:24
This turned out to be easier than I thought. Let $n$ be equal to the maximum of the number of factors of 2 in $b$ and the number of factors of 5 in $b$. Now write $\frac{a}{b}$ as $$\frac{10^n\frac{a}{b}}{10^n}$$ Then the new fraction you have in the numerator will now have have a denominator that's coprime to 10, since the $10^n$ gets rid of all the factors of 2's and 5's that were present in the denominator. And we can now use the procedure given in the beginning of my question (after changing the fraction in the numerator into a mixed number to separate out the non-repeating and repeating parts).
| 660
| 2,181
|
{"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": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.25
| 4
|
CC-MAIN-2021-17
|
latest
|
en
| 0.884138
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.