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.gurufocus.com/news/197280/using-the-graham-number-correctly | 1,604,090,166,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107911229.96/warc/CC-MAIN-20201030182757-20201030212757-00521.warc.gz | 725,261,160 | 31,187 | SerenityStocks
# Using the Graham Number Correctly
One of the most commonly used stock selection formulas these days is the Graham Number, which Graham actually did recommend (unlike the completely misunderstood Benjamin Graham Formula).
But again, there is a very large difference between how this calculation was recommended and how it is being used today.
The Derivation:
The number itself is simple enough, and can be derived from criteria [6] and [7] from Graham's calculations for defensive stocks.
Summarized from Chapter 14 of "The Intelligent Investor" - Stock Selection for the Defensive Investor:
1. Not less than \$100 million of annual sales.
[Serenity note: This comes to \$500 million today based on the difference in CPI/Inflation from 1973]
2. (A) Current assets should be at least twice current liabilities.
(B) Long-term debt should not exceed the net current assets.
3. Some earnings for the common stock in each of the past ten years.
4. Uninterrupted payments for at least the past 20 years.
5. A minimum increase of at least one-third in per-share earnings in the past ten years.
6. Current price should not be more than 15 times average earnings.
7. Current price should not be more than 1-1â„2 times the book value.
As a rule of thumb we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5.
The optimum price for a defensive stock can easily be derived from this as the square root of (22.5 x EPS x BVPS), and this is the Graham number.
The problem however is that almost everywhere today, this number is used alone, while the other five supporting criteria for defensive stock selection are completely ignored.
The Complete Procedure
The complete stock selection procedure recommended by Graham is far more elaborate.
Step 1. First a stock is checked against all seven criteria for defensive investment above.
Step 2. If the stock fails to meet any one of the above criteria, it is then checked against the five criteria for enterprising investment (below).
Summarized from Chapter 15 of "The Intelligent Investor" - Stock Selection for the Enterprising Investor:
[Serenity note: For issues selling at PE multipliers under 10]
1A. Current assets at least 11â„2 times current liabilities.
1B. Debt not more than 110% of net current assets.
2. Earnings stability: No deficit in the last five years covered in the Stock Guide.
3. Dividend record: Some current dividend.
4. Earnings growth: Last year's earnings more than those of 1966.
[Serenity note: This corresponds approximately to the earnings of 2007 today]
5. Price: Less than 120% net tangible assets.
This second set of criteria gives us an optimum price for a stock meeting the above conditions (an "enterprising" stock) as the lower of 120% net tangible assets (book value), or 10 times current earnings.
This is a number quite different from the Graham Number but equally, if not more valuable today.
Step 3. If a stock meets neither of the above groups of checks, it is finally checked against the last two criteria for investment as an NCAV or "bargain" stock (below).
Summarized from Chapter 15 of "The Intelligent Investor" - Stock Selection for the Enterprising Investor:
"Bargain Issues, or Net-Current-Asset Stocks"
"Price less than the applicable net current assets alone-after deducting all prior claims, and counting as zero the fixed and other assets."
"Eliminated those which had reported net losses in the last 12-month period."
This last set of criteria, for a stock that meets neither of the first two sets of criteria, gives us an NCAV stock. This is a stock selling for less than the value of its cash worth alone, and with positive earnings (no losses) in the last one year.
For a complete understanding of stocks and investing, a reading of "The Intelligent Investor" by Benjamin Graham is highly recommended. This is the book that Warren Buffett himself describes (in the preface) as "by far the best book about investing ever written."
To Conclude:
If one were to apply all the Graham defensive criteria strictly, using 500 million in sales to count for inflation since 1973, there are plenty of stocks that meet most of them.
For example, these stocks meet all the defensive quality criteria but are simply too expensive:
Stock Symbol Sales Earnings growth Graham Number Current price Intel Corp INTC 125.23% 102.28% \$22.41 \$22.66 Cato Corp A CATO 102.22% 100.22% \$25.87 \$29.71 Fuller, H.B. Co FUL 104.89% 100.48% \$24.24 \$30.68 Valmont Industries Inc VMI 107.73% 100.75% \$94.51 \$131.50 SEI Investments Corp SEIC 102.21% 100.22% \$12.25 \$21.44 Lancaster Colony Corp LANC 103.03% 100.30% \$41.83 \$73.25 Sigma-Aldrich Corp SIAL 107.42% 100.72% \$40.05 \$71.97 Henry, Jack & Associates JKHY 102.41% 100.24% \$20.07 \$37.85 T Rowe Price Group Inc TROW 107.91% 100.76% \$30.59 \$63.30 Fastenal Co FAST 107.95% 100.77% \$11.90 \$42.99
And these stocks meet all the defensive criteria, including the pricing ones, but have a dividend record of less than 20 years:
Stock Symbol Sales Dividend record Earnings growth Graham Number Current price Bunge Ltd BG 125.76% 55.00% 102.32% \$104.59 \$67.05 Murphy Oil Corp MUR 121.13% 60.00% 101.94% \$63.45 \$53.69 Molson Coors Brewing Co B TAP 109.25% 60.00% 100.89% \$59.32 \$45.05 Alamo Group Inc ALG 100.03% 60.00% 100.00% \$38.21 \$33.78 Autoliv Inc ALV 113.99% 60.00% 101.32% \$75.62 \$61.97 HollyFrontier Corporation HFC 117.63% 65.00% 101.64% \$59.91 \$41.27 Brady Corporation BRC 104.10% 60.00% 100.40% \$30.31 \$29.28 Occidental Petroleum OXY 120.28% 60.00% 101.86% \$93.59 \$86.06 Chevron Corp CVX 135.30% 60.00% 103.07% \$138.69 \$116.56
Graham's various criteria are a fine balance of checks. There's no point if a stock meets just some of the criteria in a group and doesn't meet others.
For example, it's easy for a stock to show a great asset number while having lots of debt.
In any case, an automated analysis of all 4000 NYSE and Nasdaq stocks brings up plenty of stocks meeting all the necessary Graham criteria.
Also, choosing stocks that completely meet the latter of Graham's criteria is a far better approach than investing in stocks that incompletely meet the former criteria.
But just using the Graham Number, which satisfies only two of the seven defensive criteria, is not only excessively simplistic, but also potentially dangerous.
Disclaimer: The lists of stocks were arrived at by automated quantitative analysis and were not verified individually. Check for any recent changes in the data used before making an investment decision, especially for any recent stock splits.
SerenityStocks
Value Investing Software True To Benjamin Graham - SerenityStocks.com
Visit SerenityStocks's Website
Currently 4.00/512345 Rating: 4.0/5 (10 votes) Voters: | 1,716 | 6,832 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-45 | latest | en | 0.948024 |
https://accounting-financial-tax.com/2008/12/how-to-estimate-inventory-ending-balance-basic-accounting/ | 1,624,625,606,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487630175.17/warc/CC-MAIN-20210625115905-20210625145905-00615.warc.gz | 94,830,249 | 15,364 | Connect with us
# How To Estimate Inventory Ending Balance? [Basic Accounting]
Published
on
Although a physical inventory is taken once a year, there are occasions when the value of the inventory must be known during the year. When interim financial statements are requested, an inventory amount must be estimated. If no physical count is taken, the amount of inventory must be estimated. Also, in the event of fire or any other casualty, an amount must be reported as a loss. Two of the most popular methods of estimating inventory are the gross profit method and the retail method. Through this post we are going to discuss basic technique of both methods.
Gross Profit Method
Gross profit method re-arranges the Cost of Goods Sold section of the income statement. As we have known, the cost of goods sold formula is:
Right from the above formula:
• When you subtract ending inventory from the goods available for sale, the cost of goods sold is determined.
• Conversely, if you subtract the estimated cost of goods sold from the goods available for sale, the value of the ending inventory will result.
• The estimated cost of goods sold figure is arrived at by using the past year’s gross profit percentage and subtracting the resulting amount from sales.
Example: During the past five years, a company’s gross profit averaged 30 percent of sales. If the sales for this interim period are \$70,000, the inventory at the beginning of the period is \$30,000, and the net purchases are \$50,000, you would estimate the ending inventory under the gross profit method as follows:
This method of estimating ending inventory is also useful for determining casualty losses such as fires, flood, or theft, when such a calamity destroys a company’s inventory. It is obvious that a dollar amount must be assigned to the inventory lost before any insurance claim can be made.
Retail Inventory Method
The retail inventory method of inventory costing is used by retail businesses, particularly department stores. Department stores usually determine gross profit monthly but only take a physical inventory on an annual basis. The retail inventory method permits a determination of inventory at any time of the year and also produces a comparison of the estimated ending inventory with the physical inventory ending inventory, both at retail prices. This will help to identify any inventory shortages resulting from theft or other causes.
Retail inventory method (similar to the gross profit method), is used to estimate the dollar cost of the ending inventory when a physical count cannot be done, such as in the case of fire. The procedure for determination under this method is as follows:
1. Beginning inventory and purchases must be recorded at both cost and selling prices.
2. Total goods available for sale are then computed on both bases.
3. Sales for the period are deducted from the goods available for sale at selling price.
4. Ending inventory at selling price is the result of step 3.
This amount is then converted to ending inventory at cost by multiplying by the appropriate markup ratio.
The procedure is best illustrated in the example below:
In the above example, the cost percentage is 67%, which means that the inventory and purchases are marked up to yield a gross profit margin of 33%. Certainly not all items in the goods available for sale are marked up by exactly the same percentage, but it is the average. In other words, the retail method will use a percentage that represents an average of markup cost.
The major difference between the gross profit method and the retail method is that the former uses the historical gross profit rates, and the latter uses the percentage markup from the current period. The gross profit method uses past experience as a basis, whereas the retail method uses current experience.
The gross profit method is usually less reliable, because past situations may be different from current ones.
Both Gross Profit and Retail Inventory Method are useful because they allow the accountant to prepare interim financial statements more frequently without taking the time to physically count the inventory. However, the annual physical count is always necessary.
Are you looking for easy accounting tutorial? Established since 2007, Accounting-Financial-Tax.com hosts more than 1300 articles (still growing), and has helped millions accounting student, teacher, junior accountants and small business owners, worldwide. | 856 | 4,476 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-25 | latest | en | 0.919653 |
https://www.redhotpawn.com/forum/posers-and-puzzles/why-the-plane-takes-off-in-laymans-my-terms.55074 | 1,547,632,762,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583657151.48/warc/CC-MAIN-20190116093643-20190116115643-00000.warc.gz | 943,356,597 | 9,855 | # Why the plane takes off in laymans (my) terms
Marsan
Posers and Puzzles 30 Oct '06 11:39
1. 30 Oct '06 11:391 edit
Sorry for the double (triple) thread but this needs to be explained properly and the other threads got off topic talking irrelevant stuff.
The easy part:
The plane will take off.
The hard part:
Thought experiment.
Imagine you are lying on your stomach on a large skateboard. Along-side you is a horizontal rail which you grab and use to pull yourself forward. Your hand pulling on the rail generates the force that pulls you forward. Nothing to do with the ground.
Now imagine you're still on your large skateboard on a big conveyor belt. The rail is not attached to the conveyor-belt and does not move. Can you see that there is no practical speed the conveyor belt could travel that could make you move backward? Your hand holding the rail can easily overcome the friction in the bearings pulling you back, you could easily pull yourself forward as if you were on a normal floor.
Now replace you + skateboard with a plane (I like to visualise a little Cessna) and replace your hand pulling on a railing with a propeller pulling the plane through the air. The propeller pulls air backward generating the force which moves the plane forward. Again, nothing to do with the ground.
You should agree now that no matter what speed the conveyor belt moves the plane will pull itself through the air, accelerate to its required velocity and take off.
The only difference between the take-off on a conveyor-belt runway and a conventional runway is that the little wheels under the plane would spin much faster on the conveyor-belt.
NOTE 1:
The answer is the same for a jet propelled plane except that a jet is pushing the plane forward instead of pulling it like a propeller.
NOTE 2:
To those sidetracked by the propeller pulling air over the wing generating lift - you are kidding yourself.
Disagree?
Lets do another thought experiment (location Fairyland).
Your plane is anchored to an immovable pole by a strong cable stretching from the tail of your plane to the pole. You spin up the propellers to top speed generating sooooo much air movement over your wings that you get enough lift to lift off. Momentarily you are hovering held down only by the cable, you click a button releasing the cable and quickly accelerate forward and fly away.
If this were possible runways would only be for landing on and the last time i flew in a propellered plane i vaguely remember rolling forward faster and faster until the massive amount of air moving over the wings (caused by forward motion) generated the lift to get us off the ground.
I concede that with 2 very large propellers spinning extremely fast, over a specially designed wing on an extremely light plane this scenario MAY be possible but i doubt it. I don't know enough aerodynamics to explain why but i really doubt it. If anyone has evidence to the contrary, please post. I'm skilled at own-word eating.
2. 30 Oct '06 11:45
I don't think this explanation is easier to understand that the scientific one...
3. 30 Oct '06 12:051 edit
It's not the best analogy i guess but it's what jumped into my head when i explained it to my flatmate... He understood it.
Perhaps it doesn't work so well in written form...
Lucky i can't be sued.
4. 30 Oct '06 14:02
Originally posted by Marsan
Sorry for the double (triple) thread but this needs to be explained properly and the other threads got off topic talking irrelevant stuff.
The easy part:
The plane will take off.
The hard part:
Thought experiment.
Imagine you are lying on your stomach on a large skateboard. Along-side you is a horizontal rail which you grab and use to pull yourse ...[text shortened]... oubt it. If anyone has evidence to the contrary, please post. I'm skilled at own-word eating.
I am amazed that this "no-brainer" should keep apparently intelligent people occupied for so long.
1. Inless there is sufficient lift generated by airflow over the wings the plane will not fly. Let's call that critical airspeed.
2. If the the belt moves backwards at the same speed as the wheels of the plane are moving forward the airspeed remains at zero - no flight.
3 If the belt is slower then the plane will fly if the speed difference is greater than the critical airspeed and won't if it is less.
That's all folks.
5. 30 Oct '06 14:17
Originally posted by sugiezd
I am amazed that this "no-brainer" should keep apparently intelligent people occupied for so long.
1. Inless there is sufficient lift generated by airflow over the wings the plane will not fly. Let's call that critical airspeed.
2. If the the belt moves backwards at the same speed as the wheels of the plane are moving forward the airspeed remains at zero ...[text shortened]... ference is greater than the critical airspeed and won't if it is less.
That's all folks.
I'm amazed that some people still think a plane moves by turning it's wheels.
6. 30 Oct '06 14:25
Originally posted by Ian68
I'm amazed that some people still think a plane moves by turning it's wheels.
If there would be a lift because of turning the wheels...
What about planes with no wheels?
Like pontons? And... eh... what do you call those things you land on on snow with?
7. 30 Oct '06 14:53
Originally posted by Ian68
I'm amazed that some people still think a plane moves by turning it's wheels.
Irrelevant.
Powered by prop., wheels, jet, impulse, warp, steam, thought or just the pilot's farts- that plane won't fly.
8. 30 Oct '06 15:52
Originally posted by sugiezd
Irrelevant.
Powered by prop., wheels, jet, impulse, warp, steam, thought or just the pilot's farts- that plane won't fly.
And this is why the thread keeps going - because people keep failing to understand the explanation. The belt will not slow the plane down enough to stop it taking off.
9. 30 Oct '06 15:58
Originally posted by mtthw
And this is why the thread keeps going - because people keep failing to understand the explanation. The belt will not slow the plane down enough to stop it taking off.
If the prop. would move the plane at 100 kph om terra firma but the belt is moving backwards at the same speed - what is the speed of the air passing over the wings?
10. 30 Oct '06 16:19
Originally posted by sugiezd
If the prop. would move the plane at 100 kph om terra firma but the belt is moving backwards at the same speed - what is the speed of the air passing over the wings?
The prop would be moving the plane at 100kph with respect to the air. Propellers affect air speed, not ground speed. The belt is irrelevant.
11. 30 Oct '06 16:22
suqiezd please give up you are only making matters worse. Marsan i like your analogy and was hoping it would finnaly put an end to this question. Goodluck everyone!
12. 30 Oct '06 17:11
Originally posted by Marsan
Sorry for the double (triple) thread but this needs to be explained properly and the other threads got off topic talking irrelevant stuff.
The easy part:
The plane will take off.
The hard part:
Thought experiment.
Imagine you are lying on your stomach on a large skateboard. Along-side you is a horizontal rail which you grab and use to pull yourse ...[text shortened]... oubt it. If anyone has evidence to the contrary, please post. I'm skilled at own-word eating.
i'm confused the first half of your post says that the plane will take off. In the second half you give the reason why a propeller isn't enough to create air movement under the wing and so create lift.
Now for my 2 cents. propellers/jets/other forms of propulsion create
ACCELERATION. Assuming that the conveyor belt is moving at a constant rate eventually the plane will be moving far faster than the conveyor and will NOT STAY IN ONE PLACE. thus it takes longer but behaves exactly like a normal runway. If on the other hand the conveyor accelerates at the same rate as the plane then the plane will not move and its velocity will remain zero thus no lift is created.
If your gonna ask a question you should always make your conditions clear and precise. otherwise half the group answers one question the other half answers a different question and a moronic argument breaks out. I place the blame squarely at the feet of the original author of the problem.
13. 30 Oct '06 17:55
Originally posted by aginis
If your gonna ask a question you should always make your conditions clear and precise. otherwise half the group answers one question the other half answers a different question and a moronic argument breaks out. I place the blame squarely at the feet of the original author of the problem.
The question clearly stated that the plane was moving forward. You cannot blame the questioner for people who cannot understand how a plane moves and thus concluded that the plane would be stationary in relation to the surrounding air.
14. 30 Oct '06 21:30
Originally posted by FabianFnas
If there would be a lift because of turning the wheels...
What about planes with no wheels?
Like pontons? And... eh... what do you call those things you land on on snow with?
skis
15. 30 Oct '06 21:31
Originally posted by sugiezd
If the prop. would move the plane at 100 kph om terra firma but the belt is moving backwards at the same speed - what is the speed of the air passing over the wings?
0 | 2,104 | 9,268 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2019-04 | latest | en | 0.940031 |
https://pastebin.com/xYkCEdWZ | 1,606,152,058,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141163411.0/warc/CC-MAIN-20201123153826-20201123183826-00467.warc.gz | 430,934,981 | 6,017 | критерии 2 сортировки
Oct 26th, 2020 (edited)
721
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
1. #include <iostream>
2. #include <cmath>
3. #include <algorithm>
4.
5. using namespace std;
6.
7. void merge_series (int **arr, int first, int last_1, int last_2, int *dubl, int *ind, int par)
8. {
9. int i = first;
10. int j = last_1+1;
11. int c = 0;
12.
13. for (c = first; c <= last_2; c++)
14. if (j > last_2)
15. dubl[c] = ind[i++];
16. else if (i > last_1)
17. dubl[c] = ind[j++];
18. else if (arr[ind[i]][par] >= arr[ind[j]][par] && par == 1)
19. dubl[c] = ind[i++];
20. else if (arr[ind[i]][par] <= arr[ind[j]][par] && par == 2)
21. dubl[c] = ind[i++];
22. else dubl[c] = ind[j++];
23. }
24.
25. void sort (int **arr, int first, int last, int *dubl, int *ind, int par)
26. {
27. int middle = (first + last)/2;
28.
29. if (first < middle)
30. sort (arr, first, middle, dubl, ind, par);
31. if (middle + 1 < last)
32. sort (arr, middle+1, last, dubl, ind, par);
33.
34. merge_series (arr, first, middle, last, dubl, ind, par);
35.
36.
37. for (int i = first; i <= last; i++)
38. {
39. ind[i] = dubl[i];
40. }
41. }
42.
43. int main ()
44. {
45. int n;
46. int **arr, *ind, *dubl;
47. cin >> n;
48.
49. arr = new int* [n];
50. ind = new int [n];
51. dubl = new int [n];
52.
53. for (int i=0; i<n; i++)
54. arr[i] = new int [3];
55.
56. for (int i=0; i<n; i++)
57. {
58. arr[i][0] = i+1;
59. ind[i] = i;
60. for (int j=1; j<3; j++)
61. cin >> arr[i][j];
62. }
63.
64. sort (arr, 0, n-1, dubl, ind, 1);
65.
66. int index = 0, shet = 0, i = n-1;
67.
68. for (int i=0; i<n; i++)
69. dubl[i] = 0;
70.
71. while(i > 0)
72. {
73. while (arr[ind[i]][1] == arr[ind[i-1]][1] && i > 0)
74. {
75. index++;
76. i--;
77. }
78. shet = i+1;
79. //cout << index << " " << shet << endl;
80. if (index != 0)
81. {
82. sort (arr, shet-1, index+shet-1, dubl, ind, 2);
83. index = 0;
84. }
85. i--;
86. }
87.
88. for (int i=0; i<n; i++)
89. cout << ind[i] + 1 << " ";
90. }
RAW Paste Data | 929 | 2,236 | {"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} | 2.90625 | 3 | CC-MAIN-2020-50 | latest | en | 0.114098 |
https://abettes-culinary.com/how-fast-is-50-km-h-update/ | 1,653,350,715,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00241.warc.gz | 126,095,638 | 19,215 | Home » How Fast Is 50 Km H? Update
# How Fast Is 50 Km H? Update
Let’s discuss the question: how fast is 50 km h. We summarize all relevant answers in section Q&A of website Abettes-culinary.com in category: MMO. See more related questions in the comments below.
## Is 1 km/h fast?
If something is traveling at 1 km/h it moves 1 kilometer every hour. 1 km/h is like a very slow walking speed.
### How to skate 50 km/h and faster?!
How to skate 50 km/h and faster?!
How to skate 50 km/h and faster?!
## What is 50km in minutes?
Kilometer/hour to Kilometer/minute Conversion Table
Kilometer/hour km/h] Kilometer/minute [km/min]
5 km/h 0.0833333333 km/min
10 km/h 0.1666666667 km/min
20 km/h 0.3333333333 km/min
50 km/h 0.8333333333 km/min
## How fast is a 100km in mph?
Answer: 100 km/h is equal to 62.14 mph
So, 100 km/h is equal to 62.14 miles per hour.
## How fast is 46 km in mph?
46 kmh ≈ 28.58 mph
Now you know how fast 46 kmh is in mph.
## Is 60 kph fast?
Minimal ang damage. At 60 kph you can use all the braking power that you have.” (In case you lose your brake, or something went wrong with your car, if you bump into something, at 60 kph it will not be instantly fatal. Damage is minimal.
## What is the speed of a car that runs 100 km in 2 hours?
A car travels a distance of 100 km in 2 hours. Its average speed is 50 km/h.
## How fast is 10 km in mph?
Kilometers per hour to Miles per hour table
Kilometers per hour Miles per hour
10 kph 6.21 mph
11 kph 6.84 mph
12 kph 7.46 mph
13 kph 8.08 mph
## How many km is a 1 hour drive?
Speed = distance (60 km) / time (1 hour) = 60km/h.
## How many hours is 50 kilometers?
Time taken to cover 50 km = 1 hour.
## How many kilometers is 30 minutes?
Beginner runners should aim to run 2 – 3 miles (3.2 – 4.8 kilometres) in 30 minutes. Even if you’re taking regular walking breaks, you should be able to run this distance in half an hour.
### 50 km/h on bicycle
50 km/h on bicycle
50 km/h on bicycle
## How many kilometers are in a minute?
Kilometer/minute to Kilometer/hour Conversion Table
Kilometer/minute [km/min] Kilometer/hour [km/h]
0.1 km/min 6 km/h
1 km/min 60 km/h
2 km/min 120 km/h
3 km/min 180 km/h
## How fast is 110km?
110 kmh ≈ 68.35 mph
Now you know how fast 110 kmh is in mph.
## How fast is 125km?
125 kmh ≈ 77.67 mph
Now you know how fast 125 kmh is in mph.
## Is kph and kmh the same?
The kilometre per hour (SI symbol: km/h; abbreviations: kph, kmph, km/hr) is a unit of speed, expressing the number of kilometres travelled in one hour.
Kilometres per hour.
kilometre per hour
A car speedometer that indicates measured speed in kilometres per hour.
General information
Unit system derived
Unit of speed
## What speed is 80 km in mph?
80 kmh ≈ 49.71 mph
Now you know how fast 80 kmh is in mph.
## What is 30km mph?
Kilometers Per Hour to Miles Per Hour Conversions
Kilometers Per Hour Miles Per Hour
15 kph 9.321 mph
20 kph 12.427 mph
25 kph 15.534 mph
30 kph 18.641 mph
## How far will a car with average speed 60km/h move in 4 hours?
Answer: 60 times 4 is 240. So, over 4 hours, but not 5, as 60 times 5 is 30. If the car is going at 60 kilometres an hour, then it’ll hit 30 kilometres every half anhour.
## What speed did the car travel at from 45 to 60 minutes?
time taken by car = 45min. = 45/60 hr = 3/4 hr. speed = 60*4/3 = 80km/hr.
## What is the average speed of the car if it covers 200 km in 5 hours?
Answer: The average speed of the car is 40km/hr.
### Max Speed Xiaomi M365 Pro (50km/h)
Max Speed Xiaomi M365 Pro (50km/h)
Max Speed Xiaomi M365 Pro (50km/h)
## What will be the average speed in kilometer per hour if the car travels 100 km in 2 hours and 30 minutes?
so average speed is 50 km/h.
## What must be your average speed to travel 100 km in 5 hours?
= 20km /hour.
Related searches
• how fast is 50 km in miles per hour
• how fast is 50 kph
• is 50 mph fast
• how fast is 50 km/h
• 50 km/h to mph
• 50 kilometers per hour
• 100 km to miles per hour
• 50 kmh to ms
• how fast is 50 km h in mph
• 50 kmh wind
• 50 km to miles
• how fast is 60 km
• is 50 km/h fast on a bike
• how fast is 53 km an hour
• at what speed does google maps calculate car time
• 50 km/h wind
• 50 km/h to m/s
• how fast is 50km
• is 50 kmh fast on a bike
• 50 kmh to mph
• what does 50 km/h mean
• how fast is 50 km an hour
## Information related to the topic how fast is 50 km h
Here are the search results of the thread how fast is 50 km h from Bing. You can read more if you want.
You have just come across an article on the topic how fast is 50 km h. If you found this article useful, please share it. Thank you very much. | 1,459 | 4,654 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2022-21 | latest | en | 0.821688 |
https://www.calnewport.com/blog/2014/07/04/how-to-read-proofs-faster-a-summary-of-useful-advice/?replytocom=200601 | 1,660,560,510,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572163.61/warc/CC-MAIN-20220815085006-20220815115006-00220.warc.gz | 609,631,876 | 21,854 | How to Read Proofs Faster: A Summary of Useful Advice
July 4th, 2014 · 18 comments
The Wisdom of (Math Nerd) Crowds
A couple weeks ago, I complained that my academic paper reading speed was slower than I would like given its importance to my productivity. I asked for your advice and you responded with over 60 comments and numerous private e-mails.
My goal in this post is to synthesize the best ideas from this feedback, as well as the results of my own self-reflection, into a clear answer. In particular, I’ve identified three big ideas relevant to trying to read technical papers — and in particular those containing mathematical proofs — as efficiently as possible.
Idea #1: There are no magic bullets…
This conversation helped cement an idea that I’ve long suspected to be true (but sometimes resist):
To develop a detailed understanding of a published mathematical proof is an ambiguous process that requires multiple attacks and can take an unpredictable amount of time (not unlike proving something in the first place).
As a result, you must be selective about what proofs you decide to dig into, as the time commitment is potentially serious. In the study of algorithms (my field), for example, in most cases when reading a relevant paper it’s sufficient to dive down just deep enough to answer the following questions:
1. What is the main result and how does it compare to what was known before (or what a naive approach would provide)?
2. What is the high-level insight/trick deployed in the bound argument that enabled this improvement?
With experience, I’ve found that I can consistently produce this level of understanding within an hour (sometimes less if the paper is well-written or building on my own results).
This knowledge is not enough by itself to deploy or extend the technique presented in the paper, but it is enough to recognize future opportunities where this technique might be relevant to a problem you care about (at which point, you’ll have to dive deeper). In other words, maybe just one out of ten papers you read will end up proving directly useful to your own work, so it makes sense to learn just enough from the papers you read to identify whether or not they’re in that crucial 10%.
Idea #2: There are ways to be more efficient…
If you must understand the details of a proof, then in addition to the high-level suggestion from above of preparing yourself psychologically for a difficult battle, the following low-level strategies might also help:
• Instead of trying to read through the proof linearly, build a hierarchy of dependencies among the lemmata and theorems. Summarize each lemma and theorem in your own words and summarize each dependency relation; e.g., how does this theorem use the following three lemmata? Once you have this map, it becomes clearer where to begin a deeper dive and provides context for what you’re reading.
(Last time I deployed this full proof-mapping process — which can be quite arduous — I ended up uncovering a flaw in a reasonably well-cited paper.)
• In general, you should never start reverse-engineering a mathematical derivation until you understand what it is trying to show, why you expect it to be true, and how it will be used. If possible to assign some of this reverse engineering to a grad student, do so: it’s helpful to both parties.
• Create your own system of notation and rewrite the relevant statements and re-derive the main results (or, rough approximations of the main results) using this notation. You’ll likely have to revise this notation system many times before you’re done, but this process will make it much easier for you to conceptualize the deeper insights of the argument.
(I had to do this last week for a proof that I needed to understand better. It took me something north of six hours to complete! But I do certainly understand better now what is going on underneath the covers of this particular line of thinking.)
• Form reading groups with like-minded academics. Something about collaboration has a tendency to bust open mental road blocks and incite more creative thinking.
Idea #3: But perhaps the best strategy of all…
Get the authors on the phone or pull them aside at a conference and have them walk you through the argument. Nothing is more efficient than having the original author fill in the details of his or her thoughts.
(This latter strategy, of course, becomes more available as your status in your field grows. It might not be advisable, for example, for a first year PhD student to apply it with too much regularity!)
18 thoughts on “How to Read Proofs Faster: A Summary of Useful Advice”
1. Jeff says:
I like the notation suggestion.
Rewriting a proof in different (often more personal) notation is like translating foreign language passages, or transcribing music from one key to another. Just the process of it cements your understanding.
1. I like that parallel, Jeff!
2. Melissa says:
On idea #3. A lower status academic might be able to use this idea a lot more often were he to create a series of good videos with formulas from important papers that he does understand well (preferably outside his main area of interest). Then, when approaching other academics, he could offer to repay their time investment by creating a similar video for them and making it available on vimeo. Preferably on a paper other than the one our lower status academic is most interested in. Or, on that paper but with a delayed “publishing schedule” of six months. The argument being that the better able other academics are able to understand his ideas, the more he will be cited, the greater his influence, the more attractive academic groupies will pander after him at conferences, etc.
3. Melissa says:
On idea #3. A lower status academic might be able to use this idea a lot more often were he to create a series of good videos with formulas from important papers that he does understand well (preferably outside his main area of interest). Then, when approaching other academics, he could offer to repay their time investment by creating a similar video for them and making it available on vimeo. Preferably on a paper other than the one our lower status academic is most interested in. Or, on that paper but with a delayed “publishing schedule” of six months. The argument being that the better able other academics are able to understand his ideas, the more he will be cited, the greater his influence, the more attractive academic groupies will follow adoringly behind him at conferences, etc.
1. dontbelievein status says:
Sorry, but this is a ridiculous level of commitment. Academics are literally institutions whose job it is to come up with and disseminate research. Even as a high school student, I could write to the most famous academics in the world with specific questions or troubles, and they would correct me right away or tell me the key missing insight.
As long as you show you’re intelligent and trying, anyone would take a minute to set you straight. It only takes them a minute!
4. Stefan says:
(This latter strategy, of course, becomes more available as your status in your field grows. It might not be advisable, for example, for a first year PhD student to apply it with too much regularity!)
Why is that? Why dissuade anyone from doing this? With a proper explanation / introduction (“I’m a university student interested in [topic] and came across your paper; I was hoping you could explain this point to me…”), I don’t see any real downside to this — unless you harass or repeatedly bug the same professor or department without having first thought about the proof / paper considerably.
5. Nal Cewport says:
FOR GREAT INCREASE OF MATHEMATICKAL EFFIECIENCY IN GREAT REPUBLICK OF MATHAKHSTAN!!!
But with a comment like “you should never start reverse-engineering…” I can’t take you seriously. I Pity the fools who listen to you.
6. Stefan says:
(This latter strategy, of course, becomes more available as your status in your field grows. It might not be advisable, for example, for a first year PhD student to apply it with too much regularity!)
Why? Why dissuade anyone from doing this? With a proper explanation / introduction (“I’m a university student interested in [topic] and came across your paper; I was hoping you could explain this point to me…”), I don’t see any real downside to this — unless you harass or repeatedly bug the same professor or department without having first thought about the proof / paper considerably.
1. Sam says:
Conferences serve a lot of purposes. Some people have scheduled meetings. Others are are trying to squeeze in some research in the spur of the moment. Others are desperately trying to get a hold of the speaker from the last session, but unfortunately he or she is stuck with someone who refuses to let the speaker go to the bathroom before the next session starts. Conferences are also social gatherings where researchers meet their friends, and the more senior researchers go back 20 or 30 years together.
As flattering as it is to meet people who like and have read your work, there’s a limit on how much time people are prepared to spend explaining it. What that limit is depends on the person, but assume that a bigger name/more senior means less free time on their hands.
Looking at stereotypes I think it’s basically two distinct sets of students. The first set haven’t done their homework or thought much about the problem at all, and they have no qualms in endlessly stalking the top names with any trivial question they can think of (ask a fellow student or supervisor those questions instead). The second set have spent weeks preparing, and they are too shy to approach the person at all.
7. Ivan Savov says:
I would like to add to this a general strategy I learned from my colleague about reading papers in general: read the abstract then skip ahead to the theorems.
This is in contrast to my usual strategy of reading linearly from the beginning: abstract, introduction, previous work, results, etc. Reading linearly, I learn a lot about the field, but it’s inefficient because I get tired by reading so deeply…
8. Sorry, I eventually forgot to add a proper comment yesterday. 🙂
After reading that other post that led to this one, there’s something I’d like to comment on:
You said that reading the text surrounding a theorem and its proof often takes you longer than reading the formulas and unambiguous statements of the theorem, lemma or definition.
Well, I can relate. I’m not very good in Mathematics, but I can tell you things began to improve when I stopped reading anything else but the theorem and the proof on page. Only *after* I had at least a general understanding of the subject at hand I went reading the explanatory text. It was easier and didn’t feel like a heavy rock in my chest.
Don’t know if that’s your case, but emotions and schematization play an important role in my understanding of sciences (as well as any other subject) – they need to *flow* so I have no time to waste over a passage that confuses me. I study non-linearly, and starting with theorems, formulas and proofs (and then all the rest) helps me keep the flow going.
And I read aloud if I can. Listening to myself talking creates a duality, so to speak – a part of me talks, another part thinks. But the effort is reduced to a bare minimum. I even found connections between topics when I did this while prepping for a Math exam three years ago.
Well, that’s my two cents, I guess.
– Luana S.
9. PhDHacker says:
Thanks for the great post, Cal. Will definitely use your suggestions to become better at understanding papers. Also, this is a good example for employing deliberate practice to become better at a task for which there are no straightforward quantitative measures.
What I wanted to ask you is if you have any suggestions on how to administrate and collect all the information you’re getting. I often find myself spending an hour or so trying to understand a paper, hoping to be able to use it in the future, but I do not really have a system for dealing with the information, so I usually just end up accumulating huge piles of unreadable notes. How do you deal with this?
10. Jeremy says:
I respect all the answers here, but it’s things like this that make me glad I pursued other fields of study than forcing myself to continue with deep math study. The intense thinking involved makes my head hurt just thinking about it!
11. Ian Engelbrecht says:
Not specifically related to this post, but I see that those handy little tags you used to have on your blog aren’t available anymore. Not sure if you could add them back in again but it would be wonderful to be able to track down all the deep work, hard focus, or deliberate practice posts relatively quickly.
Cheers,
Ian | 2,664 | 12,838 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-33 | latest | en | 0.95592 |
http://www.sailnet.com/forums/gear-maintenance/78634-loads-my-turning-blocks-2.html#post774179 | 1,480,780,687,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698540975.18/warc/CC-MAIN-20161202170900-00049-ip-10-31-129-80.ec2.internal.warc.gz | 689,575,373 | 30,797 | Loads on my turning blocks? - Page 2 - SailNet Community
Old 09-13-2011
Bluenoser
Join Date: Jul 2008
Location: St. Margaret's Bay
Posts: 190
Thanks: 0
Thanked 2 Times in 2 Posts
Rep Power: 9
Thanks to knuterikt for correcting my mistake on counting mechanical advantage of a purchase (I SAID it was a long time ago...). However, gut feeling tells me that the load on the head of a mainsail is a lot less than mainsheet load? And does the boom act as a lever? Oh my, time to go back to the books...
Old 09-13-2011
Senior Member
Join Date: Aug 2009
Posts: 208
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 8
There is another consideration here, in terms of shiv load on turning blocks. Regardless of sail size and wind speed, there is a functional limit to how much force can be imparted.
Consider this:
You are sailing with full rig in a hurricane. Good times! Wind speed, lets say, 3000 knots. Why not? In this situation, your turning blocks will be under no more stress than, say, 35 knots of wind.
The boat heels. So, in that hurricane, your boat isn't going to accept all that extra wind force.. it's just going to lay over and take a little rest in the water. So the maximum loads on your turning blocks is not just a function of sail size, but also how much force your boat can exert on the wind to keep itself upright. That force has been called "righting moment" by people much smarter than myself.
I only bring this up to suggest that one can do a lot of math - which we all agree is a ton of fun! - but in the end, it's more of an exercise in mental acrobatics more than sailboat mechanics.
Don't get me wrong.. I do love me some good mental acrobatics. But lets try this.. what type and size rope is your current halyard? Determine the max load on that line, assume it's the max load for your rig (safe assumption, since the halyard hasn't snapped in two on you (I hope)) and double that number. The result is the size of turning block you need.
I know it's not sexy.. but it'll get you on the water, if that's where you want to be
... or I'm wrong.
Living aboard, currently in the Chesapeake
O'Day 37, still new to us
CapTim is offline
Old 09-13-2011
Senior Member
Join Date: Nov 2008
Location: Deale, MD
Posts: 2,924
Thanks: 1
Thanked 84 Times in 83 Posts
Rep Power: 9
I see some folks did remember basic physics!
I guess not everyone hid in the back!
Another thing to consider is the maximum force the main sheet is likely to add. After all, often the maximum force boils down to the maximum the sailor can crank. Say, the purchase times 50 pounds. For design purposes, 80 pounds. See how that adds up. Again, I suspect the mast will be in the water before that. In general, the reefing tackle is matched to the mainsheet tackle. On my boat, at least, the loads are equal.
(when asked how he reached the starting holds on a difficult rock climbing problem that clearly favored taller climbers - he was perhaps 5'5")
"Well, I just climb up to them."
by Joe Brown, English rock climber
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
pdqaltair is offline
Old 09-13-2011
Senior Member
Join Date: Sep 2008
Posts: 4,304
Thanks: 1
Thanked 34 Times in 34 Posts
Rep Power: 9
Despite what you think of SA there was a great thread with some good info in a civil form i cant find it right now BUT
There were some really good pictures of this posted on SA and the purchase depends on what is anchored wear and the load on the block does depend on the angles
1970 Cal 29 Sea Fever
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
1981 J24 Tangent 2930
Tommays
Northport NY
If a dirty bottom slows you down what do you think it does to your boat
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
tommays is offline
Old 09-14-2011
Señor Member
Join Date: Sep 2007
Posts: 1,446
Thanks: 8
Thanked 20 Times in 20 Posts
Rep Power: 10
Great points, folks.
The physics and mechanical engineering involved in arriving at a definitive answer are obviously beyond what any of us have covered here.
The bottom line is that I would tend to trust the recommendations of a reputable manufacturer like Harken when it comes to selcting block sizes. I'd bet that they've done the research, run the numbers , and added a safety factor to their calculations before making any such recommendation.
PorFin is offline
Old 09-14-2011
Senior Member
Join Date: Sep 2008
Posts: 7,761
Thanks: 0
Thanked 109 Times in 100 Posts
Rep Power: 10
Harken used to have all these numbers on line for hundreds of designs - CompuSpec. But they have apparently removed it all because they say it was dated - now they say email or call for info.
Brian
Living aboard in Victoria Harbour
mitiempo is online now
Message:
Options
By choosing to post the reply above you agree to the rules you agreed to when joining Sailnet.
## Register Now
In order to be able to post messages on the SailNet Community forums, you must first register.
Please note: After entering 3 characters a list of Usernames already in use will appear and the list will disappear once a valid Username is entered.
User Name:
OR
## Log-in
Human Verification
In order to verify that you are a human and not a spam bot, please enter the answer into the following box below based on the instructions contained in the graphic.
Currently Active Users Viewing This Thread: 1 (0 members and 1 guests) | 1,400 | 5,534 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-50 | latest | en | 0.952605 |
https://www.codeflu.com/post/minimum-index-sum-of-two-lists | 1,674,889,594,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00440.warc.gz | 711,700,861 | 5,844 | ## Minimum Index Sum of Two Lists
• Time:O(m + n), where m = |\texttt{list1}| \cdot \max(|\texttt{list1[i]}|) and n = |\texttt{list2}| \cdot \max(|\texttt{list2[i]}|)
• Space:O(n)
## C++
class Solution {
public:
vector<string> findRestaurant(vector<string>& list1, vector<string>& list2) {
vector<string> ans;
unordered_map<string, int> restaurantToIndex;
int minSum = INT_MAX;
for (int i = 0; i < list1.size(); ++i)
restaurantToIndex[list1[i]] = i;
for (int i = 0; i < list2.size(); ++i) {
const string& restaurant = list2[i];
if (restaurantToIndex.count(restaurant)) {
const int sum = restaurantToIndex[restaurant] + i;
if (sum < minSum) {
minSum = sum;
ans = {restaurant};
} else if (sum == minSum) {
ans.push_back(restaurant);
}
}
}
return ans;
}
};
## JAVA
class Solution {
public String[] findRestaurant(String[] list1, String[] list2) {
List<String> ans = new LinkedList<>();
Map<String, Integer> restaurantToIndex = new HashMap<>();
int minSum = Integer.MAX_VALUE;
for (int i = 0; i < list1.length; ++i)
restaurantToIndex.put(list1[i], i);
for (int i = 0; i < list2.length; ++i) {
final String restaurant = list2[i];
if (restaurantToIndex.containsKey(restaurant)) {
final int sum = restaurantToIndex.get(restaurant) + i;
if (sum < minSum) {
minSum = sum;
ans.clear();
ans.add(restaurant);
} else if (sum == minSum) {
ans.add(restaurant);
}
}
}
return ans.toArray(new String[0]);
}
}
## Python
class Solution:
def findRestaurant(self, list1: List[str], list2: List[str]) -> List[str]:
ans = []
restaurantToIndex = {restaurant: i for i,
restaurant in enumerate(list1)}
minSum = math.inf
for i, restaurant in enumerate(list2):
if restaurant in restaurantToIndex:
sum = restaurantToIndex[restaurant] + i
if sum < minSum:
ans.clear()
if sum <= minSum:
ans.append(restaurant)
minSum = sum
return ans | 522 | 1,818 | {"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} | 3.109375 | 3 | CC-MAIN-2023-06 | longest | en | 0.254687 |
https://www.askiitians.com/forums/Analytical-Geometry/tangents-are-drawn-to-the-hyperbola-4-x-2-y-2-36_235496.htm | 1,643,352,646,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305420.54/warc/CC-MAIN-20220128043801-20220128073801-00522.warc.gz | 663,768,123 | 36,278 | #### Thank you for registering.
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
CART 0
• 0
MY CART (5)
Use Coupon: CART20 and get 20% off on all online Study Material
ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.
There are no items in this cart.
Continue Shopping
# Tangents are drawn to the hyperbola 4 x^2 - y^2=36 at point P and Q.If these tangents intersect at point T(0,3) find area of triangle formed
Arun
25763 Points
3 years ago
Dear student
Hyperbola: 4x²-y²=36 or x²/9 -y²/36 = 1. It’s tangent may be written as: ax/9 -by/36 = 1 and it is given that it passes through (0,3). Then, 0 - 3b/36=1 or b=- 12. Substitute this in our hyperbola eqn to obtain the value of a:4a² -144=36 which yields: a = ±3√5. So P:( -3√5,-12) and Q:(3√5, -12). This implies that the height of the triangle PQT = (12+3)=15 while PQ =6√5. Area of Tr. PQT = 15*6√5/2 = 45√5 s.u. | 338 | 948 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2022-05 | latest | en | 0.790004 |
https://www.doubtnut.com/question-answer/if-fxx2-then-evaluate-fx-1-fx-1-4x-30619865 | 1,623,961,741,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487633444.37/warc/CC-MAIN-20210617192319-20210617222319-00028.warc.gz | 664,183,054 | 65,348 | Class 11
MATHS
Relations And Functions
# If f(x)=x^(2) , then evaluate : (f(x+1)-f(x-1))/(4x)
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 11-9-2020
Apne doubts clear karein ab Whatsapp par bhi. Try it now.
Watch 1000+ concepts & tricky questions explained!
24.6 K+
16.7 K+
Text Solution
1
Image Solution
30619864
1.1 K+
22.6 K+
1:05
30619891
16.6 K+
28.5 K+
3:55
3350709
18.5 K+
135.8 K+
1:28
30619866
2.1 K+
41.7 K+
1:36
1216153
6.0 K+
120.9 K+
2:49
9562686
3.0 K+
59.9 K+
5:11
51236229
3.0 K+
60.8 K+
1:43
354013
2.9 K+
59.1 K+
1:46
30619755
12.6 K+
12.8 K+
0:43
7287
91.9 K+
179.3 K+
2:40
17122
14.7 K+
53.6 K+
2:10
5719089
2.8 K+
56.1 K+
3:30
34209
43.1 K+
250.6 K+
2:19
9677704
2.3 K+
47.4 K+
1:45
77345
31.9 K+
93.1 K+
2:13
## Latest Questions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions
Class 11th
Relations And Functions | 465 | 1,207 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2021-25 | latest | en | 0.52437 |
http://www.algebra.com/algebra/homework/quadratic/word/Quadratic_Equations.faq?question=278254 | 1,386,170,500,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163035819/warc/CC-MAIN-20131204131715-00056-ip-10-33-133-15.ec2.internal.warc.gz | 300,471,640 | 5,025 | # SOLUTION: hmm..ok. I got, 2(r^2+3r-40)=0 2(r-5) (r+8)=0 r-5= 0 r+8= 0 +5 +5 -8 -8 r=5 r=-8....? Is that good
Algebra -> Quadratic Equations and Parabolas -> Quadratic Equation Customizable Word Problems -> SOLUTION: hmm..ok. I got, 2(r^2+3r-40)=0 2(r-5) (r+8)=0 r-5= 0 r+8= 0 +5 +5 -8 -8 r=5 r=-8....? Is that good Log On
Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo . Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!
Quadratics: solvers Practice! Answers archive Lessons Word Problems In Depth
Click here to see ALL problems on Quadratic Equations Question 278254: hmm..ok. I got, 2(r^2+3r-40)=0 2(r-5) (r+8)=0 r-5= 0 r+8= 0 +5 +5 -8 -8 r=5 r=-8....? Is that goodAnswer by jim_thompson5910(29613) (Show Source): You can put this solution on YOUR website!You are correct. Good job. | 346 | 999 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-48 | latest | en | 0.721298 |
http://www.math.kochi-u.ac.jp/docky/kogi/kogi2012_1/chushodaisu/regular01/index.html | 1,513,128,584,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948520218.49/warc/CC-MAIN-20171213011024-20171213031024-00157.warc.gz | 416,789,797 | 2,866 | Next: Bibliography
# Commutative algebra
Yoshifumi Tsuchimoto
DEFINITION 01.1 A (unital associative) ring is a set equipped with two binary operations (addition (+'') and multiplication ( '')) such that the following axioms are satisfied.
Ring-1.
is an additive group with respect to the addition.
Ring-2.
distributive law holds. Namely, we have
Ring-3.
The multiplcation is associative.
Ring-4.
has a multiplicative unit.
In this lectuer we are mainly interested in commutative rings, that means, rings on which the multiplication satisfies the commutativity law.
For any ring , we denote by (respectively, ) the zero element of (respectively, the unit element of ). Namely, and are elements of characterized by the following rules.
• , .
• , .
When no confusion arises, we omit the subscript ` ' and write instead of .
DEFINITION 01.2 A map from a unital associative ring to another unital associative ring is said to be ring homomorphism if it satisfies the following conditions.
Ringhom-1.
Ringhom-2.
Ringhom-3.
Our aim is to show the following.
THEOREM 01.3 Any regular local ring is UFD.
DEFINITION 01.4 A commutative ring is said to be a local ring if it has only one maximal ideal.
EXAMPLE 01.5 We give examples of local rings here.
• Any field is a local ring.
• For any commutative ring and for any prime ideal , the localization is a local ring with the maximal ideal .
LEMMA 01.6
1. Let be a local ring. Then the maximal ideal of coincides with .
2. A commutative ring is a local ring if and only if the set of non-units of forms an ideal of .
Next: Bibliography
2012-04-13 | 417 | 1,619 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2017-51 | latest | en | 0.842687 |
https://documents.pub/document/on-some-theorems-on-circulant-matrices-on-some-theorems-on-circulant-matrices.html | 1,713,496,933,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817253.5/warc/CC-MAIN-20240419013002-20240419043002-00872.warc.gz | 188,220,654 | 31,940 | Home > Documents > On Some Theorems on Circulant Matrices · On Some Theorems on Circulant Matrices Paolo Zellini and...
# On Some Theorems on Circulant Matrices · On Some Theorems on Circulant Matrices Paolo Zellini and...
Date post: 16-Feb-2019
Category:
View: 222 times
13
On Some Theorems on Circulant Matrices Paolo Zellini and Angela Mack lstituto di Scienze dell’lnformuzione Universitci di Pisa Pisa, Ztaly Submitted by David H. Carlson ABSTRACT In [2] some theorems on n Xn circulant matrices were introduced under the hypothesis n a prime number. We extend these theorems to the case nE2.r where T is a prime greater then 2. 1. INTRODUCTION In [2] the spaces Z, of nXn matrices A(a)=Z;LiakJk were introduced, where a k are complex and Jo, J1,. . . , .I,_ 1 satisfy the following condition: (*) &={J0,J1,...J,-~} is a set of nXn permutation matrices one of which is I and such that Z;!tJ, =J= ( j,, ,), where i,, s = 1 (r, s=O, 1,. . . , n - 1). The following two theorems have been proved in [2] under the hypothesis n a prime number: THEOREM 3.2. Zf \$ satisfies ( * ) and the Jk commute, then for P,,, the permutation matrix corresponding to the permutation (12 . . . n), the following holds: ( * *) For same permutation matrix P, and reindexing, Jk = PTP,kP, k=O,l,..., n-l. THEOREM 4.1. Zf &= {JO, JI,. . . , J,, ~ I} satisfies ( * ) and is closed under multiplication, then ( * *) holds. LINEAR ALGEBRA AND ITS APPLICATIONS 41:137-149 (1981) 137 ‘r Elsevier North Holland, Inc., 1981 ri2 Vanderbilt Ave., New York, NY 10017 00243795/81/070137+ 13\$02.50
Transcript
On Some Theorems on Circulant Matrices
Paolo Zellini and Angela Mack lstituto di Scienze dell’lnformuzione Universitci di Pisa
Pisa, Ztaly
Submitted by David H. Carlson
ABSTRACT
In [2] some theorems on n Xn circulant matrices were introduced under the hypothesis n a prime number. We extend these theorems to the case nE2.r where T is a prime greater then 2.
1. INTRODUCTION
In [2] the spaces Z, of nXn matrices A(a)=Z;LiakJk were introduced, where a k are complex and Jo, J1, . . . , .I,_ 1 satisfy the following condition:
(*) &={J0,J1,...J,-~} is a set of nXn permutation matrices one of which is I and such that Z;!tJ, =J= ( j,, ,), where i,, s = 1 (r, s=O, 1,. . . , n - 1).
The following two theorems have been proved in [2] under the hypothesis n a prime number:
THEOREM 3.2. Zf \$ satisfies ( * ) and the Jk commute, then for P,,, the
permutation matrix corresponding to the permutation (12 . . . n), the following
holds:
( * *) For same permutation matrix P, and reindexing,
Jk = PTP,kP, k=O,l,..., n-l.
THEOREM 4.1. Zf &= {JO, JI,. . . , J,, ~ I} satisfies ( * ) and is closed under
multiplication, then ( * *) holds.
LINEAR ALGEBRA AND ITS APPLICATIONS 41:137-149 (1981) 137
‘r Elsevier North Holland, Inc., 1981 ri2 Vanderbilt Ave., New York, NY 10017 00243795/81/070137+ 13\$02.50
138 PAOLO ZELLINI AND ANGELA MACK
An obvious consequence of Theorem 3.2 and Theorem 4.1 is stated in the following.
THEOREM 4.2 (see [2]). 172e only Z, which constitute a commutative algebra are the spaces of n X n matrices ( n prime) of the form P“CP, where C is circulant, and P, which depends on the choice of the set { .I,), is the permutation matrix or the identity.
An alternative proof of Theorem 3.2 and Theorem 4.1 has been intro duced in [l] by using the centralizers of a permutation group. In [l] Theorems 3.2 and 4.1 appear as corollaries of the following results:
THEOREM 1. Let n he a positive integer. IJet :/ satisfy ( *) and the Jk commute. Then for P,,, the permutation matm’x corresponding to the permuta-
tion (0 12 . . n - l), ( * * ) holds if and only if there exist.s a J, in j which is an n-cycle.
THEOREM 2. Let n be a positive integer, and zj satisfy (* ) and be closed under multiplication. Then ( * * ) ho1d.s if and only if there exists a 4, in j which is an n-cycle.
In the present paper we find an extension of Theorem 3.2 and Theorem 4.1 to the case n = 2. r, where r is a prime > 2. More precisely, Theorem 3.2 is still true in the case n=2.r, while for the closure under multiplication some different spaces of matrices A(a) are to be introduced beside the circulant. .4 new class of algebras of n X n matrices on the complex field is then introduced at the end of Section 3.
If ij satisfies ( * ), then we shall suppose, in the remainder of the paper, Jo =I.
2. ON THE COMMUTATIVITY OF THE MATRICES OF THE SPACES Z,
The following Propositions are in some sense implicit in the results in [2] and in their proofs. In the following Ip,y ‘ck) is the element (p, a) of the matrix II, and lick) is the permutation mapping 4 to p in the case j:f’A = 1, i.e. II(“) gives the exact disposition in the row k of A(a) of the complex parameters
a,, a i, . . . , a ,, ~ r (see [2, p. 371). We suppose that [ aOal . . .a ,I ,] is the first row of A(a), i.e. \$1 =l.
CIRCULANT MATRICES 139
PROPOSITION 2.1. Let &= {J,,, J1,. . . , Jn_1} satisfy (*) and Jk commute. Then lick’, for a k#O, is an n-cycle if and only if Jk is an n-cycle. Also, if nCk’ or ./k is 972 n+&?, then & satisfies ( * * ).
Proof. Proposition 2.1 follows immediately from Lemma 3.4 in 2 , I1 which states that, if the commutativity of the Jk is assumed, then ijp) = ii,“k =
ii”,’ = 1 implies 1,. k - ‘(‘) - 1. Hence, from &“L = @) = i&r’i = 1 we deduce ig”! = 1, and analogously, i:“) = 1 is a consequence of lo, p ‘(P) = i(k) = ih”L = 1, ~0 we: have p, r , the equivalence
i:p)=l w i(k) ~1. ,r P.T (2.1)
Now it is easy to see that if the permutation (ha h, . . . h, _I) defines IICk’, then (ha h,_, . . .h,) defines lk (and vice versa). The last part of Proposition 2.1 has been pointed out in [ 11. It is also a direct consequence of the proof of Theorem 3.2 in [2]. n
PROPOSITION 2.2. Let \$= {Jo, J1,. . . , .l,_ I} satisfy ( * ). Then the matrices
Jk commute with each other only if flCk’, for every k#O, is the product of
disjoint cycles of the same length r where r=n or r/n.
Proof. Let the J, commute, and let IICt) be the product of cycles rr, . . , TV, such that at least two of them have different lengths. Without loss of generality suppose that rr and rl, for an index I, have lengths, respectively, r
and s, with r # s. Then there are indices p,, p,, . . . , p, with p0 = pT =O and p T P1=t (we have ii”;’ fii”j=l) and 90,91,...,9, (90=9S) such that -7, .
i(Pl) t.Pz 1
=l, ii:;;;,! 1=1, i=l,...,r, m=l,...,s.
Successive applications of (2.1) and Lemma 3.4 in [2] define the recurrent implications
-,,-I) =I, 2.41
h=O ,..., r-l. (2.3)
140 PAOLO ZELLINI AND ANGELA MACK
(2.2) and (2.3) correspond, respectively, to the recurrent relations (3.6) and (3.7) in [2]. They lead, for r # s, to a contradiction with (*). In fact, let r > s.
Then we deduce, from (2.2), jbl;“q;) = 1. But we have also i:‘,! Q, = 1, because jj’\$I) = 1 and (2.1) holds; so, by the equality t = p, If r < s, then we have, from (2.3) i,,, ‘,,
with the equality jr(,Ts:, = 1 that is deduced from (2.2).
Now we have the following.
LEMMA 2.1. Let \$ = {Jo, Jr,. . . , .I,, 1} sutisfy ( *), and .I, commute. Let IT(‘), for some t, be the product of I, disjoint cycles of the sume length r. Then
there exist indices p,,, pI,. . . , p,, with p,, =p, =O, p, I = t, such that
J,,l . ’ ) I,,- , are completely defined by, and correspond to, r-l permutations
up, (k=l,..., r- 1) which are the product of n/r disjoint cycles of length r.
Analogously all permutations IICpk’ are defined and are the product of 1,
cycles of length r. In particular if 1, = 1 ati r= n, then any J, is an n-cycle
and(**)ho
Proof. Suppose, without loss of generality, t= 1. As II(i) is the product of r-cycles, there are indices p,, p,, . . . , p, with p, = p, = 0, p, 1 = 1 such that
ILPk 1
‘(Pk) El ’
k=1,2 ,..., r. (2.4)
By successive applications of Lemma 3.4 in [2] and (2.1) we have (the indices are all taken modulo r)
(2.5)
i.e., rw, as well as I,,, contains an r-cycle. If r = n, then we obtain the Lemma and the result of Theorem 3.2 in [2] ( see the second part of the proof of Theorem 3.2 in [2, pp. 388391). If r\n, then consider another r-cycle of H(l).
ha I
.(‘lX) El ’
k=1,2 ,..., r, (2.6)
where 9O = 9,. Successive applications of Lemma 3.4 in [2] give the following
CIRCULANT MATRICES 141
implications:
j((lk) l.qk- I
=j'Pr 2) 3
4k-,.4k-3 = iiP;;_l, = 1
. r
jh) P, 3,4k 3
=i(Pr .J) El, Qks4k 3
(2.7)
wheres=l,2 ,..., r-2andk=1,2 ,..,, r. The following recurrent relations are also deduced from Lemma 3.4 in [2]:
i:Pk) =j(Ps) = *(p,)
,Pk I Pn-l.Pa+k I ll.,, , = 1
= igkl,p,+k , =iK:,:‘i,_ ,=I,
s=2,3 ,..., r-l. (2.8)
Now let qe,qi,..., 9r_l run over the set of disjoint subcycles of II”’ which do not involve 0 or 1. Then Lemma 2.1 follows from (2.7) and (2.8). Also, observe that _/p(i) E&, where i= 1,2,. . . , r- 1. w
EXAMPLE 2.1. Let n=6 and let [a4 a,, a5 a2 a, u,~] be the second row of the matrix A(a)=Z;Zia,Jk, corresponding to the permutation CT= (04 1)(253):
a0 al a2 a3 a4 a5
a4 a0 a.5 a2 al a3
A(a)= : : :I a”:, : z: .
al a4 a3 a5 a0 a2 . . al a4 . a,
(2.9)
If the Jk commute, then the rows and the columns of A(a) corresponding, respectively, to the indices p, = 0, pi ~4, p2 = 1 and 9. ~2, 91 =5, 92 =3 are defined as in (2.9). Observe that Jp, =.I4 and Jpp2 =I1 correspond, respectively, to the permutations (I and u2, i.e. Ji =.I,“.
142, PAOLO ZELLINI AND ANGELA MACK
LEMMA 2.2. Let n=2.r where r is a prime >2. Let JO, Jl ,..., J,,_l commute and satisfy (* ). Then lIICk) cannot be, for every k, the product of 2-cycles.
Proof. Consider II(l) and IIc2’, and suppose they are the product of 2cycles. Then for some indices qil’. qi”, . . . , qL1’ 1 and q[2’. qi2’, . . . , qj;‘! 1 with
91 (1) Ix 1, 42 =qp, q1 c2) =2 q/‘) +ql’) for i>2 we have ,
Alsowehaveforsomer, ,..., r,, 1 ands:, ,..., s,,~,,with~~~jaandr,#i,
(2.12)
(2.13)
Let us observe that, if the Jk commute and II (k) has subcycles of length 2 for
every k, then each Jk is symmetric. In fact we have the foIlowing obvious implications:
This property of symmetry and successive applications of Lemma 3.4 in [2] give rise to
CIRCULANT MATRICES 143
From (2.12) and (2.15) we have
r, =si, i=3,...,n-1. (2.16)
This means that the third row of A(a)=‘C;!ia,J, is a permutation l3 of the second row such that ll is the product of 2cycles.
Now if j\$ = 1 and jr,, ‘(k”= 1 for some k and k’ then we have, as a consequence of (2.10)-(2.11) and (2.16) the following configuration for the matrix A(a) (we suppose, without loss of generality, 1~ I’< k < k’):
first row: . . . a, . . . a,, . . . (Jk.. . ak’. . .
secondrow: ..’ aks’.. ak ... a,,... (I, ... third row: ... ak ... ak,.‘. a, ... a,. ...
(2.17)
i.e. we deduce, for some E’, ~r,~, - I~,,, .(k) - .(k’) = iif:, = &‘: = ji”j = ii”), = I. Now
(2.17) is consistent only with the case 41 n; in fact if 4jn, then we obtain, for some r and s, jgl= 1, or simultaneously \$l= 1 and \$~ = 1, i.e. a contradic- tion. n
THEOREM 2.1. Let n=2.r where r is a prime >2. Let the _lk commute
and satisfy ( * ). Then ( * * ) holds.
Proof. Consider the following four cases for k= 1,2,. . . , n - 1:
(a) every ll (k) is the product of two cycles of length r;
(P) every n (k) is the product of r cycles of length 2; (y) every lick) can be the product of 2cycles or the product of r-cycles; (6) there exists a k such that lick) is an n-cycle.
These cases exhaust all the different possibilities of choice of the matrices Jk. Clearly (j3) is impossible by Lemma 2.2. We claim that (a) and (y ) are also impossible, so (S) holds and the Theorem 2.1 follows from Proposition 2.1 (or from Theorem 1 in [l]).
Let condition (a) be verified and let 11 (l) be the product of two r-cycles:
Il.Pk L
.(Pk’ xl ’ Il.,,-, ’
‘(VL) = 1
k=O,l,..., r, 9f#pi Vi,i, p,=p,=O, p,-,=l, 90=9r. c2.18)
Consider a row qk of the matrices J,. From (2.7)-(2.8) we have that Ji:,),, = 1 implies Zf pi for every i [this follows immediately from the equalities O= p,
144 PAOLO ZELLINI AND ANGELA MACK
and jby’y; 1) =l, i.e., every matrix I,,, is defined and cannot have 1 in the
position (dk,‘O)]. Also, by (2.7), i,, 4 (‘) = 1 implies Z#q, for every t, so l=p, for some i. Analogously, ii’,! pa = 1, with ‘p, #O, implies Z=q, for some i; otherwise we have a contradiction with the last equality of (2.7). From it:!4k = 1 we deduce that II has a subcycle defined by some indices prctj and CJ((,, such
that
i(QI(l1) =j(P1(21) =jtclll.ll) = . . . =j(())
OL.O ‘Ik. q/,1, Yk. PI01 =1
VI>41 ’
so II has a subcycle of length m where m is even, which is impossible. Let condition (y) be verified. Suppose that II(‘) is the product of two
r-cycles [i.e. (2.18) holds]. Then n (“k), for every k, is an n-cycle [i.e. (6) is verified] or is the product of B-cycles. Let this last condition hold. Fix a qk and
let iX’,q, = 1 [we cannot have ix! pi = 1 for some P,~; in fact 1 = p, I in (2.18) and (2.7) holds]; this implies i,“;.l = 1. From ii:,:; 1) = 1 we obtain, by the
commutativity, \$‘. ,, ‘(i - - 1 and then, as 11”‘~ * 1) has subcycles of length 2, j(Si) = 1. By the commutativity j&y:+‘) = 1, so we obtain q,s =Y~+~, iki! 41,, = 1, ~~\$~~;~,, = 1. This last equality and ii”;; 1) = 1 imply that H”’ has a subcycle of length 2, i.e. a contradiction. n
EXAMPLE 2.2. The following matrix A(a) (n= 10) shows that if the commutativity is not assumed, then condition (p) does not contradict ( *). Observe that all Jk are symmetric:
A(a) = . (2.19)
If the commutativity is assumed, then the impossibility of (j3) (Lemma 2.2) is shown in the following case (n = 10): take for instance the second row of A(a) in (2.19). As i\$, = 1, we have, according to (2.17), \$A = igi = 1 and, obvi- ously, \$A = 1. Now let for instance &?A = 1. This implies \$A = j\$ = i\$Tk = 1
CIRCULANT MATRICES
145
A(a) =
a0 a1 a2 a3 a4 Qs ub: a7 at3 a9
a1 a0 a4 at? a2 a8 a3 a9 a5 a7
a2 a4 a0 ‘5 u1 ‘3 ‘R . a6
a3 a6 . . . . . . . .
a4 a2 . . . ’ . . . .
a5 ati . . . . . . . .
a6 a3 . . . . . . . .
a7 a9 . . . . . . . .
UR a5 . . . . . . . .
a9 a7 . . . . . . . .
3. CLOSURE UNDER MULTIPLICATION OF THE SPACES Z,
We are going to introduce some preliminary results which follow roughly the same logical model of reasoning of the previous section. The conclusion will be different, because for n12.r (r prime) the circulants do not constitute the only space Z, which is closed under multiplication. We shall show this in the final Theorem 3.1. In the following we denote by i!p; O) the element (T, s) of the matrix J;J,.
LEMMA 3.1. Let n=2.r (r a prime >2). Let &={lo,./, ,..., _In_1} be closed under multiplication and satisfy (*). Then IICk’ cannot be, for every kf 0, the product of 2-cycle.s. Also, there is a k#O such that Jk does not correspond to a product of 2-cycles.
Proof Let IT (k) be the product of 2cycles for every k #O. Then, from the assumption ibid = 1 (see Section 2) and the equality ii:\ = 1, we have ilk4 = 1. By the closure of &, 1: = I, i.e., all subcycles of the permutation c&responding to ./k (k = 1,2,. . . , n - 1) have length 2. Also if ii”j ‘) = 1, then we have ilki’) = 1. Hence, from ij’tk’= 1 we deduce Jk..Jl = J,../L,, i.e., the Jk commute, which is a contradiction’by Lemma 2.2. n
LEMMA 3.2. Let &= {Jo, J1,. . ., J,, _ 1} be closed under multiplication and satisfy ( *). Zf II(‘), for some 1, has two subcycles of length, respectively, r and s-i.e.
.(PL) I/,~, ,=I, ilp;i_,=l, k=l,..., r, h=l,..., s, (3.1)
146 P,4OLO ZELLINI AND ANGELA MACK
with p, =p, ~0, p,~_ I =I, qO =q, -then the following equalities are verified:
Proof. Observe that i,, y and ibpi = 1 we have
(‘) = 1 if and only if J;jk =I,. In fact, from j,(,“: = 1 ig;“’ = 1 and vice versa.
If (3.1) holds then we have
JJ,, =I,, ,) k=l,...,r,
JJ,,,=-I,,, ,’ h=l,...,s.
From (3.3) and Jo =I we obtain the following implications:
-r,;& =J”, .kJ,,,=J,,, , =3 I,,\$,,, ,=J,,,> h=l,..., s,
(3.,3)
-r,,.l/ =Jo, .l,~1,,=.l,, , = lp;lp, ,=&, i=l,...,r;
and then, from (3.4), the following recurrence relations:
(.3.4)
h=l,..., r-l, i=h+l,..., r+h; (3.5)
h=l,..., r-l, i=h+l,..., s+h,
where the indices are taken moduIo r and S. n
CIRCULANT MATRICES 147
PROPOSITION3.1. jet&={.&,./,,..., I,_ 1} be closed under multiplication
and satisfy ( *). Then IItk’ is the product of subcycles of the same length.
Also, if rICk) is an n-cycle for some k # 0, then every .lk is an n-cycle and \$
satisfies ( * *).
Proof. We claim that r#s in (3.1) contradicts (*). In fact, let r>s; then
from (3.2) we have Jp;Jq, =.&+, =I,,, which is impossible. If T<S, then we
have, from (3.2) Jp,_, ..Z4, =.ZQ,, which is a contradiction with the equality .J(._Z,, =I,, that is deduced from (3.1) [recall that p,_, =1 in (3.1) and 9” fq,]. For the second part of the proposition, if II (k) is an n-cycle for some k, then the _Z, commute by Lemma 3.2 and its proof with r=n. By Proposition 2.1, j satisfies ( * * ), and hence each Jk is an ncycle. n
LEMMA 3.3. Let n=2r (r a prime ~2). Let \$={.l,,.l, ,..., J-1} be
closed under multiplication and satisfy (*). Then there is a k#O such that
IIck) is an n-cycle or the product of 2-cycles.
Proof. Let II ck) be a product of r-cycles (k= 1,. . . , n - 1). In particular let (2.18) hold. Consider IIcqh) and let i,,,, (I) = 1. We first show that l#p, for every pi. In fact let lqh,e ‘(PI) = 1 for some pi; then J,,;.Z, =I,,, ..Zq, =.ZO =I, so we have iLpc;l= 1. But this leads to a contradiction because the equality J,, . Jp,, =
I p +, of Lemma 2.2 implies ig,“d +, = 1 and \$‘,\$ = 1 for some p, such that t \$ i’=O module r. Then we have’ 1 L 9i for some index 9i. Now observe that .(O) 1 q,l,q,L= 1. Also, by the ewb I~,,,~ ‘(qc) =l and the second equality in (3.2) .(I) 1 9,*. 4, = 1 implies l=pk for some p,. Similarly, by the first equality in (3.2) if .(I) 1 Y/i. P,
= 1, then 1=9k for some qk. This means that IIcqr) must contain an m-cycle where m is even, which is a contradiction. n
THEOREM 3.1. Let n = 2 .r, where r is a prime > 2. Let \$ =
{&,I,,..., ],_ 1} be closed under multiplication and satisfy ( * ). Then \$ is a
finite cancellative semigroup, and hence a group. Moreover,
(i) (* *) holds, or
(ii) thereexistindicesp,,p,,...,p,(p,=p,=O)ancEq,,q,,...,q,(q,=q,) such that, for all i=l,..., r and all i=l,..., r,
148 PA4OLO ZELLINI AND ANGELA MACK
Also, the matrices Jk are completely defined, and the space 2, of muttices A(a) = Ca, Jk is a marwid (with neutral element JO = I ). This implies that 2, is closed under inversion.
Proof. By Lemma 3.1 and Lemma 3.3, the closure of j and ( * ) imply that one of the following residual possibilities must be verified (see proof of Theorem 2.1):
(S) there is an 1 such that 11”’ is an n-cycle; (y) no permutation rr (‘) is an n-cycle; there is an 1 such that ll(” is the
product of two r-cycles. In this case (3.1) holds with r = s and, by the proof of Lemma 3.3, every ll (4j) is the product of 2cycles.
If (6) holds, then (i) holds by Proposition 3.1. Now let (y) hold and let Z= 1 (without loss of generality). Then we have
.(Pk) Il.,, 1
=‘(Yk) =1 11.a I ’
(3.7)
with p, =pr =o, p,_, = 1, 4” =q,. As .I(,: = 1 for every qk, we obtain, from
I,, .I,, =J,, +, [see (3.2)1,
J,, =J,,.;J 0, ’
J,,.,.JP, =-I,,~
so all the equalities (3.6) are satisfied. The choice of ll(‘) and the condition on the permutations lIcqk) define all matrices Jk. In fact from (3.6) we have
and it is easy to see, from the dislocation of the indices in (3.8) that (n.8) is consistent with ( * ).
Now let A(a) = E;t i Ask Jk and 8, be the space of matrices A(a). Consider the matrix X whose first row [x,, xi . . . x, _l] is the first row of A-‘, computed for a particular choice of ak (say ak = ak~C), and such that X =ZE;I_hxk.lk. As \$ is a group, XAE 2,. Also, the first row of X .A is the first row of the identity. This implies XA = I and X = A i. n
Observe that, if (3.6) holds, then the Jk do not commute with each other. More precisely, the J,, are not commutative and the I,>, do not commute with
CIRCULANT MATRICES 149
the J,,. We can state the following equalities:
Jq;J~=Jp~.Jq,~
J,;J,, =(Jq;J\$
(3.9)
Now we can extend Theorem 4.2 in [2] to the following
THEOREM 3.2. The only spaces of matrices A(a)=8~~~akJk (n=iS.r, 6 E { 1,2}, r a prime ~2) which constitute a commutative algebra are the spaces of the form PTCP where C is circulunt and P is a permutation matrix or the identity.
EXAMPLE 3.1. In the following matrix A(a), Jo, II,. . . , Jn_, obey condi- tion (ii) of Theorem 3.1 and do not commute with each other (more precisely, Ji and J4 do not commute with Jz, J3, J5, and Jz, J3, J5 do not commute with each other):
It is easy to see that ail Jk are defined through the second row [ a4 a, as a2 a, a,] and the equalities Jt = Jt = Jl =I.
REFERENCES
1 Chong-Yun Chao, On circulant matrices, submitted for publication. 2 P. Zellini, On some properties of circulant matrices, Linear Algebra and Appl.
26:31-43 (1979).
Recommended | 7,495 | 20,990 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-18 | latest | en | 0.798005 |
https://cracku.in/148-frac24sqrt1225120-x-sbi-clerk-2015-3 | 1,726,540,443,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651722.42/warc/CC-MAIN-20240917004428-20240917034428-00317.warc.gz | 156,252,098 | 26,077 | Instructions
What will come in place of the question mark (?) in the given question?
Question 148
# $$\frac{24*(\sqrt{1225})}{?}=120$$
Solution
Expression : $$\frac{24*(\sqrt{1225})}{?}=120$$
=> $$\frac{24 \times 35}{x} = 120$$
=> $$x = \frac{24 \times 35}{120}$$
=> $$x = \frac{35}{5} = 7$$ | 115 | 299 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2024-38 | latest | en | 0.541609 |
https://www.freemathhelp.com/forum/threads/how-to-find-the-angle-between-the-major-axis-and-n-ray-of-an-ellipse.130137/ | 1,628,219,229,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152112.54/warc/CC-MAIN-20210806020121-20210806050121-00344.warc.gz | 783,405,059 | 13,450 | # How to find the angle between the major axis and N-ray of an ellipse.
#### LCKurtz
##### Full Member
The standard equation of an ellipse with major axis in the x direction is [MATH]\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1[/MATH]. The focal distance equation is [MATH]c^2 = a^2-b^2[/MATH]. The gradient of the left side of the equation of the ellipse is [MATH]\vec N =\langle \frac{2x}{a^2},\frac{2y}{b^2}\rangle[/MATH] and is perpendicular to the ellipse at [MATH](x,y)[/MATH]. Now, if you know [MATH]\vec N[/MATH], you can find the angle you need. Looking at what you are given and what you need, what are your thoughts?
#### Tom-
##### New member
Rather than using the focal points as inputs, could I save a step using the overall width and height of the ellipse as inputs?
This problem is my own and if I do not need the focal points to solve this I'd prefer to simplify the problem.
The back ground to this question and myself...
Solving this problem will allow me to build it into a spreadsheet where I can solve thousands of these and thus allow the configuration of a tool path on a machine with an overall elliptical form.
I'm not terrifically math savvy, but am willing to learn. I feel like I could work this out if I had graphics that explained the voids in my knowledge.
Maybe it would be better to ask; what is the best approach to this solution?
It seems the focal distance equation may be unnecessary...?
Last edited:
#### LCKurtz
##### Full Member
If you know the lengths of the major and minor semiaxes, [MATH]a[/MATH] and [MATH]b[/MATH], the vector [MATH]\vec N[/MATH] I gave you in post #2 is all you need. You can leave out the 2's and use [MATH]\vec N = \langle \frac{x}{a^2},\frac{y}{b^2}\rangle[/MATH]. Then [MATH]\tan\theta = \frac{yb^2}{xa^2}[/MATH]. You can calculate for as many (x,y) points along the ellipse as you need.
#### Tom-
##### New member
I''l try this in word form to show my interpretation.
major semi is 4
minor semi is 2
random point on the ellipse is x2.0029 y1.7312
Nray equals 2.0029 divided by 16--->0.12518125 and 1.7312 divided by 4--->0.4328
tan theta = (0.4328 times 4 ) / (1.7312 times 16)
tan theta = 1.7312 divided by 2.0029
tan theta = 0.86435
The knowledge gap here is huge. ugh
If tan theta is 0.86435 then I don't see the value...
#### LCKurtz
##### Full Member
You can use Excel's atan2 function to get the angle from the formula. I have attached a little spreadsheet to show you the idea. You input the semi axis values in the green cells, and any x values you want in the first column. The yellow cells are all calculated, so don't put anything in them. The first row illustrates your x value of 2.0029. You can copy the formulas down as many rows as you want. I have just included formulas for the top half of the ellipse. Play with it and let me know if you need more help.
I just discovered that this site won't let me upload a spreadsheet with .xlsx. If you would like to PM me with your email address, I will email it to you. I don't know why I can't just attach it here.
#### LCKurtz
##### Full Member
I'm going to try another way to upload it. I renamed it to nray.pdf. But it is NOT a pdf file. Download it and change the extension to .xlsx from .pdf, then Excel will open it. If that works I won't need to email it to you.
#### Attachments
• nray.pdf
10.6 KB · Views: 3
#### Tom-
##### New member
Thank you. I have access to Excel at work and will try it there tomorrow.
#### LCKurtz
##### Full Member
So, did it work out for you? Do you have any additional questions, or are we done here?
#### Tom-
##### New member
Yes! It works beautifully and is a solution I couldn’t have hoped to ever solve on my own. Thank you-sincerely.
I have gotten very busy with other pursuits and have not yet tried to solve for the other half but hope it is something I can come up with when it is time.
You are very kind to help folks with such things LCKurtz!
Tom-
#### LCKurtz
##### Full Member
You're welcome. For the other half just change the sign of the answer. Same degrees but negative. | 1,116 | 4,065 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2021-31 | latest | en | 0.905972 |
https://brilliant.org/problems/evaluating-a-complex-function/ | 1,618,401,097,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00224.warc.gz | 251,430,809 | 9,759 | # Evaluating a Complex Function
Algebra Level 4
Consider the function $f(x)=\frac {1} {\sqrt {1-x^2} }$ which is defined for all complex numbers apart from 1 and -1. $f^{(2011)} ( \frac {1} {5} )$ has the form $\frac {a\sqrt{b}} {c}$, where $a$ and $c$ are coprime integers and $b$ is not divisible by the square of any prime. What is the value of $a + b +c$?
Details and assumptions
$f^{(n)} (x)$ means that $f$ is applied $n$ times, e.g. $f^{(2)} (x) = f \circ f (x) = f( f( x) )$
× | 179 | 489 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-17 | latest | en | 0.83516 |
https://short-question.com/how-many-edges-does-a-truncated-icosidodecahedron-have/ | 1,696,474,167,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511717.69/warc/CC-MAIN-20231005012006-20231005042006-00561.warc.gz | 558,373,885 | 43,152 | Short-Question
# How many edges does a truncated Icosidodecahedron have?
## How many edges does a truncated Icosidodecahedron have?
180 edges
In the mathematical field of graph theory, a truncated icosidodecahedral graph (or great rhombicosidodecahedral graph) is the graph of vertices and edges of the truncated icosidodecahedron, one of the Archimedean solids. It has 120 vertices and 180 edges, and is a zero-symmetric and cubic Archimedean graph.
How many sides can a polyhedron have?
with
Every polyhedron has three parts: Face: the flat surfaces that make up a polyhedron are called its faces. These faces are regular polygons. Edge: the regions where the two flat surfaces meet to form a line segment are known as the edges….Comprehensive Curriculum.
Name No. of faces
Decahedron A polyhedron with 10 faces
### How many edges does a d20 have?
30
Icosahedron/Number of edges
There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry.
How many vertices does a truncated Icosidodecahedron?
Truncated icosahedral graph
6-fold symmetry schlegel diagram
Vertices 60
Edges 90
Automorphisms 120
#### What polyhedron has 24 edges?
Octagonal prism
Convex uniform polyhedra
Name Vertex type Edges
Cube 4.4.4 12
Pentagonal prism 4.4.5 15
Hexagonal prism 4.4.6 18
Octagonal prism 4.4.8 24
What is a 20 sided object called?
icosagon
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon’s interior angles is 3240 degrees.
## How many faces does an icosidodecahedron have?
How is the icosidodecahedron related to the Johnson solid?
The icosidodecahedron is related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotundae connected as mirror images. The icosidodecahedron can therefore be called a pentagonal gyrobirotunda with the gyration between top and bottom halves.
### Why is the truncated icosidodecahedron called a zonohedron?
Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a zonohedron . The name truncated icosidodecahedron, given originally by Johannes Kepler, is misleading.
Is the icosidodecahedron a pentagonal or gyrobirotunda?
An icosidodecahedron can be split along any of six planes to form a pair of pentagonal rotundae, which belong among the Johnson solids. The icosidodecahedron can be considered a pentagonal gyrobirotunda, as a combination of two rotundae (compare pentagonal orthobirotunda, one of the Johnson solids). | 713 | 2,670 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2023-40 | latest | en | 0.927578 |
https://www.smore.com/t74m | 1,534,867,839,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221218357.92/warc/CC-MAIN-20180821151743-20180821171743-00375.warc.gz | 970,685,839 | 12,378 | # Intermediate Unit 1
## Perimiter
The distance around a shape. Example the perimeter of a square could be 12ft. If each side is 3 ft. long.
## area
The space covered by the inside of the shape ex the area of the square Bob drew was 5 feet.
## Right angle
A 90 degree angle shaped like capital L. | 78 | 302 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2018-34 | longest | en | 0.910585 |
https://oeis.org/A265078/internal | 1,726,239,419,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651523.40/warc/CC-MAIN-20240913133933-20240913163933-00644.warc.gz | 407,877,480 | 3,268 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265078 Partial sums of A072154. 2
%I #10 Sep 08 2022 08:46:14
%S 1,4,9,16,25,37,52,69,88,109,133,160,189,220,253,289,328,369,412,457,
%T 505,556,609,664,721,781,844,909,976,1045,1117,1192,1269,1348,1429,
%U 1513,1600,1689,1780,1873,1969,2068,2169,2272,2377,2485,2596,2709,2824,2941,3061,3184,3309,3436,3565,3697
%N Partial sums of A072154.
%H Colin Barker, <a href="/A265078/b265078.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F G.f.: (1+x)^2*(1-x+x^2)*(1+x+x^2) / ((1-x)^3*(1+x+x^2+x^3+x^4)).
%F a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7). - _Vincenzo Librandi_, Jan 01 2016
%t LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 4, 9, 16, 25, 37, 52}, 60] (* _Vincenzo Librandi_, Jan 01 2016 *)
%o (PARI) Vec((1+x)^2*(1-x+x^2)*(1+x+x^2)/((1-x)^3*(1+x+x^2+x^3+x^4)) + O(x^70)) \\ _Colin Barker_, Jan 01 2016
%o (Magma) I:=[1,4,9,16,25,37,52]; [n le 7 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-5)-2*Self(n-6)+Self(n-7): n in [1..60]]; // _Vincenzo Librandi_, Jan 01 2016
%Y Cf. A072154.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 29 2015
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified September 13 10:55 EDT 2024. Contains 375904 sequences. (Running on oeis4.) | 737 | 1,679 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2024-38 | latest | en | 0.503853 |
http://mathhelpforum.com/advanced-statistics/48965-probability-statistics-help-print.html | 1,519,013,906,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812327.1/warc/CC-MAIN-20180219032249-20180219052249-00373.warc.gz | 223,855,719 | 2,718 | # Probability and statistics help
• Sep 13th 2008, 09:04 PM
cb22hawk
Probability and statistics help
Hey I was wondering if someone could double check my work on this problem:
Consider a disease present in 1 in every 2 members of a population. A diagnostic test for this disease has sensitivity = specificity. Is it true that testing positive and having the disease are independent events? Justify.
Given: P(D l +)
• Sep 14th 2008, 12:10 AM
mr fantastic
Quote:
Originally Posted by cb22hawk
Hey I was wondering if someone could double check my work on this problem:
Consider a disease present in 1 in every 2 members of a population. A diagnostic test for this disease has sensitivity = specificity. Is it true that testing positive and having the disease are independent events? Justify.
Given: P(D l +)
I've double checked and triple checked and can confidently confirm that there's no work here to check.
By the way, I doubt very much that testing positive and having the disease are independent events. | 229 | 1,014 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-09 | longest | en | 0.966465 |
https://www.kidsacademy.mobi/printable-worksheets/age-6-9/learning-skills/basic-math-application/ | 1,721,412,701,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514917.3/warc/CC-MAIN-20240719170235-20240719200235-00212.warc.gz | 755,360,893 | 51,886 | # Basic math application Worksheets for Ages 6-9
Discover engaging and effective Basic Math Application Worksheets for children ages 6-9. Our printable resources are designed to enhance foundational skills and make learning enjoyable. Perfect for both classroom and home use, these worksheets cover essential topics such as addition, subtraction, multiplication, and division. They also include real-world application problems to help young learners understand the practical use of math. With colorful designs and interactive exercises, these worksheets keep kids motivated and eager to learn. Equip your child with the tools they need to succeed in math and build a strong numerical foundation for the future.
Favorites
Interactive
• 6-9
• Basic math application
## Making a Graph: Flowers Worksheet
Kids will love this engaging PDF graph. They'll count flowers and use checkmarks to represent the number on the graph, tangibly seeing the differences in an organized way they contributed to. All while developing their number representation and concrete number sense skills without even realizing it!
Making a Graph: Flowers Worksheet
Worksheet
## Pencil Case Math Worksheet
Show students a picture of simple, colorful objects they know, like pencils and erasers. Ask them to count the objects and identify the equations in the center. Guide them in solving the equations and tracing a line to the correct answer.
Pencil Case Math Worksheet
Worksheet
## Inches, Feet and Yards Worksheet
Explain the size of measurements to your child by comparing them to objects they can visualize. For example, one inch is a bottle cap and one foot is the size of a hammer. Then, explain that one yard is the width of a door. Then, go through worksheets, circling the best estimates for each object's length.
Inches, Feet and Yards Worksheet
Worksheet
## Shape Explosion Worksheet
This worksheet shows students how some shapes explode into two or more equal parts. On the left side are four shapes, each splitting into two or more parts. Ask your child to point out which shape has the smaller share, and help them circle the correct number of shares.
Shape Explosion Worksheet
Worksheet
## Time to Catch the Train Part 1 Worksheet
Time is essential for us; it lets us know when to do various things. Your kids likely wake up at a specified hour and prepare for the school bus. Demonstrate to them that time-telling is vital, and show them there are multiple ways to show time. Point to the time written on the left and the watches in the picture. Assist your children to check the box that corresponds to the time.
Time to Catch the Train Part 1 Worksheet
Worksheet
Learning Skills
Understanding basic math applications from a young age is fundamental for children's overall academic success and daily life skills. For ages 6-9, this period, commonly right after starting school, is a crucial window for developing numeracy skills. These foundational abilities, such as addition, subtraction, multiplication, and division, set the stage for more complex mathematical concepts later on. Educators and parents should prioritize math education because it enhances problem-solving, critical thinking, and logical reasoning skills that are vital for academic subjects beyond math, including science and technology.
Moreover, basic math extends beyond the classroom. It aids children in everyday tasks such as telling time, handling money, and understanding measurements. By mastering these skills early on, children gain confidence in their abilities to manage simple life tasks. This fosters a sense of independence and responsibility. Additionally, early exposure to math can instill a positive attitude towards the subject, reducing math anxiety and promoting enthusiasm for learning.
In summary, an early focus on basic math application equips children with essential skills for academic success and daily living. Parents and teachers are instrumental in creating a positive and supportive learning environment that makes math accessible and enjoyable, thereby laying a strong foundation for future learning stages. | 773 | 4,117 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2024-30 | latest | en | 0.89753 |
https://zxi.mytechroad.com/blog/tag/suffix/ | 1,716,557,275,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058719.70/warc/CC-MAIN-20240524121828-20240524151828-00503.warc.gz | 940,901,515 | 27,840 | # Posts tagged as “suffix”
You are given a 0-indexed integer array nums of length n.
The average difference of the index i is the absolute difference between the average of the first i + 1 elements of nums and the average of the last n - i - 1 elements. Both averages should be rounded down to the nearest integer.
Return the index with the minimum average difference. If there are multiple such indices, return the smallest one.
Note:
• The absolute difference of two numbers is the absolute value of their difference.
• The average of n elements is the sum of the n elements divided (integer division) by n.
• The average of 0 elements is considered to be 0.
Example 1:
Input: nums = [2,5,3,9,5,3]
Output: 3
Explanation:
- The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3.
- The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2.
- The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2.
- The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0.
- The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1.
- The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4.
The average difference of index 3 is the minimum average difference so return 3.
Example 2:
Input: nums = [0]
Output: 0
Explanation:
The only index is 0 so return 0.
The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 0.
Constraints:
• 1 <= nums.length <= 105
• 0 <= nums[i] <= 105
Solution: Prefix / Suffix Sum
Time complexity: O(n)
Space complexity: O(1)
## C++
You and a gang of thieves are planning on robbing a bank. You are given a 0-indexed integer array security, where security[i] is the number of guards on duty on the ith day. The days are numbered starting from 0. You are also given an integer time.
The ith day is a good day to rob the bank if:
• There are at least time days before and after the ith day,
• The number of guards at the bank for the time days before i are non-increasing, and
• The number of guards at the bank for the time days after i are non-decreasing.
More formally, this means day i is a good day to rob the bank if and only if security[i - time] >= security[i - time + 1] >= ... >= security[i] <= ... <= security[i + time - 1] <= security[i + time].
Return a list of all days (0-indexed) that are good days to rob the bank. The order that the days are returned in does not matter.
Example 1:
Input: security = [5,3,3,3,5,6,2], time = 2
Output: [2,3]
Explanation:
On day 2, we have security[0] >= security[1] >= security[2] <= security[3] <= security[4].
On day 3, we have security[1] >= security[2] >= security[3] <= security[4] <= security[5].
No other days satisfy this condition, so days 2 and 3 are the only good days to rob the bank.
Example 2:
Input: security = [1,1,1,1,1], time = 0
Output: [0,1,2,3,4]
Explanation:
Since time equals 0, every day is a good day to rob the bank, so return every day.
Example 3:
Input: security = [1,2,3,4,5,6], time = 2
Output: []
Explanation:
No day has 2 days before it that have a non-increasing number of guards.
Thus, no day is a good day to rob the bank, so return an empty list.
Example 4:
Input: security = [1], time = 5
Output: []
Explanation:
No day has 5 days before and after it.
Thus, no day is a good day to rob the bank, so return an empty list.
Constraints:
• 1 <= security.length <= 105
• 0 <= security[i], time <= 105
## Solution: Pre-Processing
Pre-compute the non-increasing days at days[i] and the non-decreasing days at days[i] using prefix and suffix arrays.
Time complexity: O(n)
Space complexity: O(n)
## C++
KMP Algorithm, KMP 字符串搜索算法
Time complexity: O(m+n)
Space complexity: O(m)
## Applications
LeetCode 28. strStr()
## C++
LeetCode 459. Repeated Substring Pattern
## C++
1392. Longest Happy Prefix
## C++
Given a string s, return the last substring of s in lexicographical order.
Example 1:
Input: "abab"
Output: "bab"
Explanation: The substrings are ["a", "ab", "aba", "abab", "b", "ba", "bab"]. The lexicographically maximum substring is "bab".
Example 2:
Input: "leetcode"
Output: "tcode"
Note:
1. 1 <= s.length <= 10^5
2. s contains only lowercase English letters.
Key observation: The last substring must be a suffix of the original string, can’t a substring in the middle since we can always extend it.
e.g. leetcode -> tcode, can’t be “t”, “tc”, “tco”, “tcod”
## Solution 1: Brute Force
Try all possible suffixes.
Time complexity: O(n^2)
Space complexity: O(1)
## Solution 2: Keep max and compare with candidates
Find the first largest letter as a starting point, whenever there is a same letter, keep it as a candidate and compare with the current best. If the later is larger, take over the current best.
e.g. “acbacbc”
“c” > “a”, the first “c” becomes the best.
“c” = “c”, the second “c” becomes a candidate
starting compare best and candidate.
“cb” = “cb”
“cba” < “cbc”, cand_i is the new best.
Time complexity: O(n)
Space complexity: O(1)
# Problem
Given a list of words, we may encode it by writing a reference string S and a list of indexes A.
For example, if the list of words is ["time", "me", "bell"], we can write it as S = "time#bell#" and indexes = [0, 2, 5].
Then for each index, we will recover the word by reading from the reference string from that index until we reach a “#” character.
What is the length of the shortest reference string S possible that encodes the given words?
Example:
Input: words = ["time", "me", "bell"] Output: 10 Explanation: S = "time#bell#" and indexes = [0, 2, 5].
Note:
1. 1 <= words.length <= 2000.
2. 1 <= words[i].length <= 7.
3. Each word has only lowercase letters.
# Idea
Remove all the words that are suffix of other words.
# Solution
Time complexity: O(n*l^2)
Space complexity: O(n*l) | 1,942 | 6,013 | {"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} | 3.796875 | 4 | CC-MAIN-2024-22 | latest | en | 0.649842 |
https://www.teachoo.com/3639/699/Ex-5.3--8---Find-dy-dx-in--sin2-x---cos2-y--1---Class-12/category/Ex-5.3/ | 1,723,231,596,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640768597.52/warc/CC-MAIN-20240809173246-20240809203246-00660.warc.gz | 806,827,044 | 22,121 | Ex 5.3
Chapter 5 Class 12 Continuity and Differentiability
Serial order wise
### Transcript
Ex 5.3, 8 Find ππ¦/ππ₯ in, sin2 π₯ + cos2 π¦ = 1 sin2 π₯ + cos2 π¦ = 1 Differentiating both sides π€.π.π‘.π₯ . (π (sin2 π₯ + cos2 π¦))/ππ₯ = (π (1))/ππ₯ (π (sin2 π₯))/ππ₯ + (π (cosβ‘2 π¦))/ππ₯ = 0 Calculating Derivative of sin2 π₯ & cos^2 π¦ sepretaly Finding Derivative of ππππ π (π (sin2 π₯))/ππ₯ =2γ π ππγ^(2β1) π₯ . (π(sin^2β‘π₯))/ππ₯ =2 sinβ‘π₯ . (π(sinβ‘π₯))/ππ₯ (Derivative of constant is 0) =2 sinβ‘γπ₯ γ cosγβ‘π₯ γ Finding Derivative of γπππγ^π π (π (cos2 π¦))/ππ₯ =2γcosβ‘π¦γ^(2β1) ". " π/ππ₯ " "(cosβ‘π¦) =2 cosβ‘π¦ . (βsinβ‘π¦) . (π(π¦))/ππ₯ =β 2 cosβ‘π¦ sinβ‘π¦ . ππ¦/ππ₯ Now, (π (sin2 π₯))/ππ₯+ (π (cos2 π¦))/ππ₯ = 0 2 sinβ‘π₯ .cosβ‘π₯ + (β 2 cosβ‘π¦ sinβ‘π¦ ". " ππ¦/ππ₯)= 0 2 sinβ‘π₯ .cosβ‘π₯ β 2 sinβ‘π¦β‘γ .γ cosβ‘π¦ . ππ¦/ππ₯ = 0 β 2 sinβ‘π¦β‘γ .γ cosβ‘π¦ . ππ¦/ππ₯ = β 2 sinβ‘π₯ cosβ‘π₯ β sinβ‘2π¦β‘γ .γ ππ¦/ππ₯ = β sinβ‘2π₯ ππ¦/ππ₯ = γβ sinγβ‘2π₯/(βsinβ‘2π¦ ) π
π/π
π = πππβ‘ππ/πππβ‘ππ (2 sin x cos x = sin 2x) | 1,060 | 1,458 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2024-33 | latest | en | 0.496497 |
https://www.studypool.com/discuss/254762/trigonometry-assignment-6 | 1,477,172,462,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719045.47/warc/CC-MAIN-20161020183839-00383-ip-10-171-6-4.ec2.internal.warc.gz | 993,591,024 | 752,210 | # Trigonometry Assignment 6
Oct 14th, 2014
RockCafe
Category:
Mathematics
Price: \$5 USD
Question description
1. Side c is best described as ________________________.
a right angle a leg a hypotenuse an acute angle
3 points
1.
3 points
### QUESTION 3
1. What is the trigonometric ratio for ?
3 points
### QUESTION 4
1. What is the trigonometric ratio for ?
3 points
### QUESTION 5
1. What is the trigonometric ratio for ?
3 points
### QUESTION 6
1. Find the length of b. Round your answer to the nearest tenth.
7.9 units 12.7 units 9.4 units 13.6 units
3 points
### QUESTION 7
1. Find the length of c. Round your answer to the nearest tenth.
11.1 units 16.7 units 20.2 units 22.4 units
3 points
### QUESTION 8
1. Find . Round your answer to the nearest whole degree.
37° 53° 64° 90°
3 points
### QUESTION 9
1. Find . Round your answer to the nearest whole degree.
15° 29° 51° 90°
(Top Tutor) Daniel C.
(997)
School: Duke University
Studypool has helped 1,244,100 students
## Review from our student for this Answer
FratBro23
Oct 16th, 2014
"Excellent work as usual"
Type your question here (or upload an image)
1819 tutors are online
Brown University
1271 Tutors
California Institute of Technology
2131 Tutors
Carnegie Mellon University
982 Tutors
Columbia University
1256 Tutors
Dartmouth University
2113 Tutors
Emory University
2279 Tutors
Harvard University
599 Tutors
Massachusetts Institute of Technology
2319 Tutors
New York University
1645 Tutors
Notre Dam University
1911 Tutors
Oklahoma University
2122 Tutors
Pennsylvania State University
932 Tutors
Princeton University
1211 Tutors
Stanford University
983 Tutors
University of California
1282 Tutors
Oxford University
123 Tutors
Yale University
2325 Tutors | 521 | 1,798 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2016-44 | longest | en | 0.687193 |
https://gmatclub.com/forum/profile-evaluation-7yrs-of-international-experience-in-oil-158457.html | 1,490,877,843,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218194600.27/warc/CC-MAIN-20170322212954-00404-ip-10-233-31-227.ec2.internal.warc.gz | 795,987,259 | 52,668 | Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club
It is currently 30 Mar 2017, 05:44
# Expecting:
R2 Admission Decisions from Wharton: Join Chat Room 3
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Profile evaluation (7yrs of international experience in Oil)
Author Message
Intern
Joined: 06 Apr 2013
Posts: 11
Followers: 0
Kudos [?]: 0 [0], given: 0
Profile evaluation (7yrs of international experience in Oil) [#permalink]
### Show Tags
23 Aug 2013, 07:39
Hi Team,
I am 28yrs old, Indian male. Mechanical engineering from IIT. GPA: 7/10
In a bit of confusion. I had a GMAT score of 710 ( q:50 v:36) . Took this test in 2010. I appeared for it again 2 days back and stupidly scored 660 (foolishness).
Working in one of the largest Oil&Gas service company since 7 years on international/expat assignment. Worked in Asia, Middle East, US, Africa and UK till now. Enough leadership and international experience in every location.
The only schools I was targeting were Harvard , MIT and INSEAD, however with this screw up with GMAT, I am bit disappointed.
I have quick questions: Will they consider ONLY the higher score (710). Even in that the verbal % is in 50s , is it realistic to get into Harvard/MIT with strong apps ?
Joined: 20 Apr 2003
Posts: 5513
Location: Los Angeles CA
Followers: 77
Kudos [?]: 539 [0], given: 74
Re: Profile evaluation (7yrs of international experience in Oil) [#permalink]
### Show Tags
25 Aug 2013, 21:41
aanchi01 wrote:
Hi Team,
I am 28yrs old, Indian male. Mechanical engineering from IIT. GPA: 7/10
In a bit of confusion. I had a GMAT score of 710 ( q:50 v:36) . Took this test in 2010. I appeared for it again 2 days back and stupidly scored 660 (foolishness).
Working in one of the largest Oil&Gas service company since 7 years on international/expat assignment. Worked in Asia, Middle East, US, Africa and UK till now. Enough leadership and international experience in every location.
The only schools I was targeting were Harvard , MIT and INSEAD, however with this screw up with GMAT, I am bit disappointed.
I have quick questions: Will they consider ONLY the higher score (710). Even in that the verbal % is in 50s , is it realistic to get into Harvard/MIT with strong apps ?
The will evaluate your application using the 710, but they will see both scores. And if you got in the 50 in the verbal, that could be a red flag for these elite programs. INSEAD used to take the highest score on the quant and the highest score on the verbal, so you may be in better shape there.
Linda
_________________
Linda Abraham
Accepted ~ The Premier Admissions Consultancy
310-815-9553
Co-Author of: MBA Admission for Smarties: The No-Nonsense Guide to Acceptance at Top Business Schools
Subscribe to Accepted's Blog
Re: Profile evaluation (7yrs of international experience in Oil) [#permalink] 25 Aug 2013, 21:41
Similar topics Replies Last post
Similar
Topics:
Profile evaluation - GMAT(690) & 7Yr experience (IB & Consulting) 0 01 Dec 2014, 21:37
Profile evaluation - GMAT(690) & 7Yr experience (IB & Consulting) 3 01 Dec 2014, 21:28
Profile evaluation - GMAT(690) & 7Yr experience (IB & Consulting) 1 01 Dec 2014, 20:48
MBA profile evaluation (7yrs ,Indian, Oil&Gas) 1 23 Aug 2013, 07:40
MBA profile evaluation (7yrs ,Indian, Oil&Gas) 1 23 Aug 2013, 07:39
Display posts from previous: Sort by | 1,058 | 3,936 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2017-13 | longest | en | 0.906283 |
https://www.learnitwithmrc.co.uk/includes/LO_style/lesson_template/?name=30 | 1,624,351,511,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488512243.88/warc/CC-MAIN-20210622063335-20210622093335-00329.warc.gz | 757,849,253 | 6,560 | Computing
Computer Science LearnITWithMrC ⛯ Year 7 Year 8 Year 9 GCSE
Lesson Video 30
• Watch the Lesson video
Make notes on your notes sheet.
Make notes on your notes sheet.
• Complete the learning activities
Make any notes on your notes sheet.
• Check the Learning outcomes
What do I need to Learn?
I need to learn how to explain what data validation is.
Key Terms
validation validation checks Verification Type check Format check Length check Presence check Range check Lookup check Check digit
Data Validation - Learning Activities
Database validation is a process where the data entered in the database is checked to make sure that it is correct. The purpose of validation is to make sure that data is logical, rational, complete and within acceptable limits.
There are a range of validation methods like range check, type check etc. (see table in notes for more details)
A range check is probably the simplest validation method to understand. We give the user a range of values that are valid to enter then check they have entered a value in that range.
For example we could ask the user to enter a number between 1 and 10. Our validation routine would then check if the value entered was in that range. If the user entered say the number 11 our code should declare the value 'invalid' and ask the user to enter another value
Range Check – generally used when working with data which contains numbers, currency or date and time.
A range check lets you set appropriate limits:
Boundary Description Validation
Upper limit The maximum value is 10. <=10
Lower limit The minimum value is 1. >=1
A range Number entered must be less than or equal to 10 but greater than or equal to 1. >=1 and <=10
Data Validation in practice
I have coded the simple example above using a function called data validation. Run the code and check that it works. | 393 | 1,858 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2021-25 | latest | en | 0.867584 |
http://www.physicsforums.com/showthread.php?p=4122612 | 1,369,085,670,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699238089/warc/CC-MAIN-20130516101358-00018-ip-10-60-113-184.ec2.internal.warc.gz | 655,018,687 | 12,240 | Scaling an Axial Compressor
Let's say I have a precisely designed axial compressor, comprising of stages of rotor and stator wheels, that resembles something like this:
Such a compressor, driven by a certain torque at a certain RPM, will deliver a certain air mass per time at a certain pressure. Now, what happens if the compressor is scaled down, so that the diameter is half of what it used to be but all other angles, etc. remain the same? The RPM will be such that the speed of the blade tips is the same in both compressors, i.e. the RPM will be higher in the smaller engine.
My intuition and some quick calculations tell me that the pressure ratio will remain the same, the mass flow will be divided by 4 (since cross sectional area is divided by 4), and the torque will be divided by 8 (since I think power will be divided by 4 and RPM will be doubled). But, again, I'm not sure, and I'd like to be. Can anyone help? Thanks!
PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
Bump.
In axial and centrifugal compressors, you keep the peripheral speed when scaling. This keeps the gas pressure and as well the mechanical stress. So: angular speed *2 pressure *1 mass flow /4 torque /8 power /4 (consistent with the mass flow) Needless to say, some technological reasons speak against easy scaling, for instance leakage, Reynolds... The combustion chamber is also more difficult to build.
Scaling an Axial Compressor
Quote by Enthalpy In axial and centrifugal compressors, you keep the peripheral speed when scaling. This keeps the gas pressure and as well the mechanical stress. So: angular speed *2 pressure *1 mass flow /4 torque /8 power /4 (consistent with the mass flow) Needless to say, some technological reasons speak against easy scaling, for instance leakage, Reynolds... The combustion chamber is also more difficult to build.
That makes sense, thanks. I wasn't sure if it scaled that linearly, and it probably doesn't, but that kind of simplification is probably OK for only cutting the diameter in half. Maybe it would be smart to approximate that it will need about 2% more power than predicted, and have 2% less throughput, due to gap losses etc., too. I looked at the Reynolds number a little, and it doesn't seem like it will matter that much. In the smaller engine air should be a little less turbulent.
Happy you if you can predict flows to 2%...
Quote by Enthalpy Happy you if you can predict flows to 2%...
I have a chart of gap loss to gap width. A .07 mm width gives a gap loss of around .7%. Relative to the compressor, then, if the gap is around .07 mm, the gap will double relative to the size of the compressor since it's difficult to get the gap smaller at this size. I made a few estimates and quick calculations, and am coming up with around a 1.3% additional loss. I just decided to round up since there will probably be some other losses from building at a smaller scale since the tolerances of manufactured parts won't scale.
In general, when the length of the blades gets down to one inch, it is time to switch to a centrifugal stage. At that point the efficiency of the axial stage will be less than the centrifugal stage. Efficiency is not as simple as you say. It is a function of tip clearance/blade length ratio. But tip clearance is pretty constant regardless of length. The blade packing density also gets too high for the smaller disks. That can lead to surge problems. If you compare sections of real engines, you will see that the front of the flow path for an axial compre ssor looks very much like the flow path of a centrifugal compressor. That is because it is a hybrid design. That is something the engineers learned fairly recently to combine the physics of both into one for better overall efficiency.
Recognitions:
Quote by Pkruse If you compare sections of real engines, you will see that the front of the flow path for an axial compressor looks very much like the flow path of a centrifugal compressor.
Can you give a link to a drawing of that concept?
Probably. But not from this phone. I'll get back to my computer tonight.
Quote by Pkruse In general, when the length of the blades gets down to one inch, it is time to switch to a centrifugal stage. At that point the efficiency of the axial stage will be less than the centrifugal stage. Efficiency is not as simple as you say. It is a function of tip clearance/blade length ratio. But tip clearance is pretty constant regardless of length. The blade packing density also gets too high for the smaller disks. That can lead to surge problems. If you compare sections of real engines, you will see that the front of the flow path for an axial compre ssor looks very much like the flow path of a centrifugal compressor. That is because it is a hybrid design. That is something the engineers learned fairly recently to combine the physics of both into one for better overall efficiency.
It actually turns out that's not really the case. It's a common misconception of the model jet engine community that axial compressors are not efficient at that size. The very best small jet engines use axial compressors. Also, you can't buy any centrifugal compressor wheels that small, and it's easier/cheaper to make an axial compressor than a centrifugal one.
Then it is a misconception commonly held by all the engineers who design engines for real airplanes. I don't think you can name one engine currently in production in significant numbers that I can't in five minutes walk to the desk of at least one engineer who was on the design team. If I told any one of them that, then they would strongly disagree. As for engines on small model toys, I yield to your much better understanding. I don't know anything about them at all.
Quote by Pkruse Then it is a misconception commonly held by all the engineers who design engines for real airplanes. I don't think you can name one engine currently in production in significant numbers that I can't in five minutes walk to the desk of at least one engineer who was on the design team. If I told any one of them that, then they would strongly disagree. As for engines on small model toys, I yield to your much better understanding. I don't know anything about them at all.
As for the misconception, I was talking about the model community. What about Bladon Jets? A smaller company I believe, but their engine puts out 90+ lbs of thrust with a 4.5 in diameter, and there aren't any centrifugal stages. The very best centrifugal model engines put out ~47 lbs of thrust at that size. | 1,442 | 6,714 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-20 | latest | en | 0.927643 |
https://brainly.in/question/123276 | 1,485,139,993,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281746.82/warc/CC-MAIN-20170116095121-00393-ip-10-171-10-70.ec2.internal.warc.gz | 802,806,652 | 10,551 | # Mr. Sharma borrowed Rs 24,000 at 13% per annum simple interest and an equal sum at 12% per annum compound interest . Find the total interest earned by Mr. Sharma in two years?
2
by raniabsmarkoserani
total interest earned is zero as Mr Sharma borrowed money .. so he has to pay the interest ..
The question needs to be modified ? Kindly check and rephrase your question!! Thank You??
2015-06-04T23:31:46+05:30
P=24000,R=13,T=2
SI=(P×R×T)/100
=(24000×13×2)/100=6240
COMPOUND INTEREST R=12%
A=P(1+R/
100)²
=24000(1+12/100)²
=24000×(56/50)²
=24000×3136/2500
=48×3136/5
=30105.6
CI=A-P=30105.6-24000=6105.6
CI+SI=6105.6+6240=12345.6
interest earned??
thanks
2015-06-05T11:29:06+05:30
The question should be:
Mr. Sharma borrowed Rs 24,000 at 13% per annum simple interest and an equal sum at 12% per annum compound interest . Find the total interest given by Mr.Sharma in two years?
Solution:
For SI, P=Rs.24000 , R=13 % p.a. , T=2 years.
⇒SI=24000*13*2/100
⇒SI=Rs.6240.
For CI , P=Rs.24000 , R=12% , T=2 years.
⇒A=P(1+R/100)²
⇒A=24000(1+12/100)²
⇒A=24000(28/25)²
⇒A=24000*28/25*28/25
⇒A=Rs.30105.6.
⇒CI=A-P=30105.6-24000=Rs.6105.6.
⇒Total interest given by him=6240+6105.6
=Rs.12345.6
Ans:The total interest paid by him is 12345.6.
Click on the yellow button above please | 519 | 1,276 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-04 | latest | en | 0.826399 |
https://prepinsta.com/interview-preparation/puzzle/bank-cashier-mistake/ | 1,611,227,533,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703524743.61/warc/CC-MAIN-20210121101406-20210121131406-00477.warc.gz | 517,777,580 | 22,004 | Prime
#### Prepinsta Prime
Video courses for company/skill based Preparation
(Check all courses)
Get Prime Video
Prime
#### Prepinsta Prime
Purchase mock tests for company/skill building
(Check all mocks)
Get Prime mock
# Bank Cashier Mistake Puzzle
## Bank Cashier Mistake
You went to a bank to cash out your cheque.
By mistake the bank cashier gives you-
• Dollar amount in cent, and
• Cent amount in dollars.
On the way home you spends 5 cent, and then suddenly you notices that you have twice the amount of your cheque.
How much was have you written on cheque ?
## Solution
Method : Lets assume Cent = z and \$ = 100z , no. of dollars =x and no.of cents = y
So,Initially he had 100zx + zy
Now after cashier’s mistake it becomes 100zy + zx
After spending 5 cents it becomes double
So now equation is 100zy + zx -5z = 200zx + 2zy
or 199x = 98y -5
Now,value of y cannot be greater than 100 (otherwise it becomes \$)
so plotting values of y for 1 to 100,we get only 1 integer value for x i.e. 31 for y = 63
Hence the answer 31\$ and 63 cents | 290 | 1,060 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2021-04 | longest | en | 0.883829 |
http://www.convertit.com/Go/WaveQuest/Measurement/Converter.ASP?From=depth | 1,558,489,215,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256600.32/warc/CC-MAIN-20190522002845-20190522024845-00121.warc.gz | 258,383,240 | 3,624 | Riding the internet wave!
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: ```length = 1 meter (length) ``` Related Measurements: Try converting from "depth" to angstrom, archin (Russian archin), bottom measure, cable length, chain (surveyors chain), ell, en (typography en), engineers chain, finger, Greek palm, Greek span, Israeli cubit, ken (Japanese ken), micron, nautical league, nautical mile, parsec, shaku (Japanese shaku), stadium (Roman stadium), verst (Russian verst), or any combination of units which equate to "length" and represent depth, fl head, height, length, wavelength, or width. Sample Conversions: depth = .02818591 actus (Roman actus), 551.18 agate (typography agate), 118.11 barleycorn, 4.37 cloth quarter, .87489064 ell, 44.99 finger, .01093613 football field, .00497097 furlong (surveyors furlong), .54020415 Greek fathom, 4.32 Greek span, 9.84 hand, .47206329 ken (Japanese ken), 472.44 line, 3.38 Roman foot, .00067577 Roman mile, .16404199 rope, .00911344 skein, 33 sun (Japanese sun), 3.28 survey foot, .00062137 UK mile (British mile).
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 439 | 1,623 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2019-22 | latest | en | 0.703528 |
https://hangerspur.com/ncert-solutions/ncert-solutions-class-7-maths-chapter-13-exponents-and-powers/--24-7506c1a | 1,652,947,063,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00473.warc.gz | 355,739,708 | 13,669 | Home
# Exponents and Powers Class 8 test Paper
Online Test for Class 8 Maths Exponents and Powers . Question 1: The Base in the expression 8 100 is. 10. 100 . 8. 800. Correct Option is : 3. Solution : When a number is in the form x n , then x is the base and n is the exponent of this number. So in 8 100 , base is 8. Question 2 Important questions for class 8 maths chapter 12 - exponents and powers, with solutions are provided here by our subject experts. Practice these questions to score better marks in the exam as it covers the latest CBSE syllabus (2020-2021) and is as per NCERT book/curriculum.. The chapter exponents and powers will explain to represent very large numbers or very small numbers in a standard form These Worksheets for Grade 8 Exponents and Powers, class assignments and practice tests have been prepared as per syllabus issued by CBSE and topics given in NCERT book 2021. Class 8 Exponents and Powers test papers for all important topics covered which can come in your school exams, download in pdf free Free PDF Download - Best collection of CBSE topper Notes, Important Questions, Sample papers and NCERT Solutions for CBSE Class 8 Math Exponents and Powers. The entire NCERT textbook questions have been solved by best teachers for you Free Online Mock Test for CBSE Class 8 Exponents and Powers for important topics of all chapters in CBSE Class 8 Exponents and Powers book. Access full series of free online mock tests with answers from Exponents and Powers Class 8. Do tests many times and check your score and download certificate.Doing mock online tests will help you to check your understanding and identify areas of improvement
### Free CBSE Online Test Class 8 Maths Exponents and Power
• exponents and powers class 8 test paper . MCQ Questions for Class 8 Maths Chapter 12 Exponents and Powers with Answers. July 30, 2021 by ncertcareer. Search for: Taro's Reward Class 6 MCQ Questions with Answers English Chapter 3; How the Dog Found Himself a New Master? Class 6 MCQ Questions with Answer
• Aug 02,2021 - Olympiad Test: Exponents And Powers -1 | 20 Questions MCQ Test has questions of Class 8 preparation. This test is Rated positive by 85% students preparing for Class 8.This MCQ test is related to Class 8 syllabus, prepared by Class 8 teachers
• Get Notes Here - https://payments.pabbly.com/subscribe/5e2954ad14a2e43f1110d5ef/notes Class: 8thSubject: MathsChapter: Exponents and PowersTopic Name: Expone..
• Exponents Class 8 Maths Online Quiz/MCQ. Exponents are also known as Indices. In general sense we can call them 'Powers' to understand it easily. This online quiz from the online Maths quiz series comprises multiple choice questions on the chapter Exponents. This quiz will help you remember the concepts, laws and rules of exponents
### Important Questions Class 8 Maths Chapter 12 Exponents And
1. Exponents and Powers Class 8 Extra Questions Maths Chapter 12 Extra Questions for Class 8 Maths Chapter 12 Exponents and Powers Exponents and Powers Class 8 Extra Questions Very Short Answer Type Question 1. Find the multiplicative inverse of: (i) 3-3 (ii) 10-10 Solution: Question 2. Expand the following using exponents. (i) 0.0523 (ii) 32.005 [
2. g for high marks in their exa
3. Are you confused while solving problems on Exponents & Powers Class 8? Do not worry, Visit Math Square and learn what is Exponents & Powers Class 8 and how to solve problems on Class 8 Exponents & Powers
4. Exponents and Powers worksheet for class 8 in PDF for free download. Maths worksheets on Exponents and Powers as per NCERT syllabus. test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers
5. Chapter Tests for the Exponents And Powers, CBSE Class 8 MATH, Rational Numbers
Exponents and Powers RS Aggarwal ICSE Class-8th Mathematics Goyal Brothers Prakashan Chapter-2 Solutions. We provide step by step Solutions of Exercise / lesson-2 Exponents and Powers for ICSE Class-8 RS Aggarwal Mathematics. Our Solutions contain all type Questions with Exe-2 A, Exe-2 B (MCQ) and Mental maths to develop skill and confidence The Exponents and Powers Class 8 Important Questions that are available on the official website of Vedantu are surely the most reliable online resource. The Class 8 Maths Chapter 12 Important Questions listed on the platform have the most relevant questions and the most accurate answers, from an exam point of view Here you can get Class 8 Important Questions Maths based on NCERT Text book for Class VIII. Maths Class 8 Important Questions are very helpful to score high marks in board exams. Here we have covered Important Questions on Exponents and Powers for Class 8 Maths subject. Maths Important Questions Class 8 are given below
### Worksheets for Class 8 Exponents and Power
Get Exponents and Powers, Mathematics Chapter Notes, Questions & Answers, Video Lessons, Practice Test and more for CBSE Class 10 at TopperLearning E xponent or power is a mathematical representation that indicates the number of times that a number is multiplied by itself. If a number is multiplied by itself m times, then it can be written as: a x a x a x a x a...m times = a^m. 8th Exponent and Power CBSE Test Paper - 01. File Size: 577 kb. File Type
### CBSE 8 Math CBSE- Exponents and Powers, Free Test Papers
1. Class 8 math (India) Unit: Exponents and powers. 0. Legend (Opens a modal) Multiply & divide powers (integer exponents) Get 5 of 7 questions to level up! Powers of products & quotients Unit test. Level up on all the skills in this unit and collect up to 900 Mastery points
2. Exponents and Powers 12CHAPTER Exponent is a negative integer. in Class VII for positive exponents only. -5 is the sum of two exponents - 3 and - 2 (- 4) + (-3) = - 7 Thickness of a piece of paper is 0.0016 cm. 11. Diameter of a wire on a computer chip is 0.000003 m
3. Exponents RS Aggarwal Class 8 Maths Solutions Exercise 2A . Exponents RS Aggarwal Class 8 Maths Solutions Exercise 2A. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13. For More Resources. RS Aggarwal Class 8 Solutions; RS Aggarwal Maths Class 8 Exponents RS Aggarwal CCE Test Papers.
Access the Formula Sheet of Exponents and Powers Class 8 covering numerous concepts and use them to solve your Problems effortlessly. The numbers with negative exponents also obey the following laws: A number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10 Get Revision notes of Class 8th Mathematics Chapter 12 Exponents and powers to score good marks in your Exams. Our notes of Chapter 12 Exponents and powers are prepared by Maths experts in an easy to remember format, covering all syllabus of CBSE, KVPY, NTSE, Olympiads, NCERT & other Competitive Exams
Exponents and Powers: Questions 1-13 of 61. Get to the point IMO Level 1- Mathematics Olympiad (SOF) Class 8 questions for your exams Filed Under: Class 8, Mathematics, RS Aggarwal Tagged With: CBSE Class 8 RS Aggarwal Maths Solutions, RS Aggarwal CBSE Class 8 Maths Time and Work, RS Aggarwal Class 8 Maths Solutions, RS Aggarwal Class 8 Time and Work, RS Aggarwal Math Solutions, RS Aggarwal Maths Class 8 Time and Work RS Aggarwal CCE Test Papers, RS Aggarwal Time and Work.
Important Class 8 of Exponents Questions and Answers Paper. Get top class preparation for IMO-Level-2 right from your home: fully solved questions with step-by-step explanation - practice your way to success. Simplify and express the result in power notation with positive exponent. i. Find the value of Class 8 Maths Chapter 12 (Exponents and Powers) MCQs are available online for students. These objective questions are designed by experts, according to CBSE syllabus (2020-2021) and NCERT guidelines. The chapter-wise multiple-choice questions are available, to make students learn each concept and lead them to score good marks in exams
CBSE 8th Class Mathematics Chapter Exponent Power and Radicals and Scientific Notation CBSE TEST PAPER - 01 1. Express 256 as a power 4. (a) 48 (b) 28 4 (c) 4 (d) none of these 2. Express 729 as a power of 3 (a) 38 6 (b) 3 (c) 93 (d) none of these 3.Express 432 as a product of powers of prime factors Get Notes Here - https://payments.pabbly.com/subscribe/5e2954ad14a2e43f1110d5ef/notes Class: 8th Subject: Maths Chapter: Exponents and Powers Topic Name: Exp..
CBSE chapter wise Printable Worksheets with solution for class 8 Mathematics chapter 12 Exponents and Powers for free download in PDF format. 8th Mathematics chapter 12 Exponents and Powers have many topics. All these topics are included in CBSE solved Printable Worksheets of class 8 Mathematics chapter Exponents and Powers Practice Question for the Exponents And Powers, CBSE Class 8 MATH, Model Test Exponents RS Aggarwal Class 8 Maths Solutions CCE Test Paper. September 28, 2016 by Phani Raju
### Online mock tests CBSE Class 8 Exponents and Power
Hello friends in this video I have shared an activity to explain Power of Product Law by Paper Folding Activity , I hope you would like my efforts Thank Exponent and Power (Radicals) for class 8. 29/3/2014. 1 Comment. Negative integral Exponents, Laws of integral Exponents, Expressing Numbers in the Standard Form, Converting Numbers from Standard Form to Usual Form. Start your preparation ICSE 8 Maths > Question Paper. Revision Notes Learning Material. ICSE 8 Maths ICSE 8 Maths Question Paper is a very important resource for students preparing for examination. Solving these question papers helps students get familiar with the pattern and time required to tackle their final exams. PDF.js viewer
### exponents and powers class 8 test paper Archives » NCERT
Read and download free pdf of CBSE Class 8 Mathematics Exponents And Powers Worksheet Set A. Students and teachers of Class 8 Exponents and Powers can get free printable Worksheets for Class 8 Exponents and Powers in PDF format prepared as per the latest syllabus and examination pattern in your schools. Standard 8 students should practice questions and answers given here for Exponents and. Students can also refer to NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers for better exam preparation and score more marks. Exponents and Powers Class 8 MCQs Questions with Answers. Question 1. a m x a m is equal to (a) a m+n (b) a m-n (c) a mn (d) a n-m. Answer. Answer: (a) a m+n Hint: Formul ICSE Selina Class 8 Maths Solution of Chapter Exponents (Powers) is given here. The topics mentioned in the chapter explains about power which means a product of multiplying a number by itself which is usually represented with a base number and an exponent. The topic Laws of exponent with integral powers explains about three laws which. With our ICSE Class 8 Mathematics online learning materials, revise the laws of exponents. Also, practise exponents with our online mock tests. Relearn exponents by utilising our ICSE Maths Class 8 sample papers with solutions. During the revision of exponents, you may have doubts while trying to learn to simplify a given equation
### Olympiad Test: Exponents And Powers -1 20 Questions MCQ Tes
1. Download free CBSE Sample paper for Class 8, Math. A collection of questions on CBSE- Squares and Square Roots with solutions created by best teachers are available as a PDF download
2. Ex 12.1 Class 8 Maths Question 1. Ex 12.1 Class 8 Maths Question 2. Simplify and express the result in power notation with a positive exponent. Ex 12.1 Class 8 Maths Question 3. Ex 12.1 Class 8 Maths Question 4. Ex 12.1 Class 8 Maths Question 5. Find the value of m for which 5 m ÷ 5 -3 = 5 5. Ex 12.1 Class 8 Maths Question 6
3. MCQ Questions for Class 8 Maths with Answers: Central Board of Secondary Education (CBSE) has declared a major change in the Class 8 exam pattern from 2020.Practicing & preparing each and every chapter covered in the CBSE Class 8 Maths Syllabus is a necessary task to attempt the MCQs Section easily with full confidence in the board exam paper
5. ations. 8 × 8 can be written as 8 2. In 8 2, the number 8 is called the base and 2 is called the exponent or the power. • The value of any number raised to 0 is 1, i.e. a 0 = 1
Class 8 - Maths - Exponents and Powers. Download PDF. Exercise 12.1. Question 1: Evaluate: (i) 3-2 (ii) (-4)-2 (iii) (1/2)-5 . Answer: (i) 3-2 = 1/3 2 = 1/9 Thickness if a thick paper is 0.07 mm. Answer: (i) 1 = 1/1000000 = 1/10 6 = 1 * 10-6 m (ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb. Here you can get Class 7 Important Questions Maths based on NCERT Text book for Class VII. Exponents and Powers are very helpful to score high marks in board exams. Here we have covered Important Questions on Coordinate Geometry for Class 7 Maths subject. Maths Important Questions Class 7 are given below Free PDF download of RS Aggarwal Solutions for Class 8 Maths Chapter-2 Exponents solved by Expert Mathematics Teachers on Vedantu.com. All Chapter-2 Exponents Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams The NCERT Solutions for class 8 maths chapter 12 focus on helping students get better clarity on essential topics of exponents and powers. Exponents and powers class 8 is one of the most critical chapters of Class 8. Students can now avail of the Class 8 maths chapter 12 PDF to gain relevant insights on how to ace their exams Check the below NCERT MCQ Questions for Class 7 Maths Chapter 13 Exponents and Powers with Answers Pdf free download. MCQ Questions for Class 7 Maths with Answers were prepared based on the latest exam pattern. We have provided Exponents and Powers Class 7 Maths MCQs Questions with Answers to help students understand the concept very well
Exponents and Powers worksheet for class 7 in PDF for free download. Maths worksheets on Exponents and Powers as per NCERT syllabus test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers Filed Under: Class 8, Mathematics, RS Aggarwal Tagged With: CBSE Class 8 RS Aggarwal Maths Solutions, Cubes and Cube Roots RS Aggarwal Class 8 Math Solutions, Cubes and Cube Roots RS Aggarwal Class 8 Maths Solutions CCE Test Paper, Cubes and Cube Roots RS Aggarwal Maths Solutions, RS Aggarwal CBSE Class 8 Maths Cubes and Cube Roots, RS Aggarwal. Let x be the required number which is multiplied. Question 12. Solution: Let x be the required number. Question 13. Solution: 5 2x+1 ÷ 25 = 125. Hope given RS Aggarwal Solutions Class 8 Chapter 2 Exponents Ex 2A are helpful to complete your math homework. If you have any doubts, please comment below
Worksheet 5: Exponents. Posted on December 4, 2014. March 13, 2018. by Maths @ SHARP. This grade 9 maths worksheets has questions on all things exponents covered in the CAPS syllabus. Questions include some basic theory, scientific notation, simplifying algebraic expressions and solving basic exponential equations. There are also some story sums Solution: (b) We know that, if 'a' is a rational number, m and n are natural numbers such that m> n, then. a m ÷ a n = a m-n. So, x 8 ÷ x 2 = x 8 /x 2 = x 8-2 = x 6. Question 3: x is a non-zero rational number. Product of the square of x with the cube of x is equal to the. (a) second power of x (b) third power of x Exponents Questions with Answers for Grade 9. Grade 9 questions on exponents are presented along with solutions and detailed explanations. Rules and Properties of Exponents. The exponential form is a convenient way to write long repeated multiplications of the same number by itself
Free PDF download of Chapter 12 - Exponents and Powers Formula for CBSE Class 8 Maths. To Register Online Maths Tuitions on Vedantu.com to clear your doubts from our expert teachers and solve the problems easily to score more marks in your CBSE Class 8 Maths Exam. Vedantu is a platform that provides free NCERT Solution and other study materials for students Exponents and Powers Class 7 Extra Questions Maths Chapter 13 Extra Questions for Class 7 Maths Chapter 13 Exponents and Powers Exponents and Powers Class 7 Extra Questions Very Short Answer Type Question 1. Express 343 as a power of 7. Solution: We have 343 = 7 × 7 × 7 = 73 Thus, 343 [ Profit and Loss RS Aggarwal Class 8 Maths Solutions. Chapter 10 Profit and Loss Exercise 10A. Chapter 10 Profit and Loss Exercise 10B. Chapter 10 Profit and Loss Exercise 10C. Chapter 10 Profit and Loss Exercise 10D. Chapter 10 Profit and Loss Test Paper. YouTube There are basically three exercises in exponents and powers class 7 chapter 5. These exercises consist of a series of questions for the students to solve. The questions are arranged in order from simple to complex. To know how much they have excelled in the topic, they can solve the CCE test paper given in class 7 maths RS Aggarwal chapter 5 Question Bank for 7th Class Mathematics Exponents and Power Exponents and Powers - Studyadda.com. Customer Care : 6267349244
Blog provides NCERT solutions, CBSE, NTSE, Olympiad study material, model test papers, important Questions and Answers asked in CBSE examinations. References to Educational Sites and resources. Pages. Home; Resources; Class 12; Class 11; CBSE Class 7 - Maths - Exponents and Powers (MCQs) (#cbsenotes)(#eduvictors Test Papers of Class 7. CBSE Test Papers from Class 7 Mathematics are very important for exam preparations. Students need to practice these practice test papers of class 7th and periodic and assessment unit tests of grade 7th while preparing for final exams. Practicing these Test Papers will enable students to identify important topics of. ML Aggarwal ICSE Solutions for Class 7 Maths Chapter 4 Exponents and Powers. ML Aggarwal Solutions ICSE Solutions Selina ICSE Solutions. Understanding ICSE Mathematics Class 7 ML Aggarwal Solutions Pdf Download Chapter 4 Exponents and Powers
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers. Exponents are commonly used in algebraic expressions and can be multiplied in the same way that other numbers are multiplied. Exponents, which indicate repetitive multiplication, can easily be simplified using a few simple properties Class 7 - Exponents and Powers problems, online practice, tests, worksheets, quizzes, and teacher assignments. Take unlimited online tests on Exponents and Powers. Get instant scores and step-by-step solutions on submission. Make sure you always get your answers right in Exponents and Powers RS Aggarwal Solutions Class 7 PDF Download 2020-2021 Edition is available here. So, students can refer here to get RS Aggarwal Maths Book Class 7 Solutions PDF Download. With the help of uploaded RS Aggarwal Mathematics Class 7 PDF Solutions, CBSE Class 7 students can achieve good marks in Class 7 Maths. By preparing RS Aggarwal Class 7 Maths. Sample CBSE Class 7 Maths Exponents and Powers Worksheet Questions. 1. Write thenumber in standard form: 7 X 10 4 + 3 X 10 2 + 2 X 10 1. 2. Write the number in standard form: 2 X 10 6 + 5 X 10 5 + 2 X 10 2 + 3 X 10 0. 3
In this section, you will find 8+ past free exam papers for Maths and English. We also provide answer sheets to these 8+ past exam papers for you to refer and cross-check after your child is done solving the papers. 8 Plus Maths. King's College School - 8 Plus Maths Specimen Paper Dulwich College - 8 Plus Maths Sample Question Practice Class 8 Maths Chapter 12 Exponents and Powers MCQ online test. This Exponents and Powers Class 8 MCQ test check the understanding and concept of the chapter. You can test your knowledge and evaluate yourself. We also have Class 8 Maths Notes, NCERT solutions, worksheets and Assignment free on our website
CBSE 8th Class Mathematics Chapter Exponent Power and Radicals and Scientific Notation CBSE TEST PAPER - 02 1. The base 24 in the expression 10 is _____. (a) 1 (b) 10 (c) 0 (d) 24 2. Multiplicative inverse of 7-2 is _____ Answers (1) 9 Step 1 (327)103 × (327)199 = (327)302 Step 2 Let's see the pattern when 7 is multiplied, Last digit of 71 = 7 Last digit of 72 = (last digit of 7x7) = 9 Last digit of 73 = (last digit of 9x7) = 3 Last digit of 74 = (last digit of 3x7) = 1 Last digit of 75 = (last digit of 1x7) = 7 Last digit of 76 = (last digit of 7x7) = 9 Last digit of 77 = (last digit of 9x7) = Class VIII Math Exponents and Powers. Exponents and Powers (Quiz) Attention Class VIII standard Aspirants! Just Exam provide a platform to all students who want to make practice for various subject online. Interested students may contact us at info@justexam.in for full course access Are you confused while solving problems on Exponents & Powers Class 8? Do not worry, Visit Math Square and learn what is Exponents & Powers Class 8 and how to solve problems on Class 8 Exponents & Powers Class 8 Maths Exponents and Powers Very Short Answer Type Questions. 1. Express 729 as a power of 3. 2. Express 2048 as a power 2. 3. Simplify and write in exponential form of 2 2 × 2 5. 4. Simplify and write in exponential form of (-4) 100 × (-4) 20
### Exponents and Powers - Test Paper Questions (Part 5
NCERT Exemplar Class 8 Maths Chapter 8 Exponents and Powers. Solution. (c) We know that an is called the nth power of a; and is also read as a raised to the power n. The rational number a is called the base and n is called the exponent (power or index). In the same way in 2 n ,n is known as exponent Add the exponent, if base are same. Uses of Exponents. The exponents can be used for various purposes such as comparing large and small numbers, expressing large and small numbers in the standard forms. It is used to express the distance between any two celestial bodies which cannot be expressed in the form of normal denotion Download Class 8 IMO 2020 latest Sample Papers with detailed step by step solutions for free. Exponents and Powers: 12. Paper-folding and Paper Cutting: 13. Direct and Inverse Proportions These solutions will help the students to prepare their level best for the IMO exam. The sample paper is designed by our inhouse Cuemath math experts. Hello Students In this article, we have discussed the Class 8 Question Papers. Question Papers/Previous Year Papers is most beneficial especially for the preparation of school exam. Classes 6 to 12 students need to have a great practice of all the concept and one of the best ways to achieve the same is through Question Papers/Previous Year Papers Sample Paper is most beneficial especially for the preparation of school exam. Classes 6 to 12 students need to have a great practice of all the concept and one of the best ways to achieve the same is through Sample Papers. In this article, you can get the CBSE Class 8 Mathematics Sample Paper in pdf format which is absolutely free. 1. Summary. 2
CBSE Class 8 Worksheets, Sample Papers & Question Papers. On Ribblu.com one can download free CBSE Class 8 Worksheets, MCQ Question Papers for 8th Class, Unit Test Papers for 8th Grade, sample papers for Class 8, important questions chapter wise for All Subjects in PDF format Math Solutions for Class 8 Maths Chapter 12 - Exponents and Powers. Mathematics NCERT Grade 8, Chapter 12: Exponents and Powers- This chapter highlights all the concepts related to exponents and powers. Initially, Power with Negative Exponents and Laws of Exponents will be discussed CBSE Class 8 Revision Notes and Key Points. Exponents and Powers class 8 Notes Mathematics. CBSE quick revision note for class-8 Mathematics, Chemistry, Math's, Biology and other subject are very helpful to revise the whole syllabus during exam days
### Exponents Class 8 Maths Online Quiz/MC
Class 8 Maths Chapter 2 Exponents and Powers Chapter 2 Exponents and Powers Ex 2.1 Chapter 2 Exponents and Powers Ex 2.2 Chapter 2 Exponents and Powers Objective Type Questions Chapter 2 Exponents and Powers Check Your Progress ML Aggarwal Class 8 Maths Chapter 3 Squares and Square Roots Chapter 3 Squares and Square Roots Ex Paper 1 Model. Exponents Exercise 2A - Selina Concise Mathematics Class 8 ICSE Solutions. Question 1. Evaluate: Solution: Question 2. If 1125 = 3 m x 5 n; find m and n. Solution: Question 3. Find x, if 9 × 3 x = (27) 2x-3 8th Class Mathematics Exponents and Power Exponents and Powers EXPONENTS & POWERS . FUNDAMENTALS . Exponent:- The exponent of a number says how many times it should be used in a multiplication. Sample Papers; Online Test 3rd b. the probability that at least one person in your class is wearing brown socks c. the probability that the sum of two dice is greater than 4 d. the probability of choosing an ace of spades from a standard dec CBSE EXAM PORTAL. Online Community for CBSE, Board Exam Students. Download File : Download-NCERT-Exemplar-Problems-from-Class-8-Mathematics-Unit-8-Exponents-Powers.pdf. Disclaimer: This website is not associated with CBSE, For official website of CBSE visit - www.cbse.gov.in AIEEE, AIPMT - Papers, Mock Exams, Books, Results and More..
### Exponents and Powers Class 8 Extra - CBSE Sample Paper
Take CBSE Class 8 Maths Chapter 12 Mock Test Now. NCERT Solutions For Class 8 Maths Chapter 12: Exponents And Powers. Before we provide you with Class 8 NCERT Solutions Maths Chapter 12, let's have an overview of the topics in this chapter. Click on any topic to download the solutions as a PDF NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Exercise 12.2. Ex 12.2 Class 8 Maths Question 1. Ex 12.2 Class 8 Maths Question 2. Express the following numbers in usual form. Ex 12.2 Class 8 Maths Question 3. Express the number appearing in the following statements in standard form. (i) 1 micron is equal to m 1. Solution : When we find the square root of 629 using division method, then the remainder is 4. Now if we subtract this remainder from the number, then the remainder will be zero and. the new number will be a perfect square. Hense the required least number = 4. and the required perfect square = 629 - 4 = 625. Now √625 = 25 Get all questions and answers of Exponents of ICSE Class 8 Mathematics on TopperLearning. TopperLearning's Experts and Students has answered all of Exponents of ICSE Class 8 Mathematics questions in detail
### Class 8 Exponents & Powers - basics, problems and solved
Question Bank, Mock Tests, Exam Papers. NCERT Solutions, Sample Papers, Notes, Videos. Install Now. cbse class 7 maths worksheets Exponents and Powers CBSE chapter wise practice papers with solution for class 7 Mathematics chapter 13 Exponents and Powers for free download in PDF format. 7th Mathematics chapter 13 Exponents and Powers have many. Inviting all students to avail a 10 minutes FREE counseling session to discuss concerns related to studies, exam phobia, stream selections, time management, coping with stress, exam preparation etc. Call us today at Toll Free Number: 1800-102-5301 and get your questions answered All our CBSE NCERT Class 8 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 8 Maths will be useful to test your conceptual understanding
### Exponents and Powers - Test Paper Questions (Part 3
Download the PDF Question Papers Free for off line practice and view the Solutions online. Currently only available for. Class 10 Class 12. Exponents and Powers. Zigya App. Express the following numbers in standard form. 31860000000. 31860000000 = 3186 1000000 Class 8 Maths Chapter 12 Exponents and Powers NCERT Book PDF Download. To ace in your exam preparation, you can refer to the 8th Class NCERT Solutions prevailing in NCERT e-Book. NCERT Books for Class 8 Maths Exponents and Powers will have illustrative problems and solutions. Students can understand the concepts written in NCERT 8th Class Maths. Multiple Choice Questions (MCQ) for CBSE Class 8 Mathematics chapters on Topperlearning. These MCQ's are extremely critical for all CBSE students to score better marks
Chapter 12: Exponents and Powers. In Class 8 Maths Chapter 12, we will study the numbers having negative or positive powers. Exercise 12.1 is based on the Laws of Exponents. Questions 5, 6 and 7 are important for exams. Assignment and test papers will also be uploaded for the preparation of exams. This page is rebuilt on the basis to. Exponent is the number of times a number is multiplied by itself. Exponents are written as x y; where x is the number and y is the exponent or power. Example: 2 * 2 * 2 * 2 * 2 = 2 5 Learn more about exponents.. Radical or root is the inverse of exponent represented by the root sign \sqrt{} if b = a n then \sqrt[n]{b} = a Surd is the n th root of a number which is irrational Online Test for 7th Class Railways UPSC (79)Exponent and Powers (80)Maths Olympiad Model Test Paper-15 (81)Maths Olympiad Model Test Paper-1 (82)The Triangle and Its Properties picture_as_pdf English Olympiad Model Test Paper-8 ; picture_as_pdf General. | 7,164 | 29,199 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-21 | latest | en | 0.902186 |
https://blog.keytometals.com/engineering-stress-strain-curve-part-three/ | 1,685,491,238,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646181.29/warc/CC-MAIN-20230530230622-20230531020622-00226.warc.gz | 178,909,910 | 9,715 | Engineering Stress-strain Curve: Part Three
The engineering tension test is widely used to provide basic design information on the strength of materials and as an acceptance test for the specification of materials. In the tension test a specimen is subjected to a continually increasing uniaxial tensile force while simultaneous observations are made of the elongation of the specimen. The parameters, which are used to describe the stress-strain curve of a metal, are the tensile strength, yield strength or yield point, percent elongation, and reduction of area. The first two are strength parameters; the last two indicate ductility.
Measures of Yielding
The stress at which plastic deformation or yielding is observed to begin depends on the sensitivity of the strain measurements. With most materials there is a gradual transition from elastic to plastic behavior, and the point at which plastic deformation begins is hard to define with precision. Various criteria for the initiation of yielding are used depending on the sensitivity of the strain measurements and the intended use of the data.
1. True elastic limit based on micro strain measurements at strains on order of 2 x 10-6 in | in. This elastic limit is a very low value and is related to the motion of a few hundred dislocations.
2. Proportional limit is the highest stress at which stress is directly proportional to strain. It is obtained by observing the deviation from the straight-line portion of the stress-strain curve.
3. Elastic limit is the greatest stress the material can withstand without any measurable permanent strain remaining on the complete release of load. With increasing sensitivity of strain measurement, the value of the elastic limit is decreased until at the limit it equals the true elastic limit determined from micro strain measurements. With the sensitivity of strain usually employed in engineering studies (10-4in | in), the elastic limit is greater than the proportional limit.
4. The yield strength is the stress required to produce a small-specified amount of plastic deformation. The usual definition of this property is the offset yield strength determined by the stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by a specified strain. In the United States the offset is usually specified as a strain of 0.2 or 0.1 percent (e = 0.002 or 0.001).
(4)
A good way of looking at offset yield strength is that after a specimen has been loaded to its 0.2 percent offset yield strength and then unloaded it will be 0.2 percent longer than before the test. The offset yield strength is often referred to in Great Britain as the proof stress, where offset values are either 0.1 or 0.5 percent. The yield strength obtained by an offset method is commonly used for design and specification purposes because it avoids the practical difficulties of measuring the elastic limit or proportional limit.
Some materials have essentially no linear portion to their stress-strain curve, for example, soft copper or gray cast iron. For these materials the offset method cannot be used and the usual practice is to define the yield strength as the stress to produce some total strain, for example, e = 0.005.
Measures of Ductility
At our present degree of understanding, ductility is a qualitative, subjective property of a material. In general, measurements of ductility are of interest in three ways:
To indicate the extent to which a metal can be deformed without fracture in metalworking operations such as rolling and extrusion.
To indicate to the designer, in a general way, the ability of the metal to flow plastically before fracture. A high ductility indicates that the material is “forgiving” and likely to deform locally without fracture should the designer err in the stress calculation or the prediction of severe loads.
To serve as an indicator of changes in impurity level or processing conditions. Ductility measurements may be specified to assess material quality even though no direct relationship exists between the ductility measurement and performance in service.
The conventional measures of ductility that are obtained from the tension test are the engineering strain at fracture ef (usually called the elongation) and the reduction of area at fracture q. Both of these properties are obtained after fracture by putting the specimen back together and taking measurements of Lf and Af .
(5)
(6)
Because an appreciable fraction of the plastic deformation will be concentrated in the necked region of the tension specimen, the value of ef will depend on the gage length L0 over which the measurement was taken. The smaller the gage length the greater will be the contribution to the overall elongation from the necked region and the higher will be the value of ef. Therefore, when reporting values of percentage elongation, the gage length L0 always should be given.
The reduction of area does not suffer from this difficulty. Reduction of area values can be converted into an equivalent zero-gage-length elongation e0. From the constancy of volume relationship for plastic deformation A*L = A0*L0, we obtain
(7)
This represents the elongation based on a very short gage length near the fracture.
Another way to avoid the complication from necking is to base the percentage elongation on the uniform strain out to the point at which necking begins. The uniform elongation eu correlates well with stretch-forming operations. Since the engineering stress-strain curve often is quite flat in the vicinity of necking, it may be difficult to establish the strain at maximum load without ambiguity. In this case the method suggested by Nelson and Winlock is useful. | 1,127 | 5,756 | {"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} | 2.703125 | 3 | CC-MAIN-2023-23 | latest | en | 0.921803 |
https://www.physicsforums.com/threads/time-independence-of-original-coordinates-in-canonical-transform.727940/ | 1,513,180,543,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948527279.33/warc/CC-MAIN-20171213143307-20171213163307-00300.warc.gz | 771,487,647 | 15,221 | # Time-independence of original coordinates in canonical transform
1. Dec 12, 2013
### mjordan2nd
I am going through my professors notes on generating functions. I come across the following equation:
$$\frac{\partial}{\partial t} \frac{\partial F}{\partial \xi^k} = \frac{\partial}{\partial t} \left( \gamma_{il} \frac{\partial \eta^i}{\partial \xi^k}\eta^l - \gamma_{kl}\xi^l \right ).$$
Here $\xi$ are the original coordinates, $\eta$ are the transformed coordinates, and $\gamma_{il}$ are the components of the block matrix
$$\left( \begin{array}{ccc} 0 & -I \\ 0 & 0 \end{array} \right ).$$
When the time derivative is taken on the right hand side, the $\xi^l$ are said to be independent of time. Why is this. Certainly (q,p) depend on time, right? | 224 | 759 | {"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} | 2.65625 | 3 | CC-MAIN-2017-51 | longest | en | 0.83564 |
https://www.cut-the-knot.org/m/Algebra/KunnyWithConstraint.shtml | 1,527,014,418,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864837.40/warc/CC-MAIN-20180522170703-20180522190703-00406.warc.gz | 720,764,291 | 15,692 | # Kunihiko Chikaya's Inequality with a Constraint
### Solution 1
\displaystyle \begin{align} 4a^3-3a+1=(a+1)(2a-1)^2\ge 0,\\ 9b^3-3b+\frac{2}{3}=\left(b+\frac{2}{3}\right)(3b-1)^2\ge 0,\\ 36c^3-3c+\frac{1}{3}=\left(c+\frac{1}{3}\right)(6c-1)^2\ge 0. \end{align}
Summing up,
\displaystyle\begin{align} 4a^3+9b^3+36c^3&\ge 3(a+b+c)-\left(1+\frac{2}{3}+\frac{1}{3}\right)\\ &=3\cdot 1-2=1. \end{align}
### Solution 2
The required inequality is a special case of the following statement:
Assume $x+y+z=1$ and $a+b+c=1,$ $a,b,c,x,y,z \gt 0.$ Then
$\displaystyle \frac{a^3}{x^2} + \frac{b^3}{y^2} + \frac{c^3}{z^2} \ge 1.$
$\displaystyle \frac{a^3}{x^2} + \frac{b^3}{y^2} + \frac{c^3}{z^2}\ge\frac{(a+b+c)^3}{(x+y+z)^2} = 1.$
In this problem $\displaystyle x=\frac{1}{2},$ $\displaystyle y=\frac{1}{3},$ $\displaystyle z=\frac{1}{6}.$
### Solution 3
Obviously $\displaystyle \frac{\frac{a}{3}+\frac{a}{3}+\frac{a}{3}+\frac{b}{2}+\frac{b}{2}+c}{6} = \frac{1}{6}.$ By the power-mean theorem
\displaystyle\begin{align} \frac{3\left(\frac{a}{3}\right)^3 +2\left(\frac{b}{2}\right)^3 + c^3}{6} &\ge\left(\frac{3\frac{a}{3}+2\frac{b}{2}+c}{6}\right)^3\\ &=\left(\frac{1}{6}\right)^3. \end{align}
Multiplying both parts by $6^3$ yields the required result.
### Solution 4
\displaystyle \begin{align} a&=\frac{4}{3}\cdot 3\cdot \frac{1}{2}\cdot \frac{1}{2}\cdot a\le\frac{4}{3}\left(\frac{1}{8}+\frac{1}{8}+a^3\right)=\frac{1}{3}+\frac{4}{3}a^3\\ b&=3\cdot 3\cdot \frac{1}{3}\cdot \frac{1}{3}\cdot b\le 3\left(\frac{1}{27}+\frac{1}{27}+b^3\right)=\frac{2}{9}+3b^3\\ c&=12\cdot 3\cdot \frac{1}{6}\cdot \frac{1}{6}\cdot c\le 12\left(\frac{1}{216}+\frac{1}{216}+c^3\right)=\frac{1}{9}+12c^3 \end{align}
Summing up,
$\displaystyle 1=a+b+c\le\frac{2}{3}+\frac{4}{3}a^3+3b^3+12c^3,$
i.e.,
$\displaystyle 1=3\left(1-\frac{2}{3}\right)\le 4a^3+9b^3+36c^3.$
### Solution 5
The function $v=y^3$ is convex, so that by Jensen's inequality,
\displaystyle \begin{align} 4a^3+9b^3+36c^3 &= \frac{1}{2}(2a)^3+\frac{1}{3}(3b)^3+\frac{1}{6}(6c)^3\\ &\ge\left( \frac{1}{2}(2a)+\frac{1}{3}(3b)+\frac{1}{6}(6c)\right)^3\\ &=(a+b+c)^3=1. \end{align}
### Solution 6
We can eyeball from the constraint of the Lagrangian that $3\cdot 4a^2=3\cdot 9b^2=3\cdot 36c^2,$ giving the minimum of $4a^3+9b^3+36c^3$ at $\displaystyle (a,b,c)=\left(\frac{1}{2},\frac{1}{3},\frac{1}{6}\right).$ We know it is a minimum because the second derivatives are $24a,54b, 216c$ are all positive and the Lagrangian has no cross terms.
### Acknowledgment
Kunihiko Chikaya has shared his inequality, along with a solution of his at the mathematical inequalities facebook group. Both were first posted on the web on September 13, 2014. I am grateful to Kunihiko for the permission to reproduce his post here.
Solution 2 is by Konstantin Knop; Solution 3 is by Maxim Razin; Solution 4 is by Tran Quoc Thinh; Solution 6 is by N. N. Taleb. | 1,274 | 2,901 | {"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": 5, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2018-22 | longest | en | 0.323312 |
https://rational-equations.com/rational-equations/linear-inequalities/help-solve-algebra-problems.html | 1,524,687,334,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125947957.81/warc/CC-MAIN-20180425193720-20180425213720-00339.warc.gz | 697,305,736 | 11,472 | Algebra Tutorials!
Home Rational Expressions Graphs of Rational Functions Solve Two-Step Equations Multiply, Dividing; Exponents; Square Roots; and Solving Equations LinearEquations Solving a Quadratic Equation Systems of Linear Equations Introduction Equations and Inequalities Solving 2nd Degree Equations Review Solving Quadratic Equations System of Equations Solving Equations & Inequalities Linear Equations Functions Zeros, and Applications Rational Expressions and Functions Linear equations in two variables Lesson Plan for Comparing and Ordering Rational Numbers LinearEquations Solving Equations Radicals and Rational Exponents Solving Linear Equations Systems of Linear Equations Solving Exponential and Logarithmic Equations Solving Systems of Linear Equations DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS Solving Quadratic Equations Quadratic and Rational Inequalit Applications of Systems of Linear Equations in Two Variables Systems of Linear Equations Test Description for RATIONAL EX Exponential and Logarithmic Equations Systems of Linear Equations: Cramer's Rule Introduction to Systems of Linear Equations Literal Equations & Formula Equations and Inequalities with Absolute Value Rational Expressions SOLVING LINEAR AND QUADRATIC EQUATIONS Steepest Descent for Solving Linear Equations The Quadratic Equation Linear equations in two variables
Try the Free Math Solver or Scroll down to Resources!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
Ineq. #9:
Solve for:
Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:
### Our users:
I just wanted to first say your algebra program is awesome! It really helped me it my class! I was really worried about my Algebra class and the step through solving really increased my understanding of Algebra and allowed me to cross check my work and pointed out where I went wrong during my solutions. Thanks!
J.R. Turnston, NY
I really needed a way to get help with my homework when I wasn't able to speak with my teacher. Algebrator really solved my problem :)
D.B., Washington
What a great friendly interface, full of colors, witch make Algebrator software an easy program to work with, and also it's so easy to work on, u don't have to interrupt your thoughts stream every time u need to interact with the program.
Brian T. Gomez, SD
Thank you so much Algebrator, you saved me this year, I was afraid to fail at Algebra class, but u saved me with your step by step solving equations, am thankful.
Kathleen Becker, PA
### Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them?
#### Search phrases used on 2010-08-17:
• nonhomogeneous higher order differential equations general solutions
• maths questions for year 8 students for year end exam frre questions
• holt mathematics help
• ellipsoid math lesson 8th grade
• freee standardize practice test for school age chiildren
• how to pass the algebra clep test
• prentice hall conceptual physics answers
• "read a 12 inch ruler"
• free CAT exam guide online
• Learn Alegbra
• "modern algebra projects "
• Fraction to decimal conversion worksheet
• mixed number to decimal
• print off practise ks3 maths papers
• free math a regent questions
• VERY SIMPLE ALGEBRA WORKSHEETS
• maths shareware
• hyperbolas activities
• Whats the answer to algebra with pizzazz page 90?
• simplify variable charts
• 2-step inequalities worksheet
• what are coordinates-math term
• prentice hall mathematics Florida algebra 1 online textbook
• algebra substitution method with exponents
• algebra for idiots online tutorial
• engineering maths-exponential equation
• free slope worksheets
• world history by mcdougal littell chapter outlines
• grade 11 math area and volume worksheets
• 8th grade slope example problems
• formula for circumference fifth grade
• 3 variables 3 equations online calculator in fraction
• worksheets on greatest and least common multiples
• using derivative function on graphing calculator
• pre algebra calculator free
• pre algebra with pizzazz
• algerbra solver
• free online math curriculum for 9th grade
• algebra 2 ebook
• combination permutation worksheet doc
• fraction caculator
• enter trigonomic equations
• online fraction calculator and simplifyer
• ERB test, practice
• fractions lesson plan 1st grade
• use every digit from 1-9 exactly once to compute this sum
• ode45
• polynomials problem solving
• "ti-82" "worksheets"
• factoring worksheets
• free online absolute value for dummies lessons
• online easy mathematics aptitude test practice papers
• subtracting negative fractions calculator
• AREA WORKSHEET KS2
• adding subtracting multiplying and dividing rational numbers
• prentice hall chemistry review book answers
• difference of square roots
• math function practice worksheet
• softmath
• binomial calculator
• multiplying integer worksheet
• free pre algebra binomials problems
• factoring a polynominal
• answers for glencoe algebra 2
• Linear Equations with Decimals
• linear programming problem gcse
• adding and subtracting polynomials with algebra tiles
• elementary algabra
• qudratic function | 1,283 | 5,568 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-17 | latest | en | 0.853045 |
https://www.hanspub.org/reference/ReferencePapers.aspx?ReferenceID=126560&PaperID=17005 | 1,519,252,934,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891813818.15/warc/CC-MAIN-20180221222354-20180222002354-00200.warc.gz | 882,180,499 | 17,946 | ## 文章引用说明 更多>>(返回到该文章)
Vese, L. (2003) Multiphase Object Detection and Image Segmen-tation. Geometric Level Set Methods in Imaging, Vision, and Grahics, Springer, 175-194.
http://dx.doi.org/10.1007/0-387-21810-6_10
• 作者: 马秀, 张浩然, 王汉权
期刊名称: 《Advances in Applied Mathematics》, Vol.5 No.1, 2016-02-26
摘要: 图像分割是目标识别，资源分类等研究的基础。在医学临床诊断，视频监控计算机视觉等多个林谷都有重要的应用。水平集方法以一种紧凑的方式来表达集合主动轮廓曲线的演化，并且为之提供稳定的数值计算。Chan和Vese提出的基于简化的Mumford-Shan模型的主动轮廓模型(C-V方法)，能够很的检查出带有空洞的目标的内部区域，但只能处理两相图片的分割。基于C-V模型，Vese Chan推广到实用多个水平集函数来分割多相图像，即Vese-Chan变分多水平模型。该方法有以下优点：可以自动的避免水平集函数覆盖区域的“重叠”和“真空”问题。本文中，我们基于C-V模型以及Vese-Chan变分水平集模型，实现了如何利用单个水平集函数以及两个水平集函数来进行医学图像分割；讨论了这两种方法的优缺点。我们的图像分割数值实验结果验证了理论结果。 Image segmentation is the basic of object detection and resource classification, and it has an im-portant application in the field of medical diagnosis, video monitoring and computer vision. Level set method describes the evolution of geometric active contour in a compact way and provides a stable numerical algorithm. Chan and Vese first introduced the active contour model based sim-plified Mumford-Shah model, which could well detect the vacuum of object, but could represent only two phases or segments in the image. Vese-Chan variational level set model was proposed by Vese-Chan as the generalization of C-V model, which needed multiple level set functions for n phases image segmentation; it can represent boundaries with complex topologies. In this paper, based on the C-V model and Vese-Chan variational level set model, we show how to do medical image segmentation through one level set function and two-level set functions respectively. We discuss the advantages and disadvantages of both methods. Our numerical results validate our theoretical predication. | 583 | 1,740 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-09 | longest | en | 0.568763 |
https://isabelle.in.tum.de/repos/isabelle/file/e0dc738eb08c/src/Doc/Logics_ZF/FOL_examples.thy | 1,620,933,636,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991943.36/warc/CC-MAIN-20210513173321-20210513203321-00103.warc.gz | 348,678,909 | 2,418 | src/Doc/Logics_ZF/FOL_examples.thy
author wenzelm Tue, 31 Mar 2015 22:31:05 +0200 changeset 59886 e0dc738eb08c parent 58889 5b7a9633cfa8 child 66453 cc19f7ca2ed6 permissions -rw-r--r--
support for explicit scope of private entries;
```
section{*Examples of Classical Reasoning*}
theory FOL_examples imports "~~/src/FOL/FOL" begin
lemma "EX y. ALL x. P(y)-->P(x)"
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (rule exCI)
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (rule allI)
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (rule impI)
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (erule allE)
--{* @{subgoals[display,indent=0,margin=65]} *}
txt{*see below for @{text allI} combined with @{text swap}*}
apply (erule allI [THEN [2] swap])
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (rule impI)
--{* @{subgoals[display,indent=0,margin=65]} *}
apply (erule notE)
--{* @{subgoals[display,indent=0,margin=65]} *}
apply assumption
done
text {*
@{thm[display] allI [THEN [2] swap]}
*}
lemma "EX y. ALL x. P(y)-->P(x)"
by blast
end
``` | 387 | 1,079 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-21 | latest | en | 0.264946 |
https://www.codeproject.com/Articles/15680/How-to-write-a-Memory-Scanner-using-C | 1,695,879,181,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510358.68/warc/CC-MAIN-20230928031105-20230928061105-00070.warc.gz | 769,768,936 | 32,312 | 15,745,335 members
Articles / Programming Languages / C#
Article
Posted 23 Sep 2006
333.4K views
163 bookmarked
# How to write a Memory Scanner using C#
Rate me:
Search a process' memory to find specified 16, 32 or 64 bit data values.
## Introduction
Have you ever had a problem completing a game because your health meter shows just 5% of your health available?
Have you ever used a game trainer to solve this problem?
Have you ever wondered how this trainer freezes your health meter to 100%?
These game trainers, do a simple job!
They write a little part of the Game's memory with the 100 `value`!
But how to find the exact part of memory?
## The Question and the Answer
Q: How to find the location in which a program stores a `value` in its memory?
A: Some programs named 'Memory Scanners', are written to read and search a program's memory for exact location and help freezing it! (And I have written this article to show you, how to write a 'Memory Scanner')
## Step 1: Where to begin?
Let's have a look at a program's memory.
Think that I have written a program and we can have a look at its memory.
To have a picture in mind, we can say, it looks something like this:
As you can see, the memory is made up of a huge number of small sectors, that hold a `value` in it. Our picture, just shows a small part of the memory, from sector 0 to sector 99 and a detail of sector 0 to sector 15. But as you know, a computer just knows the meaning of 0 and 1, so what do these Hexadecimal `value`s mean?
Let's take a deep look at the memory again.
As you can see, every byte is made up of 8 bits with each of them being just that 1 or 0, and in Binary mode, they can return the `value` stored in the byte((00010111)2 = (23)10 = (17)16).
As we saw, a computer's memory stores information by holding the 0 and 1s in the memory bits, and 8 bits of memory make a section of memory named byte, so a byte can hold `value`s up to (11111111)2 = (255)10 = (FF)16, but how about the bigger `value`s?
We usually work with `value`s greater than 255!
Ok, the answer is that, we have bigger units of memory to hold the bigger `value`s.
Let's look at another picture of memory that shows the bigger units and then, I will explain everything:
So we have 3 bigger memory units: 2 `Bytes` that make a 16 bit memory unit that we call 'short' in C#, 4 `Bytes` that make a 32 bit memory unit that we call it 'int' in C#, and 8 `Bytes` that make a 64 bit memory unit, and we call it 'long' in C#.
## Step 2: What to look for?
Now that we have a simple picture of the memory in our mind, let's go back to the first picture:
I know that, you are going to say: "Hey, it's just a row of `bytes`! How to find the memory units?" And then I'll tell you that, you asked the biggest question in writing a memory scanner!
Ok, let's think that it's a part of the memory of my program, and I know, where in the memory, I have stored the `value`s and I will show you that:
As you see, a memory unit, can be stored in any part of the memory and start from any memory sector. In this program for example, I have stored a 32 bit `value` in the 0 sector, and because a 32 bit `value` takes 4 `bytes` of memory, from the sector 0 to sector 3 is assigned for a 32 bit variable in the program, and after that, from the sector 4, there is a 16 bit variable that takes 2 `bytes` of memory, next is a 64 bit variable and at the end, there is again a 16 bit variable.
Now let's think that the `value`s of the sectors are the same, but the memory units start from different sectors:
Why everything changed?
Because, a variable could be stored in any memory sector number, and most of the time, even the programmer doesn't know, where the variable is stored in the memory, and just the program knows it!
## Step 3: Where to find it?
Now, let's think that we are playing a game, and the health meter shows 83%, and we don't know the location of the variable in the memory and we want to find the variable and we start from sector 0, so the memory looks like this:
So what? Is there any 83 in the memory?
First, we know that we have the hexadecimal `value`s of the memory `bytes`. Second, we should guess the variable type to look for.
Ok, let's say that the programmers of the game have used a 32 bit (int) variable, that is the most usual data type being used for storing the `value` of the health meter. So the `value` is stored in a 4 `bytes` long part of the memory. But, how to find it?
The only way to search the memory completely, is to start from the beginning, take 4 `bytes`, test them to see if the `value` equals our digit (here 83), and find the location. Like this:
Ok, now you know the main concept of memory scanning, but there are some other things that you should know to be able to write the Memory scanner:
1. Q: How long is a program's memory? (Where to begin and where to stop?)
A: As you know, Microsoft's first OS was DOS that was a 8 bit OS, after that, the Windows 3.1 became a 16 bit OS, and after that, the Windows OS became a 32 bit OS. (I'm a real fan of Apple Co. that developed the Apple Macintosh OS, a 64 bit OS, exactly when Microsoft was working on DOS (a 8 bit OS) and today, Microsoft is going to write a 64 bit Windows (and like the first Windows versions, it still looks like the Apple OSs) but, I still recommend Apple MacOS X (Ver. 10)).
So, in the DOS OS that was a 8 bit OS, programmers named 8 bits of memory, a "Byte". After that, When the Windows 3.1 OS was a 16 bit OS, they named 16 bits of memory(2 `Bytes`) a "WORD", and 32 bits of memory(4 `Bytes`) a "DWORD"(Double Word) and 64 bits of memory(8 `Bytes`) a "QWORD"(Quad Word).
As I experienced, the length of every program's memory in Windows XP, is from "0x00000000" to the maximum `value` of a "Int"("DWORD"), and equals to "0x7FFFFFFF".
I'm not sure, but I guess, it's because of that, the Windows is a 32 bit OS and the main memory unit for it, is a 32 bit memory unit, and so, the length of a program's memory, is the maximum `value` of a 32 bit memory unit!
Ok. So, we should start our search from "0x0000000" to "0x7FFFFFFF".
2. Q: Is the first found memory address, the exact answer of our search?
A: No! As you can see, there are "0x7FFFFFFF" sectors, and when you search it for a `value` like 83, you could find so many of them. So you need to hold the memory addresses and wait for the `value`s to be changed. Then search the addresses you have, for the new `value`, and do this, until you find, just one memory address that matches your `value`.
3. Q: How to read a program's memory and search it?
A: There are some functions in Windows API that make it possible for us to read and write the memory, from another program.
Thanks goes to "Arik Poznanski" for P/Invokes and methods needed to read and write the Memory, I just used his classes to do this and didn't do the P/Invokes myself.
You can search Codeproject.com, for "Minesweeper, Behind the scenes", to find his comments about these classes.
4. Q: How to convert these `bytes` to a 16, 32 or 64 bit `value`?
A: For this, we used .NET goods! There is a class with static methods that does this for us:
C#
```byte[] bytes = new byte[] { 0x53, 0x00, 0x00, 0x00 };
int value = System.BitConverter.ToInt32(bytes, 0);
//The value is 83```
## Step 4: Let's do the final job
Ok, now you have all the information you need to write the memory scanner.
You just need to do these in your code:
1. Select a process to scan its memory.
2. Scan the whole memory for the specified `value` and hold the addresses.
3. Wait for the `value` to be changed and search the memory address list that you got from the first scan and again wait for the `value` to be changed and scan again, and do this until you find just the address that matches the `value`.
4. At the end, you can freeze the address with a new `value`, by using a timer to write the memory in every timer's tick.
If you download my code, you will find them with comments for every command and every line of code. But there it a little thing I should explain:
`ReadProcessMemory(IntPtr MemoryAddress, uint bytesToRead, out int bytesRead)` that is the most important function, returns an empty `bytes` array if reading your request's size is too big! So I had to read the memory in parts as big as 20480 `bytes` (20KB), and because, when you are searching these memory parts, byte by byte, at the end of the `bytes` array, there will be some `bytes` left! (for example, 3 `bytes` will be left when you are searching for 32 bit `value`s)!
C#
```if (/*scan requirement is less than 20480 bytes*/)
{
}
else
{
/*Loop through blocks(of length 20480 bytes),
until the whole memory is read;
After the first loop, move the current address to
[Data type bytes count - 1] steps back in the memory,
to fix the previously told problem;
After the loops, check to see if any other memory addresses
are left outside of the loops and if so, read them;*/
}```
You can see it:
## That's all
Ok folks, that's all! Hope you like and enjoy it!
And now I'm working on a Enhanced Memory Scanner that could scan all types of data, including the `Bytes`, Signed Data Types and even Strings, it just takes some time!
I'll be back soon.
Written By
Founder Sojaner AB
Sweden
UX designer and full stack developer mainly focused on .NET technologies.
Currently loving .NET Core 2.0.
First PrevNext
Hi Sojaner MegaTh12326-Feb-14 6:48 MegaTh123 26-Feb-14 6:48
Re: Hi Sojaner Rojan Gh.26-Feb-14 10:29 Rojan Gh. 26-Feb-14 10:29
Re: ask Rojan Gh.18-Nov-13 22:35 Rojan Gh. 18-Nov-13 22:35
My vote of 5 Ritschy23-Jun-13 23:53 Ritschy 23-Jun-13 23:53
Re: My vote of 5 Rojan Gh.8-Jul-13 11:42 Rojan Gh. 8-Jul-13 11:42
yaw, pitch and roll Larissa Schön3-Aug-12 13:57 Larissa Schön 3-Aug-12 13:57
DOS != 8Bit LittleFox9431-May-12 22:51 LittleFox94 31-May-12 22:51
Re: DOS != 8Bit Rojan Gh.1-Jun-12 1:34 Rojan Gh. 1-Jun-12 1:34
Re: DOS != 8Bit LittleFox941-Jun-12 3:05 LittleFox94 1-Jun-12 3:05
strings Kurtis Shafer25-May-12 8:16 Kurtis Shafer 25-May-12 8:16
Re: strings Rojan Gh.27-May-12 10:03 Rojan Gh. 27-May-12 10:03
Re: strings Kurtis Shafer29-May-12 6:50 Kurtis Shafer 29-May-12 6:50
Re: strings Rojan Gh.1-Jun-12 1:45 Rojan Gh. 1-Jun-12 1:45
My vote of 5 iliabest19-Jan-12 5:31 iliabest 19-Jan-12 5:31
Re: My vote of 5 Rojan Gh.24-Feb-12 12:10 Rojan Gh. 24-Feb-12 12:10
Need to search String please. AbuS3ood8-Jul-11 6:21 AbuS3ood 8-Jul-11 6:21
Re: Need to search String please. Rojan Gh.11-Jul-11 17:48 Rojan Gh. 11-Jul-11 17:48
Re: Need to search String please. AbuS3ood11-Jul-11 20:41 AbuS3ood 11-Jul-11 20:41
Re: Need to search String please. AbuS3ood12-Jul-11 4:41 AbuS3ood 12-Jul-11 4:41
Re: Need to search String please. Rojan Gh.24-Feb-12 12:13 Rojan Gh. 24-Feb-12 12:13
Game statistics in real-time haxballfan6-Jul-11 8:56 haxballfan 6-Jul-11 8:56
Re: Game statistics in real-time Rojan Gh.11-Jul-11 17:40 Rojan Gh. 11-Jul-11 17:40
Re: Game statistics in real-time haxballfan13-Jul-11 6:23 haxballfan 13-Jul-11 6:23
how to access a specific direction of a program memory [modified] sjstanich9-Jun-11 8:54 sjstanich 9-Jun-11 8:54
Last Visit: 31-Dec-99 18:00 Last Update: 27-Sep-23 19:33 Refresh 1234 Next ᐅ | 3,238 | 11,214 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-40 | latest | en | 0.937649 |
http://mathforum.org/kb/plaintext.jspa?messageID=9137485 | 1,524,243,635,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944479.27/warc/CC-MAIN-20180420155332-20180420175332-00019.warc.gz | 198,320,782 | 1,520 | ```Date: Jun 16, 2013 4:38 AM
Author: Bruno Luong
Subject: Re: eigenvector
"Remus " <remusac@yahoo.com> wrote in message <kpighh\$qj3\$1@newscl01ah.mathworks.com>...> > Hi guys,> I'm also looking at this problem. To answer you question John, yes I know that 1p is an Eigenvector of A. Let A be a matrix which has sum of all rows = 0, then 1p (where p=dim(a)) is an eigenvector of A. > For Example let A = [0 0 0; -1 1 0; -1 0 1]. the comand [V,D]=eig(A) returns the following eigenvectors:> V = [0 0 .5774; 1 0 .5774; 0 1 .5774], which is correct but as posted in the thread it is not normalized to 1.It *is* normalized to 1>> A = [0 0 0; -1 1 0; -1 0 1]A = 0 0 0 -1 1 0 -1 0 1>> [V,D]=eig(A) V = 0 0 0.5774 0 1.0000 0.5774 1.0000 0 0.5774D = 1 0 0 0 1 0 0 0 0>> sqrt(sum(V.^2,1)) % compute l2-norm of 3 eigen vectors ans = 1 1 1>>% Bruno
``` | 401 | 973 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-17 | latest | en | 0.826757 |
https://www.trustudies.com/question/2271/Q-2-Arrange-the-following-in-descending-order-i-frac-2-9-frac-2-3-frac-8-21-br-ii-frac-1-5-frac-3-7-frac-7-10/ | 1,611,399,718,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00664.warc.gz | 1,001,866,355 | 3,559 | Q.2 Arrange the following in descending order: (i)$$\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$$
(ii) $$\frac{1}{5} ,\frac{3}{7}, \frac{7}{10}$$
(i)$$\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$$
$$\frac{2}{9}=\frac{2×7}{9×7}=\frac{14}{63}$$ $$\frac{2}{3}=\frac{2×21}{3×21}=\frac{42}{63}$$ $$\frac{8}{21}=\frac{8×3}{21×3}=\frac{24}{63}$$ Hence $$\frac{42}{63} > \frac{24}{63} > \frac{14}{63}$$
$$\frac{2}{3} > \frac{8}{21} > \frac{2}{9}$$
(ii) $$\frac{1}{5} ,\frac{3}{7}, \frac{7}{10}$$
$$\frac{1}{5}=\frac{1×14}{5×14}=\frac{14}{70}$$ $$\frac{3}{7}=\frac{3×10}{7×10}=\frac{21}{70}$$ $$\frac{7}{10}=\frac{7×7}{10×7}=\frac{49}{70}$$ Hence $$\frac{49}{70} > \frac{21}{70} > \frac{14}{70}$$
$$\frac{7}{10} > \frac{3}{7} > \frac{1}{5}$$ | 385 | 722 | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2021-04 | latest | en | 0.318688 |
https://stats.stackexchange.com/questions/276070/testing-proportions-with-low-sample-size | 1,696,226,772,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510967.73/warc/CC-MAIN-20231002033129-20231002063129-00234.warc.gz | 581,442,070 | 41,964 | # Testing proportions with low sample size
## Question :
A student bought 8 packets of crisps to eat and decided to weigh each packet. They discovered that 5 of them weighed less than the "average contents 25g" stated on the packet.
Is this significant at the 5% level?
Comment on the suitability of the test.
## working
Assume that $P(x < \text{average}) = P(x > \text{average})$ for a packet.
This gives $p = 0.5$ , and $\hat{p} = \frac{5}{8} = 0.625$.
$\sigma = \sqrt{0.5 \times 0.5} = 0.5$
Standard error, $SE = \frac{\sigma}{\sqrt{n}} = \frac{0.5}{\sqrt{8}} \approx 0.177$
Using the above I have
$z = \frac{\frac{5}{8} - \frac{1}{2}}{0.177} = \frac{\frac{1}{8}}{0.177} = 0.706 \approx 0.71$.
Looking up this value in the table gives
$z = 0.2389$
Which is not less than $0.05$, so we don't reject $H_0$ in this case (at a $5\%$ significance level)
The suitability of the test is questionable as the sample size is quite low. It's also not very clear what's meant by 'average' here.
# binomial model
Using a binomial model instead of a $z$-test
I assume that $p = 0.5$, then I have $X \sim Bin(8, 0.5)$
To find whether the value of $\frac{5}{8}$ packets being underweight is significant (to a $95\%$ level) I use the model as
$$P(X) = {n \choose x }p^x (1 - p)^{n - x}$$
As
$$P(5) = {8 \choose 5}(0.5)^{5} (0.5)^{3}$$
Which gives $\frac{7}{32} = 0.21875$.
This is insignificant at a $5\%$ level.
The binomial test was more suitable for this situation as the values were low and easy to compute.
## improvements
if the student had recorded the actual weight rather than just whether or not they were less than the given average then they would have been able to make inferences based on that data.
• Even assuming the binomial model is suitable, your binomial calculations are not the appropriate ones to test this hypothesis. You might want to review our posts on p-values, such as stats.stackexchange.com/questions/tagged/…
– whuber
Apr 26, 2017 at 22:31
• @whuber thanks - what's unsuitable about the binomial model here? It seems that I'm finding the probability of there being (5/8) , and from this I'm seeing whether it's 'particularly' unlikely or not. Here, particularly would be a value of 0.025 or less.
– baxx
Apr 26, 2017 at 22:34
• To appreciate the error, emulate your calculations with different numbers. Suppose, for instance, there were $1000$ packets and $501$ of them were underweight. (1) Intuitively, how strong is this evidence against the hypothesis that half or more of all packets meet the stated weight? (2) What number does your calculation give you?
– whuber
Apr 26, 2017 at 22:36
• @whuber cheers, (1) it's very weak evidence against the hypothesis, as it's only 'off by one' (where 1 is 1/1000). (2) my calculation is $P(X) = {1000 \choose x} p^{x}(1 - p)^{1000 - x}$ where $x = 501$, which gives roughly $0.0252$. Which isn't less than $0.025$ and isn't therefore evidence against the hypothesis. However, I think I see an error, as changing the values to 10,000 and 5001 I have a value which is 0.0079..., but clearly this is less significant than that of the previous example (with 1000 and 501), so I'm interpreting the output wrong...
– baxx
Apr 26, 2017 at 22:44
• You comment sounds thoroughly confused concerning what a p-value is and how to compute it. I will reiterate my recommendation to review the concepts of hypothesis testing and p-values.
– whuber
Apr 27, 2017 at 13:14
Don't worry about what exactly "average" means in the question because you're given no information about how it was computed; it can only really serve as a benchmark value.
You have dichotomous data. A binomial test is a better fit for this than a $z$-test. I believe the part that says "Comment on the suitability of the test" is hinting that if you were the student, there's a better way to collect the data that would allow you to conduct a more powerful test.
• thanks - I've updated the OP with the binomial test. I'm not sure what a better approach to data collection would be though? (other than just getting loads more samples)
– baxx
Apr 26, 2017 at 22:29
• @baxx The student recorded whether each packet weighed more or less than 25g, but not its actual weight. Apr 26, 2017 at 22:49
• Oh , of course. So if they had recorded the weight of the packets then instead of a binomial model they would have been able to find the mean of the sample - then a $z$-test would have been more appropriate?
– baxx
Apr 26, 2017 at 23:02
• @baxx Right. (>'-')> Apr 27, 2017 at 2:34
• @baxx Yes, in R, binom.test(5, 8) yields .727, whereas you got .219. Apr 27, 2017 at 14:27 | 1,369 | 4,619 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2023-40 | longest | en | 0.913572 |
http://perplexus.info/show.php?pid=6034&cid=40440 | 1,542,795,963,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039747665.82/warc/CC-MAIN-20181121092625-20181121114625-00232.warc.gz | 251,964,825 | 4,379 | All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
perplexus dot info
Sum of Powers (Posted on 2008-04-21)
The numbers 184 and 345 have a special property. Their sum, the sum of their squares, and the sum of their cubes are all perfect squares:
184 + 345 = 23^2
184^2 + 345^2 = 391^2
184^3 + 345^3 = 6877^2
Find another primitive pair of non-zero integers with the same property. Note, a primitive solution is a solution which is not a multiple of any smaller solution.
If you have extended precision math software, try to find a third or fourth primitive solution.
Tip: one of the numbers may be negative.
No Solution Yet Submitted by Brian Smith Rating: 4.0000 (2 votes)
Comments: ( Back to comment list | You must be logged in to post comments.)
Solving tips | Comment 3 of 5 |
Some solving tips:
Equation 2 (a^2+b^2=y^2) is a Pythagorean equation. The general parameterization is [a=k*(x^2-y^2), b=k*(2*x*y), y=k*(x^2+y^2)]
Start with that and find a way to easily find k so that Equations 1(a+b=x^2) and 2 is satisfied simultaneously. Then move on to equation 3 (a^3+b^3=z^2).
Posted by Brian Smith on 2008-04-24 00:42:31
Search: Search body:
Forums (0) | 356 | 1,207 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2018-47 | longest | en | 0.808462 |
https://www.askiitians.com/forums/Botany/if-a-capacitor-is-placed-across-a-20-v-source-wha_198267.htm | 1,696,010,627,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510520.98/warc/CC-MAIN-20230929154432-20230929184432-00109.warc.gz | 695,183,846 | 42,916 | If a capacitor is placed across a 20 V source, what will be the amount of charge after 5 tc? 13.5 V 5.0 V 20 V 12.8 V
Arun
25757 Points
5 years ago
Dear Abhishek
Voltage = 20 v.
So, the amount of charge after 5tc= Vin * (1-e^(-t/rc))
= 20*0.993
=19.86
And its app. = 20 v.
Hence option C is correct.
Regards | 119 | 310 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2023-40 | latest | en | 0.849076 |
http://gpuzzles.com/interview/aptitude/time-to-work-problem/ | 1,485,108,971,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281492.97/warc/CC-MAIN-20170116095121-00290-ip-10-171-10-70.ec2.internal.warc.gz | 121,437,024 | 12,333 | • Views : 20k+
• Sol Viewed : 10k+
Aptitude Questions : Time To Work Problem
Difficulty Popularity
If a class project is completed by all the Girls in X hours.
How much time is taken by Girls and Boys together?
Discussion
Suggestions
• Views : 70k+
• Sol Viewed : 20k+
Aptitude Questions : Measure Water Supply Brain Teaser
Difficulty Popularity
You had an infinite supply of water and a 5 ml and 3 ml gallons.
How would you measure exactly 4 ml in least number of steps ?
• Views : 80k+
• Sol Viewed : 20k+
Aptitude Questions : Classic Lateral Thinking Problem
Difficulty Popularity
There are two glasses in front of you. One of the glasses is full of coke and the other glass is full of lemonade. You take a spoonful of coke and mix it into the glass of lemonade. Now the lemonade glass has a mixture of coke and lemonade. You take a spoonful of that mixture and mix it inside the coke glass.
Now what do you think? - The glass with coke has more quantity of lemonade or the glass with lemonade have more quantity of coke mixed with it?
• Views : 90k+
• Sol Viewed : 30k+
Aptitude Questions : Tough Two Jug Measuring Puzzle
Difficulty Popularity
I got two jugs of
A) 11 liter
B) 6 liter
How can I measure exactly 9 liters ?
• Views : 70k+
• Sol Viewed : 20k+
Aptitude Questions : Tricky Math Race Riddle
Difficulty Popularity
Rooney, Hernandez, and Robin race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Rooney beats Hernandez by 20 meters.
Hernandez beats Robin by 20 meters.
How many meters does Rooney beat Robin by ?
• Views : 70k+
• Sol Viewed : 20k+
Aptitude Questions : Hard Logic Puzzle
Difficulty Popularity
A great meeting is held by a great logician where all the other logicians are called upon. The master logician takes them in a room and makes them sit in circle. A hat is placed on each of their heads. Now all of them can see the color of hats others are wearing but can’t see his own. They are told that there different colors of hats.
The master logician explains that a bell will be rung at regular intervals and the moment when a logician knows the color of his hat, he will leave on the next bell. If anyone leaves at the wrong bell, he will be disqualified and sent home.
All of them are assured of one thing that the puzzle will not be impossible for anyone of them. How will they manage the situation?
• Views : 80k+
• Sol Viewed : 20k+
Aptitude Questions : Logic Problem Brain Teaser
Difficulty Popularity
The world is facing a serious viral infection. The government of various countries have issued every citizen two bottles. You as well have been given the same. Now one pill from each bottle is to be taken every day for a month to become immune to the virus. The problem is that if you take just one, or if you take two from the same bottle, you will die a painful death.
While using it, you hurriedly open the bottles and pour the tablets in your hand. Three tablets come down in your hand and you realize they look exactly the same and have same characteristics. You can’t throw away the pill as they are limited and you can’t put them back or you may put it wrong and may die someday.
How will you ensure that you are taking the right pill?
• Views : 50k+
• Sol Viewed : 20k+
Aptitude Questions : Weight Balance Riddle
Difficulty Popularity
You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.
• Views : 50k+
• Sol Viewed : 20k+
Aptitude Questions : Move 3 MatchSticks Puzzle
Difficulty Popularity
You need to divide area in the picture below into two equal parts by using exactly three match sticks. Can you do it?
• Views : 80k+
• Sol Viewed : 20k+
Aptitude Questions : Logic Math Problem
Difficulty Popularity
David and Albert are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game?
You are a friend of David. Do you suggest him to play first or second?
• Views : 90k+
• Sol Viewed : 30k+
Aptitude Questions : Popular Interview Problem
Difficulty Popularity
I have two rectangular bars.
They have property such that when you light the fire from one end , it will take exactly 60 seconds to get completely burn.
However they do not burn at consistent speed (i.e it might be possible that 40 percent burn in 55 seconds and next 60 percent can burn in 10 seconds).
Problem is : How do you measure 45 seconds ?
Latest Puzzles
22 January
Ball Pyramid Puzzle
Can you count the numbers of the ball in...
21 January
What Am I Poem Riddle
I am the end of life but also the start ...
20 January
Most Popular Number Series IAS Problem
Can you solve the number series problem ...
19 January
Nice What Is It Riddle
It has no heart but yet it lives.
...
18 January
Number Pyramid Puzzle
Can you solve below number pyramid puzzl...
17 January
Japanese Ship Sailing Puzzle
A Japanese ship is on route back to the ...
16 January
Move Four MatchSticks Three Squares Puzzle
Can you move four matchsticks to form th... | 1,334 | 5,489 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-04 | longest | en | 0.937401 |
https://www.geeksforgeeks.org/count-distinct-regular-bracket-sequences-which-are-not-n-periodic/?ref=lbp | 1,623,533,844,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487586390.4/warc/CC-MAIN-20210612193058-20210612223058-00074.warc.gz | 720,809,044 | 28,152 | Related Articles
Count distinct regular bracket sequences which are not N periodic
• Difficulty Level : Easy
• Last Updated : 17 Mar, 2021
Given an integer N, the task is to find the number of distinct bracket sequences that can be formed using 2 * N brackets such that the sequence is not N-periodic.
A bracket sequence str of length 2 * N is said to be N-periodic if the sequence can be split into two equal substrings having same regular bracket sequence.
A regular bracket sequence is a sequence in the following way:
• An empty string is a regular bracket sequence.
• If s & t are regular bracket sequences, then s + t is a regular bracket sequence.
Examples:
Input: N = 3
Output:
Explanation:
There will be 5 distinct regular bracket sequences of length 2 * N = ()()(), ()(()), (())(), (()()), ((()))
Now, none of the sequences are N-periodic. Therefore, the output is 5.
Input: N = 4
Output: 12
Explanation:
There will be 14 distinct regular bracket sequences of length 2*N which are
()()()(), ()()(()), ()(())(), ()(()()), ()((())), (())()(), (())(()), (()())(), (()()()), (()(())), ((()))(), ((())()), ((()())), (((())))
Out of these 14 regular sequences, two of them are N periodic which are
()()()() and (())(()). They have a period of N.
Therefore, the distinct regular bracket sequences of length 2 * N which are not N-periodic are 14 – 2 = 12.
Approach: The idea is to calculate the total number of regular bracket sequences possible of length 2 * N and then to subtract the number of bracket sequences which are N-periodic from it. Below are the steps:
1. To find the number of regular bracket sequences of length 2*N, use the Catalan number formula.
2. For a sequence of length 2*N to be N periodic, N should be even because if N is odd then the sequence of length 2*N cannot be a regular sequence and have a period of N at the same time.
3. Since the concatenation of two similar non-regular bracket sequences cannot make a sequence regular, so both subsequences of length N should be regular.
4. Reduce the number of regular bracket sequences of length N(if N is even) from the number of regular bracket sequences of length 2*N to get the desired result.
Below is the implementation of the above approach:
## C++
`// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function that finds the value of``// Binomial Coefficient C(n, k)``unsigned ``long` `int``binomialCoeff(unsigned ``int` `n,`` ``unsigned ``int` `k)``{`` ``unsigned ``long` `int` `res = 1;` ` ``// Since C(n, k) = C(n, n - k)`` ``if` `(k > n - k)`` ``k = n - k;` ` ``// Calculate the value of`` ``// [n*(n - 1)*---*(n - k + 1)] /`` ``// [k*(k - 1)*---*1]`` ``for` `(``int` `i = 0; i < k; ++i) {`` ``res *= (n - i);`` ``res /= (i + 1);`` ``}` ` ``// Return the C(n, k)`` ``return` `res;``}` `// Binomial coefficient based function to``// find nth catalan number in O(n) time``unsigned ``long` `int` `catalan(unsigned ``int` `n)``{`` ``// Calculate value of 2nCn`` ``unsigned ``long` `int` `c`` ``= binomialCoeff(2 * n, n);` ` ``// Return C(2n, n)/(n+1)`` ``return` `c / (n + 1);``}` `// Function to find possible ways to``// put balanced parenthesis in an``// expression of length n``unsigned ``long` `int` `findWays(unsigned n)``{`` ``// If n is odd, not possible to`` ``// create any valid parentheses`` ``if` `(n & 1)`` ``return` `0;` ` ``// Otherwise return n/2th`` ``// Catalan Numer`` ``return` `catalan(n / 2);``}` `void` `countNonNPeriodic(``int` `N)``{` ` ``// Difference between counting ways`` ``// of 2*N and N is the result`` ``cout << findWays(2 * N)`` ``- findWays(N);``}` `// Driver Code``int` `main()``{`` ``// Given value of N`` ``int` `N = 4;` ` ``// Function Call`` ``countNonNPeriodic(N);` ` ``return` `0;``}`
## Java
`// Java program for above approach``import` `java.io.*;` `class` `GFG{`` ` `// Function that finds the value of``// Binomial Coefficient C(n, k)``static` `long` `binomialCoeff(``int` `n, ``int` `k)``{`` ``long` `res = ``1``;` ` ``// Since C(n, k) = C(n, n - k)`` ``if` `(k > n - k)`` ``k = n - k;` ` ``// Calculate the value of`` ``// [n*(n - 1)*---*(n - k + 1)] /`` ``// [k*(k - 1)*---*1]`` ``for``(``int` `i = ``0``; i < k; ++i)`` ``{`` ``res *= (n - i);`` ``res /= (i + ``1``);`` ``}` ` ``// Return the C(n, k)`` ``return` `res;``}` `// Binomial coefficient based function to``// find nth catalan number in O(n) time``static` `long` `catalan(``int` `n)``{`` ` ` ``// Calculate value of 2nCn`` ``long` `c = binomialCoeff(``2` `* n, n);` ` ``// Return C(2n, n)/(n+1)`` ``return` `c / (n + ``1``);``}` `// Function to find possible ways to``// put balanced parenthesis in an``// expression of length n``static` `long` `findWays(``int` `n)``{`` ` ` ``// If n is odd, not possible to`` ``// create any valid parentheses`` ``if` `((n & ``1``) == ``1``)`` ``return` `0``;` ` ``// Otherwise return n/2th`` ``// Catalan Numer`` ``return` `catalan(n / ``2``);``}` `static` `void` `countNonNPeriodic(``int` `N)``{`` ` ` ``// Difference between counting ways`` ``// of 2*N and N is the result`` ``System.out.println(findWays(``2` `* N) -`` ``findWays(N));``}` `// Driver code``public` `static` `void` `main (String[] args)``{`` ` ` ``// Given value of N`` ``int` `N = ``4``;`` ` ` ``// Function call`` ``countNonNPeriodic(N);``}``}` `// This code is contributed by offbeat`
## Python3
`# Python3 program for``# the above approach` `# Function that finds the value of``# Binomial Coefficient C(n, k)``def` `binomialCoeff(n, k):`` ``res ``=` `1`` ` ` ``# Since C(n, k) = C(n, n - k)`` ``if` `(k > n ``-` `k):`` ``k ``=` `n ``-` `k`` ` ` ``# Calculate the value of`` ``# [n*(n - 1)*---*(n - k + 1)] /`` ``# [k*(k - 1)*---*1]`` ``for` `i ``in` `range``(k):`` ` ` ``res ``=` `res ``*` `(n ``-` `i)`` ``res ``=` `res ``/``/` `(i ``+` `1``)`` ` ` ``# Return the C(n, k)`` ``return` `res`` ` `# Binomial coefficient based function to``# find nth catalan number in O(n) time``def` `catalan(n):`` ` ` ``# Calculate value of 2nCn`` ``c ``=` `binomialCoeff(``2` `*` `n, n)`` ` ` ``# Return C(2n, n)/(n+1)`` ``return` `c ``/``/` `(n ``+` `1``)`` ` `# Function to find possible ways to``# put balanced parenthesis in an``# expression of length n``def` `findWays(n):` ` ``# If n is odd, not possible to`` ``# create any valid parentheses`` ``if` `((n & ``1``) ``=``=` `1``):`` ``return` `0`` ` ` ``# Otherwise return n/2th`` ``# Catalan Numer`` ``return` `catalan(n ``/``/` `2``)`` ` `def` `countNonNPeriodic(N):`` ` ` ``# Difference between counting ways`` ``# of 2*N and N is the result`` ``print``(findWays(``2` `*` `N) ``-` `findWays(N))` `# Driver code``# Given value of N``N ``=` `4`` ` `# Function call``countNonNPeriodic(N)` `# This code is contributed by divyeshrabadiya07`
## C#
`// C# program for above approach``using` `System;``using` `System.Collections.Generic; ` `class` `GFG{`` ` `// Function that finds the value of``// Binomial Coefficient C(n, k)``static` `long` `binomialCoeff(``int` `n, ``int` `k)``{`` ``long` `res = 1;`` ` ` ``// Since C(n, k) = C(n, n - k)`` ``if` `(k > n - k)`` ``k = n - k;`` ` ` ``// Calculate the value of`` ``// [n*(n - 1)*---*(n - k + 1)] /`` ``// [k*(k - 1)*---*1]`` ``for``(``int` `i = 0; i < k; ++i)`` ``{`` ``res *= (n - i);`` ``res /= (i + 1);`` ``}`` ` ` ``// Return the C(n, k)`` ``return` `res;``}`` ` `// Binomial coefficient based function to``// find nth catalan number in O(n) time``static` `long` `catalan(``int` `n)``{`` ` ` ``// Calculate value of 2nCn`` ``long` `c = binomialCoeff(2 * n, n);`` ` ` ``// Return C(2n, n)/(n+1)`` ``return` `c / (n + 1);``}`` ` `// Function to find possible ways to``// put balanced parenthesis in an``// expression of length n``static` `long` `findWays(``int` `n)``{`` ` ` ``// If n is odd, not possible to`` ``// create any valid parentheses`` ``if` `((n & 1) == 1)`` ``return` `0;`` ` ` ``// Otherwise return n/2th`` ``// Catalan Numer`` ``return` `catalan(n / 2);``}`` ` `static` `void` `countNonNPeriodic(``int` `N)``{`` ` ` ``// Difference between counting ways`` ``// of 2*N and N is the result`` ``Console.Write(findWays(2 * N) -`` ``findWays(N));``}`` ` `// Driver Code``public` `static` `void` `Main(``string``[] args)``{`` ` ` ``// Given value of N`` ``int` `N = 4;`` ` ` ``// Function call`` ``countNonNPeriodic(N);``}``}` `// This code is contributed by rutvik_56`
## Javascript
``
Output:
`12`
Time Complexity: O(N)
Auxiliary Space: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.
In case you wish to attend live classes with industry experts, please refer Geeks Classes Live
My Personal Notes arrow_drop_up | 3,307 | 9,398 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2021-25 | latest | en | 0.889793 |
https://www.cfd-online.com/Forums/siemens/96992-wall-shear-stress-pipe.html | 1,516,139,059,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886739.5/warc/CC-MAIN-20180116204303-20180116224303-00063.warc.gz | 857,363,914 | 15,963 | # Wall Shear Stress in a Pipe
Register Blogs Members List Search Today's Posts Mark Forums Read
February 6, 2012, 18:38 Wall Shear Stress in a Pipe #1 Senior Member Ke Wu Join Date: Jan 2012 Posts: 179 Rep Power: 7 Hi Anyone know how to calculate the wall shear stress along the pipe in laminar flow in Star ccm? Thanks
February 6, 2012, 18:41 #2 New Member kj878 Join Date: Feb 2012 Posts: 10 Rep Power: 7 scenes>scalar scene>wall>wall shear stress report>total foce
February 6, 2012, 18:44
#3
Senior Member
Ke Wu
Join Date: Jan 2012
Posts: 179
Rep Power: 7
Quote:
Originally Posted by kj878 scenes>scalar scene>wall>wall shear stress report>total foce
Hi kj878
Is it possible to export the results of wall shear stress in your way?
February 6, 2012, 18:49
#4
New Member
kj878
Join Date: Feb 2012
Posts: 10
Rep Power: 7
Quote:
Originally Posted by itsme_kit Hi kj878 Thanks for your fast reply Is it possible to export the results of wall shear stress in your way?
no problem, i've been lurking this site on hopes that ppl can help me with my problem as well. (perhaps u can attempt to help me?)
the way that i get force due to shear stress is just running the force report and it gives a scalar answer for the total force. i've been taking a piece-wise approach to get my results. im not sure if that can be applied to ur problem
February 11, 2012, 13:32
#5
Senior Member
Ke Wu
Join Date: Jan 2012
Posts: 179
Rep Power: 7
Quote:
Originally Posted by kj878 no problem, i've been lurking this site on hopes that ppl can help me with my problem as well. (perhaps u can attempt to help me?) the way that i get force due to shear stress is just running the force report and it gives a scalar answer for the total force. i've been taking a piece-wise approach to get my results. im not sure if that can be applied to ur problem
I still can't get wall shear stress
It's zero when wall is selected in scalar plots
Do I need to creat a inner cylinder which a little smaller than original cylinder?
How to deal with the wall treatment in the laminar pipe flow?
Thread Tools Display Modes Linear Mode
Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules
Similar Threads Thread Thread Starter Forum Replies Last Post HFLUENT Fluent UDF and Scheme Programming 0 April 27, 2011 12:03 Sinead Kelly (Kelly) OpenFOAM Running, Solving & CFD 2 March 30, 2011 06:41 xiexiehezuo FLUENT 1 September 22, 2009 12:26 Andrea CFX 2 October 11, 2004 05:12 Andreas Borg FLUENT 0 June 7, 2000 06:27
All times are GMT -4. The time now is 17:44. | 758 | 2,740 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2018-05 | latest | en | 0.933353 |
https://forum.xojo.com/t/rotate-picture-without-distortion/43676 | 1,656,775,850,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00556.warc.gz | 318,722,521 | 6,458 | Rotate Picture without distortion.
My application needs to rotate a picture.
What works so far is to get a ref to the picture,
Create a PixmapShape with the picture as the image.
Rotate the PixmapShape,
Use .Graphics.DrawObject to return the rotated image.
This works but distorts the image. Although, if I rotate it back to it’s original position, it looks perfect again.
So see if you think I am on the right track.
Assume that the picture coming into the method is a rectangle.
If I take the longer side,
And make the new picture area a square of the longest side,
Now If I rotate, I won’t get any distortion as the area being used will not require distortion.
This may crop the PixmapShape if centered.
So I’ll take the longer side and multiply it by sqroot(2). This would give me a square larger than the longest side by the hypotenuse. I am assuming this:
TO rotate a square in another square, the outer square need only be the hypotenuse in length.
That is, take a leg of the inner square, and multiply it by root(2), and you’ll have a leg for the outer square large enough.
A leg large enough to rotate the inner square.
So …
1. Find the longer side of a OriginalPicture to be rotated.
2. Mul that by root 2.
3. Make a NewPicture, square, of the size of the new leg,
4. Use PixmapShape to draw the OriginalPicture into the NewPicture - centered.
(to center use the width/2 and height/2 to center the PixmapShape)
Graphics.DrawObject(PMap, Pic.Width/2, Pic.Height/2) - here PMap is my PixMapShpe.
With that all done, …
5) Rotate the image with PixMapShape.
6) Place the rotated PixMapShape into FinalPicture and return that from the routine.
I’m off to try this. … let’s see if it works …
Eric
Rotation will always distort to some degree. Anti-aliasing is used to mask some of the effects by blending colors, usually.
Having a larger area to do the rotation within just avoids losing some of the pixels from the corners
This might help…
Did you search the forum?
https://forum.xojo.com/6865-rotate-picture-90-degrees
[quote=389517:@LangueR]Did you search the forum?
https://forum.xojo.com/6865-rotate-picture-90-degrees%5B/quote%5D
last I checked, there were more angles than just multiples of 90
@Dave S
You are correct. The post I reffered to has four options that allow rotation to whatever angle is desired. And it shows 4 different ways to skin the same cat, one which may provide better results to Eric (I’m thinking imageMagick, but Eric may find a better option).
Here is the solution I ended up with.
RotateSameSizeV2(Degrees as Integer, Pic as Picture)
// we pass the picture to be rotated and the desired rotation in degrees.
'Create a new picture with width and height of the picture passed to this routine.
Dim NewPic as Picture // this will hold the new picture in a bigger frame.
Dim NewPic2 as Picture // this will hold the rotated picture
Dim NewSide As Double // we need to calculate a value for a long side.
// Which side of the passed picture is the longest?
If Pic.Width > Pic.Height Then
NewSide=Pic.Width
Else // = or H is larger
NewSide=Pic.Height
End
// Now we have the longest side.
// if we make a new picture that is a square, with the longest side for each leg, we’ll end up cropping
// the picture as we rotate it. So we need to add some length.
'NewSide=NewSide*Sqrt(2) // find the diag of the square made of the longer side.
NewPic = new Picture(NewSide,NewSide) // make a picrure with this as it’s new width and height
’ create a pixmap shape to hold the rotation map
Dim PMap as PixmapShape
PMap = New PixmapShape
Pmap.Height=NewSide
PMap.Width=NewSide
PMap.Image=Pic
Pmap.SourceLeft=0 // not sure these are important.
PMap.SourceTop=0// not sure these are important.
Pmap.SourceHeight=Pic.Height // not sure these are important.
Pmap.SourceWidth=Pic.Width // not sure these are important.
PMap.Rotation=(Degrees/57.296) // rotate the passed picture
// you MUST center the object
NewPic.Graphics.DrawObject(PMap, NewSide/2, NewSide/2)
// draw the rotated picture cropped to the frame
// What’s odd is that I needed to center the PMap and
// I found the XOJO docs on Pixel Maps did not tell me why.
// But this works.
// now I return the rotated picture.
Return NewPic
// There is a little cropping but I think this is due to a rounding error and could be fixed by making
// NewSide a little longer to compensate. | 1,091 | 4,382 | {"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} | 3.125 | 3 | CC-MAIN-2022-27 | latest | en | 0.870956 |
http://nieonline.com/starledger/2011footballscience.cfm | 1,430,198,286,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246660724.78/warc/CC-MAIN-20150417045740-00061-ip-10-235-10-82.ec2.internal.warc.gz | 194,104,410 | 9,500 | For Teachers
Lessons & Classroom Activities
For Students
Interactive features
Cool Web Sites
Special Video Report:
Are you ready for some football (science)?
Courtesy: National Science Foundation, NBC Learn and The National Football League
Think you know football? Ok, what's a prolate spheroid?
NBC Learn, the educational arm of NBC News, has teamed up with the National Science Foundation (NSF) and the National Football League (NFL) to produce this 10-part video series focusing on the science behind NFL football.
This groundbreaking project uses the global spotlight of the NFL games to make science more accessible and more interesting to students, by showing how science helps athletes accomplish their goals by exploring concepts from geometry like the Pythagorean Theorem, physics concepts like torque, velocity and accelleration and more.
By the way, prolate spheroid roughly describes the three-dimensional shape of a football.
Select a video by clicking on a topic below
Passing and Vectors
This segment looks at the role vectors play every time an NFL quarterback throws a pass. With the help of former NFL quarterback Joey Harrington, NSF-funded scientists explain how to use vectors to calculate the speed and direction needed for a completed pass.
Watch the video
Punting and projectile motion and parabolas
This segment looks at the science of projectile motion and parabolas with the help of former NFL punter Craig Hentrich. NSF-funded scientists explain the significance of vertical and horizontal velocity on the trajectory every time an NFL punter kicks a football into the sky.
Watch the video
Training Camp: Nutrition, Hydration & Health
This segment looks at the physically demanding pre-season ritual of NFL training camp. Professor Douglas Casa, head of the Korey Stringer Institute at the University of Connecticut, and athletic trainers from the Pittsburgh Steelers explain what NFL players must do to stay hydrated and replenish the essential nutrients needed to maintain good health during rigorous practices.
Watch the video
Kinematics and running backs: Position, Velocity & Acceleration
This segment explores kinematics on the playing field. Scientists Tony Schmitz from the University of Florida and John Ziegert of Clemson University explain how the kinematic concepts of position, velocity and acceleration can be used to define how a running back moves.
Watch the video
Geometric Shapes: Spheres, Ellipses & Prolate Spheroids
In this segment, NBC's Lester Holt explores the prolate spheroid, the three-dimensional shape of a football, and how it helps an NFL quarterback throw a hard, accurate pass.
Watch the video
Newton's First Law of Motion
In this segment, NBC's Lester Holt looks at Newton's First Law of Motion and the role that unbalanced forces play whenever a ball carrier goes head to head with a defender.
Watch the video
Newton's Second Law of Motion
NBC's Lester Holt and former NFL kicker, Morten Andersen, look at what's really behind powerful field goal kicks--Newton's Second Law of Motion.
Watch the video
Newton's Third Law of Motion
NBC's Lester Holt looks at Newton's Third Law of Motion and the role that conservation of momentum plays whenever players collide on the football field, with former NFL linebacker Hardy Nickerson, Tony Schmitz of the University of Florida and Jim Gates of the University of Maryland.
Watch the video
Offensive linemen and torque
NBC's Lester Holt looks at how the physics concepts of torque and center of mass are applied in football by some of the games most massive players--the offensive linemen.
Watch the video
Tackling and the Pythagorean Theorem
In the last segment of this video series, Lester Holt explores the path a defender must take in order to tackle a ball carrier, and how this distance--called the "angle of pursuit"--can be calculated by using the Pythagorean Theorem to find the hypotenuse of a right triangle, and the distance of a defender's angle of pursuit.
Watch the video | 810 | 4,030 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-18 | longest | en | 0.911955 |
http://www.convertit.com/Go/ConvertIt/Measurement/Converter.ASP?From=firkin&To=capacity | 1,550,630,944,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247494424.70/warc/CC-MAIN-20190220024254-20190220050254-00278.warc.gz | 328,298,789 | 3,854 | Partner with ConvertIt.com
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: ```firkin = 0.034068706056 volume (volume) ``` Related Measurements: Try converting from "firkin" to acre foot, bath (Israeli bath), beer gallon (English beer gallon), cord (of wood), displacement ton, freight ton, hogshead, jigger, minim, oil arroba (Spanish oil arroba), petroleum barrel, pint (fluid pint), pipe, quart (fluid quart), Roman amphora, salmanazar, strike, teaspoon, UK quart (British quart), wine arroba (Spanish wine arroba), or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: firkin = .87378641 amphora (Greek amphora), 2.25 balthazar, 144 cup, .034375 displacement ton, .29464286 dry barrel, 7.73 dry gallon, 61.87 dry pint, 30.94 dry quart, 45 fifth, .18907563 koku (Japanese koku), .01208485 last, 552,960 minim, 3.87 peck (dry peck), .07142857 pipe, .32226263 sack, 3 salmanazar, .48339394 strike, 3.28 tou (Chinese tou), 1,199.05 UK oz fluid (British fluid ounce), 3.75 UK peck (British peck).
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 455 | 1,651 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2019-09 | longest | en | 0.67123 |
http://www.thefreelibrary.com/Back+to+basics%3A+estimating+energy+requirements+for+adult+hospital+...-a0169311678 | 1,469,924,918,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469258944256.88/warc/CC-MAIN-20160723072904-00263-ip-10-185-27-174.ec2.internal.warc.gz | 596,628,415 | 28,692 | # Back to basics: estimating energy requirements for adult hospital patients.
Abstract
Predictive equations are a quick and non-invasive way to estimate a patient's energy requirements, and can be a useful tool when used appropriately. However, as with any tool, the skill and experience of the user will affect the quality of the result. This paper looks at the origins and limitations of some of the more commonly used equations. Considerations in their use and interpretation, such as the use of injury and activity factors, adjusting weight and non-protein calories, are also discussed.
Key words: basal metabolism, energy metabolism, nutrition assessment, nutrition support.
INTRODUCTION
The estimation of a patient's requirements is an essential component of nutrition support, ensuring that the patient's nutritional needs are met without significant over- or underfeeding. In everyday hospital practice, several different equations are used, often without an adequate understanding of their origins and limitations. (1,2) This can lead to significant variation in energy provision, which could have serious implications for patient care. A previous review of prediction equations concluded that none is sufficiently accurate to be useful in practice. (3) However, the reality is that equations are the most widely used method for assessing nutrition support that patients need in hospital. When used appropriately, a predictive equation can be a useful tool. Although it is not a 'magic formula' to tell us the answer, it enables us to make a good prediction as a starting point for ongoing patient care. Like any tool, the equation is only as good as the person using it: skill and experience will significantly inform the use and interpretation of these prediction equations.
BASIC CONCEPTS
The body's energy expenditure is usually described as consisting of three components: the basal metabolic rate (BMR), the energy expended in physical activity, and the thermic effect of feeding (TEF). The BMR is the minimum amount of energy required to sustain the body's essential metabolic processes. It is the value for metabolic rate that would be obtained when the subject first awakes (remaining relaxed, and motionless) after an overnight fast, in a thermoneutral setting. Resting metabolic rate (RMR) approximates the BMR when it is not possible to meet all of the above conditions. It is usually measured in a subject who has fasted and has been lying quietly for at least 30 minutes before measurement. (4) The TEF is the amount of energy consumed by the body after eating, in digesting and absorbing the nutrients from food and converting them for use or storage. It can be measured using indirect calorimetry, by comparing the BMR with energy expenditure measured (in the same conditions) after a meal. TEF is usually assumed to be about 10-15% of the BMR, but is affected by a wide range of factors, such as the subject's nutritional status and the composition of the diet. Other terms used for the TEF include: 'diet-induced thermogenesis', 'postprandial thermogenesis', and 'thermic effect of a meal'. (5) The total energy expenditure is the total of basal energy expenditure (BMR), the TEF and activity. Increased activity raises the total, as does increased food intake (by increasing TEF) and illness/inflammation (by increasing BMR).
The rate of energy consumption in the body changes from moment to moment, and varies between different body organs and tissues, but an individual's BMR changes very little, even over significant periods of time. (6,7) Metabolic rate measurements produce a 'snapshot' of energy expenditure over a short period, which is then used to estimate the average rate of energy expenditure for the whole day. However, the measurement period may not reflect the true energy expenditure, as there is necessarily some variation and error involved. Similarly, the energy released from food will not provide exactly the calculated amount, because of losses as unabsorbed nutrient, losses due to energy conversion inefficiencies, and losses as heat. Decreased activity and muscle mass with ageing, and smaller muscle mass in women, generally contribute to a lower energy expenditure; however, variation between individuals is significant. A group of people of the same age and sex who have similar body weight and body composition will not have identical BMRs; even when intake and activity are controlled, the variation in BMRs between different members of the group will be as much as 10%. (8)
EQUATIONS FOR ESTIMATING ENERGY REQUIREMENTS
Clearly, it would be best if it were possible to measure actual energy expenditure, rather than just estimating it. For this reason, indirect calorimetry is considered to be the 'gold standard' for assessing energy expenditure in hospitalised patients. This uses respiratory gas exchange to estimate fuel consumption, and can produce accurate results when implemented correctly by trained personnel. It is not infallible, however, as its results are affected by factors such as oxygen therapy, haemodynamic instability, fever, nursing care activities and difficulties obtaining a steady state. (9) It is time-intensive and requires expensive equipment, and at present, most dietitians do not have access to this method for everyday estimation of their patients' needs.
Other measurement methods are generally not useful for hospital patients. Direct calorimetry is not in wide use even for research purposes, as it measures energy expenditure by monitoring the body's heat production and requires a specially designed sealed room with tightly controlled conditions. The doubly labelled water technique is the only research method that allows energy expenditure to be estimated in free-living subjects. This uses orally administered 'heavy' water (containing stable isotopes of hydrogen and oxygen) to measure the body's carbon dioxide production as indicated by the gradual loss of the isotopes from the body over 1-3 weeks. (4) The energy expenditure can then be estimated in a similar way to that in indirect calorimetry. The time frame for doubly labelled water studies is too long for the assessment of most hospital patients, and the heavy water is expensive. As an alternative to these measurement methods, predictive equations provide a cheap, quick and non-invasive method for estimating requirements, based on the main factors that affect energy expenditure: age and sex (which both affect body composition), and body size.
Researchers developing predictive equations have attempted to validate these against measurements of energy expenditure, often using statistical regression or correlation. When assessing the literature, it should be noted that correlation does not necessarily indicate how closely the equation can estimate the patient's expenditure. For example, if an equation always produced a result that was exactly double the true energy expenditure, it would lead to dangerous over-feeding if it was used for predicting patients' requirements. Statistically, though, it is considered a perfect correlation, with a correlation coefficient r = 1. The correlation therefore does not indicate how useful the equation would be in practice. Validation of predictive equations should always consider residuals, limits of agreement, or other indication of fit, rather than just the correlation coefficient. (10)
Various equations have been developed for the estimation of energy requirements, but the most commonly used equations are the Harris-Benedict equation and the Schofield equation. More recently developed equations have attracted attention; these include the Mifflin-St Jeor equation and the Ireton-Jones equation.
Schofield equation (11,12)
The Schofield equations are an extension of the FAO/WHO/UNU work on energy requirements (13) and, as a result, are sometimes referred to, incorrectly, as the WHO equation. (14) Having since been revised by Schofield, the equation now in use is slightly different due to the incorporation of some extra data. It is the most commonly used by Australian dietitians (1) and has been preferred, because it does not require a value for height and, therefore, introduces fewer sources of error if no measured height or weight are available. Schofield did develop an additional equation that included height, but it did not significantly increase the accuracy of the prediction when compared with the simpler equation. The Schofield equation (Table 1) estimates basal requirement. It is based on a very large data set (pooled BMR data from 114 studies, with more than 7000 healthy subjects from 23 different countries). The results may have been affected by significant differences in ambient temperatures for some of the data, and also some of the subjects were significantly underweight and may have been malnourished. The age and weight range of subjects is wide, but the group contains many more men than women, and a significant number (about 1000) of the subjects were young male Italian soldiers and cadets. The average subject in Schofield's data set would therefore be significantly younger, leaner and fitter than an average Australian hospital patient. This may mean that the equations overestimate requirements (15,16) even in young healthy Australian men. (17) Other validating studies have suggested that it may overestimate for those with low requirements and underestimate for those with high requirements, deviating towards the mean for both. (14) In 1991, a British panel of experts, the Panel on Dietary Reference Values, published a modified version of the Schofield equation for use in Britain. (18) They added data from an additional 451 European subjects, particularly from older age groups, and also excluded some of Schofield's original data which were 'collected in the tropics' and were not felt to reflect the requirements of better-nourished British people. The original data set may in fact have been more appropriate for multicultural Australia; however, the modifications affect only the older (over 60 years) age group. In any case, the majority of Australian dietitians are likely to be using the original, unmodified equations, because these are generally the ones to be found in textbooks and other widely used resources, such as the Dietitians' Pocketbook, (19) the previous Recommended Dietary Intakes for Use in Australia (20) and the Nutrient Reference Values for Australia and New Zealand, which replaced it. (21)
Harris-Benedict equation (22)
This equation was developed from a single smaller study, with only 239 subjects, all healthy Americans. The participants may not be reflective of modern Australians because they were relatively young (average age 29 [+ or -] 11 years) and lean (average body mass index 21 [+ or -] 3 kg/[m.sup.2]). Repeated measurements were made in each subject, with careful attention to factors such as subject inactivity; however, the limitations of the testing conditions mean that some subjects may not have been in a true 'basal' state, leading to over-estimation of their energy needs. (8,15) The Harris-Benedict equation (Table 2) is thought to overestimate requirements in healthy people, perhaps by 5% in men or 15% in women. (23-25) A disadvantage of this equation is that it requires both weight and height, which may often not be available. However, as it remains the most commonly used equation in the world, particularly in the USA, it is essential to be familiar with it when assessing the medical literature.
Mifflin-St Jeor equation (26)
This equation used 498 healthy adult subjects with a wide range of ages and weights (about half of the subjects were obese) and measured resting metabolic rate. The equation uses actual weight, and notably it predicts significantly lower requirements when weight is very high, compared with the Schofield and Harris-Benedict equations. An advantage of the Mifflin-St Jeor equation (Table 3) is that it is very simple and easy to remember; however, like the Harris-Benedict equation, it requires values for both weight and height. Because of its wider range of subjects, it is considered to reflect the requirements of the modern US population with less estimation bias than other equations, and has recently been endorsed by the American Dietetic Association. (27) Its use may increase in those populations among whom obesity is becoming more common, but it does not yet appear to be in common use in Australia (1) and has not been subjected to as much critical scrutiny as the older equations, having been developed more recently Further research may help establish whether it will be of lasting use in practice.
Activity and injury factors
All three of the equations above were developed using healthy subjects, and may not accurately reflect the requirements of hospitalised patients. They estimate only basal or resting requirements, and therefore, it is customary to make adjustments to the value obtained, to allow for energy expended in activity and for the increased requirements due to illness. In practice, these adjustment factors are often applied in different ways. Typically, the result from the equation is multiplied by an activity factor (which may be only 1.0 for a sedated patient lying still in bed) and a stress or injury factor pertaining to the individual patient's condition. There is no evidence to support the less-common practice of adding the activity and stress factors before multiplying by the basal energy expenditure. It may be based on different assumptions about how activity and stress would increase requirements.
The activity and stress factors were not developed by the authors of the equations, but have been suggested by researchers investigating total energy expenditure in different states of illness or exercise. Table 4 lists activity factors derived from the FAO/WHO/UNU Expert Consultation Report and from a variety of other studies, mostly in healthy people. (13,28-33) Physical activity levels (PALs) are obtained by measuring total energy expenditure in free-living individuals and dividing by their BMR. This produces a multiple of the BMR that expresses the average energy requirement for that individual's level of daily activity. When the measured energy cost of a particular activity (climbing a ladder, for example) is expressed as a multiple of BMR, this is called the physical activity ratios (PARs) for that activity. Both PALs and PARs are expressed as a multiple of the BMR, and are therefore affected by any errors in measurement of BMR and total energy expenditure. (34) The PAR and PAL values are generated from non-fasting subjects, so they include the TEF: this means that an additional factor for TEF is not necessary when using these as activity factors to predict an individual's energy requirement. Illness may have an effect on TEF: the thermic response to nutrition can be increased in stress situations, while continuous tube feeding may reduce TEF close to the fasting level. (9) It is important to consider that illness and sedation cause a decrease in activity, so the activity component of total energy expenditure is likely to be lower for a hospital patient than for a healthy person performing the same activity. For example, studies of healthy people with sedentary jobs found that their activity factor averaged 1.5-1.7, (29,35) while Elia reports a variety of studies showing activity factors of only 1.15-1.3 in free-living people with chronic illnesses, and 1.0-1.2 in hospitalised people with acute diseases. (28)
Although illness tends to cause a decrease in physical activity, it can also cause an increase in energy requirements, by several different mechanisms. For example, inflammatory or infective illness can increase the BMR. Large wounds, such as in burn injury, cause loss of heat and body tissue. A fever may increase energy expenditure by about 10% of BMR for every centigrade degree above normal body temperature, (36) while inducing hypothermia (such as after stroke or cardiac arrest) decreases energy expenditure. (37) Pain and stress, too, increase energy expenditure, while sedation and pain control can decrease it. Energy expenditure is reduced further with heavier sedation. (38)
Since the early studies of energy expenditure were published, changes in patient care (particularly in the critically ill) such as improved pain management and respiratory support, avoidance of overfeeding, and more effective treatment of infections, have reduced the impact of illness on energy consumption. This means that older recommendations for injury factors are mostly too high. Newer research has also revealed a surprisingly wide variation in metabolic rates of patients with conditions that were previously assumed to be consistently hypermetabolic, such as cancer (39) and sepsis. (40,41) Such patients may have BMRs that are close to normal, or even below normal, and even where hypermetabolism occurs, it may be short-lived, peaking within a few days. (28) Unfortunately, the injury factors that are still in wide use (and which still appear in many textbooks) are those from the original classic paper by Long et al. from 1979, (42) and use of these may significantly overestimate requirements, as indicated by more recent studies. (28,43-45) One of the more comprehensive approaches is the study by Barak et al., (43) who derived injury factors for the critically ill using indirect calorimetry and compared them with existing factors in the literature. The paper by Elia (28) is a compilation of energy expenditure data for a variety of both acute and chronic illnesses. Table 5 displays some injury factors based on these recent studies.
The studies that derived these injury factors have most commonly used the Harris-Benedict equation, and consequently it has been argued that the factors are not valid to use with other equations. However, the injury factors represent the estimated degree of hypermetabolism as a multiple of the BMR, so in theory they should be applicable to any equation that accurately estimates BMR. In reality, none of the equations is free of bias or error, and this error may be increased if the injury factors are treated as fully transferable between equations. Even with equations known to have a similar bias (such as the Schofield and Harris-Benedict equations, which both tend to overestimate BMR) conservative selection of activity and injury factors may be necessary, to avoid overfeeding. Careful evaluation of the individual patient, with attention to biochemical parameters (such as albumin, C-reactive protein) and clinical signs (such as body temperature, minute ventilation, cardiac output, weight changes), can also help identify whether hypermetabolism is likely, justifying the use of a larger injury factor.
In critically ill patients, even when the energy requirement is significantly increased, it may be difficult, and even inappropriate, to meet these needs. Stress metabolism can interfere with utilisation of the extra energy, leading to an increased risk of overfeeding, and undesirable complications. (46) Conservative provision of nutrition support, or even deliberate underfeeding, is increasingly being recommended in these patients (47,48) despite their known increase in requirements.
Ireton-Jones equation (49)
This is one of the few equations available that have been developed and validated for use in hospitalised patients, rather than healthy people, and is notable for its lower estimates for heavier patients when compared with other commonly used equations. (50) The original equation (Table 6) was developed from a single study of 200 hospitalised patients, including patients with trauma and burns. Advantages of the Ireton-Jones equation include the fact that it uses the patient's actual weight, does not require a value for height, predicts total energy expenditure (therefore does not require activity or stress factors), and is subject to ongoing review by its authors and, therefore, may be more reflective of contemporary medical management than other, older equations. It takes into account specific clinical conditions, such as mechanical ventilation or trauma. However, it is important to be aware of the many assumptions made in developing this equation, which affect its use and interpretation. These include:
1 A patient is critically ill only while ventilated.
2 All burns and trauma are of the same severity, and affect energy requirement during the ventilated/critical illness phase only. This means that the equation does not account for an anabolic period of convalescence.
3 All modes of ventilation have the same impact on energy requirements.
4 All obese patients have the same body size and body composition at a given weight.
Several study groups have tested this equation on their own patients, usually by comparing the results of the equation (which estimates total energy expenditure) with indirect calorimetry measures of resting expenditure. This may be appropriate in a sedated critically ill patient, but is not a valid comparison if the patient has significant activity. Unsurprisingly, the Ireton-Jones equation produces a result that is significantly greater than the resting energy expenditure in such situations. (51,52) In a number of studies of sedated mechanically ventilated patients, the Ireton-Jones equations performed better than other equations (including the Harris-Benedict equation), but did show some bias towards underestimation. (50,53-56) Two studies of acutely ill hospital patients found that the Harris-Benedict equation used with an injury factor was more accurate than the Ireton-Jones equation. One of these studies looked at normal-weight ventilated critically ill patients (using a factor of 1.2); (55) the other was in acutely ill obese patients and used an adjusted weight value (with an injury factor of 1.3). (57)
OTHER CONSIDERATIONS
Which value to use for body weight has been a controversial issue for some time. All of the equations discussed above were developed using the actual weight of each subject, and the authors make no recommendations regarding the use of any other value. Use of an arbitrary adjusted weight value introduces an additional source of possible error, increasing the variability of the result. (58) However, there are many situations in which the patient's weight differs significantly from normal, and the use of the actual weight value can lead to unacceptable errors in estimating requirements. (59-61) It may therefore be appropriate sometimes to use a different value in the calculation.
If the patient is underweight, the use of the patient's current weight is likely to be the best way to estimate current energy requirements. However, in some patients, such as the critically ill, this may be an underestimate. (59) If it is appropriate to aim for weight gain, ideal weight can be used to estimate an ideal energy intake. However, this approach may be too aggressive for frail or unstable patients, and it may be necessary to select a more conservative goal weight at first, particularly in very underweight people. Close monitoring is desirable to ensure that the patient does not develop overfeeding-related complications. The risk of overfeeding is increased during illness, as stress metabolism alters fuel utilisation. (46) During this time, any weight gained will be mainly fat and fluid. (62) As a guide, weight change (either gain or loss) is not an appropriate goal during the period that an injury/stress factor applies to the patient.
If the patient is overweight or obese, or severely oedematous, using the actual weight can lead to an overestimation of the patient's requirements. The metabolic activity of adipose tissue is lower compared with other tissue, (63,64) so an obese patient has a lower metabolic rate per kg body weight. It has been suggested that the ratio of lean tissue to fat tissue changes as weight increases. That is, an increase in adipose tissue is supported by an increase in muscle and organ mass but, at the point of obesity, the fat stores are increasing disproportionately. (65,66) Studies using indirect calorimetry have obtained conflicting results on this point. (23-26,43,67,68) Some suggest that the ratio of lean tissue to fat tissue remains the same as weight increases, even in obesity; others indicate that equations using actual weight can grossly overestimate requirements in the obese. Use of an adjusted weight value is clearly problematic, (69) but may still be appropriate in order to avoid overestimating the patient's requirements in cases where overfeeding is particularly undesirable. These may include situations such as:
1 Where an obese or oedematous patient is not mobilising, such as bedbound or critically ill patients. An ambulant obese or oedematous patient has greater energy expenditure in everyday activities as a result of moving the extra body weight around. If the patient is not mobilising, this contribution to energy expenditure is absent.
2 Where overfeeding may be difficult to detect and is very undesirable, such as in mechanical ventilation or other respiratory compromise, or patients receiving parenteral nutrition.
3 Where the patient is sedentary in the long term, and muscle is not being maintained by activity (therefore, any extra weight is more likely to be adipose tissue), such as elderly patients or those who are otherwise mobility disabled.
4 In patient groups with known reduced energy needs, such as head injury patients after the acute period.
Usually the adjustment consists of using the ideal weight plus 25-50% of the excess weight. (43,57,67) For example, a patient weighing 100 kg whose ideal weight is 60 kg would have an adjusted weight value of 70-80 kg for use in predictive equations. Ideally, the choice of weight adjustment should be based on a physical assessment of the patient's tissue stores. A very muscular patient can be 'overweight' yet be very lean, and it would be appropriate to use actual weight in predicting the energy requirement. For most patients requiring an adjusted weight calculation, an average between ideal and actual weights would be appropriate, (43,57) while in extreme adiposity, where lean tissue stores appear depleted, or in oedema, where lean tissue is not contributing to the extra weight, an even lower adjusted weight might better reflect the patient's reduced metabolic activity. (67) Using an adjusted weight value requires caution, as it increases the risk of underfeeding in overweight patients. (27) If the patient is ambulant, it may be more appropriate to use an obesity-validated equation, such as the Mifflin-St Jeor equation (if height information is available) or the Ireton-Jones equation using the obesity factor.
Total energy or 'non-protein calories'?
In the past it has been suggested (most commonly in the context of parenteral nutrition) that a patient's energy requirements should be provided as 'non-protein calories', in order to spare the protein for healing and anabolism. However, predictive equations estimate the consumption rate of all energy, not just non-protein energy. If it is assumed that the estimated requirement refers only to the non-protein energy requirement, overfeeding will result, and beyond a certain point, giving extra energy will not improve protein sparing at all. As long as the protein requirement is met, it is sufficient to provide the estimated energy needs as the total energy input. (70,71)
CONCLUSION
The use of predictive equations for energy requirements has many pitfalls. There is little benefit in blindly applying an equation without paying attention to the individual characteristics of the patient and the situation. This can affect the credibility of the nutrition support dietitian, attracting terms like 'mumbo-jumbo' and 'dietitian's fudge factor'. An understanding of the origins and limitations of the equations is important for any dietitian who uses them.
The complex appearance of the equations unfortunately seems to give them more authority than they deserve. An equation is not a magic formula, and will not transform incorrect or inaccurate data into a useful result. For example, using an equation with both an estimated height and an estimated weight is probably no better than just making a conservative guess about an appropriate feed rate, or approximating requirements with a simple rule of thumb (such as a 'calories-per-kilo' method). Expressing the predicted requirement as a range, rather than a fixed value, may help avoid implying an unrealistic level of accuracy.
Most importantly, it is often forgotten that the equation only provides a suggested starting point for energy provision: the aim is not just to obtain the 'right answer' at the beginning and then walk away. Ongoing monitoring of the patient is essential, and this may involve regular re-estimation of requirements and adjustment of the feeding regimen as the patient's condition changes. An equation cannot replace other forms of assessment, such as physical examination, and is no substitute for quality patient care. However, when used by an informed and experienced practitioner, predictive equations can still be a valuable and time-saving tool, and retain a role in a dietitian's evidence-based clinical practice.
ACKNOWLEDGEMENTS
The authors wish to acknowledge Kathryn Marshall, Nicola Riley and Kellie Draffin for their valuable contributions to this paper.
REFERENCES
1 Reeves MM, Capra S. Variation in the application of methods used for predicting energy requirements in acutely ill patients: a survey of practice. Eur J Clin Nutr 2003; 57: 1530-35.
2 Elia M. Energy expenditure in the whole body. In: Kinney JM, Tucker HN, eds. Energy Metabolism: Tissue Determinants and Cellular Corollaries. New York: Raven Press, 1992; 19-59.
3 Reeves MM, Capra S. Predicting energy requirements in the clinical setting: are current methods evidence-based? Nutr Rev 2003; 61: 143-51.
4 van Raaij J. Energy. In: Mann J, Truswell AS, eds. Essentials of Human Nutrition, 2nd edn. New York: Oxford University Press, 2003; 81-94.
5 James WPT. From SDA to DIT to TEF. In: Kinney JM, Tucker HN, eds. Energy Metabolism: Tissue Determinants and Cellular Corollaries. New York: Raven Press, 1992; 163-86.
6 Black AE, Cole TJ. Within- and between-subject variation in energy expenditure measured by the doubly-labelled water technique: implications for validating reported dietary energy intake. Eur J Clin Nutr 2000; 54: 386-94.
7 Soares MJ, Shetty PS. Intra-individual variations in resting metabolic rates of human subjects. Hum Nutr Clin Nutr 1986; 40C: 365-9.
8 Daly JM, Heymsfield SB, Head CA et al. Human energy requirements: overestimation by widely-used prediction equation. Am J Clin Nutr 1985; 42: 1170-74.
9 McClave SA, Snider HL. Use of indirect calorimetry in clinical nutrition. Nutr Clin Pract 1992; 7: 207-21.
10 Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1: 307-10.
11 Schofield WN, Schofield C, James WPT. Basal metabolic rate--review and prediction. Hum Nutr Clin Nutr 1985; 39C (Suppl. 1): 5-96.
12 Schofield WN. Predicting basal metabolic rate, new standards and review of previous work. Hum Nutr Clin Nutr 1985; 39C: 1-41.
13 World Health Organisation. Energy and protein requirements. Report of a Joint FAO/WHO/UNU Meeting. WHO Technical Report Series; 724. Geneva: World Health Organisation; 1985.
14 Muller MJ, Bosy-Westphal A, Klaus S et al. World Health Organization equations have shortcomings for predicting resting energy expenditure in persons from a modern, affluent population: generation of a new reference standard from a retrospective analysis of a German database of resting energy expenditure. Am J Clin Nutr 2004; 80: 1379-90.
15 Clark HD, Hoffer LJ. Reappraisal of the resting metabolic rate of normal young men. Am J Clin Nutr 1991; 53: 21-6.
16 Hayter JE, Henry CJ. A re-examination of basal metabolic rate predictive equations: the importance of geographic origin of subjects in sample selection. Eur J Clin Nutr 1994; 48: 702-7.
17 Piers LS, Diffey B, Soares MJ et al. The validity of predicting the basal metabolic rate of young Australian men and women. Eur J Clin Nutr 1997; 51: 333-7.
18 UK Department of Health. Report on health and social subjects 41: dietary reference values for food energy and nutrients for the United Kingdom. Report of the Panel on Dietary Reference Values of the Committee on Medical Aspects of Food Policy. London: Her Majesty's Stationery Office; 1991.
19 Snell R, ed. Dietitians' Pocket Book. Perth: Department of Nutrition, Dietetics and Food Science School of Public Health, Curtin University of Technology, 2006.
20 National Health and Medical Research Council (NHMRC). Recommended Dietary Intakes for Use in Australia. Canberra: National Health and Medical Research Council, 1991.
21 National Health and Medical Research Council (NHMRC) and New Zealand Ministry of Health. Nutrient Reference Values for Australia and New Zealand. Canberra: National Health and Medical Research Council, 2006.
22 Harris JA, Benedict FG. A Biometric Study of Basal Metabolism in Man. Carnegie Institute Publication no. 279. Washington: Carnegie Institute, 1919.
23 Owen OE, Kavle E, Owen RS et al. A reappraisal of the caloric requirements of healthy women. Am J Clin Nutr 1986; 44: 1-19.
24 Owen OE, Holup JL, D'Alessio DA et al. A reappraisal of the caloric requirements of healthy men. Am J Clin Nutr 1987; 46: 875-85.
25 Frankenfeld DC, Muth ER, Rowe WA. The Harris-Benedict studies of human metabolism: history and limitations. J Am Diet Assoc 1998; 98: 439-45.
26 Mifflin MD, St Jeor ST, Hill LA et al. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 1990; 51: 241-7.
27 Frankenfield D, Roth-Yousey L, Compher C. Comparison of predictive equations for resting metabolic rate in healthy non-obese and obese adults: a systematic review. J Am Diet Assoc 2005; 105: 775-89.
28 Elia M. Insights into energy requirements in disease. Public Health Nutr 2005; 8: 1037-52.
29 Black AE, Coward WA, Cole TJ, Prentice AM. Human energy expenditure in affluent societies: analysis of 574 doubly-labelled water measurements. Eur J Clin Nutr 1996; 50: 72-92.
30 Goldberg GR, Black AE, Jebb SA et al. Critical evaluation of energy intake data using fundamental principles of energy physiology: 1. Derivation of cut-off limits to identify under-recording. Eur J Clin Nutr 1991; 45: 569-81.
31 Irsigler K, Veitl V, Sigmund A, Tschegg E, Kunz K. Calorimetric results in man: energy output in normal and overweight subjects. Metabolism 1979; 28: 1127-32.
32 James WPT, Ferro-Luzzi A, Waterlow JC. Definition of chronic energy deficiency in adults. Eur J Clin Nutr 1988; 42: 969-81.
33 Vaz M, Karaolis N, Draper A, Shetty P. A compilation of energy costs of physical activities. Public Health Nutr 2005; 8: 1153-83.
34 Shetty P. Energy requirements of adults. Public Health Nutr 2005; 8: 994-1009.
35 Westerterp KR, Plasqui G. Physical activity and human energy expenditure. Curr Opin Clin Nutr Metab Care 2004; 7: 607-13.
36 DuBois E. The basal metabolism in fever. JAMA 1921; 77: 352-7.
37 Bardutzky J, Georgiadis D, Kollmar R, Schwab S. Energy expenditure in ischemic stroke patients treated with moderate hypothermia. Int Care Med 2004; 30: 151-4.
38 Terao Y, Miura K, Saito M, Sekino M, Fukusaki M, Sumikawa K. Quantitative analysis of the relationship between sedation and resting energy expenditure in postoperative patients. Crit Care Med 2003; 31: 830-33.
39 Bauer J, Reeves MM, Capra S. The agreement between measured and predicted resting energy expenditure in patients with pancreatic cancer: a pilot study. JOP 2004; 5: 32-40.
40 McClave SA, Snider HL. Understanding the metabolic response to critical illness: factors that cause patients to deviate from the expected pattern of hypermetabolism. New Horiz 1994; 2: 139-46.
41 Weissman C, Kemper M. Assessing hypermetabolism and hypometabolism in the postoperative critically ill patient. Chest 1992; 102: 1566-71.
42 Long C, Schaffel N, Geiger J, Schiller W, Blakemore W. Metabolic response to injury and illness: estimation of energy and protein needs from indirect calorimetry and nitrogen balance. JPEN J Parenter Enteral Nutr 1979; 3: 452-6.
43 Barak N, Wall-Alonso E, Sitrin MD. Evaluation of stress factors and body weight adjustments currently used to estimate energy expenditure in hospitalized patients. JPEN J Parenter Enteral Nutr 2002; 26: 231-8.
44 Swinamer DL, Grace MG, Hamilton SM, Jones RL, Roberts P, King EG. Variation in the resting metabolic rate of mechanically ventilated critically ill patients. Crit Care Med 1990; 18: 657-61.
45 Uehara M, Plank L, Hill G. Components of energy expenditure in patients with severe sepsis and major trauma: a basis for clinical care. Crit Care Med 1999; 27: 1295-302.
46 Klein CJ, Stanek GS, Wiles CE. Overfeeding macronutrients to critically ill adults: metabolic complications. J Am Diet Assoc 1998; 98: 795-806.
47 Patino J, Echeverri de Pimiento S, Vergara A, Savino P, Rodriguez M, Escallon J. Hypocaloric support in the critically ill. World J Surg 1999; 23: 553-9.
48 Jeejeebhoy K. Permissive underfeeding of the critically ill patient. Nutr Clin Pract 2004; 19: 477-80.
49 Ireton-Jones C, Jones J. Improved equations for predicting energy expenditure in patients. Nutr Clin Pract 2002; 2: 29-40.
50 MacDonald A, Hildebrandt L. Comparison of fomulaic equations to determine energy expenditure in the critically ill. Nutrition 2003; 19: 233-9.
51 Das SK, Saltzman E, McCrory MA et al. Energy expenditure is very high in extremely obese women. J Nutr 2004; 134: 1412-16.
52 Hirano KM, Heiss CJ, Olson KE, Beerman KA, Brahler CJ. A comparison of calculated and measured resting energy expenditure in obese women. Top Clin Nutr 2001; 16 (61-69): 85-8.
53 Amato P, Keating KP, Quercia RA, Karbonic J. Formulaic methods of estimating calorie requirements in mechanically ventilated obese patients: a reappraisal. Nutr Clin Pract 1995; 10: 229-332.
54 Flancbaum L, Choban PS, Sambucco S, Verducci J, Burge JC. Comparison of indirect calorimetry, the Fick method, and prediction equations in estimating the energy requirements of critically ill patients. Am J Clin Nutr 1999; 69: 461-6.
55 Alexander E, Susla GM, Burstein AH, Brown DT, Ognibene FP. Retrospective evaluation of commonly used equations to predict energy expenditure in mechanically ventilated, critically ill patients. Pharmacotherapy 2004; 24 (12 I): 1659-67.
56 Frankenfield D, Smith JS, Cooney RN. Validation of two approaches to predicting resting metabolic rate in critically ill patients. JPEN J Parenter Enteral Nutr 2004; 28: 259-64.
57 Glynn CC, Greene GW, Winkler MF. Predictive versus measured energy expenditure using limits-of-agreement analysis in hospitalised obese patients. JPEN J Parenter Enteral Nutr 1999; 23: 147-54.
58 Frankenfield DC, Rowe WA, Smith JS, Cooney RN. Validation of several established equations for resting metabolic rate in obese and nonobese people. J Am Diet Assoc 2003; 103: 1152-9.
59 Campbell CG, Zander E, Thorland W. Predicted vs measured energy expenditure in critically ill, underweight patients. Nutr Clin Pract 2005; 20: 276-80.
60 Horgan GW, Stubbs J. Predicting basal metabolic rate in the obese is difficult. Eur J Clin Nutr 2003; 57: 335-40.
61 Shetty PS. Adaptation to low energy intakes: the responses and limits to low intakes in infants, children and adults. Eur J Clin Nutr 1999; 53 (Suppl.): S14-33.
62 Streat SJ, Beddoe AH, Hill GL. Aggressive nutritional support does not prevent protein loss despite fat gain in septic intensive care patients. J Trauma 1987; 27: 262-6.
63 McClave S, Snider H. Dissecting the energy needs of the body. Curr Opin Clin Nutr Metab Care 2001; 4: 143-7.
64 Elia M. Organ and tissue contribution to metabolic rate. In: Kinney JM, Tucker HN, eds. Energy Metabolism: Tissue Determinants and Cellular Corollaries. New York: Raven Press, 1992; 61-79.
65 Naeye RL, Roode P. The sizes and numbers of cells in visceral organs in human obesity. Am J Clin Path 1970; 54: 251-3.
66 Forbes GB. Lean body mass-body fat interrelationships. Nutr Rev 1987; 45: 225-31.
67 Cutts ME, Dowdy RP, Ellersieck MR, Edes TE. Predicting energy needs in ventilator-dependent critically ill patients: effect of adjusting weight for edema or adiposity. Am J Clin Nutr 1997; 66: 1250-56.
68 Ireton-Jones CS, Turner WW. Actual or ideal body weight: which should be used to predict energy expenditure? J Am Diet Assoc 1991; 91: 193-5.
69 Ireton-Jones C. Clinical controversies: adjusted body weight, con: why adjust body weight in energy expenditure equations? Nutr Clin Pract 2005; 20: 474-9.
70 VanWay C. Total calories vs non-protein calories. Nutr Clin Pract 2001; 16: 271-2.
71 Miles JM, Klein JA. Should protein calories be included in caloric calculations for a TPN prescription? Point-counterpoint. Nutr Clin Pract 1996; 11: 204-6.
Suzie FERRIE (1) and Meagan WARD (2)
(1) Royal Prince Alfred Hospital, Sydney, New South Wales, and (2) Department of Nutrition and Dietetics, Austin Health, Melbourne, Victoria, Australia
S. Ferrie, M.Nutr.Diet, APD, Critical Care Dietitian
M. Ward, M.Nutr.Diet, APD, Senior Dietitian
Correspondence: S. Ferrie, Department of Nutrition and Dietetics, Royal Prince Alfred Hospital, Missenden Road, Camperdown, NSW 2050, Australia. Email: suzie.ferrie@cs.nsw.gov.au
```Table 1 Schofield equation for estimating basal metabolic rate
(kJ/day) (11,12)
Age (years) Men Women
10-17 74 W + 2754 56 W + 2898
18-29 63 W + 2896 62 W + 2036
30-59 48 W + 3653 34 W + 3538
Original equations over 60 49 W + 2459 38 W + 2755
Modified equations 60-74 49.9 W + 2930 38.6 W + 2875
Modified equations over 75 35 W + 3434 41 W + 2610
W = weight (kg).
Table 2 Harris-Benedict equation for estimating resting energy
expenditure (kcal/day) (22)
Men 66.5 + 13.8 W + 5.0 H - 6.8 A
Women 655.1 + 9.6 W + 1.8 H - 4.7 A
Coefficients are rounded to one decimal place.
W = weight (kg); H = height (cm); A = age (year).
Table 3 Mifflin-St Jeor equation for estimating resting energy
expenditure (kcal/day) (26)
Men 10 W + 6.25H - 5 A + 5
Women 10 W + 6.25H - 5 A - 161
W = weight (kg); H = height (cm); A = age (year).
Table 4 Activity factors for adult hospital patients (13,28-33)
resting (lying or sitting)# 1.0-1.4 X
BMR
lying still, sedated or asleep 0.9-1.1
lying still, conscious 1.0-1.1
bedrest (moving self around bed) 1.15-1.2
sitting out of bed long periods 1.1-1.3
mobilising occasionally on ward 1.15-1.4
sedentary/light activity (standing for long periods)# 1.4-1.6
mobilising frequently on ward 1.4-1.5
+regular, intensive physiotherapy 1.5-1.6
moderate activity (continuous movement/slow walking)# 1.6-1.8
Factors in bold were obtained in healthy, free-living people.
BMR = basal metabolic rate.
Note: Factors indicated with # were obtained in healthy, free-living
people.
Table 5 Stress/injury factors for adult hospital patients (28,43-45)
Medical 1.1-1.2
(e.g. inflammatory bowel disease, liver or pancreatic disease)
Surgical 1.1-1.4
(e.g. transplant, fistula)
Cancer 1.1-1.4
(e.g. tumour or leukaemia)
Trauma 1.2-1.4
(e.g. skeletal or head injury or minor burns)
Sepsis 1.3-1.4
or other major infection
Major burns 1.4-1.6
Critical illness and/or major surgery/trauma
* With mechanical ventilation 1.2-1.4
* After the first week, for next 2-3 weeks (note limitations >1.6-1.8
on utilisation and risk of overfeeding)
Table 6 Ireton-Jones equation for estimating total energy expenditure
(kcal/day) (49)
Non-ventilated patients
629 - 11 A + 25 W - 609 O
Ventilated patients
1784 - 11 A + 5 W + 244 S + 239 T + 804 B
A = age (year); W = weight (kg).
O = 1 if obese (body mass index > 27); 0 otherwise.
S = 1 if patient is male; 0 otherwise.
T = 1 if trauma (include major surgery) is present; 0 otherwise.
B = 1 if burns are present; 0 otherwise.
```
COPYRIGHT 2007 Dietitians Association of Australia
No portion of this article can be reproduced without the express written permission from the copyright holder. | 10,131 | 44,322 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-30 | latest | en | 0.941098 |
https://www.convertunits.com/from/petabyte/to/kilobyte | 1,624,604,571,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487622113.11/warc/CC-MAIN-20210625054501-20210625084501-00388.warc.gz | 626,772,724 | 13,097 | ## ››Convert petabyte to kilobyte
petabyte kilobyte
How many petabyte in 1 kilobyte? The answer is 9.0949470177293E-13.
We assume you are converting between petabyte and kilobyte.
You can view more details on each measurement unit:
petabyte or kilobyte
The main non-SI unit for computer data storage is the byte.
1 byte is equal to 8.8817841970013E-16 petabyte, or 0.0009765625 kilobyte.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between petabytes and kilobytes.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of petabyte to kilobyte
1 petabyte to kilobyte = 1099511627776 kilobyte
2 petabyte to kilobyte = 2199023255552 kilobyte
3 petabyte to kilobyte = 3298534883328 kilobyte
4 petabyte to kilobyte = 4398046511104 kilobyte
5 petabyte to kilobyte = 5497558138880 kilobyte
6 petabyte to kilobyte = 6597069766656 kilobyte
7 petabyte to kilobyte = 7696581394432 kilobyte
8 petabyte to kilobyte = 8796093022208 kilobyte
9 petabyte to kilobyte = 9895604649984 kilobyte
10 petabyte to kilobyte = 10995116277760 kilobyte
## ››Want other units?
You can do the reverse unit conversion from kilobyte to petabyte, or enter any two units below:
## Enter two units to convert
From: To:
## ››Definition: Petabyte
Most users prefer the non-SI common usage for this term, so on this site a petabyte is the same as a pebibyte, which equals 250 bytes.
## ››Definition: Kilobyte
A kilobyte is a unit of information or computer storage equal to 1024 bytes, assuming a binary system. This is not a standard SI definition, which would use kibibyte to represent 1024 bytes. However, most people have requested the more common usage, so the non-SI version is used on this site.
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 631 | 2,265 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-25 | latest | en | 0.724984 |
https://forums.ni.com/t5/DIAdem/Formatting-curve-colors-on-report/m-p/4351093 | 1,713,779,801,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818105.48/warc/CC-MAIN-20240422082202-20240422112202-00246.warc.gz | 236,686,626 | 149,347 | cancel
Showing results for
Did you mean:
Solved!
Go to solution
## Formatting curve colors on report
Hello!
From the plot below, I need to change the color of the parts of the curve that goes to 0 (so basically all the vertical segments). I don't know if it is possible directly from the report window or maybe throyugh a script. The priority is to delete them in order to show only the values <> 0, and the vertical segments introduce difficulty in reading the graph. Could you please help me? Thanks in advance!
Message 1 of 5
(742 Views)
## Re: Formatting curve colors on report
Hey.
The data points which are equal to zero are valid and will be shown.
If you want to "switch off" these, you can set them to "invalid" (via script, all values =0 to change in "NoValue").
Then - I guess - the result should fit your expectations.
Don't forget to switch off the "interpolation of the curve between NoValues".
Greetings,
Vassili
Message 2 of 5
(694 Views)
## Re: Formatting curve colors on report
Hello! Could you please help me by writing some strings to replace all the 0 values of the channel into "NoValue"? I'm not able to do it... thanks!
Message 3 of 5
(683 Views)
Solution
Accepted by topic author Piacioo
## Re: Formatting curve colors on report
An easy way looks e.g. like this:
``````ChnEventResultList = ChnEventFind("A=0", Array("A"), Array(Data.GetChannel("[1]/MyDataChn")))
Call ChnEventCreateStatusChn("/WOZero", ChnEventResultList, "[1]/MyDataChn", 1, NOVALUE)
Call ChnMul("[1]/WOZero","[1]/MyDataChn", "/MyResultChn")
``````
The first line is the code to a Diadem function "Event Search".
The formula is A=0, and the A is linked to your data channel (I used the name "MyDataChn" and assumed, it's in the 1st group).
The resulting channel is just a state (named "WOZero"), where the zeros are replaced by NV and others by 1.
Finally, multiplying this state channel with your data provides a new data channel, where zero values are replaced by NV.
I use to keep the original data unchanged, and create such new channels instead of "deleting" any information at all...
Greetings
Message 4 of 5
(677 Views)
## Re: Formatting curve colors on report
Fantastic, it works! Thanks a lot, unfortunately I only received an ultra-basic training, I'm trying to learn by myself but no-paper material found, so...
Anyway, thanks again!
Message 5 of 5
(670 Views) | 611 | 2,395 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-18 | latest | en | 0.882755 |
https://study.com/academy/topic/cahsee-logic-tutoring-solution.html | 1,569,224,728,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514576122.89/warc/CC-MAIN-20190923064347-20190923090347-00540.warc.gz | 677,748,592 | 26,542 | # Ch 21: CAHSEE - Logic: Tutoring Solution
The Logic chapter of this CAHSEE Tutoring Solution is a flexible and affordable path to learning about mathematical logic. These simple and fun video lessons are each about five minutes long and they teach all of the operations involving logic covered in the CAHSEE math exam.
## How it works:
• Begin your CAHSEE math exam prep.
• Identify the mathematical logic concepts that you're stuck on.
• Find fun videos on the topics you need to understand.
• Press play, watch and learn!
• Complete the quizzes to test your understanding.
• As needed, submit a question to one of our instructors for personalized support.
## Who's it for?
This chapter of our CAHSEE Tutoring Solution will benefit any student who is trying to learn about mathematical logic and earn passing scores on the exam. This resource can help students including those who:
• Struggle with understanding logical equivalence or fallacies, truth tables or values, conditional statements or any other logic topic
• Have limited time for studying
• Want a cost effective way to supplement their math learning
• Prefer learning about math visually
• Find themselves struggling to prepare for the CAHSEE math exam
• Want to get ahead in high school math
## Why it works:
• Engaging Tutors: We make learning about mathematical logic simple and fun.
• Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
• Consistent High Quality: Unlike a live math tutor, these video lessons are thoroughly reviewed.
• Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about mathematical logic on the go!
• Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.
## Learning Objectives
• Describe the different types of logical equivalence.
• Become familiar with different types of logical fallacies.
• Understand how logic and critical thinking are used in mathematics.
• Learn how to work with truth values, truth tables and propositions.
• Take a look at conditional statements in math.
• Identify conjunctions and disjunctions.
7 Lessons in Chapter 21: CAHSEE - Logic: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken
### Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. | 593 | 2,837 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-39 | longest | en | 0.897372 |
https://chrischona2015.org/7-9-as-a-percent/ | 1,652,773,731,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00646.warc.gz | 233,757,730 | 4,680 | It"s really common as soon as learning around fractions to desire to understand how transform a fraction like 7/9 into a percentage. In this step-by-step guide, we"ll show you just how to rotate any fraction into a percent really easily. Let"s take a look!
Want to easily learn or show students just how to transform 7/9 come a percentage? play this an extremely quick and also fun video now!
Before we gain started in the portion to portion conversion, let"s go over some really quick portion basics. Remember that a numerator is the number over the portion line, and the denominator is the number below the portion line. We"ll usage this later in the tutorial.
You are watching: 7/9 as a percent
When we space using percentages, what we room really speak is that the portion is a portion of 100. "Percent" method per hundred, and so 50% is the same as saying 50/100 or 5/10 in portion form.
So, due to the fact that our denominator in 7/9 is 9, we could readjust the fraction to make the denominator 100. To do that, we divide 100 through the denominator:
100 ÷ 9 = 11.111111111111
Once we have actually that, we deserve to multiple both the numerator and denominator by this multiple:
7 x 11.111111111111/9 x 11.111111111111=77.777777777778/100
Now we can see that our portion is 77.777777777778/100, which method that 7/9 together a portion is 77.7778%.
We can also work this the end in a simpler way by an initial converting the portion 7/9 come a decimal. To perform that, we merely divide the numerator by the denominator:
7/9 = 0.77777777777778
Once we have actually the answer to the division, we deserve to multiply the answer by 100 to do it a percentage:
0.77777777777778 x 100 = 77.7778%
And over there you have actually it! Two various ways to transform 7/9 come a percentage. Both are pretty straightforward and easy come do, but I personally like the transform to decimal an approach as the takes much less steps.
I"ve watched a the majority of students get confused whenever a question comes up around converting a portion to a percentage, yet if you monitor the procedures laid out below it should be simple. That said, you might still require a calculator because that more complex fractions (and you can always use our calculator in the type below).
See more: What Food Is Used As The Base Of Guacamole ? What To Put In Guacamole To Make It Even Tastier!
If you desire to practice, grab you yourself a pen, a pad, and a calculator and shot to convert a couple of fractions to a percentage yourself.
Hopefully this tutorial has actually helped you to understand how to transform a portion to a percentage. You deserve to now walk forth and convert fractions to percentages as much as your small heart desires!
## Fraction as Percentage
Enter a numerator and denominator | 659 | 2,808 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2022-21 | latest | en | 0.940374 |
http://www.mathworks.com/help/control/ref/rss.html?requestedDomain=www.mathworks.com&nocookie=true | 1,516,298,816,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887535.40/warc/CC-MAIN-20180118171050-20180118191050-00613.warc.gz | 482,977,454 | 14,421 | # Documentation
### This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.
Generate random continuous test model
## Syntax
```rss(n) rss(n,p) rss(n,p,m,s1,...,sn) ```
## Description
`rss(n) ` generates an `n-`th order model with one input and one output and returns the model in the state-space object `sys`. The poles of `sys` are random and stable with the possible exception of poles at ```s = 0``` (integrators).
`rss(n,p) ` generates an `n`th order model with one input and `p` outputs, and `rss(n,p,m)` generates an `n-`th order model with `m` inputs and `p` outputs. The output `sys` is always a state-space model.
`rss(n,p,m,s1,...,sn)` generates an s1-by-...-by-sn array of n-th order state-space models with `m` inputs and `p` outputs.
Use `tf`, `frd`, or `zpk` to convert the state-space object `sys` to transfer function, frequency response, or zero-pole-gain form.
## Examples
collapse all
Generate a random SISO state-space model with two states.
`sys2 = rss(2)`
```sys2 = A = x1 x2 x1 -1.101 0.3733 x2 0.3733 -0.9561 B = u1 x1 0.7254 x2 -0.06305 C = x1 x2 y1 0 -0.205 D = u1 y1 -0.1241 Continuous-time state-space model. ```
Generate a model with four states, three outputs, and two inputs. The input arguments to `rss` are arranged in the order states, outputs, inputs.
`sys4 = rss(4,3,2)`
```sys4 = A = x1 x2 x3 x4 x1 -0.6722 -3.145 -4.692 -4.391 x2 2.312 -0.3352 8.041 6.791 x3 5.398 -7.51 -0.5229 1.114 x4 4.087 -7.059 -0.3362 -0.4294 B = u1 u2 x1 0 -0.2256 x2 1.533 0 x3 -0.7697 0 x4 0 0.03256 C = x1 x2 x3 x4 y1 0.5525 0.08593 -1.062 0.7481 y2 1.101 0 2.35 -0.1924 y3 1.544 0 -0.6156 0.8886 D = u1 u2 y1 0 0.4882 y2 -1.402 0 y3 0 -0.1961 Continuous-time state-space model. ```
Generate a 4-by-5 array of SISO models with three states each.
```sysarray = rss(3,1,1,4,5); size(sysarray)```
```4x5 array of state-space models. Each model has 1 outputs, 1 inputs, and 3 states. ``` | 723 | 2,004 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-05 | latest | en | 0.647084 |
https://coderanch.com/t/608735/java/Double-equality | 1,477,137,548,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988718957.31/warc/CC-MAIN-20161020183838-00261-ip-10-171-6-4.ec2.internal.warc.gz | 834,555,695 | 9,507 | # Double equality
Janis Strautins
Greenhorn
Posts: 20
Hi.
I have to do a double comparison, I have tried many things, but nothing really works.. they are responsible for stopping a cycle.
First off, compared double's them selves using (double) Math.round(x*10000000)/10000000, worked fine but then.. Numbers were the same, but weren't(and vice versa), so the cycle continued endlessly.
Tried rounding them and comparing long values, still the same.
Lastly, tried using Big-decimal, ran into problems yet again.
Whats wrong with this code? As far as i know, it's best to use the string constructor, so I'm using it. The second line returns a juicy "java.lang.NumberFormatException", if I edit the 2nd line to, for example, 5.3222, after a while, the first line returns the same error. Should I replace doubles with BigDecimals, only for this comparison? That seems silly to me, there has to be an easy way to do this comparison.
Jesper de Jong
Java Cowboy
Saloon Keeper
Posts: 15559
46
Janis Strautins wrote:As far as i know, it's best to use the string constructor, so I'm using it.
You should understand why people say it's best to use the constructor that takes a string, then you'd realise that if you already have a double, it makes no sense to first convert it to a string so that you can use BigDecimal's constructor that takes a string.
The reason why someone told you that it's best to use the constructor that takes a string, is because double is inherently imprecise, and it can't accurately store values such as for example 0.1. For example, if you do this:
you get:
0.1000000000000000055511151231257827021181583404541015625
If you specify the number in the form of a string "0.1", you won't suffer from the fact that double can't store it precisely:
I don't know what your code looks like, but precise comparisons of double values, using ==, often return false, because there are small rounding errors. Don't use == to compare double values; instead of that, check if they are close enough to each other. For example: | 491 | 2,037 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-44 | longest | en | 0.927501 |
http://mizar.uwb.edu.pl/version/current/html/proofs/matrix15/22 | 1,571,214,808,000,000,000 | text/plain | crawl-data/CC-MAIN-2019-43/segments/1570986666467.20/warc/CC-MAIN-20191016063833-20191016091333-00116.warc.gz | 134,271,821 | 4,340 | let k, m, n be Nat; :: thesis: for D being non empty set
for A being Matrix of n,m,D
for B being Matrix of n,k,D holds
( Segm ((A ^^ B),(Seg n),(Seg ())) = A & Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B )
let D be non empty set ; :: thesis: for A being Matrix of n,m,D
for B being Matrix of n,k,D holds
( Segm ((A ^^ B),(Seg n),(Seg ())) = A & Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B )
let A be Matrix of n,m,D; :: thesis: for B being Matrix of n,k,D holds
( Segm ((A ^^ B),(Seg n),(Seg ())) = A & Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B )
let B be Matrix of n,k,D; :: thesis: ( Segm ((A ^^ B),(Seg n),(Seg ())) = A & Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B )
set AB = A ^^ B;
A1: card (Seg n) = n by FINSEQ_1:57;
A2: len A = n by MATRIX_0:def 2;
then reconsider A9 = A as Matrix of n, width A,D by MATRIX_0:51;
set S1 = Segm ((A ^^ B),(Seg n),(Seg ()));
A3: card (Seg ()) = width A by FINSEQ_1:57;
A4: len (A ^^ B) = n by MATRIX_0:def 2;
now :: thesis: for i, j being Nat st [i,j] in Indices A9 holds
(Segm ((A ^^ B),(Seg n),(Seg ()))) * (i,j) = A * (i,j)
let i, j be Nat; :: thesis: ( [i,j] in Indices A9 implies (Segm ((A ^^ B),(Seg n),(Seg ()))) * (i,j) = A * (i,j) )
assume A5: [i,j] in Indices A9 ; :: thesis: (Segm ((A ^^ B),(Seg n),(Seg ()))) * (i,j) = A * (i,j)
reconsider I = i, J = j as Element of NAT by ORDINAL1:def 12;
A6: dom A = Seg n by ;
n <> 0 by ;
then Indices A9 = [:(Seg n),(Seg ()):] by MATRIX_0:23;
then A7: I in Seg n by ;
A8: J in Seg () by ;
then A9: J = (idseq ()) . J by FINSEQ_2:49
.= (Sgm (Seg ())) . J by FINSEQ_3:48 ;
dom (Segm ((A ^^ B),(Seg n),(Seg ()))) = Seg (len (Segm ((A ^^ B),(Seg n),(Seg ())))) by FINSEQ_1:def 3
.= Seg n by ;
hence (Segm ((A ^^ B),(Seg n),(Seg ()))) * (i,j) = (Col ((Segm ((A ^^ B),(Seg n),(Seg ()))),J)) . I by
.= (Col ((A ^^ B),((Sgm (Seg ())) . J))) . I by
.= (Col (A,J)) . I by A8, A9, Th16
.= A * (i,j) by ;
:: thesis: verum
end;
hence A = Segm ((A ^^ B),(Seg n),(Seg ())) by ; :: thesis: Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B
set w = () + ();
set SS = (Seg (() + ())) \ (Seg ());
set S2 = Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())));
A10: len B = n by MATRIX_0:def 2;
then reconsider B9 = B as Matrix of n, width B,D by MATRIX_0:51;
width A <= () + () by NAT_1:11;
then ( card (Seg (() + ())) = () + () & Seg () c= Seg (() + ()) ) by ;
then A11: card ((Seg (() + ())) \ (Seg ())) = (() + ()) - () by
.= width B ;
now :: thesis: for i, j being Nat st [i,j] in Indices B9 holds
(Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))) * (i,j) = B9 * (i,j)
A12: dom B = Seg n by ;
let i, j be Nat; :: thesis: ( [i,j] in Indices B9 implies (Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))) * (i,j) = B9 * (i,j) )
assume A13: [i,j] in Indices B9 ; :: thesis: (Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))) * (i,j) = B9 * (i,j)
reconsider I = i, J = j as Element of NAT by ORDINAL1:def 12;
A14: J in Seg () by ;
n <> 0 by ;
then Indices B9 = [:(Seg n),(Seg ()):] by MATRIX_0:23;
then A15: I in Seg n by ;
dom (Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))) = Seg (len (Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))))) by FINSEQ_1:def 3
.= Seg n by ;
hence (Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))) * (i,j) = (Col ((Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ())))),J)) . I by
.= (Col ((A ^^ B),((Sgm ((Seg (() + ())) \ (Seg ()))) . J))) . I by
.= (Col ((A ^^ B),(() + J))) . I by
.= (Col (B,J)) . I by
.= B9 * (i,j) by ;
:: thesis: verum
end;
hence Segm ((A ^^ B),(Seg n),((Seg (() + ())) \ (Seg ()))) = B by ; :: thesis: verum | 1,436 | 3,624 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2019-43 | latest | en | 0.753042 |
https://cs.stackexchange.com/questions/37461/is-it-possible-to-minimize-pushdown-automata?noredirect=1 | 1,719,341,114,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198866218.13/warc/CC-MAIN-20240625171218-20240625201218-00488.warc.gz | 163,273,393 | 42,423 | # is it possible to minimize pushdown automata?
is it possible to minimize pushdown automata? If no, why? Is it because for minimization the equivalence classes need to have a finite index and we cannot guarantee that for CFG?
Unfortunately the problem is not computable. It is undecidable even to tell if two arbitrary PDAs are equivalent; minimizing a PDA is even harder.
I answered basically the same question (put more generally) here.
The argument in short: if you could do this, you could decide universality, and a couple of other undecidable properties of PDA/CFG. Hence, by reduction, there can be no such minimizer.
Sorry, minimize in terms of what?
Every PDA has an equivalent one having a single state.
• Huh, true. :) I guess "size of a reasonable encoding", e.g. the transition table. The other answers would work with that, wouldn't they? Commented Jan 21, 2015 at 20:42
I don't know about minimizing in the way you do with non-pushdown automata, but...
You can convert a CFG to PDA right? And that conversion according to Hopcroft has only one state, which is very minimized dont you think? So, all you have to do, is, convert your PDA to CFG, and then your CFG back to PDA, you'll have a 1-state PDA.
• Note that this is state-minimal, but not transition minimal. As DW says, making it transition and state minimal is uncomputable. Commented Apr 13, 2015 at 12:17
"minimize" typically means "global minimum" but sometimes can refer to a "local minimum" in which case there do exist heuristics ie strategies that can result in some reduction but not consistently find the global minimum. and also some special classes of PDAs can be minimized or "trimmed". "non guaranteed terminating" machine learning optimization algorithms eg genetic algorithms can be employed here also. here are two papers on "visibly push down automata" a subclass. 2 example papers along these lines: | 442 | 1,902 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-26 | latest | en | 0.942331 |
https://www.sharebazaar.com/financial-planning/the-first-aid-kit-of-personal-finance/ | 1,726,110,071,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651420.25/warc/CC-MAIN-20240912011254-20240912041254-00074.warc.gz | 923,575,583 | 63,061 | Thursday, September 12, 2024
HomeFinancial PlanningThe First Aid Kit Of Personal Finance
# The First Aid Kit Of Personal Finance
Just as you reach for a medical first aid kit when you’re unwell, personal finance has its own first aid kit. However, this financial first aid kit is meant to be used proactively, not as a reaction to specific events. Its primary purpose is to serve as the starting point for your personal wealth management journey.
## Here We Open The First Aid Box Of Personal Finance:
### Rule of 72, 114, and 144: Doubling, Tripling, and Quadrupling Your Money
1. Rule of 72: This rule helps you estimate how long it will take to double your money at a given interest rate. Simply divide 72 by the interest rate to find the number of years required. For example, with an 8% interest rate, it would take 9 years to double your money.
2. Rule 114: Similar to Rule 72, this rule calculates the time needed to triple your money. Divide 114 by the interest rate to get the number of years. For instance, at a 12% interest rate, it would take 9.5 years to triple your investment.
3. Rule of 144: This rule helps you determine the time required to quadruple your money. Divide 144 by the interest rate to find the number of years needed. At a 12% interest rate, it would take 12 years to quadruple your investment.
### Rule of 70: Dealing with Inflation
To understand how fast your investment’s value will decrease due to inflation, divide 70 by the current inflation rate. For example, if inflation is at 7%, your money’s value will halve in about 10 years.
### 4% Rule for Financial Freedom
This rule is about achieving financial independence. To calculate the corpus required for retirement, multiply your annual expenses by 25. For example, if your annual expenses are 5,00,000, you’ll need 1.25 crore for retirement. Allocate 50% to fixed income and 50% to equity and withdraw 4% annually, which is 5 lakh. This rule works for 96% of the time in a 30-year period.
### 100 Minus Your Age Rule: Asset Allocation
This rule helps determine the asset allocation in your portfolio. Subtract your age from 100 to decide how much of your portfolio should be allocated to equities. For example, if you’re 30, allocate 70% to equities and 30% to debt, and if you’re 60, go for 40% equities and 60% debt.
### 10-5-3 Rule: Reasonable Returns Expectations
Set realistic return expectations for your investments: 10% for equities or mutual funds, 5% for debts (like fixed deposits), and 3% for savings accounts.
### 50-30-20 Rule: Income Allocation
Divide your income into three categories: 50% for needs (e.g., groceries, rent, EMI), 30% for wants (entertainment, vacations), and 20% for savings (equity, mutual funds, debt). Strive to save at least 20% of your income.
### 3X Emergency Rule: Building Emergency Funds
Always keep at least three times your monthly income in an emergency fund to cover unexpected expenses like job loss or medical emergencies. You can aim for six times your monthly income for added security.
### 40% EMI Rule: Managing Loan Payments
Ensure that your total monthly EMIs do not exceed 40% of your monthly income. For instance, if you earn 50,000 per month, limit your EMIs to 20,000.
### Life Insurance Rule: Protecting Your Loved Ones
Secure your family’s financial future with life insurance. Aim for a sum assured that is 20 times your annual income. For example, if you earn 5 lakhs annually, your insurance should be at least 1 crore.
### 70-20-10 Rule for Equity Investing
When investing in equities, consider allocating 70% to large-cap stocks, 20% to mid-cap stocks, and 10% to small-cap stocks.
`Disclaimer: This blog has been written exclusively for educational purposes. The securities mentioned are only examples and not recommendations. It is based on several secondary sources on the internet and is subject to changes. Please consult an expert before making related decisions.`
RELATED ARTICLES
Continue to the category | 948 | 3,992 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-38 | latest | en | 0.92742 |
https://bigfrontend.dev/problem/pickup-the-stones/aisolution | 1,686,324,575,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224656737.96/warc/CC-MAIN-20230609132648-20230609162648-00491.warc.gz | 153,363,012 | 12,400 | This solution is generated by ChatGPT, correctness is not guaranteed.
# AI solution for JavaScript Coding Question on BFE.dev 147. Pick up stones
Here's one solution using recursion and memoization to avoid redundant calculations:
``````function winningStonePicking(n) {
const memo = new Map();
function canWin(numStones) {
if (numStones <= 0) {
return false;
}
if (numStones === 1 || numStones === 2) {
return true;
}
if (memo.has(numStones)) {
return memo.get(numStones);
}
const canWinTakingOne = !canWin(numStones - 1);
const canWinTakingTwo = !canWin(numStones - 2);
const result = canWinTakingOne || canWinTakingTwo;
memo.set(numStones, result);
return result;
}
if (canWin(n)) {
return 'A';
}
return 'B';
}``````
The `canWin(numStones)` function recursively determines whether the player whose turn it is to move can win with `numStones` remaining in the pile. We first check for the base cases where there are only 1 or 2 stones left, since in that case the player who moves first (A) can win by simply taking that number of stones. If there are no stones left, the current player cannot move and therefore cannot win, so we return `false` in that case.
If we have not seen this `numStones` value before (i.e., it's not in the memoization map), we recursively calculate whether we can win by taking 1 or 2 stones. If taking 1 stone results in the opponent winning (i.e., `!canWin(numStones - 1)`), or if taking 2 stones results in the opponent winning (i.e., `!canWin(numStones - 2)`), then the current player can win by taking either 1 or 2 stones, respectively. Otherwise, the opponent has a winning strategy, so we return `false`.
Once we've determined whether A can win with `n` stones, we return `'A'` if she can, or `'B'` otherwise.
This solution has a time complexity of O(n), where n is the number of stones, since we only have to compute `canWin` once for each possible number of stones. The space complexity is also O(n), since we use a memoization map to store the results of previous calculations. | 520 | 2,026 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2023-23 | longest | en | 0.812535 |
https://stthomasbarrowford.org/and-pdf/125-patterning-and-algebra-grade-8-worksheets-pdf-859-350.php | 1,642,686,639,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301863.7/warc/CC-MAIN-20220120130236-20220120160236-00343.warc.gz | 597,316,134 | 7,847 | # Patterning And Algebra Grade 8 Worksheets Pdf
By Pete W.
On Monday, November 16, 2020 10:11:43 AM
File Name: patterning and algebra grade 8 worksheets .zip
Size: 1156Kb
Published: 16.11.2020
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Grade Level. Resource Type.
## grade 8 math worksheets pdf
First things first, prioritize major topics with our printable compilation of 8th grade math worksheets with answer keys. Pursue conceptual understanding of topics like number systems, expressions and equations, work with radicals and exponents, solve linear equations and inequalities, evaluate and compare functions, understand similarity and congruence, know and apply the Pythagorean Theorem, find volume and surface area, develop an understanding of statistics and probability and much more. Our free math worksheets for grade 8 students make sure they start right! Convert each fraction with a multiple of 10 as its denominator into a decimal number by placing the decimal point at the right spot. Finding the Square Roots of Perfect Squares.
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? Grade Level. Resource Type. Log In Join Us. View Wish List View Cart.
Melaine Ninon February 13, Worksheet. Teachers use printable writing paper sheets. They let their students trace the numbers, letters, words or dots as this is the perfect way for a child to practice the controlled movements of his fingers and wrist. With continued practice or tracing, he will soon be able to write more legibly and clearly. There are many types of worksheets you can use as a teaching aid. First is coloring pages. This is good in teaching kids the different colors and their names, and the proper way to color.
where worksheets are printed or photocopied by teachers for use by students, 8 + 3. 10 + 3. Number pattern. 5. 7. 9. Function rule. Multiply by 2 and.
Posted in worksheet, November 13, , am by Amanda. Simple algebra worksheet templates word free premium algebraic expressions pdf. Simple algebra worksheet templates word free premium algebraic expressions pdf — discreetly assembled and subsequently posted at November 13, , am, This simple algebra worksheet templates word free premium algebraic expressions pdf above is one of the pictures in algebraic expressions worksheet pdf in conjunction with other worksheet pictures. Words Tracing Worksheets ear words worksheet worksheets tracing.
Grade 8 maths linear equation in one variable multiple choice questions mcqs 1. This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. Algebra equations worksheets grade 8.
Испания не славится эффективностью бюрократического аппарата, и Беккер понял, что ему придется простоять здесь всю ночь, чтобы получить информацию о канадце. За конторкой сидела только одна секретарша, норовившая избавиться от назойливых пациентов. Беккер застыл в дверях, не зная, как поступить.
Он набрал номер. - Escortes Belen, - ответил мужчина. И снова Беккер изложил свою проблему: - Si, si, senor. Меня зовут сеньор Ролдан.
Халохот остановился у одного из окон, расположенных на уровне его плеча, и посмотрел на улицу. Он находился на северной стороне башни и, по всей видимости, преодолел уже половину подъема. За углом показалась смотровая площадка.
Что значит у вас? - крикнул директор. Это могло оказаться лучшей новостью за весь день. Смит потянулся к объективу камеры, чтобы направить его в глубь кузова. На экране промелькнула внутренняя часть мини-автобуса, и перед глазами присутствующих предстали два безжизненных тела у задней двери. Один из мужчин был крупного телосложения, в очках в тонкой металлической оправе с разбитыми стеклами.
Обсуждая шифры и ключи к ним, он поймал себя на мысли, что изо всех сил пытается соответствовать ее уровню, - для него это ощущение было новым и оттого волнующим. Час спустя, когда Беккер уже окончательно опоздал на свой матч, а Сьюзан откровенно проигнорировала трехстраничное послание на интеркоме, оба вдруг расхохотались. И вот эти два интеллектуала, казалось бы, неспособные на вспышки иррациональной влюбленности, обсуждая проблемы лингвистической морфологии и числовые генераторы, внезапно почувствовали себя подростками, и все вокруг окрасилось в радужные тона. Сьюзан ни слова не сказала об истинной причине своей беседы с Дэвидом Беккером - о том, что она собиралась предложить ему место в Отделе азиатской криптографии. Судя по той увлеченности, с которой молодой профессор говорил о преподавательской работе, из университета он не уйдет.
Я бы хотел задержаться. - Значит, вы видели башню. Гиральду.
Ты лжешь. У меня есть доказательство! - Сьюзан встала и подошла к терминалам.
### Medical billing payment posting interview questions and answers pdf
12.03.2021 at 04:16
### Cleaning supervisor duties and responsibilities pdf
20.02.2021 at 17:01
### Pocket obstetrics and gynecology pdf
04.08.2020 at 00:48 | 1,358 | 5,378 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-05 | latest | en | 0.929668 |
https://pedagogue.app/how-to-understand-percentiles-3/ | 1,719,197,251,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198864986.57/warc/CC-MAIN-20240624021134-20240624051134-00576.warc.gz | 388,763,018 | 26,390 | # How to Understand Percentiles
Standardized tests are quite common. If you are a student, then you must have encountered them one way or another. Some examples include an aptitude test, an intelligence test, the SAT, or GRE. Once you’ve taken these, you will be sent a report about your scores for each section of the test. These standardized tests are not usually the pass-or-fail type of tests. They show you how your skills and knowledge rank among other people who have taken the same test. The results are presented in a different way, which is called percentile rank scores.
Knowing your percentile ranking will allow you to compare your performance with the other people who have also taken the test. For this article, I will explain percentile ranks in terms of SAT scores.
Percentile Rank Scores
Let us say that you are eyeing a school that is quite popular and known for having high academic standards. You are about to take the SAT and decided to research some information about admitted applicants last year. Here is an example of how percentile rank scores might be presented:
SAT Score: 1400
Percentile Rank: 30th percentile
SAT Score: 1570
Percentile Rank: 70th percentile
To summarize, 30% of admitted applicants had SAT scores of 1570 and above, while the rest of the admitted applicants scored 1400 or above. If your SAT score is anywhere between 1400 and 1570, you have a good chance of getting into this school.
Interpreting Results
Aptitude tests usually have several components. Aside from reporting the standard score for each component, the results will also tell you the percentile ranking of your score. For example:
Verbal Reasoning: 30th percentile
Numerical Reasoning: 80th percentile
Mechanical Reasoning: 90th percentile
What do these scores mean in layman’s terms?
Verbal reasoning: this area needs improvement. Your score is higher than only 30% of people who took the test.
Numerical Reasoning: this area is okay. Your score is higher than 80% of people who took the test.
Mechanical Reasoning: you did well in this area. Your score is higher than 90% of people who took the test.
Purpose and Significance
In the context of SAT scores and college applications, percentile rankings are important because they will give you an idea of whether your SAT score is enough to be considered by the college or university of your choice. However, your percentile score is only one part of the admissions requirements for college. Make sure to prepare for the other requirements that may include but are not limited to the following: interview, transcript of records from your high school, and recommendation letters.
Final Thoughts
It is important to note that while the percentile rank scores are designed so that you can gauge how well you did compare to everyone else who took the exam. The result depends on the number of people who took the test and how well they performed. | 614 | 2,927 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2024-26 | latest | en | 0.951529 |
https://forum.ozgrid.com/forum/index.php?user-post-list/117316-widgetwonka/&pageNo=5 | 1,675,291,901,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499953.47/warc/CC-MAIN-20230201211725-20230202001725-00386.warc.gz | 278,596,698 | 22,342 | # Posts by widgetwonka
Something like this (replace the ranges as needs and names as needed):
• ## INDEX Function within IF Formula
Re: INDEX Function within IF Formula
This will find if any of your conditions are true:
=IF(OR(ISERROR(VLOOKUP("*AAA*",\$A2,1,FALSE))=FALSE,ISERROR(VLOOKUP("*BBB*",\$A2,1,FALSE))=FALSE,ISERROR(VLOOKUP("*CCC*",\$A2,1,FALSE))=FALSE)=TRUE,\$B\$1,"No Match")
• ## Compare Two Columns to Receive a Specific Result
Re: Compare Two Columns to Receive a Specific Result
I can think of two ways to do this.
1. use IF(AND(C2="whatever",D2="whatever"),10,something else
you can nest 7 IFs that way
2. Concatenate the field, then use a lookup to return the value you want
so, Cell E2 formula is =C2&D2
and J2 = IF(ISERROR(VLOOKUP(E2,LOOKUP_RANGE,2,FALSE)),"New String",VLOOKUP(E2,LOOKUP_RANGE,2,FALSE))
Where LOOKUP_RANGE has the combinations you want
• ## Profiling Duration in months between 2 dates
Re: Profiling Duration in months between 2 dates
What is the fiscal year in this case? There are 23 months between the two dates specified, but only 20 in your formulas.
• ## Find row with closest value
Re: Find row with closest value
I found one way to do it. It involves sorting the row in descending order, then copying the row and sorting in ascending order.
My Desc row starts in D16. My Asc row starts in E16. My formula to find the row value is:
=MATCH(IF(ABS(G16-INDEX(E16:E33,MATCH(G16,E16:E33,1)))<ABS(G16-INDEX(D16:D33,MATCH(G16,D16:D33,-1))),INDEX(E16:E33,MATCH(G16,E16:E33,1)),INDEX(D16:D33,MATCH(G16,D16:D33,-1))),E16:E33,0)+15
It is an inelegant solution, so maybe someone else can get you closer...
• ## Auto Scaling & auto formating major/minor grid lines
Re: Auto Scaling & auto formating major/minor grid lines
This is getting close to what you want I believe.
• ## Auto Scaling & auto formating major/minor grid lines
Re: Auto Scaling & auto formating major/minor grid lines
Where does this get you:
replacing the [f1] obviously
• ## Deny save if cell empty
Re: Deny save if cell empty
You will need to put the worksheet name that you want to drive the action in place of Sheet1. You will have to put this in the Worksheet section of the VBE.
• ## Multiple users sending data from UserForms to a single sheet
Re: Multiple users sending data from UserForms to a single sheet
You should be using a database program. You probably could code around this in Excel, but it is going to be more work than it is worth.
• ## too many vlookups in a formula
Re: too many vlookups in a formula
Take a look: forum.ozgrid.com/index.php?attachment/37445/
I didn't change you vlookups...I just made it so you don't have to update anything. Just add the Rd# sheets and the sheet will auto populate.
The trick here is to use INDIRECT().
Also, you could easily add 6 to all your lookups. Don't do it in the cell, do it via a reference. That is what I did for your formulas in this workbook. I didn't have to, but I figured it would be illustrative..
• ## Auto Scaling & auto formating major/minor grid lines
Re: Auto Scaling & auto formating major/minor grid lines
I am not terribly familiar with the chat object, but it seems your reference to [f1] needs to reference a value like range("F1").
• ## Formula to deduct value from one cell and add to a different one
Re: Formula to deduct value from one cell and add to a different one
B3
=IF(AND(Details!A2="Apples",Details!B2="A",Details!D2="ordered"),0,-Details!C2)
E3
=IF(AND(Details!A2="Apples",Details!B2="A",Details!D2="Ordered"),Details!C2,-B3)
You could substitute "apples for whatever you want, like a link a cell that has a dynamic value.
You can also add more tests to the AND().
• ## Return a cell value based on 3 text criterias
Re: Return a cell value based on 3 text criterias
maybe you should try the solution I posted to your previous thread:
MODERATOR NOTICE: This topic has also been posted on other sites and may already have an answer elsewhere. Please take this into consideration when answering this question
• ## VBA - How to make Evaluate INDEX MATCH work with Variables as Criteria?
Re: VBA - How to make Evaluate INDEX MATCH work with Variables as Criteria?
break it into two parts:
Code
``````dim str1 as string
dim str2 as string
str1 = worksheetFormula("INDEX(PromoNumber&""2"",Promotions1&Promotions7,0)")
str2 = Application.Index(promotions8,str1,1)
EditPromo.ProdNo2.value = str2``````
• ## Copying New First/Last names from Roster and Inserting into New Rows in diff sheet
Re: Copying New First/Last names from Roster and Inserting into New Rows in diff shee
application.screenupdating = false
application.screenupdating = true
The 0s and 1s are for determining if a value is in the list. for the delete list, it determines if the value is in the imported data. for the addNew, it determines if the the entry is already in the caseload sheet.
The formatting is in reference to your desire to format the rows afterwards. You can record a macro to do it, and copy down any formulas that you have.
I used the offset function so that when you delete a row, you don't create a reference error in the mechanics sheet.
• ## Dynamic Chart based on drop down selection
Re: Dynamic Chart based on drop down selection
I see what you mean after looking at how the data is setup...I would advise changing it to be in a flat database format. It will be tremendously easier to work with.
Here is the solution:
forum.ozgrid.com/index.php?attachment/37421/
It uses INDEX(INDIRECT()) to get what you need.
• ## Checkbox activating sub function
Re: Checkbox activating sub function
Glad to help. I finally joined this site after years of coming here to get quick code. I am happy to see I can give back a little.
• ## Copying New First/Last names from Roster and Inserting into New Rows in diff sheet
Re: Logic Process
I added a sheet called mechanics that will do the sorting for you. I have written the code to compare the old and delete and then add the new:
So, just run compareAndContrast and it will do the rest.
I ran out of steam for the format...I'll let someone else tackle that
forum.ozgrid.com/index.php?attachment/37420/
I had to zip it...I added an arbitrary number of comparative rows, you can adjust if you want it bigger/smaller...
• ## Checkbox activating sub function
Re: Checkbox activating sub function
OK, I have changed your code somewhat. The problem was with how you were using the form. While segregating code is a good idea, skipping from the form to the modules, etc and using the same variable names defined several times was causing the form to think that one of your check boxes was always on, and the other was always off, because FEthernet was used for both boxes.
Also, I changed the directory structure so I could use it on my computer. You will need to change it back in your worksheet.
Here is the code:
Sheet12 private sub:
Code
``````Private Sub BtnCreate_Click()
Call Generate
End Sub``````
frmstart code:
principalmod code:
FastEthernetmod was redundant at this point, so I deleted it.
forum.ozgrid.com/index.php?attachment/37418/ -- here is the workbook as well. Don't forget to change the directories back.
In summary, when using a button on a form, drive the actions within the button code. Don't reference back to a module that also uses the same variable.
Hope this helped. Sorry if I inadvertently deleted some functionality. You can add it back, just do it in line with the form.
• ## Get a cell value based on multiple criteria
Re: Get a cell value based on multiple criteria
Steps:
1. Make a pivot table of the Source data. Include all the rows you want, just de-select blank in the drop down later.
2. Use GETPIVOTDATA for the rest:
Original formula:
=GETPIVOTDATA("Sum of Product",\$A\$3,"Company","Astrix"," Service"," Posting ")
Formula that is driven by Customer Name:
=GETPIVOTDATA("Sum of Product",\$A\$3,"Company",B3," Service"," Posting ")
The GETPIVOTDATA formula can be manipulated a number of ways. So, if you don't want posting, just change "posting" to the service reference: you are done. Go have a beer and tell the boss you worked on it all night. | 2,075 | 8,211 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2023-06 | latest | en | 0.805839 |
http://mathhelpforum.com/algebra/134014-two-linear-equations-problem-print.html | 1,526,923,362,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864461.53/warc/CC-MAIN-20180521161639-20180521181639-00503.warc.gz | 177,549,639 | 3,678 | # Two linear equations problem.
• Mar 15th 2010, 08:47 PM
bnk0430
Two linear equations problem.
I have two problems that I'm having a hard time solving.
Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?
I need to get 2 equations out of it and use the matrix to solve the problem...
The first equation I got from it is...
U + D = 5 and the second is 2U = D...?
The other problem I'm having trouble with is...
Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.
I can't figure out the 2nd one at all. (Headbang)
• Mar 15th 2010, 11:07 PM
earboth
Quote:
Originally Posted by bnk0430
I have two problems that I'm having a hard time solving.
Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?
I need to get 2 equations out of it and use the matrix to solve the problem...
The first equation I got from it is...
U + D = 5 and the second is 2U = D...? <<<<<<< that's correct. Since you have to use a matrix maybe this is better:
U + D = 5
2U - D = 0
The other problem I'm having trouble with is...
Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.
I can't figure out the 2nd one at all. (Headbang)
There are 2 different distances: The jogging distance j and the bus riding distance b:
\$\displaystyle j + b = 16\$
According to the formula \$\displaystyle speed = \dfrac{distance}{time}\$ the time for jogging is:
\$\displaystyle t_j=\dfrac j{4\ \tfrac{mi}{h}}\$
and the busriding time is
\$\displaystyle t_b= \dfrac b{20\ \tfrac{mi}{h}}\$
Both periods add up to 1 hour:
\$\displaystyle \dfrac j{4\ \tfrac{mi}{h}}+\dfrac b{20\ \tfrac{mi}{h}} = 1\ h\$
Can you take it from here?
• Mar 15th 2010, 11:39 PM
bnk0430
Thank you earboth, but for the 2nd question it is actually set up like this...
J+B = 1
4J+20B = 16
I used the first question for time and 2nd question for distance instead of how you provided it. At first when I followed your steps the answer came out to be J = 1 and B = 12. After a couple of minutes of hard thinking and several times of rereading, I thought it would make more sense if the first equation would equal to time instead of distance and that's it! Without your guidance I would've never reach the conclusion on my own so thank you very much!(Happy)
Also I would have never thought of 2U-D = 0 on my own so again thank you.
• Mar 16th 2010, 04:24 AM
HallsofIvy
Quote:
Originally Posted by bnk0430
I have two problems that I'm having a hard time solving.
Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?
I need to get 2 equations out of it and use the matrix to solve the problem...
The first equation I got from it is...
U + D = 5 and the second is 2U = D...?
I can't imagine why you would use matrices to solve this- if D= 2U then the first equation becomes U+ 2U= 3U= 5.
Quote:
The other problem I'm having trouble with is...
Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.
I can't figure out the 2nd one at all. (Headbang)
If J+B = 1 then 4J+ 4B= 4.
subtract that from 4J+20B = 16. | 1,205 | 4,372 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2018-22 | latest | en | 0.964712 |
https://discusstest.codechef.com/t/balls-editorial/4452 | 1,627,732,637,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154089.6/warc/CC-MAIN-20210731105716-20210731135716-00582.warc.gz | 227,038,114 | 3,874 | # BALLS - Editorial
Contest
EASY
### PROBLEM:
Given N(<=10^5) balls, each with a number on top and bottom, find minimum number of flips that can make at least half of the balls show same number on their top. Print “impossible”, if not possible.
### EXPLANATION:
This problem can be solved by keeping a track of how many times a number has occurred on top/bottom. Iterate through all possible numbers that we have and suppose that this number occurs on top, then find total number of moves for this number to show up on at least half of the total balls. The minimal number through all this will be the answer. To find the minimal number of turns to make we need to know two numbers: the number of balls with current color on the top and the number of balls with the current number on bottom (but not at the same time). Let it be integers a and b. Let m = (n + 1) / 2 — the minimal number count of current number to win the game. Then if a + b < m it is impossible won the game using current number at all. If a ≥ m then the answer is 0, otherwise the answer is m - a.
### CODE:
setter.cpp By Prateek Sachdev
// | 271 | 1,118 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-31 | latest | en | 0.896461 |
https://www.xach.com/rpw3/articles/sp6dndOAdvezmV7ZnZ2dnUVZ_u6dnZ2d%40speakeasy.net.html | 1,696,441,721,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511386.54/warc/CC-MAIN-20231004152134-20231004182134-00198.warc.gz | 1,180,641,403 | 2,392 | ``` Subject: Re: Squeezing blood from a turnip From: rpw3@rpw3.org (Rob Warnock) Date: Sun, 23 Jul 2006 00:07:58 -0500 Newsgroups: comp.lang.lisp Message-ID: <sp6dndOAdvezmV7ZnZ2dnUVZ_u6dnZ2d@speakeasy.net> ```
```Bob Felts <wrf3@stablecross.com> wrote:
+---------------
| One of the standard problems is to implement "countBits",
| which counts all of the bits set in an integer. [1]
| One solution uses the fact that and'ing n with (n - 1)
| removes the leastmost bit set in n:
| int countBits(int n)
| { int count;
| for (count = 0; n; n &= (n - 1))
| ++count;
| return (count);
| }
+---------------
Unless you have some strong reason to expect that a *very* small
number of bits in "n" will be set on average, this method is horribly
slow. Much better is the standard iterated comb method, variations
of which were already well-known in the early days of computing
<http://www.inwap.com/pdp10/hbaker/hakmem/hacks.html#item169>:
int countBits(int n) /* Assumes 32-bit ints */
{
n = (n & 0x55555555) + ((n >> 1) & 0x55555555);
n = (n & 0x33333333) + ((n >> 2) & 0x33333333);
n = (n & 0x0f0f0f0f) + ((n >> 4) & 0x0f0f0f0f);
n += (n >> 8);
n += (n >> 16);
return n & 0xff;
}
This is branch-free, and runs in a constant number of cycles for all
inputs. [For 64 bits, add one more line and use wider constants.]
Of course, in Common Lisp one would simply use the built-in LOGCOUNT,
though if you allow negative arguments you will have to pick a
presumed "machine word size" for the result to be meaningful,
either this way:
(defparameter +count-bits-word-width+ 64) ; For example
(defun count-bits (n)
(if (minusp n)
(- +count-bits-word-width+ (logcount n)) ; See def'n of LOGCOUNT
(logcount n)))
or this way:
(defun count-bits (n &optional (bits-per-word 64))
(if (minusp n)
(- bits-per-word (logcount n))
(logcount n)))
[Of course, some error-checking for the value being in range
of ints with BITS-PER-WORD bits would be nice.]
-Rob
-----
Rob Warnock <rpw3@rpw3.org>
627 26th Avenue <URL:http://rpw3.org/>
San Mateo, CA 94403 (650)572-2607
``` | 685 | 2,090 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-40 | latest | en | 0.764506 |
https://goprep.co/ex-7.1-q9b-3-5-3-1-1-3-1-4-name-the-type-of-quadrilateral-i-1nkgge | 1,611,368,383,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00791.warc.gz | 360,723,536 | 34,083 | Q. 9 B
# Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.(-3, 5), (3, 1), (1, -3), (-1,-4)
Let A(-3, 5), B(3, 1), C(1, -3) and D(-1,-4)
Let us see the points on coordinate axes.
Let us first calculate the length of the sides,
We know that distance between two points A(x1, y1) and B(x2, y2) is given by,
Therefore,
Now calculating BC,
Calculating CD,
Calculating DA,
From the lengths we can see that, none of the sides are equal.
Hence, the quadrilateral formed is of no specific type.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Section Formula30 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE Questions29 mins
Smart Revision | Become a Master in Coordinate Geometry54 mins
Distance Formula and Section Formula44 mins
NCERT | Quiz on Section Formula43 mins
Champ Quiz | Coordinate Geometry Problems38 mins
Quiz | Solving Important Questions on Section Formula54 mins
NCERT Solutions of Distance Formula43 mins
Champ Quiz | Distance Formula30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses | 348 | 1,385 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2021-04 | latest | en | 0.826059 |
https://www.britannica.com/science/ideal-mathematics | 1,701,822,870,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100575.30/warc/CC-MAIN-20231206000253-20231206030253-00807.warc.gz | 757,017,850 | 18,750 | Introduction References & Edit History Related Topics
Science & Tech
# ideal
mathematics
ideal, in modern algebra, a subring of a mathematical ring with certain absorption properties. The concept of an ideal was first defined and developed by German mathematician Richard Dedekind in 1871. In particular, he used ideals to translate ordinary properties of arithmetic into properties of sets.
A ring is a set having two binary operations, typically addition and multiplication. Addition (or another operation) must be commutative (a + b = b + a for any a, b) and associative [a + (b + c) = (a + b) + c for any a, b, c], and multiplication (or another operation) must be associative [a(bc) = (ab)c for any a, b, c]. There must also be a zero (which functions as an identity element for addition), negatives of all elements (so that adding a number and its negative produces the ring’s zero element), and two distributive laws relating addition and multiplication [a(b + c) = ab + ac and (a + b)c = ac + bc for any a, b, c]. A subset of a ring that forms a ring with respect to the operations of the ring is known as a subring.
More From Britannica
algebra: Ideals
For a subring I of a ring R to be an ideal, ax and xa must be in I for all a in R and x in I. In other words, multiplying (on the left or right) any element of the ring by an element of the ideal produces another element of the ideal. Note that ax may not equal xa, as multiplication does not have to be commutative.
Furthermore, each element a of R forms a coset (a + I), where every element from I is substituted into the expression to produce the full coset. For an ideal I, the set of all cosets forms a ring, with addition and multiplication, respectively, defined by: (a + I) + (b + I) = (a + b) + I and (a + I)(b + I) = ab + I. The ring of cosets is called a quotient ring R/I, and the ideal I is its zero element. For example, the set of integers (ℤ) forms a ring with ordinary addition and multiplication. The set 3ℤ formed by multiplying each integer by 3 forms an ideal, and the quotient ring ℤ/3ℤ has only three elements:
1. 0 + 3ℤ = 3ℤ = {0, ±3, ±6, ±9,…}
2. 1 + 3ℤ = {…, −8, −5, −2, 1, 4, 7,…}
3. 2 + 3ℤ = {…, −7, −4, −1, 2, 5, 8,…}
William L. Hosch | 682 | 2,233 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2023-50 | latest | en | 0.879562 |
https://www.gophotonics.com/calculators/focal-length-calculator-thick-lens | 1,660,817,644,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00678.warc.gz | 664,115,700 | 22,986 | Focal Length Calculator (Thick Lens)
This is an online calculator to find the focal length of a thick lens. Just enter the radius of curvature, refractive index, and thickness to get the nominal power, effective power, and focal length value.
• mm
• mm
• mm
Result
• Nominal Power
• Effective Power
• Effective Focal Length
mm
Thick lens is a physically large lens whose spherical surfaces are separated by a distance. In other words, it is a lens whose thickness cannot be neglected when compared to its focal length.
Focal length is the distance between the focal point and the optical center of a lens. It is the measure of the ability of a lens to converge or diverge a ray of light. The plane perpendicular to the principal axis of the lens and passing through its focal point is known as the focal plane.
Focal Point is the point to which a set of rays parallel to the principal axis is set to converge (in the case of a convex lens) or appear to diverge (in the case of a concave lens).
Optical Center is a point on the principal axis for which the rays passing through it are not deviated by the lens. Any ray passing through the optic center emerges in a direction parallel to the incident ray, i.e. the ray emerges undeviated.
Principle Axis is the line joining the centers of curvature of the two curved surfaces of a lens.
A lens has two curved surfaces and each surface has a curvature.
Radius of Curvature of a lens is the radius of that circle of which the curvatures of the lens is a part.
Power of a lens is the measure of its ability to produce convergence of a parallel beam of light. A convex lens has a converging effect and thus its power is taken as positive, but a concave lens produces divergence and so its power is taken as negative. The unit in which the power of a lens is measured is called Dioptre. Mathematically,
In the case of a thick lens, the optical power of the surfaces depends on the refractive index of the lens. Thus the power output of both surfaces will be different.
Where nlens is the refractive index of the lens, nobject space is the refractive index of the medium in which the object is kept and R1 is the radius of curvature of surface 1.
nimage space is the refractive index of the medium in which the image is formed, and R2 is the radius of curvature of surface 2.
Nominal Power of a lens is algebraically the sum of optical powers of each surface. It is denoted as 'DNP'.
Where, DNP = D1 + D2
Since the thickness is non-negligible, the Effective Power is not just simply the sum of the individual powers, but it depends on the thickness of the lens. The equation for the effective power of a lens is given by the Gullstrand Equation as,
where 't' is the thickness of the lens.
In such a lens where the power depends on the thickness of the lens, the effective focal length cannot be taken as the sum of individual foci of the two surfaces. So, we define Effective Focal Length as the reciprocal of the effective power of the lens, showing the thickness dependence of the lens. | 688 | 3,050 | {"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} | 3.6875 | 4 | CC-MAIN-2022-33 | longest | en | 0.933309 |
https://datascience.stackexchange.com/questions/80635/poisson-model-with-overdisperssion | 1,713,216,760,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817033.56/warc/CC-MAIN-20240415205332-20240415235332-00080.warc.gz | 185,196,264 | 41,431 | I'm working with a dataset $$X$$ (of length $$N$$) of count data, which looks like:
I developed a statistical model which can be improved, so I'm asking for any suggestions, for instance, differnet likelihoods or prior selection, different approach, anything...
My model
I'm trying to get the parameters of the likelihood of the data, so thaht I can get a posterior predictive density function, credible intervals and so on. Let's say, I want to model the generative process of the data given some parameters, $$f(X|\theta)$$
This data shows a large overdispersion ($$\bar X << var(X)$$), thus a Poisson likelihood, $$f(X|\lambda) \sim \mathcal{Poisson}(\lambda)$$, is not a good choice.
Reading literature about count data with overdisperssion, I decided to model $$f(X|\lambda)$$ as a Negative Binomial distribution, thus $$f(X|\lambda) \sim \mathcal NB(r, p)$$
Parameter estimation
In order to not to end up with a very complex set-up, I've performed bayesian estiamtion of the hyperameter $$p$$, letting $$r$$ be computed from the data: in a Neagative Binomial distribution, $$r$$ is related to the first and second moments of the distribution following:
$$r = \frac{\mu^2}{\sigma^2 - \mu}, \text then$$
$$\hat r = \frac{\bar X^2}{var(X) - \bar X}$$
The whole set-up is:
• Likelihood: $$f(X|p) = \mathcal NB(\hat r, p)$$
• Prior: $$f(p) = \mathcal Beta (0, 0)$$ (non informative, improper prior)
• Posterior: $$f(p|X) = \mathcal Beta (0 + \hat rN, 0 + \sum X)$$
which returned the following posterior predictive distribution:
The first and second moments of the predictive posterior distribution are very close to those in the data (I've let the data have a huge impact in the posteriors since I've choosen a non-informative prior). Also, the point estimate posterior predictive (using $$\mu_p$$) does not differ from an averaged predictive posterior distribution over all possible values of $$p$$.
Once again, any suggestions for improvement?
EDIT
What about a zero-truncated negative binomial distribution?
• How many data points do you have? How many features? Aug 21, 2020 at 19:29
• 10^4 data points, no features at the moment... are you thinking in performin regression with some features? I could add as features the number of pages per document, for instance Aug 21, 2020 at 19:45
• I was mistaken, thinking you are doing regression here... Maybe you can add a little context Aug 21, 2020 at 19:51
• I trying to estimate the parameter $p$ of the likelihood function, so that I can end up with credible intervals, momemts, and so on... I'll clarify it in the post Aug 21, 2020 at 19:53 | 691 | 2,613 | {"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": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2024-18 | latest | en | 0.824825 |
http://www.kwiznet.com/p/takeQuiz.php?ChapterID=2495&CurriculumID=38&Num=1.113 | 1,585,572,924,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00184.warc.gz | 251,082,719 | 4,015 | Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!
#### Online Quiz (WorksheetABCD)
Questions Per Quiz = 2 4 6 8 10
### MEAP Preparation - Grade 7 Mathematics1.113 Profit and Loss Table
The following table gives details of certain transactions involving buying and selling of items. Review the table and answer the questions.
Cost PriceSelling PriceProfitLoss% of Profit% of Loss
\$30\$27...(1)...(2)
\$240\$290(3)...(4)...
360(5)\$45...(6)...
(7)\$680\$40...(8)...
\$96(9)...\$16...(10)
Directions: Find the missing values in the above table.
Q 1: What is the value in place (6)?12 1/2%1 1/6%6 1/12% Q 2: What is the value in place (3) ?\$45\$50\$40 Q 3: What is the value in place (10)?16 2/3%3 1/8%2 3/16% Q 4: What is the value in place (1)?\$3\$50\$5 Q 5: What is the value in place (2)?20%15%10% Q 6: What is the value in place (5)?\$400\$405\$350 Q 7: What is the value in place (7)?\$640\$600\$650 Q 8: What is the value in place (4)?6 5/20%5 6/20%20 5/6% Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only! | 379 | 1,138 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-16 | latest | en | 0.803923 |
https://byjus.com/questions/calculate-the-volume-strength-of-1-5-n-h2-o2-is-a-4-8-b-8-4-c-3-0-d-8-0/ | 1,628,045,240,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154500.32/warc/CC-MAIN-20210804013942-20210804043942-00701.warc.gz | 163,576,176 | 36,543 | # Calculate the volume strength of 1.5 n h2 o2 is a. 4.8 b. 8.4 c. 3.0 d. 8.0
1.5 N = 1.5 g eqwt in 1 L solution.
N= weight/eq.wt (eq wt for hydrogen peroxide = 17 g)
Therefore, 1.5 = wt/17 or wt = 1.5 X17 = 25.5 g
Now, from equation we know that 68 g of H2O2 gives 22.4 L of Oxygen.
Therefore, 25.5 g of Hydrogen peroxide gives-
22.4 X25.5/68
= 8.4 L
So the answer will be ‘b’ | 168 | 385 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-31 | latest | en | 0.804003 |
https://e2e.ti.com/support/audio-group/audio/f/audio-forum/921421/tlv320aic3110-how-to-calculate-power-consumption-from-the-spec?tisearch=e2e-sitesearch&keymatch=TLV320AIC3110 | 1,656,317,320,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00222.warc.gz | 273,873,047 | 30,317 | If you have a related question, please click the "Ask a related question" button in the top right corner. The newly created question will be automatically linked to this question.
# TLV320AIC3110: How to calculate power consumption from the spec?
Part Number: TLV320AIC3110
From the specification, we have Tj(max)=105℃ and Ta=85℃, Rθja=32.7℃/W, Rθja=23.3℃/W
Can we use Tj = Ta+ Θja * P to calculate the power consumption? Is Ta=85℃ when Tj(max) is 105℃?
In other words, which formula is correct in this figure?
thanks.
• Hello Mike,
Power dissipation depends on the voltage and load, which is figured out first, then back calculated to see if Tj (junction temperature) operating at Ta (expected operating environment) will be exceeded. This is done to see if you may need additional airflow or some external heat sink to dissipate heat from the device before it gets too hot.
Regards,
Aaron | 232 | 903 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2022-27 | latest | en | 0.880346 |
https://uk.mathworks.com/matlabcentral/fileexchange/41813-runlength | 1,652,917,202,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662522556.18/warc/CC-MAIN-20220518215138-20220519005138-00738.warc.gz | 672,848,130 | 19,835 | RunLength
version 1.2.0.0 (18.7 KB) by
RunLength coding as fast MEX and M-code
5.9K Downloads
Updated 08 Apr 2017
View License
RUNLENGTH - Run-length coding
Run-length encoding splits a vector into one vector, which contains the
elements without neighboring repetitions, and a second vector, which
contains the number of repetitions.
This can reduce the memory for storing the data or allow to analyze sequences.
Encoding: [B, N, BI] = RunLength(X)
Decoding: X = RunLength(B, N)
INPUT / OUTPUT:
X: Full input signal, row or column vector.
Types: (U)INT8/16/32/64, SINGLE, DOUBLE, LOGICAL, CHAR.
B: Compressed data, neighboring elements with the same value are removed.
B and X have the same types.
N: Number of repetitions of the elements of B in X as DOUBLE or UINT8 row vector.
BI: Indices of elements in B in X as DOUBLE row vector.
RunLength(X, 'byte') replies N as UINT8 vector.
You can find a lot of RLE tools in the FileExchange already. This C-Mex is
about 5 times faster than good vectorized M-versions.
The M-file RunLength_M contains vectorized and loop M-code for education.
EXAMPLES:
Encode and decode:
[b, n] = RunLength([8, 9, 9, 10, 10, 10, 11])
x = RunLength(b, n)
% b = [8,9,10,11], n = [1,2,3,1], x = [8,9,9,10,10,10,11]
Limit counter to 255:
[b, n] = RunLength(ones(1, 257), 'byte')
% b = [1, 1], n = uint8([255, 2])
LOGICAL input:
[b, n] = RunLength([true(257, 1); false])
% b = [true; false], n = [257, 1]
Find the longest sequence:
x = floor(rand(1, 1e6) * 2);
[b, n, bi] = RunLength(x);
[longestRun, index] = max(n);
longestPos = bi(index);
The C-code is compiled automatically the first time RunLength is called.
See "RunLength_ReadMe.txt" for more details.
The unit-test uTest_RunLength tests validity and speed.
Tested: Matlab 6.5, 7.7, 7.8, 7.13, WinXP/32, Win7/64
Compiler: LCC3.8, BCC5.5, OWC1.8, MSVC2008/2010
Does not compile under LCC2.4 shipped with Matlab/32!
Assumed Compatibility: higher Matlab versions, Linux, MacOS.
Cite As
Jan (2022). RunLength (https://www.mathworks.com/matlabcentral/fileexchange/41813-runlength), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Created with R2011b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements
Inspired: runindex, FillGaps_ez
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 724 | 2,406 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2022-21 | latest | en | 0.828121 |
http://www.primenumbers.net/prptop/prptop.php?page=23 | 1,696,005,130,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510520.98/warc/CC-MAIN-20230929154432-20230929184432-00312.warc.gz | 64,813,552 | 12,128 | ## PRP Records
### Probable Primes Top 10000
#### (293510 PRPs in the top)
What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
See the Top discoverers
See the Latest PRPs
Search by form
1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000
Rank Probable prime Digits (> 50000) Who ? When ? 5501 2^365838-461267 110129 Enzo Doria 07/2015 5502 30152^4491+4491^30152 110126 Hans Havermann 11/2020 5503 10^110111+464019 110112 Patrick De Geest 05/2021 5504 10^110111-40001 110111 Robert Price 01/2021 5505 2^365763-6555 110106 Lelio R Paula 04/2017 5506 (2^365689+2^182845+1)/5 110083 11/2006 5507 2^365666-459161 110077 Enzo Doria 05/2015 5508 3*10^110076-7 110077 Robert Price 08/2015 5509 13^98785-72 110041 Lelio R Paula 03/2017 5510 (25^78707+1)/26 110027 Robert Price 06/2013 5511 (7*10^110027-277)/9 110027 Robert Price 02/2022 5512 (16*10^110014-73)/3 110015 Robert Price 07/2020 5513 (7*10^110006-151)/9 110006 Robert Price 02/2018 5514 6^141361-7 110001 Lelio R Paula 11/2014 5515 20^84536+81 109984 Lelio R Paula 03/2017 5516 5*2^365347-9 109982 Lelio R Paula 09/2014 5517 9*6^141303+7 109957 Lelio R Paula 11/2014 5518 27635^9522+9522^27635 109953 Hans Havermann 11/2020 5519 78^58099+77 109929 Norbert Schneider 02/2015 5520 2*10^109928-7 109929 Robert Price 10/2015 5521 30580^3933+3933^30580 109927 Hans Havermann 11/2020 5522 26380^14689+14689^26380 109926 Hans Havermann 11/2020 5523 (2^365161+1130)/2 109925 Stefano Morozzi 09/2020 5524 (27*2^365137-1)/2021 109916 Lelio R Paula 03/2014 5525 (4441*29^75152-24)/7 109905 Curtis Bright 05/2015 5526 (2^365087+7)/6015 109899 Lelio R Paula 01/2014 5527 (2^365069+3774)/2 109897 Stefano Morozzi 02/2021 5528 29652^5083+5083^29652 109894 Mark Rodenkirch 10/2020 5529 (2^365049+722)/2 109891 Stefano Morozzi 09/2020 5530 (35*10^109888-89)/9 109889 Robert Price 02/2022 5531 18^87533-11 109878 Lelio R Paula 04/2017 5532 2^364982-5 109871 Henri Lifchitz 04/2006 5533 3*10^109861+59 109862 Robert Price 08/2018 5534 5*10^109860-69 109861 Robert Price 02/2021 5535 2^364936-1867979 109857 Enzo Doria 04/2016 5536 27013^11652+11652^27013 109846 Hans Havermann 10/2020 5537 2^364867-112087 109836 Enzo Doria 06/2014 5538 4^182415-85061 109825 Mike Oakes 06/2011 5539 (2^364809+1034)/2 109819 Stefano Morozzi 09/2020 5540 (53*10^109809-287)/9 109810 Robert Price 02/2022 5541 (52*10^109807-133)/9 109808 Robert Price 09/2021 5542 25708^18675+18675^25708 109806 Hans Havermann 10/2020 5543 (17^89227+16^89227)/33 109788 Robert Price 08/2013 5544 2^364687-187 109782 Lelio R Paula 01/2012 5545 2^364644+67 109769 Lelio R Paula 01/2012 5546 (9787*2^364625-1)/24947 109763 Lelio R Paula 05/2015 5547 (2^364616+5)/9 109760 Lelio R Paula 01/2014 5548 (55*10^109759+89)/9 109760 Robert Price 03/2019 5549 (14*32^72921+4171)/31 109757 Eric Chen 04/2023 5550 12^101694+73 109747 Lelio R Paula 03/2017 5551 13^98518-66 109744 Lelio R Paula 03/2017 5552 (8*10^109721-269)/9 109721 Robert Price 09/2021 5553 2^364478-113261 109719 Enzo Doria 07/2014 5554 (2^364513+1)/(3*44290516579) 109719 Gord Palameta 08/2018 5555 (24737*2^364454+1)/3 109716 Lelio R Paula 07/2014 5556 27814^8777+8777^27814 109681 Hans Havermann 10/2020 5557 (62*10^109673+1)/9 109674 Serge Batalov 11/2010 5558 3^229824+340 109654 Lelio R Paula 03/2017 5559 (16623*33^72206-8095)/16 109649 Eric Chen 05/2023 5560 (2*10^109645-71)/3 109645 Robert Price 12/2017 5561 2^364169-112813 109626 Enzo Doria 06/2014 5562 28822^6359+6359^28822 109622 Hans Havermann 11/2020 5563 10^109615+21 109616 Lelio R Paula 03/2017 5564 10^109615-456267 109615 Patrick De Geest 03/2017 5565 2^364094-113 109604 Lelio R Paula 01/2012 5566 25251^21898+21898^25251 109600 Hans Havermann 11/2020 5567 (4^182026+11)/3 109591 Robert Price 02/2017 5568 2^364041-6883 109588 Lelio R Paula 09/2011 5569 12^101545+11 109586 Lelio R Paula 03/2017 5570 26536^13475+13475^26536 109582 Hans Havermann 11/2020 5571 2^363842-2787101 109528 Enzo Doria 03/2016 5572 (2^363812+3570)/2 109519 Stefano Morozzi 09/2020 5573 (22699*2^363782+1)/763 109511 Lelio R Paula 07/2014 5574 2^363769+5711 109506 Lelio R Paula 04/2017 5575 (31*2^363748+1)/49 109499 Lelio R Paula 03/2014 5576 (2^363670+100280245065) 109476 Paul Bourdelais 05/2022 5577 p(22245)#/2-8 109462 Robert Price 01/2017 5578 2^363556+55 109442 Lelio R Paula 01/2012 5579 (509*10^109414+31)/9 109416 Robert Price 08/2022 5580 (2^363437+1682)/2 109406 Stefano Morozzi 09/2020 5581 (55459*2^363411+1)/81 109401 Lelio R Paula 07/2014 5582 2^363406+1871569 109397 Enzo Doria 05/2016 5583 (2^363370+1338)/2 109385 Stefano Morozzi 02/2021 5584 (2^363349+7)/9 109378 Lelio R Paula 01/2014 5585 3^229236+100 109374 Lelio R Paula 03/2017 5586 (2^363315+3258)/2 109369 Stefano Morozzi 02/2021 5587 2^363268-58695 109355 Lelio R Paula 04/2017 5588 2^363191-112321 109332 Enzo Doria 06/2014 5589 26231^14718+14718^26231 109327 Hans Havermann 10/2020 5590 25461^19672+19672^25461 109326 Hans Havermann 10/2020 5591 4*10^109316-63 109317 Robert Price 10/2018 5592 2^363120+3 109311 Donovan Johnson 04/2006 5593 (10^109297-1)/9 109297 Paul Bourdelais, Harvey Dubner 04/2007 5594 2^363042-114641 109287 Enzo Doria 04/2015 5595 2^363020-112793 109280 Enzo Doria 06/2014 5596 (85*10^109253+203)/9 109254 Robert Price 09/2020 5597 24990^23431+23431^24990 109202 Hans Havermann 10/2020 5598 (2^362746+3738)/2 109198 Stefano Morozzi 09/2020 5599 (2^362716+1282)/2 109189 Stefano Morozzi 01/2021 5600 (67607*2^362695+1)/70499 109183 Lelio R Paula 07/2014 5601 25060^22737+22737^25060 109180 Hans Havermann 10/2020 5602 (9*2^362644+1)/5 109167 Lelio R Paula 03/2014 5603 5^156181+38 109166 Lelio R Paula 02/2017 5604 (2^362623+3618)/2 109161 Stefano Morozzi 09/2020 5605 25138^21993+21993^25138 109157 Hans Havermann 10/2020 5606 4*10^109142+91 109143 Robert Price 08/2018 5607 3^228750+68 109142 Lelio R Paula 03/2017 5608 (2^362561+786)/2 109142 Stefano Morozzi 09/2020 5609 (23*10^109113+61)/3 109114 Robert Price 01/2022 5610 2*10^109100-49 109101 Robert Price 09/2020 5611 (10223*2^362376+1)/9 109090 Lelio R Paula 07/2014 5612 65^60167-64^60167 109078 Robert Price 08/2013 5613 7*3^228589-2 109066 Lelio R Paula 09/2014 5614 24874^24243+24243^24874 109063 Hans Havermann 11/2020 5615 (17*10^109059-161)/9 109060 Robert Price 02/2021 5616 29158^5495+5495^29158 109050 Hans Havermann 11/2020 5617 (78557*2^362188+1)/189 109033 Lelio R Paula 07/2014 5618 2*7^129008+9 109025 Lelio R Paula 11/2014 5619 88*10^109022+7 109024 Robert Price 03/2020 5620 28194^7337+7337^28194 108985 Hans Havermann 10/2020 5621 (5*10^108960+91)/3 108961 Robert Price 04/2018 5622 2^361957+76367 108960 Enzo Doria 05/2016 5623 2^361873-1411 108935 Yves Minet 01/2013 5624 (24737*2^361857+1)/35 108933 Lelio R Paula 07/2014 5625 115^52842-114 108892 Norbert Schneider 07/2018 5626 13^97745-24 108883 Lelio R Paula 03/2017 5627 (2^361696+2562)/2 108882 Stefano Morozzi 09/2020 5628 17^88475+8 108864 Lelio R Paula 04/2017 5629 2^361567+51 108843 Lelio R Paula 01/2012 5630 2^361563-109501 108842 Enzo Doria 04/2014 5631 12^100852+83 108838 Lelio R Paula 03/2017 5632 2^361497+767 108822 Lelio R Paula 01/2012 5633 28019^7630+7630^28019 108785 Hans Havermann 10/2020 5634 24723^24758-24758^24723 108765 Norbert Schneider 11/2020 5635 2^361280-112349 108757 Enzo Doria 06/2014 5636 2^361271-5955 108754 Lelio R Paula 04/2017 5637 12^100757+19 108736 Lelio R Paula 03/2017 5638 25368^19333+19333^25368 108735 Hans Havermann 11/2020 5639 (2^361195+3618)/2 108731 Stefano Morozzi 09/2020 5640 2^361153-111546435 108718 Paul Bourdelais 10/2021 5641 14^94849-61 108710 Lelio R Paula 05/2017 5642 27267^9700+9700^27267 108708 Hans Havermann 11/2020 5643 (19^85009-5^85009)/14 108705 Robert Price 07/2013 5644 24832^23853+23853^24832 108704 Hans Havermann 11/2020 5645 27502^8963+8963^27502 108701 Hans Havermann 11/2020 5646 25807^16278+16278^25807 108689 Hans Havermann 11/2020 5647 (11*2^361027+1)/40463 108677 Lelio R Paula 03/2014 5648 2^360973+1299 108664 Lelio R Paula 04/2017 5649 2^360959-109101 108660 Enzo Doria 04/2014 5650 6*5^155454+7 108659 Lelio R Paula 11/2014 5651 10^108656+79 108657 Lelio R Paula 02/2017 5652 10^108656-50001 108656 Patrick De Geest 03/2017 5653 2^360918-35 108648 Lelio R Paula 01/2012 5654 4*10^108646-47 108647 Robert Price 10/2021 5655 (11*2^360886-1)/7 108638 Lelio R Paula 03/2014 5656 3*10^108624-49 108625 Robert Price 07/2018 5657 (2^360831+666)/2 108621 Stefano Morozzi 09/2020 5658 (134*10^108610+7)/3 108612 Robert Price 02/2020 5659 2*10^108609+29 108610 Robert Price 02/2021 5660 (10^108604+7)/71/191 108600 Alfred Reich 06/2021 5661 (2^360742+3222)/2 108594 Stefano Morozzi 09/2020 5662 2^360706-458903 108584 Enzo Doria 04/2015 5663 31112^3087+3087^31112 108567 Hans Havermann 11/2020 5664 2^360641-113185 108564 Enzo Doria 07/2014 5665 (29*10^108559-71)/3 108560 Robert Price 07/2021 5666 2^360618+75019 108557 Enzo Doria 04/2016 5667 2^360607-216367 108554 Harrison Mesh 06/2022 5668 (14*10^108545-221)/9 108546 Robert Price 04/2018 5669 (44*10^108544-233)/9 108545 Robert Price 01/2019 5670 3*5^155286+2 108541 Lelio R Paula 11/2014 5671 7^128422+4 108530 Lelio R Paula 11/2014 5672 7^128421-80 108529 Lelio R Paula 03/2017 5673 2^360497+53807 108521 Yves Minet 07/2010 5674 2^360468-4559 108512 Yves Minet 03/2019 5675 (2^360451+578)/2 108507 Stefano Morozzi 09/2020 5676 2^360366+1459 108481 Lelio R Paula 09/2011 5677 2^360364-1499 108481 Yves Minet 05/2013 5678 25662^16871+16871^25662 108477 Hans Havermann 10/2020 5679 25009^21748+21748^25009 108475 Hans Havermann 10/2020 5680 14^94642-23 108472 Lelio R Paula 05/2017 5681 (197*10^108446-11)/3 108448 Robert Price 03/2020 5682 (2^360229+1290)/2 108440 Stefano Morozzi 01/2021 5683 4*10^108412+9 108413 Robert Price 05/2015 5684 (259*10^108409-1)/3 108411 Robert Price 12/2020 5685 (2^360122+1194)/2 108408 Stefano Morozzi 09/2020 5686 133^51042-132 108406 Norbert Schneider 02/2019 5687 2^360093-351103 108399 Enzo Doria 06/2015 5688 2^360042+723 108384 Lelio R Paula 01/2012 5689 85^56164-2 108364 Lelio R Paula 10/2013 5690 2^359937-29323 108352 Enzo Doria 07/2015 5691 (2^359922+1762)/2 108348 Stefano Morozzi 09/2020 5692 (2^359903+758)/2 108342 Stefano Morozzi 09/2020 5693 2^359898-19997 108341 Enzo Doria 06/2013 5694 (2^359886+2122)/2 108337 Stefano Morozzi 09/2020 5695 2*5^154948-7 108305 Lelio R Paula 11/2014 5696 10^108303+13 108304 Lelio R Paula 02/2017 5697 10^108303-207959 108303 Patrick De Geest 03/2017 5698 7*10^108300+69 108301 Robert Price 07/2019 5699 2^359730+753 108290 Lelio R Paula 12/2011 5700 (8*10^108273+13)/3 108274 Robert Price 06/2018 5701 2^359650-19797 108266 Enzo Doria 06/2013 5702 (47*10^108261+259)/9 108262 Robert Price 03/2022 5703 91^55259-90^55259 108255 Robert Price 07/2015 5704 10^108251+85749 108252 Patrick De Geest 02/2021 5705 10^108251-50000000001 108251 Robert Price 12/2020 5706 10^108251-252081 108251 Patrick De Geest 02/2021 5707 4*10^108238-71 108239 Robert Price 12/2018 5708 3^226845+68 108233 Lelio R Paula 03/2017 5709 31836^2509+2509^31836 108227 Hans Havermann 10/2020 5710 5^154822-12866 108216 Enzo Doria 05/2014 5711 (9*2^359480+1)/5 108215 Lelio R Paula 03/2014 5712 2^359454-177 108207 Lelio R Paula 12/2011 5713 (19*10^108184+191)/3 108185 Robert Price 05/2019 5714 6^139022-59 108181 Lelio R Paula 02/2017 5715 (19*10^108176-43)/3 108177 Robert Price 05/2019 5716 2^359352-179 108176 Lelio R Paula 12/2011 5717 2^359338-1858781 108172 Enzo Doria 04/2016 5718 12^100230-97 108167 Lelio R Paula 03/2017 5719 27028^10043+10043^27028 108163 Hans Havermann 11/2020 5720 (25*2^359297-1)/137 108159 Lelio R Paula 03/2014 5721 (2^359262-509203)/9 108148 Lelio R Paula 12/2013 5722 26583^11702+11702^26583 108147 Hans Havermann 11/2020 5723 (3^226648-8)/352715633 108131 Lelio R Paula 12/2013 5724 6^138956-59 108129 Lelio R Paula 02/2017 5725 2^359184+30285 108126 Lelio R Paula 04/2017 5726 13^97059+10 108119 Lelio R Paula 03/2017 5727 2^359137-81 108112 Lelio R Paula 12/2011 5729 (15185*2^359105-1)/567 108103 Lelio R Paula 05/2015 5728 2^359110-11655 108103 Lelio R Paula 04/2017 5730 2^359069-933075 108091 Paul Bourdelais 06/2021 5731 26227^13222+13222^26227 108090 Hans Havermann 10/2020 5732 8*6^138875+5 108067 Lelio R Paula 11/2014 5733 2^358987-216919 108066 Enzo Doria 05/2014 5734 (2^358977+2714)/2 108063 Stefano Morozzi 09/2020 5735 39^67918-67918^39 108062 Norbert Schneider 02/2017 5736 24^78283-1*78283^24 108048 Dylan Delgado 12/2019 5737 25282^18767+18767^25282 108040 Hans Havermann 11/2020 5738 2^358785-16933 108006 Enzo Doria 05/2013 5739 (2^358783+5)/33383 108000 Lelio R Paula 12/2013 5740 6^138770-77 107985 Lelio R Paula 02/2017 5741 (2^358727-1017)/94178479 107980 Lelio R Paula 12/2013 5742 10^107976+19 107977 Lelio R Paula 02/2017 5743 10^107976-202103 107976 Patrick De Geest 03/2017 5744 2^358684+75781 107975 Enzo Doria 04/2016 5745 24928^21411+21411^24928 107955 Hans Havermann 10/2020 5746 99^54094+2 107952 Lelio R Paula 06/2013 5747 (2^358583-9)/391 107942 Lelio R Paula 12/2013 5748 (2^358562+838)/2 107938 Stefano Morozzi 02/2021 5749 2^358538+55 107931 Lelio R Paula 12/2011 5750 2^358517-109009 107925 Enzo Doria 03/2014
Find by discoverer :
Created by Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)
Go back | 6,607 | 14,147 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-40 | latest | en | 0.39099 |
https://www.toppr.com/guides/chemistry/some-basic-concepts-of-chemistry/concentrations/ | 1,606,487,700,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141193221.49/warc/CC-MAIN-20201127131802-20201127161802-00537.warc.gz | 889,799,051 | 41,355 | > > Concentrations
# Concentrations
Do you like your coffee thick or more ‘watery’? What do we mean by this? Maybe the ratio of water to milk? Or, maybe the concentration of milk in water! We always discuss a solution being diluted or concentrated. However, this is a qualitative way of expressing the concentration of the solution.
### Suggested Videos
Atomic Mass
Dalton's Atomic Theory
Stoichiometry
## Dilute and Concentrated Solutions
A dilute solution means the quantity of solute is relatively very small. On the other hand, a concentrated solution implies that the solution has a large amount of solute. But, unfortunately, these are relative terms. They do not give us an idea of the quantitative concentration of the solution.
So, to quantitatively describe the concentrations of various solutions around us, we commonly express levels of concentration in different ways. Let us look at a few of them below.
## Quantitative Measurement of Concentration
### 1) Mass Percentage (w/w)
When we express the concentration of a solution as the percent of one component in the solution, we call it the mass percentage (w/w). Suppose, we have a solution containing component A as the solute and B as the solvent, then its mass percentage is expressed as:
Mass % of A = Mass of component A in the solution/Total mass of the solution×100
10% solution of sugar by mass means that 10 grams of sugar is present in 100 grams of the solution, i.e., 10 grams of sugar has been dissolved in 90 grams of water.
### 2) Volume percentage (V/V)
Sometimes, we express the concentration as a percent of one component in the solution by volume. In such cases, it is the volume percentage. It is given as:
Volume % of A = Volume of component A in the solution/Total volume of the solution×100
For example, if a solution of NaCl in water is said to be 10 % by volume that means a 100 ml solution will contain 10 ml NaCl.
### 3) Mass by Volume Percentage (w/V)
This unit is majorly used in pharmaceutical industry. It is the mass of a solute dissolved per 100 mL of the solution.
### Â 4)Â Molarity (M)
One of the most commonly used methods for expressing the concentrations is molarity. It is the number of moles of solute dissolved in one litre of a solution. Thus, if one gram molecule of a solute is present in 1 litre of the solution, the concentration of the solution is said to be one molar. Unit of molarity: mol L-1
Suppose a solution of ethanol is labelled as 0.25 M. By this, we mean that in one litre of the given solution 0.25 moles of ethanol is dissolved.
### 5) Molality (m)
Molality represents the concentration regarding moles of solute and the mass of solvent. It is given by moles of solute dissolved per kg of the solvent. The molality formula is given as:
 Molality(m) = Moles of solute/Mass of solvent in kg
### Relationship Between Molality and Molarity
Â
Â
Let the density of the solution be ‘d’. Unit= g mL−1  Â
Mass of solution = V × d
The mass of solute = number of moles × molecular mass of solute   = n mA
Mass of solvent, W = mass of solution – mass of solute   = V × d – n × mA
Thus,
Where mA is the molecular mass of solvent.
### 6) Mole Fraction
If the solution has a solvent and the a solute, mole fraction gives a concentration as the ratio of moles of one component to the total moles present in the solution. It is denoted by x.
The above-mentioned methods are commonly used ways of expressing the concentration of solutions. All the methods describe the same thing that is, the concentration of a solution, each of them has their own advantages and disadvantages. Molarity depends on temperature while mole fraction and molality are independent of temperature. All these methods are used on the basis of requirement of expressing the concentrations.
## Solved Example for You
Q: What do you mean by the formality of a solution?
Answer:Â It is the number of formula mass in grams present per litre of solution. In case, formula mass is equal to molecular mass, formality is equal to molarity. Like molarity and normality, the formality also depends on temperature.
Share with friends
## Customize your course in 30 seconds
##### Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
Ashhar Firdausi
IIT Roorkee
Biology
Dr. Nazma Shaik
VTU
Chemistry
Gaurav Tiwari
APJAKTU
Physics
Get Started
## Browse
##### Some Basic Concepts of Chemistry
0 Followers
Most reacted comment
1 Comment authors
Recent comment authors
Subscribe
Notify of
Guest
Where are Equivalent weight video in chapter
## Question Mark?
Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps. | 1,236 | 4,923 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-50 | longest | en | 0.920609 |
https://www.brightstorm.com/tag/graphs/page/6 | 1,524,158,461,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937015.7/warc/CC-MAIN-20180419165443-20180419185443-00375.warc.gz | 771,310,218 | 11,929 | # graphs 105 videos
• #### Optimization Using the First Derivative Test
##### CalculusApplications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
• #### Optimization Using the Second Derivative Test
##### CalculusApplications of the Derivative
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.
• #### More Transformations of Sine and Cosine
##### TrigonometryTrigonometric Functions
How the value of h affects the shape of the graph y = A sin(B(x-h)).
transformations sine period amplitude phase shift horizontal shift
• #### Find an Equation of the Polynomial Function
##### PrecalculusPolynomial and Rational Functions
How we identify the equation of a polynomial function when we are given the intercepts of its graph.
polynomial functions cubic functions x intercepts factors end behavior leading coefficient stretch factor
• #### More Transformations of Sine and Cosine
##### PrecalculusTrigonometric Functions
How the value of h affects the shape of the graph y = A sin(B(x-h)).
transformations sine period amplitude phase shift horizontal shift | 256 | 1,245 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-17 | latest | en | 0.733923 |
https://www.mersenneforum.org/sendmessage.php?s=23da6157c96a70a9e8e217b3ddff4b46&do=sendtofriend&t=23892 | 1,652,786,936,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662517245.1/warc/CC-MAIN-20220517095022-20220517125022-00634.warc.gz | 1,039,533,687 | 5,769 | mersenneforum.org Email to Friend
User Name Remember Me? Password
Register FAQ Search Today's Posts Mark Forums Read
Thread: Predict M52 Send Page to a Friend
Your Username: Click here to log in
Random Question
how many two decimal digit primes exist?
Recipient Name:
Recipient Email Address:
Email Subject:
Message:
All times are UTC. The time now is 11:28.
Tue May 17 11:28:56 UTC 2022 up 33 days, 9:30, 0 users, load averages: 1.34, 1.10, 0.92
Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.
This forum has received and complied with 0 (zero) government requests for information.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.
≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔 | 639 | 1,219 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2022-21 | latest | en | 0.725795 |
https://mathoverflow.net/questions/322358/algorithm-for-calculating-spheric-convex-hulls-of-finite-pointsets | 1,555,629,871,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578526904.20/warc/CC-MAIN-20190418221425-20190419003425-00199.warc.gz | 494,502,352 | 29,858 | # Algorithm for Calculating Spheric Convex Hulls of Finite Pointsets
Let the Spheric Convex Hull ($$\mathrm{CH}_S$$) denote the intersection of all closed spheres that contain a compact $$\Sigma\subset\mathbb{R}^n$$ and on their boundary at least $$n+1$$ distinct points of $$\Sigma$$
Question:
how can the cell structure of $$\mathrm{CH}_S(\Sigma)$$ be efficiently determined from the cell structure of $$\mathrm{CH}(\Sigma)$$ in case $$\quad n+1\ \le\ \partial\mathrm{CH}(\Sigma)\cap\Sigma\ \lt\ \infty,\quad \Sigma\subset\mathbb{R}^n\$$, when $$\mathrm{CH}$$ denotes the standard convex hull and $$\partial\mathrm{CH}$$ the set of its boundary points?
An example that shows that the cell structures actually can be different:
take the corners of triangle plus three further points, one to each side of the triangle and slightly outside the circum circle. The cell structure of $$\partial\mathrm{CH}$$ contains 6 line segments, whereas $$\mathrm{CH}_S$$ contains only three circular arcs.
The bigger red dots mark the delimiters of the circular arcs of $$\mathrm{CH}_S$$
Edit
just realized, the spheres that contribute $$\mathrm{CH}_S$$ can be characterized as follows: after a stereographic projection of $$\Sigma$$ onto the unit sphere of appropriate dimension the contributing hyperspheres correspond to hyperplanes through $$n+1$$ stereo-projected points that separate the origin from the projected points that are not on that hyperplane; maybe that observation simplifies matters.
• Are not the cell structures identical? For spheres with very large radii through the corners of a triangle face of the hull will approach halfplanes tangent to that triangle. For finite pointsets, the limit as the radii go to $\infty$ is the regular convex hull. – Joseph O'Rourke Feb 3 at 14:03
• @JosephO'Rourke yes you are right; I will edit my question and add an important restriction, that makes the cell structures possibly different – Manfred Weis Feb 3 at 14:33
• Note that the spherical hull of $n+1$ general-position points in $\mathbb{R}^n$ is in fact a sphere. – Joseph O'Rourke Feb 3 at 15:52
• @JosephO'Rourke yes, that is the degenerate case; thanks for mentioning it. I wrote "at least n+1" to not rule out that case. – Manfred Weis Feb 3 at 16:00 | 579 | 2,261 | {"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": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2019-18 | latest | en | 0.8447 |
https://www.thestudentroom.co.uk/showthread.php?t=3887361 | 1,524,168,875,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937016.16/warc/CC-MAIN-20180419184909-20180419204909-00204.warc.gz | 890,097,330 | 46,650 | x Turn on thread page Beta
You are Here: Home >< Maths
# An A-level integral watch
1. I have decided to take a leaf out of TeeEm's book
Evaluate
I initially posted this on 'the hard integral thread', but I think it deserves a wider audience because, after all, it only requires knowledge of the regular A-level Maths syllabus
Enjoy!
2. (Original post by Indeterminate)
I have decided to take a leaf out of TeeEm's book in order to invoke some kind of a discussion on this forum
Evaluate
I initially posted this on 'the hard integral thread', but I think it deserves a wider audience because, after all, it only requires knowledge of the regular A-level Maths syllabus
Enjoy!
very good
3. (Original post by TeeEm)
very good
Shame we haven't had any replies yet
4. (Original post by Indeterminate)
Shame we haven't had any replies yet
maths died about a year ago ...
5. (Original post by Indeterminate)
Shame we haven't had any replies yet
I'd give it a bash but I'm swamped with FP3.
6. (Original post by Zacken)
I'd give it a bash but I'm swamped with FP3.
Lol, that's fair enough
So I think it's time to tag a few people...
7. I'll give it a try, be back soonish with my answer hopefully
8. Spoiler:
Show
Posted from TSR Mobile
9. (Original post by Zacken)
I'd give it a bash but I'm swamped with FP3.
I'd give it a bash but I can't be bothered as it looks hard.
Though maybe you can look for an IBP inspired approach? The exponential would seem to point that way.
10. (Original post by Indeterminate)
Lol, that's fair enough
So I think it's time to tag a few people...
I'm honoured to be tagged in one of Indeterminate's integral posts, but my integration skills are quite laughable.
I've attempted to separate them into individual functions using simplification and have tried trigonometric substitutions, but it's not looking too pretty... Any hints?
11. (Original post by aymanzayedmannan)
I'm honoured to be tagged in one of Indeterminate's integral posts, but my integration skills are quite laughable.
I've attempted to separate them into individual functions using simplification and have tried trigonometric substitutions, but it's not looking too pretty... Any hints?
You don't need to use a substitution. Play around with what's inside the brackets and see what you get
12. Spoiler:
Show
Posted from TSR Mobile
13. correct?
14. (Original post by drandy76)
Spoiler:
Show
Posted from TSR Mobile
Try differentiating that and then compare it to the expression to be integrated
Posted from TSR Mobile
15. (Original post by KFazza)
Try differentiating that and then compare it to the expression to be integrated
Posted from TSR Mobile
oh dear
16. I don't think this can be classed as a solution cause I did a lot of this question by observation which I tried to explain with the notes as I go along
IMPORTANT EDIT: at the end there should be a minus not a plus. IntA - IntB
But anyway is this correct? Hopefully you can follow along..
Spoiler:
Show
17. Having had a quick look through all the responses, I am now delighted to announce that the winners are Student403 and KFazza
I guess I should write up a solution using LATEX, so here goes...
Spoiler:
Show
Let denote our integral.
We have
by recognition
18. (Original post by Indeterminate)
Having had a quick look through all the responses, I am now delighted to announce that the winners are Student403 and KFazza
I guess I should write up a solution using LATEX, so here goes...
Spoiler:
Show
Let denote our integral.
We have
by recognition
Thanks I cannot understand how people can write in LaTeX :O
19. (Original post by Student403)
Thanks I cannot understand how people can write in LaTeX :O
Congrats.
20. (Original post by Zacken)
Congrats.
Thanks also to you b/c the Cambridge thread won a community award!
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: February 13, 2016
Today on TSR
### Negatives of studying at Oxbridge
What are the downsides?
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 | 1,043 | 4,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-17 | latest | en | 0.971347 |
https://www.conwaylife.com/forums/viewtopic.php?f=2&t=1828&start=0 | 1,611,568,342,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00748.warc.gz | 754,753,757 | 37,379 | ## Still-life 'factories'
For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
M. I. Wright
Posts: 372
Joined: June 13th, 2015, 12:04 pm
### Still-life 'factories'
I think it'd be useful to have a collection of these, especially the "edgy" variety. Here are all the factories I know of.
G->block:
Code: Select all
x = 18, y = 21, rule = LifeHistory
2.A11.E$2.3A8.E$5.A7.3E$4.2A4$4.A$3.A.A$4.2A10.2A$16.2A$2D$2D4$9.2A$3.2A4.A$3.A6.3A$4.3A5.A$6.A!
G->beehive:
Code: Select all
x = 38, y = 39, rule = LifeHistory
33.C$31.3C$30.C$30.2C5$9.2A$10.A$10.A.A$11.2A4$2A$.A$.A.A30.2A$2.2A 30.A$35.3A$20.2A15.A$20.2A$13.2D$12.D2.D$13.2D$2.2C$.C.C$.C$2C4$13.2A
$13.2A3$3E$2.E$.E!
G->beehive:
Code: Select all
x = 25, y = 24, rule = LifeHistory
2.E$E.E$.2E6$2A5.D$2A4.D.D$6.D.D$7.D$21.2A$21.A.A$23.A$12.2A9.2A$5.2A 5.2A$4.A.A$4.2A2$7.2A$7.A$8.3A$10.A! I know there were some others from a LifeNews article, but I can't find them anymore (and pentadecathlon.com is down again) Edge-shooters H->boat: Code: Select all x = 28, y = 38, rule = LifeHistory 17.A$17.3A$20.A$19.2A5$20.2A$20.2A5$7.2A$8.A$8.A.A$9.2A7$9.E$9.E.E$9. 3E$11.E5$2.2C$3.C$3C$C25.2D$25.D.D$26.D!
H->boat:
Code: Select all
x = 34, y = 32, rule = LifeHistory
21.2D$21.D.D$22.D7$9.2A$4.2A2.A2.A17.2A$.A2.A4.A.A17.A.A$A.A.A5.A20.A
$.A2.A.2A23.2A$4.A2.A$5.A4.A$6.5A2$8.A12.3E$7.A.A2.2A8.E$8.2A3.A6.3E$
10.3A$10.A6$30.2C$30.C.C$32.C$32.2C! H->beehive (the first part can be deleted to turn this into a dependent conduit): Code: Select all x = 54, y = 31, rule = LifeHistory 30.2C$31.C$6.A24.C.C$6.3A23.2C$9.A$8.2A8.2A$18.A$16.A.A$16.2A$2.2A35.
3E$2.2A26.2C7.E$30.C7.3E$28.C.C$28.2C$2.2A$2.2A3$52.2A$52.2A$26.2A.D$
26.2A.3D$2C27.D.D$.C29.D15.2A$.C.C43.2A$2.2C47.2A$51.2A3$45.2A$45.2A! Are there any other edgy beehive factories? Last edited by M. I. Wright on October 2nd, 2019, 12:02 am, edited 1 time in total. gamer54657 wrote:God save us all. God save humanity. hgkhjfgh nutshelltlifeDiscord 'Conwaylife Lounge' simeks Posts: 369 Joined: March 11th, 2015, 12:03 pm Location: Sweden ### Re: Still-life 'factories' M. I. Wright wrote:Are there any other edgy beehive factories? Well, there is this: Code: Select all x = 30, y = 26, rule = LifeHistory 5.A$3.A.A$4.2A12.A$16.3A$15.A13.A$15.2A10.3A$2A24.A$.A24.2A$.A.2A$2.A
2.A$3.2A$18.2A$18.2A7$21.2A.A$21.2A.3A$27.A$21.2A.3A$22.A.A$22.A.A$
23.A!
dvgrn
Moderator
Posts: 7582
Joined: May 17th, 2009, 11:00 pm
Contact:
### Re: Still-life 'factories'
M. I. Wright wrote:Are there any other edgy beehive factories?
There must be many thousands of good converters out there waiting to be catalogued. Another one showed up in the new-conduits thread back in June:
Code: Select all
x = 143, y = 75, rule = LifeHistory
113.A$111.3A$110.A$110.2A$101.2A$101.A.A37.A$102.A37.A.A$140.A.A$141.
A$109.D3.2A15.D$109.2D2.2A15.D.D$27.D69.2D11.2D18.3D$26.DBD69.2D10.D
21.D$25.BDBDB68.D10.D$25.2BD2B$24.6B$23.8B$22.9B92.2C$16.13B95.C$15. 16B90.3C$15.17B89.C$15.17B$17.16B$14.B.17B$13.2AB.17B49.2A$13.2A20B 48.2A$14.B.14B3.B2A68.2A$16.13B4.A2.A66.A2.A$16.12B6.2A.A66.2A.A$16. 13B8.A69.A$16.12B9.2A68.2A$16.10B$16.10B$15.10B107.2A$15.10B107.A$7. 2A6.10B52.2A55.A$8.A7.9B53.A35.2A14.5A$8.A.AB4.9B.2B50.A.A34.A13.A$9.
2AB.14B2A50.2A16.2A16.A.A12.3A$11.16B2A68.2A17.2A15.A$11.14B.2B102.4A
$12.13B100.2A3.A3.2A$11.14B.2B97.2A4.3A2.A$9.18B2A68.2A34.A.2A$7.18B.
B2A68.2A34.A$7.2BC15B2.B51.C52.2A$6.3BCBC4B.8B54.C.C$7.2B3C4B2.7B54. 3C$6.5BC4B2.7B56.C42.2A$5.10B3.7B99.A$4.4B11.6B.BA69.A27.3A$4.3B12.7B A.A67.A.A28.A$2.4B13.8BA69.A4.A$2.2C16.5B.B45.2C26.3A$3.C14.6B49.C25.
A$3C15.6B46.3C26.2A$C17.4B48.C16.2A$18.2B2AB63.A.A$20.2A64.A$85.2A3$
89.2A$88.A.A5.2A$88.A7.2A$87.2A2$101.A$97.2A.A.A$96.A.A.A.A$93.A2.A.A .A.A.2A$93.4A.2A2.A2.A$97.A4.2A$95.A.A$95.2A! Restarting the active reaction with a beehive+glider collision seems like a neat trick. There are a few period-multiplying conduits that have a beehive as one of the stages. If it happened to work out, for example, you could send a couple of signals into simeks' new period quadrupler, and then do something with the beehive. Here are the other H-to-beehive converters I have in my old collection: Code: Select all x = 168, y = 52, rule = LifeHistory 81.2A6.A15.B40.2A.2A$73.A6.B2AB5.3A11.4B4.B34.2A.2A$73.3A5.3B8.A9.5B 3.B2D$22.2B52.A3.B.B8.2A9.6B2.D2BD32.5A2.A$20.3B2D50.2A2.6B6.7B4.9B2D B31.A4.A2.3A9.2A$19.3BD2BD49.10B6.8B2.13B30.A.BAB7.A6.2B2AB$7.2A10.4B 2DB41.2A8.11B2.25B26.A2.A.2AB6.2A6.4B$8.A9.8B42.A8.22B.15B25.A.A.A.4B
A4.5B2.4B$8.A.AB5.10B41.A.AB6.20B2.14B27.A2.A3.BABA5.10B$9.2AB.3B.11B
41.2AB.3B2.33B33.2A2.A2BA3.12B$11.17B43.40B38.2A2B.12B$11.16B44.38B
42.16B$12.13B47.37B42.17B$11.14B.2B43.36B.B2A40.17B$9.18B2A40.21B.7B 2.6B2.BA.A37.18B$6.19B.B2A38.19B5.6B14.A34.22B$4.5BA15B2.B39.2BA15B7. 6B13.2A32.4BA17B$4.5BABA4B.7B42.3BABA4B.7B8.5B48.4BABA15B$4.5B3A4B.7B 43.2B3A4B2.6B9.2B50.4B3A14B$4.7BA4B2.7B41.5BA4B3.6B7.2A51.6BA14B$4. 11B4.6B40.10B6.4B7.A52.22B$4.4B10.7B39.4B12.B2A2B8.3A48.4B.17B$4.3B 12.4B40.4B14.2A.B2A8.A48.3B2.17B$2.4B14.5B37.4B18.BA.A54.4B.17B$2.2C 19.2A36.B2CB22.A54.2C3.17B$3.C19.A36.3BC23.2A54.C3.13B2DB$3C21.3A32.B 3C77.3C4.12BD2BD$C25.A33.C79.C7.12B2D$148.5B2A7B$150.3B2A7B$151.10B$
151.6B.2B$150.7B$150.6B7.A$151.6B4.3A$151.8B.A$150.9BA.A$150.7B.2BAB$150.6B3.2B$149.2B3D2B2.2B$149.4BD2B.B2AB$144.3B.4B3DB2.2A$143.13B$
142.14B$141.15B$141.14B$142.13B$142.14B$143.12B$145.3B2A3B$146.BA2BA 2B$148.2AB!
The third one on the right doesn't use up the Herschel -- the beehive is generated in passing. It was used at one point in a G->LWSS converter, and then Guam figured out how to turn it into a clean conduit, if I recall correctly. The other two are terminal converters that have pretty good clearance and "edginess".
I have another H-to-beehive saved, that drops the beehive right in the middle of the conduit on top of the input Herschel. Unless there's some reason why it's useful in a specific case, I suspect that anything as non-edgy as this will not be worth posting on this thread -- there are way too many millions of similar converters.
Code: Select all
#C sample not-really-worth-posting Herschel-to-beehive converter
x = 41, y = 27, rule = LifeHistory
30.A$30.3A$33.A$2A30.2A4.2B$A.A25.B3.6B.B$2.A22.3B.B4.B5.B$2.2A20.B5.
B.2B6.B$3.B20.B6.B8.B$3.3B18.B15.B$2.B3.2B15.B16.B$.B6.3B11.B16.B$B 10.B3.2B2.3B16.B$.A3.2A5.3B2.2B3.A15.B$.2A2.2A15.A2D14.2B$2.2A18.C2AD
14.B$.2A20.DC15.B$3B13.B4.B18.B$3.B6.B.4B.B2.B.3B15.B$3.7B.B4.B2.B5.B
14.B$15.B2.B7.B12.B$15.2AB9.B11.B$16.A10.B11.B$13.3A11.B11.B$13.A14.B 10.B$29.B7.2B$30.B5.B$31.5B!
A for awesome
Posts: 2292
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: Still-life 'factories'
A small dependent edgeshooting H-to-block:
Code: Select all
x = 12, y = 4, rule = B3/S23
3bo$b3o5b3o$o9bo$2o6b3o! praosylen#5847 (Discord) x₁=ηx V*_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ simsim314 Posts: 1766 Joined: February 10th, 2014, 1:27 pm ### Re: Still-life 'factories' H->Mango Code: Select all xx = 40, y = 31, rule = LifeHistory .C10.3B3.2C3.2C$.3C6.6B.B2CB.B2CB$4.C4.7B.4B.3B$3.2C4.8B.2B3.B6.2B$3. 5B.25B$5.31B$4.32B.B$4.33B2C$4.33B2C$2.2CB.27B.4B$.C.CB2.23B4.4B$.C6.
BD17B$2C6.DBD15B$8.D2BD4B2.11B$8.BDBDB5.12B$10.DB6.12B$19.11B$17.4B.
4B3CB$17.2C4.4BC2B$18.C4.2B3C2B$15.3C6.6B$15.C8.7B$26.B.4B$29.4B$30. 4B$31.4B$32.4B$33.4B$34.4B$35.4B$36.4B! H->long barge (notice long barge is rarer than eater and LWSS) Code: Select all x = 55, y = 34, rule = LifeHistory 7$25.2C3.2C$12.C12.2C3.2C$12.3C$15.C$14.2C3$44.2C$44.2C3$13.2C$14.C$11.3C$11.C3$33.3C$34.C$32.3C! dvgrn Moderator Posts: 7582 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: ### Re: Still-life 'factories' A for awesome wrote:A small dependent edgeshooting H-to-block... That's a nice simple one -- not a lot of clearance, but you don't always need much. Here's another single-eater H-to-block with similarly low clearance that turned out to be useful in signal circuitry. In the example at the right, a glider gets out past the tub-with-tail eater only if the block has been placed: Code: Select all x = 122, y = 54, rule = LifeHistory 89.2A$82.2A5.2A$82.2A3$84.2A27.2A$84.2A27.2A$78.2A$78.2A$119.2A$119. 2A$115.2A$115.2A4$120.2A$120.2A2$85.2C$85.2C$77.A$77.3A9.2A$80.A8.A$79.A.A8.3A$18.2A60.A11.A$18.2A5.2A$25.2A$81.2A31.2A$81.2A31.A.A$23.2A 44.A46.A$23.2A44.3A44.2A$29.2A41.A$29.2A40.2A11.2A$84.2A3$9.A$9.A.A$
9.3A$11.A58.A44.2A$70.A.A19.2A21.2A$70.3A20.A15.2A$72.A17.3A16.2A$22. 2D66.A$2.2C18.2D$3.C107.2A$3C15.2A84.2A5.2A$C18.A43.2C39.2A$16.3A45.C
$16.A44.3C20.2A$61.C22.A$85.3A$87.A!
Blocks are relatively easy for a Herschel signal to produce "in passing", without using up the Herschel. A B-heptomino makes a natural block if you leave it to its own devices, and a Herschel makes an edgy block just after the first natural glider. There are also several period multipliers that can be used as block generators.
Here are the other H-to-block converters from my small collection. The one on the right is really a period tripler:
Code: Select all
x = 118, y = 53, rule = LifeHistory
59.A$58.A.A$58.A.A$57.2A.2A$48.4B6.B2.A$47.2D5B3.2ABA$47.2D7B.2A.A.A$48.7B.3B2.2A$47.10B$45.13B$43.15B$43.2BC12B$42.3BCBC4B.4B$43.2B3C4B2. B$42.5BC4B$41.10B$40.4B$40.3B$38.4B$38.2C$39.C$36.3C$36.C3$97.2A$88.
2A6.B2AB$89.A7.3B$89.A.AB3.B.B$90.2AB2.6B$92.9B8.2A$83.2A7.12B3.2B2AB$84.A8.12B2.4B3.B$84.A.AB6.23B$48.4B33.2AB.3B2.23B$47.2D5B33.29B2D$
47.2D7B31.29B2D$48.10B30.29B$4.A42.12B28.29B$3.A.A39.14B26.21B.9B$4.A
38.15B25.19B6.7B$5.4B34.2BC14B23.2BC15B8.6B$3.5B2D32.3BCBC4B.3B2.2A
22.3BCBC4B.7B7.5B$.7B2D33.2B3C4B2.B3.A24.2B3C4B2.6B7.2A$.2BC6B32.5BC
4B7.3A20.5BC4B3.6B7.A$3BCBC4B31.10B10.A19.10B6.4B4.3A$.2B3C4B30.4B36.
4B12.B2A2B4.A$.4BC4B30.3B36.4B14.2A.B2A$2.7B29.4B36.4B18.BA.A$38.2C 38.2C23.A$39.C39.C23.2A$36.3C37.3C$36.C39.C!
And here's something from 2003 that I'd totally forgotten about -- yet another stop-and-restart circuit, using a block-on-beehive of all things. It could potentially be turned into a period multiplier: if the restart glider doesn't appear, the next Herschel will reset the circuit cleanly. Looks like there are ways to clear the restart glider's output path if the block-on-beehive is missing, too. Maybe these stop-and-restart circuits should be collected in a separate thread?
Code: Select all
x = 199, y = 86, rule = LifeHistory
77.C$76.C120.C$76.3C117.C$196.3C22$25.A$24.A.A7.A110.A$24.A.A7.3A107.
A.A7.A$22.3A.2A9.A106.A.A7.3A$21.A14.2A104.3A.2A9.A$22.3A.2A113.A14. 2A$24.A.2A114.3A.2A$144.A.2A6$26.A$26.A.A117.A$26.3A11.D105.A.A$28.A 7.2D.D.D104.3A11.D$36.2D.D.D106.A7.2D.D.D$40.D115.2D.D.D$160.D$45.2A$
19.2C24.2A118.2A$20.C118.2C24.2A$17.3C6.2A112.C$17.C9.A109.3C$27.A.A
4.2D2.D98.C9.2C$28.2A5.3D6.2A102.C5.2D2.D$36.D7.A.A101.C.C4.3D37.2A$9.2A35.A102.2C5.D37.A2.A$9.2A35.2A147.2A4$2A$.A$.A.A$2.2A$190.3D$191.
D$191.3D3$49.2A129.2A$49.2A129.2A$23.2A.D$23.2A.3D121.2A.2A$26.D.D
122.A.A$28.D15.2A103.A.A.A.A$44.2A103.2A3.2A$48.2A140.2A$48.2A140.2A
2$155.A$42.2A109.3A$42.2A108.A37.2A$152.2A36.2A2$156.2A23.2A$155.A.A
12.2A9.2A$155.A14.2A$154.2A!
M. I. Wright
Posts: 372
Joined: June 13th, 2015, 12:04 pm
### Re: Still-life 'factories'
Not a still-life, but here's a TL factory I found while trying to do something else.
Code: Select all
x = 20, y = 15, rule = B3/S23
2bo$3o$obo$o$18b2o$18b2o8$12b2o$12b2o! Edit: Another! Code: Select all x = 44, y = 28, rule = LifeHistory 17.A$17.3A$20.A$19.2A8$38.2C$38.2C2$9.C$9.C.C29.D$9.3C29.D.D$11.C29.
3D$43.D4$2.2A$3.A$3A25.2A$A27.A.A$21.2A7.A$21.2A7.2A! This one's dependent (the actual converter is just the block - everything else is part of an H->H), and there are a number of conduits that can come before it. Last edited by M. I. Wright on September 19th, 2015, 12:53 am, edited 1 time in total. gamer54657 wrote:God save us all. God save humanity. hgkhjfgh nutshelltlifeDiscord 'Conwaylife Lounge' Kazyan Posts: 1062 Joined: February 6th, 2014, 11:02 pm ### Re: Still-life 'factories' I found a few factories here and there in the conduits thread while hunting for a Spartan syringe: G->beehive: Code: Select all x = 29, y = 25, rule = B3/S23 21bo$19b3o$10bo7bo$8b3o7b2o$7bo$7b2o2$4b2o10b2o7b2o$4bobo8bo2bo6bo$5b 2o4b2o2bo2bo4bobo$2o9b2o3b2o5b2o$bo$bobo$2b2o3$27b2o$27b2o5$22bo$21b2o$21bobo!
Code: Select all
x = 43, y = 16, rule = B3/S23
5b2o24bobo$5bobo23b2o$6b2o24bo$2b2o$bobo37b2o$bo39b2o$2o6$23b2o$22bo2b
o$22bo2bo$23b2o!
G->Explosion:
Code: Select all
x = 20, y = 43, rule = B3/S23
18b2o$17bobo$18bo3$17b2o$16bo2bo$17b2o8$14b2o$14b2o6$b2o15b2o$b2o14b2o$19bo4$6b2o$5bo2bo$6b2o$2b2o$bobo$bo$2o5$16b2o$16bobo$18bo$18b2o! Non-spartan G->loaf: Code: Select all x = 19, y = 22, rule = B3/S23 11b2o$10bobo$5b2o2bo$5bo2bob2o$7b2obobo$11bo$17b2o$17bo$8b2o5bobo$7bo
2bo4b2o$8b2o5$o2bob2o$4obo10b2o$5bobo8bobo$2b2o2b2o8bo$2bo$3bo$2b2o!
Simkin also found this G->block, modified from my G->beehive:
Code: Select all
x = 29, y = 28, rule = B3/S23
21bo$19b3o$10bo7bo$8b3o7b2o$7bo$7b2o2$4b2o10b2o7b2o$4bobo8bo2bo6bo$5b
2o4b2o2bo2bo4bobo$2o9b2o3b2o5b2o$bo$bobo$2b2o3$27b2o$27b2o6$21b3o$7b2o
12bo$6bobo13bo$6bo$5b2o! He also found a few p2 factories based on a transparent blinker reaction. There's some other glider-activated factories around here, and a lot of them are turned into receivers, so, go search for those. --- As for H->object conduits/factories, I've mentioned the idea of collecting an H-to-Block for as many relative locations of blocks as possible--not necessarily because that would be useful right now, but for the heck of it. Perhaps later on they'd find a use. And I've certainly seen a whole bunch of conduit prospects that terminate in a block instead of a signal, but typically, those aren't reported. I've been looking for something to do, so I'll start saving those in a folder somewhere in case they're ever needed. Tanner Jacobi Coldlander, a novel, available in paperback and as an ebook. Now on Amazon. dvgrn Moderator Posts: 7582 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: ### Re: Still-life 'factories' M. I. Wright wrote:Not a still-life, but here's a TL factory I found while trying to do something else... That one seems to come up fairly regularly. Here's a February posting by simsim314 containing the same converter. It would be nice to find a conduit that can reliably turn traffic lights into something else. But it will probably need a transparent catalyst or two, found with CatForce or ptbsearch, unless Bellman can come up with something. There's a known conduit that might be called a "TL-to-glider converter", but it's not really. It probably only works for the one specific H-to-TL above. Code: Select all x = 35, y = 40, rule = LifeHistory .3D2.5D.5D.5D2.3D3.3D$D3.D.D5.D7.D3.D3.D.D3.D$D5.D5.D7.D7.D5.D$.3D2. 3D4.3D4.D6.D4.2D$4.D.D9.D3.D5.D7.D$D3.D.D5.D3.D3.D4.D4.D3.D$.3D2.5D2. 3D4.D3.5D2.3D6$22.2A$8.2A10.2B2AB$9.A10.4B$9.A.AB6.7B$10.2AB.3B.8B$12.14B$12.14B$13.13B$12.14B.2B$10.18B2A$8.18B.B2A$8.2BC15B2.B$7.3BCBC 4B.7B$8.2B3C4B.8B$7.5BC4B2.7B$6.10B3.7B$5.4B11.8BA$5.3B12.7BA.A$3.4B 13.2BD5BA$3.2A15.2BD3B.B$4.A15.2BD2B$.3A15.7B$.A16.ACD3B3D$17.A.A8B$ 17.A3.BDB.4B$16.2A3.BDB2.4B$22.D4.3B$28.2B! #C [[ VIEWONLY THUMBNAIL ZOOM 10 ]] At the time that the eater and tub interact, the pre-traffic-light reaction is still strongly connected to a fading spark from higher up, which plays a big part in the creation of the glider. It seems pretty unlikely that any other traffic light source will have the same exact pre-TL predecessor. To be generally useful as a connector, it seems as if a hypothetical TL-to-something-else converter would have to have its first interaction less than ten ticks before the formation of the traffic light. simsim314 Posts: 1766 Joined: February 10th, 2014, 1:27 pm ### Re: Still-life 'factories' SL factories are very common. Here is a list from depth 1 + combine option from CatForce search: Code: Select all x = 1081, y = 1920, rule = LifeHistory F$F$F$F84.F$F84.F$F84.F$F84.F$F84.F85.F$F84.F85.F$F84.F85.F$F84.F85.F$F84.F85.F$F84.F85.F$F84.F85.F104.F$F84.F85.F104.F241.F$F84.F85.F104.
F241.F$F84.F85.F104.F241.F$F84.F85.F104.F241.F$F84.F85.F104.F241.F$F
84.F85.F104.F127.F113.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F
127.F113.F87.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F127.F113.F
87.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F127.F113.F87.F84.F$F 84.F85.F104.F127.F113.F87.F84.F$F48.2C34.F85.F104.F127.F113.F87.F84.F
181.F$F48.2C34.F85.F104.F127.F113.F87.F84.F84.F96.F$F84.F85.F104.F
127.F113.F87.F84.F84.F96.F$F84.F41.C43.F104.F127.F113.F87.F84.F84.F 96.F$F84.F41.3C41.F104.F127.F113.F87.F84.F84.F96.F$F40.2C42.F44.C40.F 104.F127.F113.F46.C40.F84.F84.F96.F102.F$F40.2C42.F43.2C40.F104.F127.
F113.F46.3C38.F84.F84.F96.F102.F$F84.F85.F50.2C52.F127.F113.F49.C37.F 40.C43.F84.F96.F102.F$F84.F85.F50.2C52.F127.F113.F48.2C37.F40.3C41.F
84.F96.F102.F$F56.2C26.F40.C44.F104.F127.F113.F69.2C16.F43.C40.F84.F 96.F102.F$F56.C.C25.F39.C.C43.F38.2C64.F127.F113.F69.C17.F42.2C40.F
84.F96.F102.F$F58.C25.F39.2C44.F38.2C64.F56.C70.F113.F67.C.C17.F84.F 84.F96.F102.F$F58.2C24.F85.F104.F56.3C68.F113.F67.2C18.F45.2C37.F38.
2C44.F42.C53.F102.F$F84.F85.F104.F59.C67.F113.F87.F44.C.C37.F30.2C6. 2C6.2C36.F41.C.C52.F102.F$F84.F49.3C33.F104.F58.2C15.C51.F70.C42.F87.
F36.2C6.2C3.2C33.F31.C14.2C36.F42.C53.F102.F$F84.F50.C34.F104.F74.C.C 50.F68.3C42.F38.2C47.F37.C11.2C33.F31.C.C50.F28.2C66.F51.C50.F$F84.F
48.3C34.F104.F75.C51.F43.2C22.C45.F37.C.C47.F37.C.C44.F32.2C50.F28.2C
66.F50.C.C49.F103.F$F51.3C30.F85.F104.F127.F43.C.C21.2C44.F37.C27.2C 20.F38.2C44.F84.F96.F51.C50.F47.C55.F$F42.2C8.C31.F85.F32.2C70.F127.F
44.2C67.F36.2C27.C21.F84.F84.F96.F102.F46.C.C54.F$F43.C6.3C31.F85.F 31.C.C70.F127.F40.2C71.F66.3C18.F84.F84.F96.F35.2C65.F37.C9.C55.F$F
40.3C41.F85.F31.C72.F127.F39.C.C71.F68.C18.F84.F84.F96.F36.C65.F36.C.
C64.F$F40.C43.F85.F30.2C72.F48.2C77.F39.C73.F87.F84.F84.F96.F36.C.C 63.F37.C65.F$F84.F85.F67.2C35.F47.C.C28.2C47.F38.2C28.2C43.F87.F84.F
51.2C31.F96.F37.2C63.F103.F$F84.F85.F67.C36.F47.C30.C.C46.F68.C.C42.F 87.F54.C29.F51.C32.F22.2C72.F102.F103.F$F84.F85.F68.3C33.F46.2C32.C
46.F70.C42.F56.3C28.F53.C.C28.F52.3C29.F21.C.C72.F102.F103.F$F84.F85. F70.C33.F80.2C45.F49.2C19.2C41.F47.2C8.C29.F54.2C28.F54.C29.F21.C74.F 102.F103.F$F84.F85.F104.F127.F50.C62.F48.C6.3C29.F84.F84.F20.2C74.F
37.2C63.F103.F$F84.F85.F54.3C47.F127.F47.3C63.F45.3C39.F84.F84.F57.2C 37.F36.C.C63.F103.F$F84.F85.F45.2C8.C48.F127.F47.C65.F45.C41.F84.F84.
F57.C38.F36.C65.F28.2C73.F$F84.F85.F46.C6.3C48.F127.F113.F87.F84.F41. 3C40.F52.C5.3C35.F35.2C65.F27.C.C73.F$F84.F85.F43.3C58.F66.3C58.F63.
3C47.F87.F46.3C35.F32.2C8.C41.F51.C.C6.C35.F40.2C25.2C33.F27.C75.F$F 84.F85.F43.C60.F57.2C8.C59.F54.2C8.C48.F87.F37.2C8.C36.F33.C6.3C41.F 52.C43.F41.C25.C34.F26.2C75.F$F84.F85.F104.F58.C6.3C59.F55.C6.3C48.F
87.F38.C6.3C36.F30.3C51.F44.3C49.F38.3C21.C5.3C31.F63.2C38.F$F84.F85. F104.F55.3C69.F52.3C58.F87.F35.3C46.F30.C53.F35.2C8.C50.F38.C22.C.C6. C31.F63.C39.F$F84.F85.F104.F55.C71.F52.C60.F87.F35.C48.F84.F36.C6.3C
50.F62.C39.F58.C5.3C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F33.3C60. F54.3C45.F57.C.C6.C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F33.C62.F
45.2C8.C46.F58.C44.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F46.C6.3C 46.F50.3C50.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F43.3C56.F41.2C
8.C51.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F43.C58.F42.C6.3C51.F$
F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F39.3C61.F$F84.F85.F104.F 127.F113.F87.F84.F84.F96.F102.F39.C63.F$F84.F85.F104.F127.F113.F87.F
84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F39.2C44.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F40.C44.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F40.C.C42.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F41.2C42.
F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F 87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F53.C33.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F52.C.C32.F84.F84.F96.F102.F103.F$F84.F85.F104. F127.F113.F53.C33.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40.
2C45.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40.2C45.F84.F84. F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F63.2C39.F
127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F63.C40.F127.F113.F87.F 84.F84.F96.F102.F47.C55.F$F84.F85.F61.C.C40.F127.F113.F67.2C18.F84.F
84.F96.F102.F45.3C55.F$F84.F44.2C7.3C29.F61.2C41.F127.F113.F67.2C18.F 84.F84.F96.F102.F44.C58.F$F84.F43.C.C8.C30.F42.2C60.F127.F113.F34.2C
51.F84.F84.F96.F102.F44.2C57.F$F84.F43.C8.3C30.F42.2C60.F127.F113.F 33.C.C51.F84.F84.F96.F102.F103.F$F84.F42.2C41.F104.F127.F113.F33.C53.
F84.F84.F96.F102.F41.2C60.F$F84.F85.F104.F127.F113.F32.2C53.F36.C47.F 84.F96.F102.F41.C.C59.F$F84.F85.F41.2C61.F127.F113.F87.F36.3C45.F84.F
39.C56.F102.F42.2C59.F$F84.F85.F42.C61.F127.F113.F87.F39.C44.F47.2C6. C28.F38.C.C55.F102.F103.F$F84.F85.F39.3C62.F127.F113.F87.F38.2C44.F
47.2C4.3C28.F39.C56.F49.2C10.C40.F56.2C45.F$F84.F85.F39.C64.F127.F 113.F87.F60.2C22.F52.C31.F26.2C68.F41.2C6.2C3.2C3.3C40.F56.2C6.2C37.F$F84.F85.F104.F127.F113.F87.F60.C23.F52.2C30.F26.2C68.F42.C11.2C2.C
43.F64.C38.F$F84.F85.F104.F127.F42.2C27.2C40.F56.3C28.F58.C.C23.F84.F 96.F42.C.C13.2C42.F62.C.C38.F$F84.F85.F104.F127.F43.C27.2C40.F47.2C8.
C29.F58.2C24.F84.F96.F43.2C57.F62.2C39.F$F84.F85.F43.2C7.3C49.F56.C 70.F43.C.C67.F48.C6.3C29.F84.F22.2C60.F96.F102.F103.F$F84.F85.F42.C.C
8.C50.F56.3C68.F44.2C67.F45.3C39.F84.F21.C2.C59.F21.C74.F102.F103.F$F 84.F85.F42.C8.3C50.F59.C67.F113.F45.C41.F28.2C54.F22.2C29.2C29.F20.C. C73.F102.F103.F$F39.2C43.F85.F41.2C61.F58.2C67.F113.F87.F27.C.C54.F
53.C.C28.F20.2C74.F102.F36.2C65.F$F38.C.C20.2C21.F85.F104.F80.2C45.F 113.F87.F27.C56.F55.C28.F96.F61.2C39.F37.C22.2C41.F$F38.C22.C.C20.F
85.F104.F80.C46.F44.2C67.F87.F26.2C56.F55.2C27.F96.F61.C.C38.F34.3C
23.C42.F$F37.2C24.C20.F85.F104.F78.C.C46.F43.C.C67.F87.F54.2C28.F84.F 96.F63.C38.F34.C26.3C39.F$F63.2C19.F85.F104.F78.2C47.F43.C69.F87.F54.
2C28.F84.F96.F63.2C37.F63.C39.F$F84.F85.F104.F127.F42.2C69.F87.F84.F 84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F55.C40.F
102.F103.F$F84.F85.F104.F48.2C77.F113.F87.F84.F44.3C37.F50.C5.3C37.F 102.F103.F$F84.F85.F104.F47.C.C77.F69.2C42.F87.F46.3C35.F35.2C8.C38.F
49.C.C6.C37.F102.F51.3C49.F$F52.3C29.F85.F104.F47.C79.F69.2C42.F87.F 37.2C8.C36.F36.C6.3C38.F50.C45.F52.3C47.F42.2C8.C50.F$F43.2C8.C30.F
85.F104.F46.2C79.F113.F87.F38.C6.3C36.F33.3C48.F42.3C51.F43.2C8.C48.F
43.C6.3C50.F$F44.C6.3C30.F85.F104.F127.F61.3C49.F87.F35.3C46.F33.C50. F33.2C8.C52.F44.C6.3C48.F40.3C60.F$F41.3C40.F85.F104.F127.F62.C50.F
87.F35.C48.F84.F34.C6.3C52.F41.3C58.F40.C62.F$F41.C42.F85.F104.F127.F 60.3C50.F87.F84.F84.F31.3C62.F41.C60.F103.F$F84.F85.F104.F127.F113.F
87.F84.F84.F31.C64.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F84.F85.F104.F66.3C58.F113.F87.F84.F84.F96.F102.F103.F
$F84.F85.F104.F57.2C8.C59.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F58.C6.3C59.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F55.3C 69.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F55.C71.F113.F87.F
84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F46.2C39.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F46.2C39.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F38.2C47.F84.F84.F96.F102.F103.F$F84.F85.F104.F
127.F113.F39.C47.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F39.C .C45.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40.2C45.F84.F84.
F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F 113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F84.F85.F104.F127.F113.F60.2C25.F42.2C10.C29.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F60.C.C24.F42.2C8.3C29.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F62.C24.F51.C32.F84.F96.F50.C51.F 103.F$F84.F85.F104.F127.F113.F62.2C23.F51.2C31.F84.F96.F50.3C49.F103.
F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F53.C48.F103.F$F84.F85.F104.
F127.F113.F87.F34.2C48.F84.F96.F41.2C9.2C48.F103.F$F84.F85.F104.F127. F113.F87.F34.2C48.F84.F96.F42.C59.F103.F$F84.F85.F104.F127.F113.F87.F
84.F37.C46.F96.F42.C.C57.F103.F$F84.F85.F104.F127.F113.F51.3C33.F84.F 37.3C44.F96.F43.2C22.2C33.F103.F$F84.F85.F104.F127.F113.F42.2C8.C34.F
52.2C30.F40.C15.C27.F96.F67.2C33.F103.F$F84.F85.F104.F127.F113.F43.C 6.3C34.F52.C.C29.F39.2C13.3C27.F45.2C6.C42.F102.F51.2C10.C39.F$F84.F
85.F104.F127.F113.F40.3C44.F54.C29.F53.C30.F45.2C4.3C42.F102.F51.2C8.
3C39.F$F84.F43.2C40.F104.F127.F113.F40.C46.F54.2C28.F53.2C29.F50.C45. F102.F60.C42.F$F84.F43.2C40.F104.F127.F113.F87.F84.F84.F50.2C44.F102.
F60.2C41.F$F84.F85.F104.F127.F113.F87.F84.F84.F32.2C62.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F84.F32.2C62.F40.2C60.F43.2C58.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F39.C.C60.F43.2C58.F$F84.F85.F104.F
127.F113.F87.F45.3C36.F29.2C53.F96.F39.C62.F103.F$F84.F39.2C44.F104.F 127.F113.F87.F36.2C8.C37.F28.C.C23.2C28.F96.F38.2C62.F103.F$F84.F39.
2C44.F104.F127.F113.F87.F37.C6.3C37.F28.C25.C.C27.F50.C45.F102.F103.F
$F84.F47.3C35.F104.F127.F113.F87.F34.3C47.F27.2C27.C27.F49.C.C44.F 102.F62.C40.F$F84.F48.C36.F104.F127.F113.F87.F34.C49.F56.2C26.F50.2C
44.F102.F61.C.C39.F$F84.F46.3C36.F104.F127.F113.F87.F84.F84.F96.F71. 2C29.F62.2C39.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F71.2C29.F103.
F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F62.3C37.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F53.2C8.C38.F103.F$F84.F85.F104.F127.F 113.F87.F84.F47.3C34.F42.3C51.F54.C6.3C38.F103.F$F84.F85.F104.F127.F
113.F87.F84.F38.2C8.C35.F33.2C8.C52.F51.3C48.F54.3C46.F$F84.F85.F104. F127.F113.F87.F84.F39.C6.3C35.F34.C6.3C52.F51.C50.F45.2C8.C47.F$F84.F
85.F104.F127.F113.F87.F84.F36.3C45.F31.3C62.F102.F46.C6.3C47.F$F62.2C 20.F85.F104.F127.F113.F87.F84.F36.C47.F31.C64.F102.F43.3C57.F$F62.C
21.F85.F104.F127.F113.F87.F84.F84.F96.F102.F43.C59.F$F63.3C18.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F65.C18.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F36.2C46.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F37.C46.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F
$F34.3C13.3C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F34.C6.
2C8.C32.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F42.C6.3C32.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F39.3C42.F85.F104.F127.
F113.F87.F84.F84.F96.F102.F103.F$F39.C44.F85.F104.F127.F113.F87.F84.F 84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F
$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F
127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F 84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F
$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F
127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F 84.F96.F102.F103.F$F84.F85.F104.F127.F113.F39.C47.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F39.3C21.C23.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F42.C18.3C23.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F41.2C17.C26.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.
F113.F60.2C25.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84. F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.
F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F
127.F113.F87.F47.C36.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61. 2C24.F45.3C36.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61.C.C23.F
44.C39.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F63.C23.F44.2C38.F 84.F96.F102.F103.F$F84.F85.F104.F127.F113.F63.2C22.F84.F45.2C37.F96.F
60.2C40.F103.F$F84.F85.F104.F127.F113.F87.F41.2C41.F45.2C37.F96.F60. 2C40.F103.F$F84.F85.F104.F127.F113.F87.F41.C.C40.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F42.2C40.F33.2C49.F96.F48.2C52.F53.2C48.F$
F84.F85.F104.F127.F113.F87.F84.F33.2C49.F37.C58.F48.2C19.2C31.F53.2C
12.C35.F$F84.F85.F104.F127.F113.F56.3C28.F56.2C26.F84.F37.3C56.F69.2C 31.F45.2C18.3C35.F$F84.F85.F104.F127.F113.F47.2C8.C29.F56.2C6.2C18.F
84.F40.C55.F102.F46.C17.C38.F$F84.F85.F104.F127.F113.F48.C6.3C29.F64. C19.F84.F39.2C17.C37.F102.F46.C.C15.2C37.F$F84.F85.F104.F127.F113.F
45.3C39.F62.C.C19.F84.F56.3C37.F102.F47.2C54.F$F84.F85.F104.F127.F 113.F45.C41.F62.2C20.F84.F55.C40.F102.F103.F$F84.F85.F104.F127.F113.F
87.F84.F84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F27.2C 55.F96.F42.2C58.F103.F$F84.F85.F104.F127.F113.F87.F84.F26.C.C30.2C23.
F96.F41.C.C58.F103.F$F84.F85.F104.F127.F113.F87.F36.2C46.F26.C32.C.C 22.F96.F41.C60.F67.2C34.F$F84.F85.F104.F127.F113.F87.F37.C22.2C22.F
25.2C34.C22.F30.2C64.F40.2C60.F67.C.C33.F$F84.F85.F104.F127.F113.F87. F34.3C23.C23.F61.2C21.F29.C.C64.F102.F69.C33.F$F84.F85.F104.F127.F
113.F87.F34.C26.3C20.F84.F29.C25.C40.F102.F69.2C32.F$F84.F85.F104.F 127.F113.F87.F63.C20.F84.F28.2C24.C.C39.F102.F103.F$F84.F85.F104.F
127.F113.F87.F84.F84.F55.2C39.F74.2C26.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F75.C26.F103.F$F84.F85.F104.F127.F113.F87.F84.F49.3C
32.F96.F64.3C8.C.C24.F103.F$F84.F85.F104.F127.F113.F87.F51.3C30.F40. 2C8.C33.F96.F55.2C8.C10.2C24.F58.3C42.F$F84.F85.F104.F127.F113.F87.F
52.C31.F41.C6.3C33.F96.F56.C6.3C36.F49.2C8.C43.F$F84.F85.F104.F127.F 113.F87.F50.3C31.F38.3C43.F47.3C46.F53.3C46.F50.C6.3C43.F$F84.F85.F
104.F127.F113.F87.F84.F38.C45.F38.2C8.C47.F53.C48.F47.3C53.F$F84.F85. F104.F127.F113.F87.F84.F84.F39.C6.3C47.F102.F47.C55.F$F84.F85.F104.F
127.F113.F87.F84.F84.F36.3C57.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F36.C59.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F59.2C23.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F59.C24.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F57.C.C24.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F57.2C25.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F40.2C42.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 39.C.C42.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F39.C44.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F38.2C44.F85.F104.F127.F 113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F 113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F42.2C7.3C30.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F41.C.C8.C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 41.C8.3C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F40.2C42.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F42.C44.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F 113.F42.3C42.F45.2C37.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F45.
C41.F45.2C37.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F44.2C41.F57. 2C25.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61.2C24.F57.C26.F84.
F96.F102.F103.F$F84.F85.F104.F127.F113.F61.C25.F55.C.C26.F84.F96.F 102.F59.C43.F$F84.F85.F104.F127.F113.F59.C.C25.F37.2C16.2C27.F84.F96.
F58.C43.F58.C.C42.F$F84.F85.F104.F127.F113.F59.2C26.F37.2C45.F84.F96. F56.3C43.F59.C43.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F55.C46.F
103.F$F84.F85.F104.F127.F113.F87.F84.F62.2C20.F96.F55.2C45.F47.2C15. 2C37.F$F84.F85.F104.F127.F113.F87.F84.F62.C21.F96.F102.F48.C15.2C37.F
$F84.F85.F104.F127.F113.F87.F84.F60.C.C21.F96.F52.2C48.F48.C.C52.F$F
84.F85.F104.F127.F113.F87.F84.F60.2C22.F96.F52.C.C47.F49.2C52.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F53.2C47.F103.F$F84.F85.F104.F127.F
113.F87.F84.F84.F46.2C48.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F 36.2C46.F38.2C6.2C8.C39.F64.2C36.F103.F$F84.F85.F104.F127.F113.F87.F
84.F35.C.C46.F39.C14.3C39.F64.2C6.2C28.F103.F$F84.F85.F104.F127.F113. F87.F84.F35.C22.2C24.F39.C.C11.C42.F72.C29.F69.2C32.F$F84.F85.F104.F
127.F113.F87.F48.3C33.F34.2C22.C25.F40.2C11.2C41.F70.C.C29.F69.C.C31.
F$F84.F85.F104.F127.F113.F52.3C32.F39.2C8.C34.F59.3C22.F96.F70.2C30.F 71.C31.F$F84.F85.F104.F127.F113.F43.2C8.C33.F40.C6.3C34.F61.C22.F96.F
102.F71.2C30.F$F84.F85.F104.F127.F113.F44.C6.3C33.F37.3C44.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F41.3C43.F37.C46.F84.F96.F102.F103.
F$F84.F85.F104.F127.F113.F41.C45.F84.F84.F54.2C40.F47.2C53.F103.F$F
84.F85.F104.F127.F113.F87.F84.F49.3C32.F54.C.C39.F48.C53.F103.F$F84.F 85.F104.F127.F113.F87.F84.F40.2C8.C33.F56.C39.F45.3C54.F62.3C38.F$F
84.F85.F104.F127.F113.F87.F84.F41.C6.3C33.F56.2C38.F45.C56.F53.2C8.C
39.F$F84.F85.F104.F127.F113.F87.F84.F38.3C43.F96.F102.F54.C6.3C39.F$F
84.F85.F104.F127.F113.F87.F84.F38.C45.F96.F102.F51.3C49.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F51.C51.F$F84.F85.F104.F127.F113.F
87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F49.3C 44.F62.3C37.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F40.2C8.C45.F
53.2C8.C38.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F41.C6.3C45.F54. C6.3C38.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F38.3C55.F51.3C48.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F38.C57.F51.C50.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F42.C41.F84.F
96.F102.F103.F$F42.C41.F85.F104.F127.F113.F87.F42.3C39.F84.F96.F102.F 103.F$F42.3C39.F85.F104.F127.F113.F87.F45.C38.F84.F96.F102.F103.F$F 45.C38.F85.F104.F127.F113.F87.F44.2C38.F84.F96.F102.F59.C43.F$F44.2C
38.F85.F104.F127.F113.F87.F84.F84.F96.F102.F58.C.C42.F$F84.F85.F104.F 127.F113.F87.F84.F84.F96.F102.F59.C43.F$F84.F85.F104.F127.F113.F87.F
84.F84.F96.F102.F46.2C55.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F46.2C55.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 57.2C25.F85.F104.F127.F113.F87.F84.F46.2C36.F96.F102.F103.F$F57.2C25.
F85.F104.F127.F113.F87.F84.F38.2C6.2C36.F96.F102.F103.F$F84.F85.F104. F127.F113.F87.F59.2C23.F39.C44.F96.F102.F103.F$F84.F85.F104.F127.F
113.F87.F59.2C23.F39.C.C42.F96.F102.F103.F$F84.F85.F104.F127.F113.F 87.F84.F40.2C42.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F69.2C31.F40.2C61.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F69.C 32.F39.C.C61.F$F84.F85.F104.F127.F113.F87.F39.2C43.F84.F96.F67.C.C32.
F39.C63.F$F84.F85.F104.F127.F113.F87.F38.C.C43.F84.F96.F67.2C33.F38. 2C63.F$F84.F85.F104.F127.F113.F87.F38.C45.F84.F96.F53.2C47.F103.F$F 84.F85.F104.F127.F113.F87.F37.2C45.F84.F46.2C48.F53.2C47.F103.F$F52.
3C29.F85.F104.F127.F113.F87.F84.F61.2C21.F46.2C48.F102.F103.F$F43.2C 8.C30.F85.F104.F127.F113.F87.F84.F61.C22.F38.2C13.2C7.C33.F102.F72.2C 29.F$F44.C6.3C30.F85.F104.F127.F113.F87.F54.3C27.F62.3C19.F39.C13.2C
5.3C33.F52.2C48.F73.C29.F$F41.3C40.F85.F104.F127.F113.F87.F45.2C8.C 28.F64.C19.F39.C.C17.C36.F53.C48.F62.3C8.C.C27.F$F41.C42.F85.F104.F
127.F113.F87.F46.C6.3C28.F84.F40.2C17.2C35.F50.3C49.F53.2C8.C10.2C27.
F$F84.F85.F104.F127.F113.F87.F43.3C38.F84.F96.F50.C51.F54.C6.3C39.F$F
84.F85.F104.F127.F113.F87.F43.C40.F49.3C32.F96.F102.F51.3C49.F$F84.F 85.F104.F127.F113.F87.F84.F40.2C8.C33.F96.F102.F51.C51.F$F84.F85.F
104.F127.F113.F87.F84.F41.C6.3C33.F96.F102.F103.F$F84.F85.F104.F127.F 113.F87.F84.F38.3C43.F96.F54.2C7.3C36.F103.F$F84.F85.F104.F127.F113.F
87.F84.F38.C45.F96.F53.C.C8.C37.F103.F$F84.F85.F104.F127.F113.F87.F 84.F84.F96.F53.C8.3C37.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.
F52.2C48.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F 113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F51.3C42.F102.F103. F$F84.F85.F104.F127.F113.F87.F84.F84.F42.2C8.C43.F102.F103.F$F84.F85. F104.F127.F113.F87.F84.F84.F43.C6.3C43.F102.F103.F$F84.F85.F104.F127.
F113.F87.F84.F84.F40.3C53.F102.F103.F$F84.F85.F104.F127.F113.F87.F84. F84.F40.C55.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F40.C43.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F40.3C41.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F43.C40.F96.F102.F103.F$F84.F85.F104.F 127.F113.F87.F84.F42.2C40.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F45.2C37.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F44.C.C37.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F35.2C7.2C38.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F36.C47.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F43.2C12.C26.F36.C.C45.F96.F102.F103.F$F84.F85.F104.F127.F113.F
87.F44.C10.3C26.F37.2C45.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F 44.C.C7.C29.F84.F96.F57.C44.F103.F$F84.F85.F104.F127.F113.F87.F45.2C
7.2C28.F84.F96.F57.3C42.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F60.C41.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F59.2C15.C
25.F103.F$F84.F85.F104.F127.F113.F87.F84.F54.2C28.F96.F75.C.C24.F53.C 49.F$F84.F85.F104.F127.F113.F87.F84.F54.C.C27.F48.C47.F76.C25.F53.3C
47.F$F84.F85.F104.F127.F113.F87.F84.F56.C27.F47.C.C46.F102.F56.C46.F$
F50.2C32.F85.F104.F127.F113.F87.F84.F56.2C26.F48.C47.F102.F55.2C46.F$F50.C.C31.F85.F104.F127.F113.F87.F84.F84.F65.2C29.F102.F48.C54.F$F51.
2C31.F85.F104.F127.F113.F87.F84.F84.F31.2C32.C30.F102.F48.3C21.C30.F$F47.2C35.F85.F104.F127.F113.F87.F84.F84.F32.C30.C.C30.F49.2C51.F51.C 18.3C30.F$F46.C.C35.F85.F104.F127.F113.F87.F84.F84.F32.C.C28.2C31.F
48.C.C51.F50.2C17.C33.F$F46.C37.F85.F104.F127.F113.F87.F84.F46.3C35.F 33.2C61.F48.C53.F69.2C32.F$F45.2C37.F85.F104.F127.F113.F87.F84.F37.2C
8.C36.F96.F47.2C53.F103.F$F84.F85.F104.F127.F113.F87.F44.2C7.3C28.F 38.C6.3C36.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F43.C.C8.C29.F
35.3C46.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F43.C8.3C29.F35.C 48.F33.2C61.F102.F103.F$F84.F85.F104.F127.F113.F87.F42.2C40.F84.F32.C
.C61.F102.F70.2C31.F$F84.F85.F104.F127.F113.F87.F84.F84.F32.C63.F102. F70.C.C30.F$F84.F85.F104.F127.F113.F87.F84.F84.F31.2C63.F67.3C32.F72.
C30.F$F59.3C22.F85.F104.F127.F113.F87.F84.F84.F96.F58.2C8.C33.F72.2C 29.F$F50.2C8.C23.F85.F104.F127.F113.F87.F84.F84.F96.F59.C6.3C33.F103.
F$F51.C6.3C23.F85.F104.F127.F113.F87.F84.F84.F96.F56.3C43.F103.F$F48.
3C33.F85.F104.F127.F113.F87.F84.F84.F96.F56.C45.F103.F$F48.C35.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F50.3C43.F102.F65.3C35.F$F84.F85.F104.F127.F113.F87.F84.F84.F 41.2C8.C44.F102.F56.2C8.C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F42.
C6.3C44.F102.F57.C6.3C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F39.3C 54.F102.F54.3C46.F$F84.F85.F104.F127.F113.F87.F84.F84.F39.C56.F102.F
54.C48.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F52.2C42.F102.F103.F$F84.F85.F104.F127.F 113.F87.F52.2C30.F84.F52.2C42.F102.F103.F$F84.F85.F104.F127.F113.F87.
F52.2C30.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F50.2C32.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F50.2C32.F69.2C25.F52.C49.F103.F$F84.F
85.F104.F127.F113.F87.F84.F42.2C14.2C24.F69.C26.F52.3C47.F103.F$F84.F 85.F104.F127.F113.F87.F84.F43.C14.2C24.F67.C.C26.F55.C14.2C30.F103.F$
F84.F85.F104.F127.F113.F87.F84.F43.C.C38.F67.2C27.F54.2C14.C31.F103.F
$F63.C20.F85.F104.F127.F113.F87.F84.F44.2C38.F96.F68.C.C31.F103.F$F
61.3C20.F85.F104.F127.F113.F87.F84.F84.F96.F68.2C32.F59.2C42.F$F60.C 23.F85.F104.F127.F113.F87.F84.F84.F34.2C60.F102.F59.2C42.F$F60.2C22.F
85.F104.F127.F113.F87.F84.F84.F33.C.C60.F102.F103.F$F84.F85.F104.F 127.F113.F87.F84.F84.F33.C31.2C29.F52.2C48.F103.F$F84.F85.F104.F127.F
113.F87.F84.F84.F32.2C31.C30.F51.C.C48.F103.F$F84.F85.F104.F127.F113. F87.F56.3C25.F84.F66.3C27.F51.C50.F103.F$F84.F85.F104.F127.F113.F87.F
47.2C8.C26.F84.F68.C27.F50.2C50.F71.2C30.F$F61.2C21.F85.F104.F127.F 113.F87.F48.C6.3C26.F84.F96.F102.F71.C31.F$F61.C.C20.F85.F104.F127.F
113.F87.F45.3C36.F84.F96.F102.F69.C.C31.F$F63.C20.F85.F104.F127.F113. F87.F45.C38.F84.F96.F102.F52.2C15.2C32.F$F42.2C19.2C19.F85.F104.F127.
F113.F87.F84.F84.F56.3C37.F102.F52.2C49.F$F43.C40.F85.F104.F127.F113. F87.F84.F84.F47.2C8.C38.F102.F103.F$F40.3C41.F85.F104.F127.F113.F87.F
84.F55.3C26.F48.C6.3C38.F66.3C33.F103.F$F40.C43.F85.F104.F127.F113.F 87.F84.F46.2C8.C27.F45.3C48.F57.2C8.C34.F69.2C32.F$F84.F85.F104.F127.
F113.F87.F84.F47.C6.3C27.F45.C50.F58.C6.3C34.F69.C.C31.F$F56.3C25.F 85.F104.F127.F113.F87.F84.F44.3C37.F96.F55.3C44.F71.C31.F$F47.2C8.C
26.F85.F104.F127.F113.F87.F84.F44.C39.F96.F55.C46.F71.2C30.F$F48.C6. 3C26.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F45.3C36.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F45.C38.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F62.3C38.F$F
84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F53.2C8.C39.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F54.C6.3C39.F$F84.F85.F104.F127.F
113.F87.F84.F84.F96.F102.F51.3C49.F$F84.F85.F104.F127.F113.F87.F84.F 84.F96.F102.F51.C51.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F55.
2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F53.2C29.F43.2C51.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F53.2C6.2C21.F43.2C51.F102.F103.F$F84.F85.F104.
F127.F113.F87.F84.F61.C22.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F59.C.C22.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F41.2C
16.2C23.F96.F102.F103.F$F84.F190.F127.F113.F87.F84.F41.2C41.F96.F102. F64.C38.F$F84.F190.F127.F113.F87.F84.F84.F96.F102.F62.3C38.F$F84.F 190.F127.F113.F87.F84.F84.F96.F102.F61.C41.F$F84.F190.F127.F113.F87.F
84.F84.F37.2C57.F102.F61.2C40.F$F84.F190.F127.F113.F87.F84.F84.F36.C. C57.F50.C51.F103.F$F84.F190.F127.F113.F87.F84.F84.F36.C59.F50.3C49.F
58.2C43.F$F84.F318.F113.F87.F84.F84.F35.2C34.2C23.F53.C48.F58.C.C42.F$F84.F318.F201.F84.F84.F71.C24.F52.2C13.C34.F59.2C42.F$F84.F318.F201. F84.F84.F72.3C21.F65.3C34.F77.C25.F$F84.F318.F201.F84.F84.F74.C21.F
64.C37.F70.2C3.3C25.F$F84.F318.F201.F84.F84.F96.F64.2C36.F70.2C2.C28. F$F84.F318.F201.F84.F51.3C30.F96.F102.F74.2C27.F$F84.F520.F84.F42.2C 8.C31.F59.3C34.F102.F103.F$F84.F605.F43.C6.3C31.F50.2C8.C35.F102.F
103.F$F84.F605.F40.3C41.F51.C6.3C35.F49.2C51.F103.F$F84.F605.F40.C43.
F48.3C45.F48.C.C51.F103.F$F84.F605.F84.F48.C47.F48.C53.F55.2C46.F$F
38.C45.F605.F84.F96.F47.2C53.F54.C.C46.F$F37.C.C44.F605.F84.F96.F102. F54.C48.F$F37.C.C44.F605.F84.F96.F102.F53.2C48.F$F38.C14.2C29.F605.F 84.F96.F102.F103.F$F53.2C6.2C21.F605.F84.F96.F102.F103.F$F61.C22.F 605.F84.F96.F102.F103.F$F59.C.C22.F605.F84.F96.F51.2C7.3C39.F103.F$F 59.2C23.F605.F84.F96.F50.C.C8.C40.F103.F$F84.F605.F84.F96.F50.C8.3C
40.F68.3C32.F$F84.F605.F84.F96.F49.2C51.F59.2C8.C33.F$F35.2C47.F605.F
84.F96.F102.F60.C6.3C33.F$F34.C.C47.F605.F84.F96.F102.F57.3C43.F$F34.
C22.2C25.F605.F84.F96.F102.F57.C45.F$F33.2C22.C26.F605.F84.F96.F102.F 103.F$F58.3C23.F605.F84.F96.F102.F103.F$F60.C23.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F48.3C33.F605.F84.F96.F102.F103.F$F39.2C8.C
34.F605.F84.F96.F102.F103.F$F40.C6.3C34.F605.F84.F96.F102.F103.F$F37.
3C44.F605.F84.F96.F102.F103.F$F37.C46.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F51.2C31.F72.2C22.F102.F103.F$F84.F
605.F41.2C8.2C5.C25.F72.C23.F102.F103.F$F84.F605.F42.C13.3C25.F70.C.C 23.F102.F103.F$F84.F605.F42.C.C10.C28.F70.2C24.F102.F103.F$F84.F605.F 43.2C10.2C27.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F 84.F96.F55.C46.F103.F$F84.F605.F84.F44.2C50.F55.3C44.F103.F$F84.F605. F84.F45.C22.2C26.F58.C43.F103.F$F84.F605.F84.F42.3C23.C27.F46.2C9.2C
43.F103.F$F84.F605.F84.F42.C26.3C24.F47.C54.F66.2C35.F$F84.F605.F84.F
71.C24.F47.C.C52.F66.2C35.F$F84.F605.F84.F96.F48.2C22.2C28.F60.2C41.F$F84.F605.F84.F96.F72.2C28.F61.C13.2C26.F$F84.F605.F84.F96.F102.F61.C .C11.C27.F$F84.F605.F84.F59.3C34.F102.F62.2C9.C.C27.F$F84.F605.F84.F 50.2C8.C35.F102.F73.2C28.F$F84.F605.F54.3C27.F51.C6.3C35.F102.F103.F$F84.F605.F45.2C8.C28.F48.3C45.F102.F103.F$F84.F605.F46.C6.3C28.F48.C
47.F102.F103.F$F84.F605.F43.3C38.F96.F102.F103.F$F84.F605.F43.C40.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F67.3C32.F62.2C7.3C29.F$F84.F605.F84.F96.F58.2C8.C33.F61.C.C8.C30.
F$F84.F605.F84.F96.F59.C6.3C33.F61.C8.3C30.F$F84.F605.F84.F96.F56.3C
43.F60.2C41.F$F84.F605.F84.F96.F56.C45.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F45.2C37.F96.F102.F103.F$F84.F605.F 45.2C3.2C5.C26.F96.F102.F103.F$F84.F605.F50.2C4.C.C25.F96.F102.F103.F
$F84.F605.F57.C26.F51.C44.F102.F103.F$F84.F605.F84.F51.3C42.F102.F
103.F$F84.F605.F84.F54.C41.F102.F103.F$F84.F605.F84.F53.2C41.F102.F
103.F$F84.F605.F84.F71.2C23.F102.F103.F$F84.F605.F84.F71.C24.F102.F
103.F$F84.F605.F84.F69.C.C24.F102.F103.F$F84.F605.F84.F69.2C25.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F43.2C51.F102.F103.F$F84.F605.F84.F42.C.C51.F102.F103.F$F84.F 605.F84.F42.C53.F102.F103.F$F84.F605.F84.F41.2C53.F102.F103.F$F84.F 605.F48.3C33.F96.F47.C54.F103.F$F84.F605.F39.2C8.C34.F96.F47.3C52.F
56.2C45.F$F84.F605.F40.C6.3C34.F96.F50.C51.F55.C.C45.F$F84.F605.F37.
3C44.F96.F49.2C51.F55.C47.F$F84.F605.F37.C46.F96.F102.F54.2C47.F$F84.
F605.F84.F61.3C32.F102.F103.F$F84.F605.F84.F52.2C8.C33.F102.F103.F$F
84.F605.F84.F53.C6.3C33.F69.2C31.F77.C25.F$F84.F605.F84.F50.3C43.F69. C32.F76.C.C24.F$F84.F605.F84.F50.C45.F67.C.C32.F77.C25.F$F84.F605.F 84.F96.F67.2C33.F69.3C31.F$F84.F605.F84.F96.F102.F60.2C8.C32.F$F84.F 605.F84.F96.F102.F61.C6.3C32.F$F84.F605.F84.F96.F54.2C46.F58.3C42.F$F 84.F605.F84.F96.F53.C.C46.F58.C44.F$F84.F605.F84.F96.F53.C48.F103.F$F 84.F605.F84.F96.F52.2C48.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F56.2C7. 3C34.F103.F$F84.F605.F84.F96.F55.C.C8.C35.F103.F$F84.F605.F84.F96.F 55.C8.3C35.F103.F$F84.F605.F84.F96.F54.2C46.F103.F$F84.F605.F84.F96.F 102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$
F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F
84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F35.2C47.F
96.F102.F103.F$F84.F605.F36.C24.2C21.F96.F102.F103.F$F84.F605.F36.C.C
22.C22.F96.F102.F103.F$F84.F605.F37.2C20.C.C22.F96.F102.F103.F$F84.F
605.F59.2C23.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F
84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F51.C44.
F102.F103.F$F84.F605.F84.F51.3C42.F102.F103.F$F84.F605.F38.2C44.F54.C
41.F102.F103.F$F84.F605.F39.C44.F53.2C41.F102.F103.F$F84.F605.F36.3C
45.F96.F102.F103.F$F84.F605.F36.C47.F56.2C38.F102.F103.F$F84.F605.F
84.F55.C.C38.F102.F103.F$F84.F605.F84.F46.2C7.2C39.F102.F103.F$F84.F
605.F52.3C29.F47.C17.2C29.F102.F103.F$F84.F605.F43.2C8.C30.F47.C.C15. C30.F102.F103.F$F84.F605.F44.C6.3C30.F48.2C13.C.C30.F102.F103.F$F84.F 605.F41.3C40.F63.2C31.F102.F103.F$F84.F605.F41.C42.F96.F102.F103.F$F 84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F 84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F 102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$
F84.F605.F84.F96.F102.F59.C11.C31.F$F84.F605.F84.F96.F102.F59.3C7.3C 31.F$F84.F605.F84.F96.F102.F62.C5.C34.F$F84.F605.F84.F57.3C36.F102.F 61.2C5.2C33.F$F84.F605.F84.F48.2C8.C37.F102.F103.F$F84.F605.F84.F49.C 6.3C37.F102.F103.F$F84.F605.F84.F46.3C47.F55.2C45.F103.F$F84.F605.F 84.F46.C49.F55.C.C44.F103.F$F84.F605.F84.F96.F56.C45.F103.F$F84.F605. F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F 102.F103.F$F84.F605.F84.F96.F102.F69.3C31.F$F84.F605.F84.F96.F102.F 60.2C8.C32.F$F84.F605.F84.F96.F102.F61.C6.3C32.F$F84.F605.F84.F96.F 65.3C34.F58.3C42.F$F84.F605.F84.F96.F56.2C8.C35.F58.C44.F$F84.F605.F 84.F96.F57.C6.3C35.F103.F$F84.F605.F84.F96.F54.3C45.F103.F$F84.F605.F 84.F96.F54.C47.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F 102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$
F84.F605.F84.F96.F102.F103.F$F84.F605.F47.2C35.F96.F102.F103.F$F84.F
605.F47.2C35.F96.F102.F103.F$85.F605.F84.F96.F102.F103.F$85.F605.F84.
F96.F102.F103.F$85.F605.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F57.2C25.F96.F102.F103.F$691.F57.2C25.F 96.F102.F103.F$691.F41.2C41.F96.F102.F103.F$691.F40.C.C41.F96.F102.F 103.F$691.F40.C43.F96.F102.F103.F$691.F39.2C43.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F52.3C29.F96.F 102.F103.F$691.F43.2C8.C30.F96.F102.F103.F$691.F44.C6.3C30.F96.F102.F 103.F$691.F41.3C40.F62.2C32.F102.F103.F$691.F41.C42.F62.C33.F102.F 103.F$691.F84.F60.C.C33.F102.F103.F$691.F84.F60.2C34.F102.F103.F$691.
F84.F44.2C50.F102.F103.F$691.F84.F44.2C50.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F43.2C51.F102.F103.F$691.F 84.F44.C51.F102.F103.F$691.F84.F41.3C52.F66.2C34.F103.F$691.F84.F41.C 54.F66.2C34.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F45.2C7.3C39.F102.F103.F$691.F84.F44.
C.C8.C40.F102.F103.F$691.F84.F44.C8.3C40.F102.F103.F$691.F84.F43.2C
51.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F61.2C7.3C29.F103.F$691.F84.F96.F60.C.C8.C30.F103.F$691.F
84.F96.F60.C8.3C30.F103.F$691.F84.F96.F59.2C41.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F33.C50.F96.F102.F103.F$691.F33.3C48.F96.F102.F103.F$691.F36.C12. C34.F96.F102.F103.F$691.F35.2C11.C.C33.F96.F102.F103.F$691.F49.C34.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F30.C53.F96.F102.F103.F$691.F29.C.C52.F96.F102.F103.F$691.F29.2C 53.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F61.2C21.F96.F102.F 103.F$691.F61.C.C20.F65.C30.F102.F103.F$691.F63.C20.F58.2C3.3C30.F 102.F103.F$691.F63.2C19.F58.2C2.C33.F102.F103.F$691.F84.F62.2C32.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F43.2C51.F102.F103.F$691.F
84.F43.2C51.F102.F103.F$691.F51.3C30.F96.F102.F103.F$691.F52.C31.F96.
F102.F103.F$691.F50.3C31.F96.F102.F103.F$691.F84.F96.F102.F103.F$691. F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F56.3C37.F102.F103.F$691.F84.F47.2C8.C38.F102.F103.F$691.F84.F48.C6.3C38.F102.F103.F$691.F84.F45.3C48.F102.F103.F$691.F84. F45.C50.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F58.2C36.F102.F103.F$691.F84.F58.2C36.F 102.F103.F$691.F84.F70.2C24.F102.F103.F$691.F84.F70.C25.F102.F103.F$
691.F84.F68.C.C25.F102.F103.F$691.F84.F68.2C26.F102.F103.F$691.F84.F
44.2C50.F102.F103.F$691.F84.F44.2C50.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F39.2C
43.F96.F102.F103.F$691.F39.2C43.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F61.3C32.F102.F103.F$691.F38.2C44.F52.2C8.C33.F102.F
103.F$691.F39.C44.F53.C6.3C33.F102.F103.F$691.F36.3C45.F50.3C43.F102.
F103.F$691.F36.C47.F50.C45.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F40.2C7.3C32.F96.F102. F103.F$691.F39.C.C8.C33.F96.F102.F103.F$691.F39.C8.3C33.F96.F102.F 103.F$691.F38.2C44.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F62.2C32.F102.F103.F$691.F84.F54.2C6.2C32. F102.F103.F$691.F84.F55.C13.2C25.F102.F103.F$691.F84.F55.C.C11.C26.F 102.F103.F$691.F84.F56.2C9.C.C26.F102.F103.F$691.F84.F67.2C27.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F56.2C7.3C28.F102.F103.F$691.F84.F55.C.C8.C29.F102.F103.F$691.F84.F55.C8.3C29.F102.F103.F$691.F84.F54.2C40.F102.F103.F$691.F84. F96.F102.F103.F$691.F53.2C29.F96.F102.F103.F$691.F53.2C29.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F30.2C52.F96.F102.F103.F$691.F29.C.
C52.F96.F102.F103.F$691.F29.C54.F96.F102.F103.F$691.F28.2C54.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F48.3C33.F96.F102.F103.F$
691.F39.2C8.C34.F96.F102.F103.F$691.F40.C6.3C34.F96.F102.F103.F$691.F
37.3C44.F96.F102.F103.F$691.F37.C46.F96.F102.F103.F$691.F84.F96.F102.
F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F48.C47.F102.F103.F$691.F84.F48.3C45.F102.F
103.F$691.F84.F51.C44.F102.F103.F$691.F84.F44.2C4.2C44.F102.F103.F$691.F84.F45.C21.2C27.F102.F103.F$691.F84.F45.C.C19.C28.F102.F103.F$691.F84.F46.2C17.C.C28.F102.F103.F$691.F84.F65.2C29.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
58.3C35.F102.F103.F$691.F84.F49.2C8.C36.F102.F103.F$691.F84.F50.C6.3C
36.F102.F103.F$691.F84.F47.3C46.F102.F103.F$691.F84.F47.C48.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F46.2C36.F96.F102.F 103.F$691.F46.C37.F96.F102.F103.F$691.F44.C.C37.F96.F102.F103.F$691.F
44.2C38.F96.F102.F103.F$691.F30.2C52.F96.F102.F103.F$691.F30.2C52.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F31.2C7.3C41.F96.F102.F103.F$691.F 30.C.C8.C42.F96.F102.F103.F$691.F30.C8.3C42.F96.F102.F103.F$691.F29. 2C53.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F206.F$691.F84.F96.F206.F$691.F84.F96.F206.F$691.F84.F96.F206.F$691.F84.F96.
F206.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F 84.F56.C39.F$691.F84.F55.C.C38.F$691.F84.F56.C39.F$691.F84.F96.F$691. F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$
691.F84.F96.F$691.F84.F96.F$691.F84.F36.2C58.F$691.F84.F35.C.C30.2C 26.F$691.F84.F35.C32.C.C25.F$691.F84.F34.2C34.C25.F$691.F84.F70.2C24.
F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F 58.3C35.F$691.F84.F49.2C8.C36.F$691.F84.F50.C6.3C36.F$691.F84.F47.3C
46.F$691.F84.F47.C48.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691. F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$
691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F
$691.F84.F96.F$691.F34.2C48.F96.F$691.F35.C18.2C28.F96.F$691.F35.C.C
16.C29.F96.F$691.F36.2C14.C.C29.F96.F$691.F52.2C30.F96.F$691.F84.F96. F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F
96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84. F96.F$691.F41.2C7.3C31.F96.F$691.F40.C.C8.C32.F96.F$691.F40.C8.3C32.F
96.F$691.F39.2C43.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F39.2C16.2C37.F$691.F84.F40.C16.
2C37.F$691.F84.F40.C.C53.F$691.F84.F41.2C53.F$691.F84.F96.F$691.F84.F
96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F62.2C32.F$691.F84.F62.C.C
31.F$691.F84.F64.C31.F$691.F84.F64.2C30.F$691.F84.F96.F$691.F84.F96.F
$691.F84.F96.F$691.F84.F96.F$691.F84.F43.2C7.3C41.F$691.F84.F42.C.C8.
C42.F$691.F84.F42.C8.3C42.F$691.F84.F41.2C53.F$691.F84.F96.F$691.F84.
F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F 84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.
F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.
F$691.F50.C33.F96.F$691.F48.3C33.F96.F$691.F47.C36.F96.F$691.F47.2C
35.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691. F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$
691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F46.3C35.F96.F$691.F37.
2C8.C36.F96.F$691.F38.C6.3C36.F96.F$691.F35.3C46.F46.2C48.F$691.F35.C 48.F46.2C48.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.
F$691.F84.F65.2C29.F$691.F84.F56.3C6.2C29.F$691.F84.F47.2C8.C38.F$
691.F84.F48.C6.3C38.F$691.F84.F45.3C48.F$691.F84.F45.C50.F$691.F84.F 96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.
F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F 84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.
F84.F96.F$691.F84.F96.F$776.F96.F$776.F96.F$776.F96.F$735.2C39.F96.F$
735.2C39.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$739.3C34.F96.F$740.C35.F96.F$738.3C35.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F62.2C32.F$
776.F62.C33.F$776.F60.C.C33.F$776.F60.2C34.F$776.F96.F$776.F96.F$776. F96.F$776.F39.2C55.F$776.F40.C55.F$776.F37.3C56.F$776.F37.C58.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F56.3C37.F$776.F47.2C8.C38.F$
776.F48.C6.3C38.F$776.F45.3C48.F$776.F45.C50.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F42.2C52.F$776.F41.C.C17.2C33.F$776.F41.
C19.C.C32.F$776.F40.2C21.C32.F$776.F63.2C31.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F53.3C40.F$776.F44.2C8.C41.F$776.F45.C6.3C41. F$776.F42.3C51.F$776.F42.C53.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F39.2C55.F$776.F38.C.C21.2C32.F$776.F38.C23.C.C31.F$
776.F37.2C25.C31.F$776.F64.2C30.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F52.3C41.F$776.F43.2C8.C42.F$776.F44.C6.3C42.F$776.F41.3C52. F$776.F41.C54.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F58.2C36.F$776.F58.C37.F$776.F56.C.C37.F$776.F39.2C15.2C38. F$776.F39.2C55.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F52.3C41.F$776.
F43.2C8.C42.F$776.F44.C6.3C42.F$776.F41.3C52.F$776.F41.C54.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F58.2C36.F$776. F58.C37.F$776.F56.C.C37.F$776.F42.2C12.2C38.F$776.F42.2C52.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F43.2C7.3C41.F$776.F42.C.C8.C42.F$776.F 42.C8.3C42.F$776.F41.2C53.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 48.C47.F$776.F48.3C45.F$776.F51.C44.F$776.F50.2C44.F$776.F96.F$776.F
96.F$776.F46.2C48.F$776.F46.C.C47.F$776.F47.C48.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F56.3C37.F$776.F47.2C8.C 38.F$776.F48.C6.3C38.F$776.F45.3C48.F$776.F45.C50.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F55.C40.F$776.F54.C.C39.F$776.F55.C7.2C31.F$
776.F63.C32.F$776.F61.C.C32.F$776.F61.2C33.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F48.3C45.F$776.F39.2C8.C 46.F$776.F40.C6.3C46.F$776.F37.3C56.F$776.F37.C58.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$873.F$873.F$873.F$873.F$873.F$873.F$873.F$873.F$873.F$873.F!
A for awesome
Posts: 2292
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: Still-life 'factories'
simsim314 wrote:SL factories are very common. Here is a list from depth 1 + combine option from CatForce search:
Code: Select all
x = 1081, y = 1920, rule = LifeHistory
F$F$F$F84.F$F84.F$F84.F$F84.F$F84.F85.F$F84.F85.F$F84.F85.F$F84.F85.F
$F84.F85.F$F84.F85.F$F84.F85.F104.F$F84.F85.F104.F241.F$F84.F85.F104. F241.F$F84.F85.F104.F241.F$F84.F85.F104.F241.F$F84.F85.F104.F241.F$F 84.F85.F104.F127.F113.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F 127.F113.F87.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F127.F113.F 87.F$F84.F85.F104.F127.F113.F87.F$F84.F85.F104.F127.F113.F87.F84.F$F
84.F85.F104.F127.F113.F87.F84.F$F48.2C34.F85.F104.F127.F113.F87.F84.F 181.F$F48.2C34.F85.F104.F127.F113.F87.F84.F84.F96.F$F84.F85.F104.F 127.F113.F87.F84.F84.F96.F$F84.F41.C43.F104.F127.F113.F87.F84.F84.F
96.F$F84.F41.3C41.F104.F127.F113.F87.F84.F84.F96.F$F40.2C42.F44.C40.F
104.F127.F113.F46.C40.F84.F84.F96.F102.F$F40.2C42.F43.2C40.F104.F127. F113.F46.3C38.F84.F84.F96.F102.F$F84.F85.F50.2C52.F127.F113.F49.C37.F
40.C43.F84.F96.F102.F$F84.F85.F50.2C52.F127.F113.F48.2C37.F40.3C41.F 84.F96.F102.F$F56.2C26.F40.C44.F104.F127.F113.F69.2C16.F43.C40.F84.F
96.F102.F$F56.C.C25.F39.C.C43.F38.2C64.F127.F113.F69.C17.F42.2C40.F 84.F96.F102.F$F58.C25.F39.2C44.F38.2C64.F56.C70.F113.F67.C.C17.F84.F
84.F96.F102.F$F58.2C24.F85.F104.F56.3C68.F113.F67.2C18.F45.2C37.F38. 2C44.F42.C53.F102.F$F84.F85.F104.F59.C67.F113.F87.F44.C.C37.F30.2C6.
2C6.2C36.F41.C.C52.F102.F$F84.F49.3C33.F104.F58.2C15.C51.F70.C42.F87. F36.2C6.2C3.2C33.F31.C14.2C36.F42.C53.F102.F$F84.F50.C34.F104.F74.C.C
50.F68.3C42.F38.2C47.F37.C11.2C33.F31.C.C50.F28.2C66.F51.C50.F$F84.F 48.3C34.F104.F75.C51.F43.2C22.C45.F37.C.C47.F37.C.C44.F32.2C50.F28.2C 66.F50.C.C49.F103.F$F51.3C30.F85.F104.F127.F43.C.C21.2C44.F37.C27.2C
20.F38.2C44.F84.F96.F51.C50.F47.C55.F$F42.2C8.C31.F85.F32.2C70.F127.F 44.2C67.F36.2C27.C21.F84.F84.F96.F102.F46.C.C54.F$F43.C6.3C31.F85.F
31.C.C70.F127.F40.2C71.F66.3C18.F84.F84.F96.F35.2C65.F37.C9.C55.F$F 40.3C41.F85.F31.C72.F127.F39.C.C71.F68.C18.F84.F84.F96.F36.C65.F36.C. C64.F$F40.C43.F85.F30.2C72.F48.2C77.F39.C73.F87.F84.F84.F96.F36.C.C
63.F37.C65.F$F84.F85.F67.2C35.F47.C.C28.2C47.F38.2C28.2C43.F87.F84.F 51.2C31.F96.F37.2C63.F103.F$F84.F85.F67.C36.F47.C30.C.C46.F68.C.C42.F
87.F54.C29.F51.C32.F22.2C72.F102.F103.F$F84.F85.F68.3C33.F46.2C32.C 46.F70.C42.F56.3C28.F53.C.C28.F52.3C29.F21.C.C72.F102.F103.F$F84.F85.
F70.C33.F80.2C45.F49.2C19.2C41.F47.2C8.C29.F54.2C28.F54.C29.F21.C74.F
102.F103.F$F84.F85.F104.F127.F50.C62.F48.C6.3C29.F84.F84.F20.2C74.F 37.2C63.F103.F$F84.F85.F54.3C47.F127.F47.3C63.F45.3C39.F84.F84.F57.2C
37.F36.C.C63.F103.F$F84.F85.F45.2C8.C48.F127.F47.C65.F45.C41.F84.F84. F57.C38.F36.C65.F28.2C73.F$F84.F85.F46.C6.3C48.F127.F113.F87.F84.F41.
3C40.F52.C5.3C35.F35.2C65.F27.C.C73.F$F84.F85.F43.3C58.F66.3C58.F63. 3C47.F87.F46.3C35.F32.2C8.C41.F51.C.C6.C35.F40.2C25.2C33.F27.C75.F$F
84.F85.F43.C60.F57.2C8.C59.F54.2C8.C48.F87.F37.2C8.C36.F33.C6.3C41.F
52.C43.F41.C25.C34.F26.2C75.F$F84.F85.F104.F58.C6.3C59.F55.C6.3C48.F 87.F38.C6.3C36.F30.3C51.F44.3C49.F38.3C21.C5.3C31.F63.2C38.F$F84.F85.
F104.F55.3C69.F52.3C58.F87.F35.3C46.F30.C53.F35.2C8.C50.F38.C22.C.C6.
C31.F63.C39.F$F84.F85.F104.F55.C71.F52.C60.F87.F35.C48.F84.F36.C6.3C 50.F62.C39.F58.C5.3C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F33.3C60.
F54.3C45.F57.C.C6.C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F33.C62.F 45.2C8.C46.F58.C44.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F46.C6.3C
46.F50.3C50.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F43.3C56.F41.2C 8.C51.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F43.C58.F42.C6.3C51.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F39.3C61.F$F84.F85.F104.F
127.F113.F87.F84.F84.F96.F102.F39.C63.F$F84.F85.F104.F127.F113.F87.F 84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F39.2C44.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F40.C44.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F40.C.C42.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F41.2C42. F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F
87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F53.C33.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F52.C.C32.F84.F84.F96.F102.F103.F$F84.F85.F104.
F127.F113.F53.C33.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40. 2C45.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40.2C45.F84.F84.
F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F63.2C39.F 127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F63.C40.F127.F113.F87.F
84.F84.F96.F102.F47.C55.F$F84.F85.F61.C.C40.F127.F113.F67.2C18.F84.F 84.F96.F102.F45.3C55.F$F84.F44.2C7.3C29.F61.2C41.F127.F113.F67.2C18.F
84.F84.F96.F102.F44.C58.F$F84.F43.C.C8.C30.F42.2C60.F127.F113.F34.2C 51.F84.F84.F96.F102.F44.2C57.F$F84.F43.C8.3C30.F42.2C60.F127.F113.F
33.C.C51.F84.F84.F96.F102.F103.F$F84.F42.2C41.F104.F127.F113.F33.C53. F84.F84.F96.F102.F41.2C60.F$F84.F85.F104.F127.F113.F32.2C53.F36.C47.F
84.F96.F102.F41.C.C59.F$F84.F85.F41.2C61.F127.F113.F87.F36.3C45.F84.F 39.C56.F102.F42.2C59.F$F84.F85.F42.C61.F127.F113.F87.F39.C44.F47.2C6.
C28.F38.C.C55.F102.F103.F$F84.F85.F39.3C62.F127.F113.F87.F38.2C44.F 47.2C4.3C28.F39.C56.F49.2C10.C40.F56.2C45.F$F84.F85.F39.C64.F127.F
113.F87.F60.2C22.F52.C31.F26.2C68.F41.2C6.2C3.2C3.3C40.F56.2C6.2C37.F
$F84.F85.F104.F127.F113.F87.F60.C23.F52.2C30.F26.2C68.F42.C11.2C2.C 43.F64.C38.F$F84.F85.F104.F127.F42.2C27.2C40.F56.3C28.F58.C.C23.F84.F
96.F42.C.C13.2C42.F62.C.C38.F$F84.F85.F104.F127.F43.C27.2C40.F47.2C8. C29.F58.2C24.F84.F96.F43.2C57.F62.2C39.F$F84.F85.F43.2C7.3C49.F56.C
70.F43.C.C67.F48.C6.3C29.F84.F22.2C60.F96.F102.F103.F$F84.F85.F42.C.C 8.C50.F56.3C68.F44.2C67.F45.3C39.F84.F21.C2.C59.F21.C74.F102.F103.F$F
84.F85.F42.C8.3C50.F59.C67.F113.F45.C41.F28.2C54.F22.2C29.2C29.F20.C.
C73.F102.F103.F$F39.2C43.F85.F41.2C61.F58.2C67.F113.F87.F27.C.C54.F 53.C.C28.F20.2C74.F102.F36.2C65.F$F38.C.C20.2C21.F85.F104.F80.2C45.F
113.F87.F27.C56.F55.C28.F96.F61.2C39.F37.C22.2C41.F$F38.C22.C.C20.F 85.F104.F80.C46.F44.2C67.F87.F26.2C56.F55.2C27.F96.F61.C.C38.F34.3C 23.C42.F$F37.2C24.C20.F85.F104.F78.C.C46.F43.C.C67.F87.F54.2C28.F84.F
96.F63.C38.F34.C26.3C39.F$F63.2C19.F85.F104.F78.2C47.F43.C69.F87.F54. 2C28.F84.F96.F63.2C37.F63.C39.F$F84.F85.F104.F127.F42.2C69.F87.F84.F
84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F55.C40.F 102.F103.F$F84.F85.F104.F48.2C77.F113.F87.F84.F44.3C37.F50.C5.3C37.F
102.F103.F$F84.F85.F104.F47.C.C77.F69.2C42.F87.F46.3C35.F35.2C8.C38.F 49.C.C6.C37.F102.F51.3C49.F$F52.3C29.F85.F104.F47.C79.F69.2C42.F87.F
37.2C8.C36.F36.C6.3C38.F50.C45.F52.3C47.F42.2C8.C50.F$F43.2C8.C30.F 85.F104.F46.2C79.F113.F87.F38.C6.3C36.F33.3C48.F42.3C51.F43.2C8.C48.F 43.C6.3C50.F$F44.C6.3C30.F85.F104.F127.F61.3C49.F87.F35.3C46.F33.C50.
F33.2C8.C52.F44.C6.3C48.F40.3C60.F$F41.3C40.F85.F104.F127.F62.C50.F 87.F35.C48.F84.F34.C6.3C52.F41.3C58.F40.C62.F$F41.C42.F85.F104.F127.F
60.3C50.F87.F84.F84.F31.3C62.F41.C60.F103.F$F84.F85.F104.F127.F113.F 87.F84.F84.F31.C64.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F84.F85.F104.F66.3C58.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F57.2C8.C59.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F58.C6.3C59.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F55.3C
69.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F55.C71.F113.F87.F 84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F46.2C39.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F46.2C39.F84.F84.F96.F102.F103.F$F
84.F85.F104.F127.F113.F38.2C47.F84.F84.F96.F102.F103.F$F84.F85.F104.F 127.F113.F39.C47.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F39.C
.C45.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F40.2C45.F84.F84. F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F
113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F84.F85.F104.F127.F113.F60.2C25.F42.2C10.C29.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F60.C.C24.F42.2C8.3C29.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F62.C24.F51.C32.F84.F96.F50.C51.F
103.F$F84.F85.F104.F127.F113.F62.2C23.F51.2C31.F84.F96.F50.3C49.F103. F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F53.C48.F103.F$F84.F85.F104. F127.F113.F87.F34.2C48.F84.F96.F41.2C9.2C48.F103.F$F84.F85.F104.F127.
F113.F87.F34.2C48.F84.F96.F42.C59.F103.F$F84.F85.F104.F127.F113.F87.F 84.F37.C46.F96.F42.C.C57.F103.F$F84.F85.F104.F127.F113.F51.3C33.F84.F
37.3C44.F96.F43.2C22.2C33.F103.F$F84.F85.F104.F127.F113.F42.2C8.C34.F 52.2C30.F40.C15.C27.F96.F67.2C33.F103.F$F84.F85.F104.F127.F113.F43.C
6.3C34.F52.C.C29.F39.2C13.3C27.F45.2C6.C42.F102.F51.2C10.C39.F$F84.F 85.F104.F127.F113.F40.3C44.F54.C29.F53.C30.F45.2C4.3C42.F102.F51.2C8. 3C39.F$F84.F43.2C40.F104.F127.F113.F40.C46.F54.2C28.F53.2C29.F50.C45.
F102.F60.C42.F$F84.F43.2C40.F104.F127.F113.F87.F84.F84.F50.2C44.F102. F60.2C41.F$F84.F85.F104.F127.F113.F87.F84.F84.F32.2C62.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F84.F32.2C62.F40.2C60.F43.2C58.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F39.C.C60.F43.2C58.F$F84.F85.F104.F 127.F113.F87.F45.3C36.F29.2C53.F96.F39.C62.F103.F$F84.F39.2C44.F104.F
127.F113.F87.F36.2C8.C37.F28.C.C23.2C28.F96.F38.2C62.F103.F$F84.F39. 2C44.F104.F127.F113.F87.F37.C6.3C37.F28.C25.C.C27.F50.C45.F102.F103.F$F84.F47.3C35.F104.F127.F113.F87.F34.3C47.F27.2C27.C27.F49.C.C44.F
102.F62.C40.F$F84.F48.C36.F104.F127.F113.F87.F34.C49.F56.2C26.F50.2C 44.F102.F61.C.C39.F$F84.F46.3C36.F104.F127.F113.F87.F84.F84.F96.F71.
2C29.F62.2C39.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F71.2C29.F103. F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F62.3C37.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F53.2C8.C38.F103.F$F84.F85.F104.F127.F
113.F87.F84.F47.3C34.F42.3C51.F54.C6.3C38.F103.F$F84.F85.F104.F127.F 113.F87.F84.F38.2C8.C35.F33.2C8.C52.F51.3C48.F54.3C46.F$F84.F85.F104.
F127.F113.F87.F84.F39.C6.3C35.F34.C6.3C52.F51.C50.F45.2C8.C47.F$F84.F 85.F104.F127.F113.F87.F84.F36.3C45.F31.3C62.F102.F46.C6.3C47.F$F62.2C
20.F85.F104.F127.F113.F87.F84.F36.C47.F31.C64.F102.F43.3C57.F$F62.C 21.F85.F104.F127.F113.F87.F84.F84.F96.F102.F43.C59.F$F63.3C18.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F65.C18.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F36.2C46.F85.F104.F127.F113.F87.F84.F84.F
96.F102.F103.F$F37.C46.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F34.3C13.3C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F34.C6. 2C8.C32.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F42.C6.3C32.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F39.3C42.F85.F104.F127. F113.F87.F84.F84.F96.F102.F103.F$F39.C44.F85.F104.F127.F113.F87.F84.F
84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F 127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F
84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F 127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F
84.F96.F102.F103.F$F84.F85.F104.F127.F113.F39.C47.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F39.3C21.C23.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F42.C18.3C23.F84.F84.F96.F102.F103.F$F84.F85.F
104.F127.F113.F41.2C17.C26.F84.F84.F96.F102.F103.F$F84.F85.F104.F127. F113.F60.2C25.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.
F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103. F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F 127.F113.F87.F47.C36.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61.
2C24.F45.3C36.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61.C.C23.F 44.C39.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F63.C23.F44.2C38.F
84.F96.F102.F103.F$F84.F85.F104.F127.F113.F63.2C22.F84.F45.2C37.F96.F 60.2C40.F103.F$F84.F85.F104.F127.F113.F87.F41.2C41.F45.2C37.F96.F60.
2C40.F103.F$F84.F85.F104.F127.F113.F87.F41.C.C40.F84.F96.F102.F103.F$
F84.F85.F104.F127.F113.F87.F42.2C40.F33.2C49.F96.F48.2C52.F53.2C48.F$F84.F85.F104.F127.F113.F87.F84.F33.2C49.F37.C58.F48.2C19.2C31.F53.2C 12.C35.F$F84.F85.F104.F127.F113.F56.3C28.F56.2C26.F84.F37.3C56.F69.2C
31.F45.2C18.3C35.F$F84.F85.F104.F127.F113.F47.2C8.C29.F56.2C6.2C18.F 84.F40.C55.F102.F46.C17.C38.F$F84.F85.F104.F127.F113.F48.C6.3C29.F64.
C19.F84.F39.2C17.C37.F102.F46.C.C15.2C37.F$F84.F85.F104.F127.F113.F 45.3C39.F62.C.C19.F84.F56.3C37.F102.F47.2C54.F$F84.F85.F104.F127.F
113.F45.C41.F62.2C20.F84.F55.C40.F102.F103.F$F84.F85.F104.F127.F113.F 87.F84.F84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F27.2C
55.F96.F42.2C58.F103.F$F84.F85.F104.F127.F113.F87.F84.F26.C.C30.2C23. F96.F41.C.C58.F103.F$F84.F85.F104.F127.F113.F87.F36.2C46.F26.C32.C.C
22.F96.F41.C60.F67.2C34.F$F84.F85.F104.F127.F113.F87.F37.C22.2C22.F 25.2C34.C22.F30.2C64.F40.2C60.F67.C.C33.F$F84.F85.F104.F127.F113.F87.
F34.3C23.C23.F61.2C21.F29.C.C64.F102.F69.C33.F$F84.F85.F104.F127.F 113.F87.F34.C26.3C20.F84.F29.C25.C40.F102.F69.2C32.F$F84.F85.F104.F
127.F113.F87.F63.C20.F84.F28.2C24.C.C39.F102.F103.F$F84.F85.F104.F 127.F113.F87.F84.F84.F55.2C39.F74.2C26.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F75.C26.F103.F$F84.F85.F104.F127.F113.F87.F84.F49.3C 32.F96.F64.3C8.C.C24.F103.F$F84.F85.F104.F127.F113.F87.F51.3C30.F40.
2C8.C33.F96.F55.2C8.C10.2C24.F58.3C42.F$F84.F85.F104.F127.F113.F87.F 52.C31.F41.C6.3C33.F96.F56.C6.3C36.F49.2C8.C43.F$F84.F85.F104.F127.F
113.F87.F50.3C31.F38.3C43.F47.3C46.F53.3C46.F50.C6.3C43.F$F84.F85.F 104.F127.F113.F87.F84.F38.C45.F38.2C8.C47.F53.C48.F47.3C53.F$F84.F85.
F104.F127.F113.F87.F84.F84.F39.C6.3C47.F102.F47.C55.F$F84.F85.F104.F 127.F113.F87.F84.F84.F36.3C57.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F36.C59.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F59.2C23.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F59.C24.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F
$F57.C.C24.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F57.2C25.F
85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113. F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F40.2C42.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
39.C.C42.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F39.C44.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F38.2C44.F85.F104.F127.F
113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F
113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F42.2C7.3C30.F85.F104.F127.F113.F87.F84.F84.F96.F102.F
103.F$F41.C.C8.C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
41.C8.3C31.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F40.2C42.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F42.C44.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F
113.F42.3C42.F45.2C37.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F45. C41.F45.2C37.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F44.2C41.F57.
2C25.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F61.2C24.F57.C26.F84. F96.F102.F103.F$F84.F85.F104.F127.F113.F61.C25.F55.C.C26.F84.F96.F
102.F59.C43.F$F84.F85.F104.F127.F113.F59.C.C25.F37.2C16.2C27.F84.F96. F58.C43.F58.C.C42.F$F84.F85.F104.F127.F113.F59.2C26.F37.2C45.F84.F96.
F56.3C43.F59.C43.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F55.C46.F 103.F$F84.F85.F104.F127.F113.F87.F84.F62.2C20.F96.F55.2C45.F47.2C15.
2C37.F$F84.F85.F104.F127.F113.F87.F84.F62.C21.F96.F102.F48.C15.2C37.F$F84.F85.F104.F127.F113.F87.F84.F60.C.C21.F96.F52.2C48.F48.C.C52.F$F 84.F85.F104.F127.F113.F87.F84.F60.2C22.F96.F52.C.C47.F49.2C52.F$F84.F
85.F104.F127.F113.F87.F84.F84.F96.F53.2C47.F103.F$F84.F85.F104.F127.F 113.F87.F84.F84.F46.2C48.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F
36.2C46.F38.2C6.2C8.C39.F64.2C36.F103.F$F84.F85.F104.F127.F113.F87.F 84.F35.C.C46.F39.C14.3C39.F64.2C6.2C28.F103.F$F84.F85.F104.F127.F113.
F87.F84.F35.C22.2C24.F39.C.C11.C42.F72.C29.F69.2C32.F$F84.F85.F104.F 127.F113.F87.F48.3C33.F34.2C22.C25.F40.2C11.2C41.F70.C.C29.F69.C.C31. F$F84.F85.F104.F127.F113.F52.3C32.F39.2C8.C34.F59.3C22.F96.F70.2C30.F
71.C31.F$F84.F85.F104.F127.F113.F43.2C8.C33.F40.C6.3C34.F61.C22.F96.F 102.F71.2C30.F$F84.F85.F104.F127.F113.F44.C6.3C33.F37.3C44.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F41.3C43.F37.C46.F84.F96.F102.F103. F$F84.F85.F104.F127.F113.F41.C45.F84.F84.F54.2C40.F47.2C53.F103.F$F 84.F85.F104.F127.F113.F87.F84.F49.3C32.F54.C.C39.F48.C53.F103.F$F84.F
85.F104.F127.F113.F87.F84.F40.2C8.C33.F56.C39.F45.3C54.F62.3C38.F$F 84.F85.F104.F127.F113.F87.F84.F41.C6.3C33.F56.2C38.F45.C56.F53.2C8.C 39.F$F84.F85.F104.F127.F113.F87.F84.F38.3C43.F96.F102.F54.C6.3C39.F$F 84.F85.F104.F127.F113.F87.F84.F38.C45.F96.F102.F51.3C49.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F51.C51.F$F84.F85.F104.F127.F113.F 87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F49.3C
44.F62.3C37.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F40.2C8.C45.F 53.2C8.C38.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F41.C6.3C45.F54.
C6.3C38.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F38.3C55.F51.3C48.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F38.C57.F51.C50.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F 85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F42.C41.F84.F 96.F102.F103.F$F42.C41.F85.F104.F127.F113.F87.F42.3C39.F84.F96.F102.F
103.F$F42.3C39.F85.F104.F127.F113.F87.F45.C38.F84.F96.F102.F103.F$F
45.C38.F85.F104.F127.F113.F87.F44.2C38.F84.F96.F102.F59.C43.F$F44.2C 38.F85.F104.F127.F113.F87.F84.F84.F96.F102.F58.C.C42.F$F84.F85.F104.F
127.F113.F87.F84.F84.F96.F102.F59.C43.F$F84.F85.F104.F127.F113.F87.F 84.F84.F96.F102.F46.2C55.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F46.2C55.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F
57.2C25.F85.F104.F127.F113.F87.F84.F46.2C36.F96.F102.F103.F$F57.2C25. F85.F104.F127.F113.F87.F84.F38.2C6.2C36.F96.F102.F103.F$F84.F85.F104.
F127.F113.F87.F59.2C23.F39.C44.F96.F102.F103.F$F84.F85.F104.F127.F 113.F87.F59.2C23.F39.C.C42.F96.F102.F103.F$F84.F85.F104.F127.F113.F
87.F84.F40.2C42.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F69.2C31.F40.2C61.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F69.C
32.F39.C.C61.F$F84.F85.F104.F127.F113.F87.F39.2C43.F84.F96.F67.C.C32. F39.C63.F$F84.F85.F104.F127.F113.F87.F38.C.C43.F84.F96.F67.2C33.F38.
2C63.F$F84.F85.F104.F127.F113.F87.F38.C45.F84.F96.F53.2C47.F103.F$F
84.F85.F104.F127.F113.F87.F37.2C45.F84.F46.2C48.F53.2C47.F103.F$F52. 3C29.F85.F104.F127.F113.F87.F84.F61.2C21.F46.2C48.F102.F103.F$F43.2C
8.C30.F85.F104.F127.F113.F87.F84.F61.C22.F38.2C13.2C7.C33.F102.F72.2C
29.F$F44.C6.3C30.F85.F104.F127.F113.F87.F54.3C27.F62.3C19.F39.C13.2C 5.3C33.F52.2C48.F73.C29.F$F41.3C40.F85.F104.F127.F113.F87.F45.2C8.C
28.F64.C19.F39.C.C17.C36.F53.C48.F62.3C8.C.C27.F$F41.C42.F85.F104.F 127.F113.F87.F46.C6.3C28.F84.F40.2C17.2C35.F50.3C49.F53.2C8.C10.2C27. F$F84.F85.F104.F127.F113.F87.F43.3C38.F84.F96.F50.C51.F54.C6.3C39.F$F 84.F85.F104.F127.F113.F87.F43.C40.F49.3C32.F96.F102.F51.3C49.F$F84.F
85.F104.F127.F113.F87.F84.F40.2C8.C33.F96.F102.F51.C51.F$F84.F85.F 104.F127.F113.F87.F84.F41.C6.3C33.F96.F102.F103.F$F84.F85.F104.F127.F
113.F87.F84.F38.3C43.F96.F54.2C7.3C36.F103.F$F84.F85.F104.F127.F113.F 87.F84.F38.C45.F96.F53.C.C8.C37.F103.F$F84.F85.F104.F127.F113.F87.F
84.F84.F96.F53.C8.3C37.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96. F52.2C48.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F
113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F 96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F51.3C42.F102.F103.
F$F84.F85.F104.F127.F113.F87.F84.F84.F42.2C8.C43.F102.F103.F$F84.F85.
F104.F127.F113.F87.F84.F84.F43.C6.3C43.F102.F103.F$F84.F85.F104.F127. F113.F87.F84.F84.F40.3C53.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.
F84.F40.C55.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F40.C43.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F40.3C41.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F43.C40.F96.F102.F103.F$F84.F85.F104.F
127.F113.F87.F84.F42.2C40.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F45.2C37.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F44.C.C37.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F35.2C7.2C38.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F36.C47.F96.F102.F103.F$F84.F85.F104.F127.F113.
F87.F43.2C12.C26.F36.C.C45.F96.F102.F103.F$F84.F85.F104.F127.F113.F 87.F44.C10.3C26.F37.2C45.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F
44.C.C7.C29.F84.F96.F57.C44.F103.F$F84.F85.F104.F127.F113.F87.F45.2C 7.2C28.F84.F96.F57.3C42.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F
96.F60.C41.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F59.2C15.C 25.F103.F$F84.F85.F104.F127.F113.F87.F84.F54.2C28.F96.F75.C.C24.F53.C
49.F$F84.F85.F104.F127.F113.F87.F84.F54.C.C27.F48.C47.F76.C25.F53.3C 47.F$F84.F85.F104.F127.F113.F87.F84.F56.C27.F47.C.C46.F102.F56.C46.F$F50.2C32.F85.F104.F127.F113.F87.F84.F56.2C26.F48.C47.F102.F55.2C46.F$
F50.C.C31.F85.F104.F127.F113.F87.F84.F84.F65.2C29.F102.F48.C54.F$F51. 2C31.F85.F104.F127.F113.F87.F84.F84.F31.2C32.C30.F102.F48.3C21.C30.F$
F47.2C35.F85.F104.F127.F113.F87.F84.F84.F32.C30.C.C30.F49.2C51.F51.C
18.3C30.F$F46.C.C35.F85.F104.F127.F113.F87.F84.F84.F32.C.C28.2C31.F 48.C.C51.F50.2C17.C33.F$F46.C37.F85.F104.F127.F113.F87.F84.F46.3C35.F
33.2C61.F48.C53.F69.2C32.F$F45.2C37.F85.F104.F127.F113.F87.F84.F37.2C 8.C36.F96.F47.2C53.F103.F$F84.F85.F104.F127.F113.F87.F44.2C7.3C28.F
38.C6.3C36.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F43.C.C8.C29.F 35.3C46.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F43.C8.3C29.F35.C
48.F33.2C61.F102.F103.F$F84.F85.F104.F127.F113.F87.F42.2C40.F84.F32.C .C61.F102.F70.2C31.F$F84.F85.F104.F127.F113.F87.F84.F84.F32.C63.F102.
F70.C.C30.F$F84.F85.F104.F127.F113.F87.F84.F84.F31.2C63.F67.3C32.F72. C30.F$F59.3C22.F85.F104.F127.F113.F87.F84.F84.F96.F58.2C8.C33.F72.2C
29.F$F50.2C8.C23.F85.F104.F127.F113.F87.F84.F84.F96.F59.C6.3C33.F103. F$F51.C6.3C23.F85.F104.F127.F113.F87.F84.F84.F96.F56.3C43.F103.F$F48. 3C33.F85.F104.F127.F113.F87.F84.F84.F96.F56.C45.F103.F$F48.C35.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87. F84.F84.F50.3C43.F102.F65.3C35.F$F84.F85.F104.F127.F113.F87.F84.F84.F
41.2C8.C44.F102.F56.2C8.C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F42. C6.3C44.F102.F57.C6.3C36.F$F84.F85.F104.F127.F113.F87.F84.F84.F39.3C
54.F102.F54.3C46.F$F84.F85.F104.F127.F113.F87.F84.F84.F39.C56.F102.F 54.C48.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F52.2C42.F102.F103.F$F84.F85.F104.F127.F
113.F87.F52.2C30.F84.F52.2C42.F102.F103.F$F84.F85.F104.F127.F113.F87. F52.2C30.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F
102.F103.F$F84.F85.F104.F127.F113.F87.F84.F50.2C32.F96.F102.F103.F$F
84.F85.F104.F127.F113.F87.F84.F50.2C32.F69.2C25.F52.C49.F103.F$F84.F 85.F104.F127.F113.F87.F84.F42.2C14.2C24.F69.C26.F52.3C47.F103.F$F84.F
85.F104.F127.F113.F87.F84.F43.C14.2C24.F67.C.C26.F55.C14.2C30.F103.F$F84.F85.F104.F127.F113.F87.F84.F43.C.C38.F67.2C27.F54.2C14.C31.F103.F$F63.C20.F85.F104.F127.F113.F87.F84.F44.2C38.F96.F68.C.C31.F103.F$F 61.3C20.F85.F104.F127.F113.F87.F84.F84.F96.F68.2C32.F59.2C42.F$F60.C
23.F85.F104.F127.F113.F87.F84.F84.F34.2C60.F102.F59.2C42.F$F60.2C22.F 85.F104.F127.F113.F87.F84.F84.F33.C.C60.F102.F103.F$F84.F85.F104.F
127.F113.F87.F84.F84.F33.C31.2C29.F52.2C48.F103.F$F84.F85.F104.F127.F 113.F87.F84.F84.F32.2C31.C30.F51.C.C48.F103.F$F84.F85.F104.F127.F113.
F87.F56.3C25.F84.F66.3C27.F51.C50.F103.F$F84.F85.F104.F127.F113.F87.F 47.2C8.C26.F84.F68.C27.F50.2C50.F71.2C30.F$F61.2C21.F85.F104.F127.F
113.F87.F48.C6.3C26.F84.F96.F102.F71.C31.F$F61.C.C20.F85.F104.F127.F 113.F87.F45.3C36.F84.F96.F102.F69.C.C31.F$F63.C20.F85.F104.F127.F113.
F87.F45.C38.F84.F96.F102.F52.2C15.2C32.F$F42.2C19.2C19.F85.F104.F127. F113.F87.F84.F84.F56.3C37.F102.F52.2C49.F$F43.C40.F85.F104.F127.F113.
F87.F84.F84.F47.2C8.C38.F102.F103.F$F40.3C41.F85.F104.F127.F113.F87.F 84.F55.3C26.F48.C6.3C38.F66.3C33.F103.F$F40.C43.F85.F104.F127.F113.F
87.F84.F46.2C8.C27.F45.3C48.F57.2C8.C34.F69.2C32.F$F84.F85.F104.F127. F113.F87.F84.F47.C6.3C27.F45.C50.F58.C6.3C34.F69.C.C31.F$F56.3C25.F
85.F104.F127.F113.F87.F84.F44.3C37.F96.F55.3C44.F71.C31.F$F47.2C8.C 26.F85.F104.F127.F113.F87.F84.F44.C39.F96.F55.C46.F71.2C30.F$F48.C6.
3C26.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F45.3C36.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F45.C38.F85.F104.F127.F113.
F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F 102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F62.3C38.F$F 84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F53.2C8.C39.F$F84.F85.F
104.F127.F113.F87.F84.F84.F96.F102.F54.C6.3C39.F$F84.F85.F104.F127.F 113.F87.F84.F84.F96.F102.F51.3C49.F$F84.F85.F104.F127.F113.F87.F84.F
84.F96.F102.F51.C51.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F 103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F 104.F127.F113.F87.F84.F84.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F84.F55.2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F55. 2C39.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F84.F96.F102.F103.F$F 84.F85.F104.F127.F113.F87.F84.F53.2C29.F43.2C51.F102.F103.F$F84.F85.F
104.F127.F113.F87.F84.F53.2C6.2C21.F43.2C51.F102.F103.F$F84.F85.F104. F127.F113.F87.F84.F61.C22.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.
F84.F59.C.C22.F96.F102.F103.F$F84.F85.F104.F127.F113.F87.F84.F41.2C 16.2C23.F96.F102.F103.F$F84.F190.F127.F113.F87.F84.F41.2C41.F96.F102.
F64.C38.F$F84.F190.F127.F113.F87.F84.F84.F96.F102.F62.3C38.F$F84.F
190.F127.F113.F87.F84.F84.F96.F102.F61.C41.F$F84.F190.F127.F113.F87.F 84.F84.F37.2C57.F102.F61.2C40.F$F84.F190.F127.F113.F87.F84.F84.F36.C.
C57.F50.C51.F103.F$F84.F190.F127.F113.F87.F84.F84.F36.C59.F50.3C49.F 58.2C43.F$F84.F318.F113.F87.F84.F84.F35.2C34.2C23.F53.C48.F58.C.C42.F
$F84.F318.F201.F84.F84.F71.C24.F52.2C13.C34.F59.2C42.F$F84.F318.F201.
F84.F84.F72.3C21.F65.3C34.F77.C25.F$F84.F318.F201.F84.F84.F74.C21.F 64.C37.F70.2C3.3C25.F$F84.F318.F201.F84.F84.F96.F64.2C36.F70.2C2.C28.
F$F84.F318.F201.F84.F51.3C30.F96.F102.F74.2C27.F$F84.F520.F84.F42.2C
8.C31.F59.3C34.F102.F103.F$F84.F605.F43.C6.3C31.F50.2C8.C35.F102.F 103.F$F84.F605.F40.3C41.F51.C6.3C35.F49.2C51.F103.F$F84.F605.F40.C43. F48.3C45.F48.C.C51.F103.F$F84.F605.F84.F48.C47.F48.C53.F55.2C46.F$F 38.C45.F605.F84.F96.F47.2C53.F54.C.C46.F$F37.C.C44.F605.F84.F96.F102.
F54.C48.F$F37.C.C44.F605.F84.F96.F102.F53.2C48.F$F38.C14.2C29.F605.F
84.F96.F102.F103.F$F53.2C6.2C21.F605.F84.F96.F102.F103.F$F61.C22.F
605.F84.F96.F102.F103.F$F59.C.C22.F605.F84.F96.F51.2C7.3C39.F103.F$F
59.2C23.F605.F84.F96.F50.C.C8.C40.F103.F$F84.F605.F84.F96.F50.C8.3C 40.F68.3C32.F$F84.F605.F84.F96.F49.2C51.F59.2C8.C33.F$F35.2C47.F605.F 84.F96.F102.F60.C6.3C33.F$F34.C.C47.F605.F84.F96.F102.F57.3C43.F$F34. C22.2C25.F605.F84.F96.F102.F57.C45.F$F33.2C22.C26.F605.F84.F96.F102.F
103.F$F58.3C23.F605.F84.F96.F102.F103.F$F60.C23.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F48.3C33.F605.F84.F96.F102.F103.F$F39.2C8.C 34.F605.F84.F96.F102.F103.F$F40.C6.3C34.F605.F84.F96.F102.F103.F$F37. 3C44.F605.F84.F96.F102.F103.F$F37.C46.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F51.2C31.F72.2C22.F102.F103.F$F84.F 605.F41.2C8.2C5.C25.F72.C23.F102.F103.F$F84.F605.F42.C13.3C25.F70.C.C
23.F102.F103.F$F84.F605.F42.C.C10.C28.F70.2C24.F102.F103.F$F84.F605.F
43.2C10.2C27.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F
84.F96.F55.C46.F103.F$F84.F605.F84.F44.2C50.F55.3C44.F103.F$F84.F605.
F84.F45.C22.2C26.F58.C43.F103.F$F84.F605.F84.F42.3C23.C27.F46.2C9.2C 43.F103.F$F84.F605.F84.F42.C26.3C24.F47.C54.F66.2C35.F$F84.F605.F84.F 71.C24.F47.C.C52.F66.2C35.F$F84.F605.F84.F96.F48.2C22.2C28.F60.2C41.F
$F84.F605.F84.F96.F72.2C28.F61.C13.2C26.F$F84.F605.F84.F96.F102.F61.C
.C11.C27.F$F84.F605.F84.F59.3C34.F102.F62.2C9.C.C27.F$F84.F605.F84.F
50.2C8.C35.F102.F73.2C28.F$F84.F605.F54.3C27.F51.C6.3C35.F102.F103.F$
F84.F605.F45.2C8.C28.F48.3C45.F102.F103.F$F84.F605.F46.C6.3C28.F48.C 47.F102.F103.F$F84.F605.F43.3C38.F96.F102.F103.F$F84.F605.F43.C40.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F67.3C32.F62.2C7.3C29.F$F84.F605.F84.F96.F58.2C8.C33.F61.C.C8.C30. F$F84.F605.F84.F96.F59.C6.3C33.F61.C8.3C30.F$F84.F605.F84.F96.F56.3C 43.F60.2C41.F$F84.F605.F84.F96.F56.C45.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F
103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F 605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F 96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F45.2C37.F96.F102.F103.F$F84.F605.F
45.2C3.2C5.C26.F96.F102.F103.F$F84.F605.F50.2C4.C.C25.F96.F102.F103.F$F84.F605.F57.C26.F51.C44.F102.F103.F$F84.F605.F84.F51.3C42.F102.F 103.F$F84.F605.F84.F54.C41.F102.F103.F$F84.F605.F84.F53.2C41.F102.F 103.F$F84.F605.F84.F71.2C23.F102.F103.F$F84.F605.F84.F71.C24.F102.F 103.F$F84.F605.F84.F69.C.C24.F102.F103.F$F84.F605.F84.F69.2C25.F102.F 103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F43.2C51.F102.F103.F$F84.F605.F84.F42.C.C51.F102.F103.F$F84.F
605.F84.F42.C53.F102.F103.F$F84.F605.F84.F41.2C53.F102.F103.F$F84.F
605.F48.3C33.F96.F47.C54.F103.F$F84.F605.F39.2C8.C34.F96.F47.3C52.F 56.2C45.F$F84.F605.F40.C6.3C34.F96.F50.C51.F55.C.C45.F$F84.F605.F37. 3C44.F96.F49.2C51.F55.C47.F$F84.F605.F37.C46.F96.F102.F54.2C47.F$F84. F605.F84.F61.3C32.F102.F103.F$F84.F605.F84.F52.2C8.C33.F102.F103.F$F 84.F605.F84.F53.C6.3C33.F69.2C31.F77.C25.F$F84.F605.F84.F50.3C43.F69.
C32.F76.C.C24.F$F84.F605.F84.F50.C45.F67.C.C32.F77.C25.F$F84.F605.F
84.F96.F67.2C33.F69.3C31.F$F84.F605.F84.F96.F102.F60.2C8.C32.F$F84.F
605.F84.F96.F102.F61.C6.3C32.F$F84.F605.F84.F96.F54.2C46.F58.3C42.F$F
84.F605.F84.F96.F53.C.C46.F58.C44.F$F84.F605.F84.F96.F53.C48.F103.F$F
84.F605.F84.F96.F52.2C48.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F
605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F
96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F56.2C7.
3C34.F103.F$F84.F605.F84.F96.F55.C.C8.C35.F103.F$F84.F605.F84.F96.F
55.C8.3C35.F103.F$F84.F605.F84.F96.F54.2C46.F103.F$F84.F605.F84.F96.F
102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F 84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F35.2C47.F 96.F102.F103.F$F84.F605.F36.C24.2C21.F96.F102.F103.F$F84.F605.F36.C.C 22.C22.F96.F102.F103.F$F84.F605.F37.2C20.C.C22.F96.F102.F103.F$F84.F 605.F59.2C23.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F 84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F51.C44. F102.F103.F$F84.F605.F84.F51.3C42.F102.F103.F$F84.F605.F38.2C44.F54.C 41.F102.F103.F$F84.F605.F39.C44.F53.2C41.F102.F103.F$F84.F605.F36.3C 45.F96.F102.F103.F$F84.F605.F36.C47.F56.2C38.F102.F103.F$F84.F605.F 84.F55.C.C38.F102.F103.F$F84.F605.F84.F46.2C7.2C39.F102.F103.F$F84.F 605.F52.3C29.F47.C17.2C29.F102.F103.F$F84.F605.F43.2C8.C30.F47.C.C15.
C30.F102.F103.F$F84.F605.F44.C6.3C30.F48.2C13.C.C30.F102.F103.F$F84.F
605.F41.3C40.F63.2C31.F102.F103.F$F84.F605.F41.C42.F96.F102.F103.F$F
84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F
84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F
102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F59.C11.C31.F$F84.F605.F84.F96.F102.F59.3C7.3C
31.F$F84.F605.F84.F96.F102.F62.C5.C34.F$F84.F605.F84.F57.3C36.F102.F
61.2C5.2C33.F$F84.F605.F84.F48.2C8.C37.F102.F103.F$F84.F605.F84.F49.C
6.3C37.F102.F103.F$F84.F605.F84.F46.3C47.F55.2C45.F103.F$F84.F605.F
84.F46.C49.F55.C.C44.F103.F$F84.F605.F84.F96.F56.C45.F103.F$F84.F605.
F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F
102.F103.F$F84.F605.F84.F96.F102.F69.3C31.F$F84.F605.F84.F96.F102.F
60.2C8.C32.F$F84.F605.F84.F96.F102.F61.C6.3C32.F$F84.F605.F84.F96.F
65.3C34.F58.3C42.F$F84.F605.F84.F96.F56.2C8.C35.F58.C44.F$F84.F605.F
84.F96.F57.C6.3C35.F103.F$F84.F605.F84.F96.F54.3C45.F103.F$F84.F605.F
84.F96.F54.C47.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F
102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F84.F96.F102.F103.F$F84.F605.F47.2C35.F96.F102.F103.F$F84.F 605.F47.2C35.F96.F102.F103.F$85.F605.F84.F96.F102.F103.F$85.F605.F84. F96.F102.F103.F$85.F605.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F57.2C25.F96.F102.F103.F$691.F57.2C25.F
96.F102.F103.F$691.F41.2C41.F96.F102.F103.F$691.F40.C.C41.F96.F102.F
103.F$691.F40.C43.F96.F102.F103.F$691.F39.2C43.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F52.3C29.F96.F
102.F103.F$691.F43.2C8.C30.F96.F102.F103.F$691.F44.C6.3C30.F96.F102.F
103.F$691.F41.3C40.F62.2C32.F102.F103.F$691.F41.C42.F62.C33.F102.F
103.F$691.F84.F60.C.C33.F102.F103.F$691.F84.F60.2C34.F102.F103.F$691. F84.F44.2C50.F102.F103.F$691.F84.F44.2C50.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F43.2C51.F102.F103.F$691.F
84.F44.C51.F102.F103.F$691.F84.F41.3C52.F66.2C34.F103.F$691.F84.F41.C
54.F66.2C34.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F45.2C7.3C39.F102.F103.F$691.F84.F44. C.C8.C40.F102.F103.F$691.F84.F44.C8.3C40.F102.F103.F$691.F84.F43.2C 51.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F61.2C7.3C29.F103.F$691.F84.F96.F60.C.C8.C30.F103.F$691.F 84.F96.F60.C8.3C30.F103.F$691.F84.F96.F59.2C41.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F33.C50.F96.F102.F103.F$691.F33.3C48.F96.F102.F103.F$691.F36.C12.
C34.F96.F102.F103.F$691.F35.2C11.C.C33.F96.F102.F103.F$691.F49.C34.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F30.C53.F96.F102.F103.F$691.F29.C.C52.F96.F102.F103.F$691.F29.2C
53.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F61.2C21.F96.F102.F
103.F$691.F61.C.C20.F65.C30.F102.F103.F$691.F63.C20.F58.2C3.3C30.F
102.F103.F$691.F63.2C19.F58.2C2.C33.F102.F103.F$691.F84.F62.2C32.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F43.2C51.F102.F103.F$691.F 84.F43.2C51.F102.F103.F$691.F51.3C30.F96.F102.F103.F$691.F52.C31.F96. F102.F103.F$691.F50.3C31.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.
F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F56.3C37.F102.F103.F$691.F84.F47.2C8.C38.F102.F103.F$
691.F84.F48.C6.3C38.F102.F103.F$691.F84.F45.3C48.F102.F103.F$691.F84.
F45.C50.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F58.2C36.F102.F103.F$691.F84.F58.2C36.F
102.F103.F$691.F84.F70.2C24.F102.F103.F$691.F84.F70.C25.F102.F103.F$691.F84.F68.C.C25.F102.F103.F$691.F84.F68.2C26.F102.F103.F$691.F84.F 44.2C50.F102.F103.F$691.F84.F44.2C50.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F39.2C 43.F96.F102.F103.F$691.F39.2C43.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F61.3C32.F102.F103.F$691.F38.2C44.F52.2C8.C33.F102.F 103.F$691.F39.C44.F53.C6.3C33.F102.F103.F$691.F36.3C45.F50.3C43.F102. F103.F$691.F36.C47.F50.C45.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F40.2C7.3C32.F96.F102.
F103.F$691.F39.C.C8.C33.F96.F102.F103.F$691.F39.C8.3C33.F96.F102.F
103.F$691.F38.2C44.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F62.2C32.F102.F103.F$691.F84.F54.2C6.2C32.
F102.F103.F$691.F84.F55.C13.2C25.F102.F103.F$691.F84.F55.C.C11.C26.F
102.F103.F$691.F84.F56.2C9.C.C26.F102.F103.F$691.F84.F67.2C27.F102.F
103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F 84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$
691.F84.F56.2C7.3C28.F102.F103.F$691.F84.F55.C.C8.C29.F102.F103.F$
691.F84.F55.C8.3C29.F102.F103.F$691.F84.F54.2C40.F102.F103.F$691.F84.
F96.F102.F103.F$691.F53.2C29.F96.F102.F103.F$691.F53.2C29.F96.F102.F
103.F$691.F84.F96.F102.F103.F$691.F30.2C52.F96.F102.F103.F$691.F29.C. C52.F96.F102.F103.F$691.F29.C54.F96.F102.F103.F$691.F28.2C54.F96.F 102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F
96.F102.F103.F$691.F84.F96.F102.F103.F$691.F48.3C33.F96.F102.F103.F$691.F39.2C8.C34.F96.F102.F103.F$691.F40.C6.3C34.F96.F102.F103.F$691.F 37.3C44.F96.F102.F103.F$691.F37.C46.F96.F102.F103.F$691.F84.F96.F102. F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F48.C47.F102.F103.F$691.F84.F48.3C45.F102.F 103.F$691.F84.F51.C44.F102.F103.F$691.F84.F44.2C4.2C44.F102.F103.F$
691.F84.F45.C21.2C27.F102.F103.F$691.F84.F45.C.C19.C28.F102.F103.F$
691.F84.F46.2C17.C.C28.F102.F103.F$691.F84.F65.2C29.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 58.3C35.F102.F103.F$691.F84.F49.2C8.C36.F102.F103.F$691.F84.F50.C6.3C 36.F102.F103.F$691.F84.F47.3C46.F102.F103.F$691.F84.F47.C48.F102.F 103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F
102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F46.2C36.F96.F102.F
103.F$691.F46.C37.F96.F102.F103.F$691.F44.C.C37.F96.F102.F103.F$691.F 44.2C38.F96.F102.F103.F$691.F30.2C52.F96.F102.F103.F$691.F30.2C52.F 96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F
84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F 103.F$691.F84.F96.F102.F103.F$691.F31.2C7.3C41.F96.F102.F103.F$691.F
30.C.C8.C42.F96.F102.F103.F$691.F30.C8.3C42.F96.F102.F103.F$691.F29.
2C53.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F102.F103.F$691.F84.F96.F206.F$
691.F84.F96.F206.F$691.F84.F96.F206.F$691.F84.F96.F206.F$691.F84.F96. F206.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F
84.F56.C39.F$691.F84.F55.C.C38.F$691.F84.F56.C39.F$691.F84.F96.F$691.
F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F36.2C58.F$691.F84.F35.C.C30.2C
26.F$691.F84.F35.C32.C.C25.F$691.F84.F34.2C34.C25.F$691.F84.F70.2C24. F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F
58.3C35.F$691.F84.F49.2C8.C36.F$691.F84.F50.C6.3C36.F$691.F84.F47.3C 46.F$691.F84.F47.C48.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.
F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F34.2C48.F96.F$691.F35.C18.2C28.F96.F$691.F35.C.C 16.C29.F96.F$691.F36.2C14.C.C29.F96.F$691.F52.2C30.F96.F$691.F84.F96.
F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F 96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.
F96.F$691.F41.2C7.3C31.F96.F$691.F40.C.C8.C32.F96.F$691.F40.C8.3C32.F 96.F$691.F39.2C43.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$
691.F84.F96.F$691.F84.F96.F$691.F84.F39.2C16.2C37.F$691.F84.F40.C16. 2C37.F$691.F84.F40.C.C53.F$691.F84.F41.2C53.F$691.F84.F96.F$691.F84.F 96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F62.2C32.F$691.F84.F62.C.C 31.F$691.F84.F64.C31.F$691.F84.F64.2C30.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F43.2C7.3C41.F$691.F84.F42.C.C8. C42.F$691.F84.F42.C8.3C42.F$691.F84.F41.2C53.F$691.F84.F96.F$691.F84. F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F
84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691. F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$
691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F
$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96. F$691.F50.C33.F96.F$691.F48.3C33.F96.F$691.F47.C36.F96.F$691.F47.2C 35.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.
F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F46.3C35.F96.F$691.F37. 2C8.C36.F96.F$691.F38.C6.3C36.F96.F$691.F35.3C46.F46.2C48.F$691.F35.C
48.F46.2C48.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F
$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96. F$691.F84.F65.2C29.F$691.F84.F56.3C6.2C29.F$691.F84.F47.2C8.C38.F$691.F84.F48.C6.3C38.F$691.F84.F45.3C48.F$691.F84.F45.C50.F$691.F84.F
96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84. F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F
84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691.F84.F96.F$691. F84.F96.F$691.F84.F96.F$776.F96.F$776.F96.F$776.F96.F$735.2C39.F96.F$735.2C39.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$739.3C34.F96.F$740.C35.F96.F$738.3C35.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F62.2C32.F$776.F62.C33.F$776.F60.C.C33.F$776.F60.2C34.F$776.F96.F$776.F96.F$776.
F96.F$776.F39.2C55.F$776.F40.C55.F$776.F37.3C56.F$776.F37.C58.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F56.3C37.F$776.F47.2C8.C38.F$776.F48.C6.3C38.F$776.F45.3C48.F$776.F45.C50.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F42.2C52.F$776.F41.C.C17.2C33.F$776.F41. C19.C.C32.F$776.F40.2C21.C32.F$776.F63.2C31.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F53.3C40.F$776.F44.2C8.C41.F$776.F45.C6.3C41.
F$776.F42.3C51.F$776.F42.C53.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F39.2C55.F$776.F38.C.C21.2C32.F$776.F38.C23.C.C31.F$776.F37.2C25.C31.F$776.F64.2C30.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F52.3C41.F$776.F43.2C8.C42.F$776.F44.C6.3C42.F$776.F41.3C52.
F$776.F41.C54.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F58.2C36.F$776.F58.C37.F$776.F56.C.C37.F$776.F39.2C15.2C38.
F$776.F39.2C55.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F52.3C41.F$776. F43.2C8.C42.F$776.F44.C6.3C42.F$776.F41.3C52.F$776.F41.C54.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F58.2C36.F$776.
F58.C37.F$776.F56.C.C37.F$776.F42.2C12.2C38.F$776.F42.2C52.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F43.2C7.3C41.F$776.F42.C.C8.C42.F$776.F
42.C8.3C42.F$776.F41.2C53.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776. F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$
776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96. F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F
48.C47.F$776.F48.3C45.F$776.F51.C44.F$776.F50.2C44.F$776.F96.F$776.F 96.F$776.F46.2C48.F$776.F46.C.C47.F$776.F47.C48.F$776.F96.F$776.F96.F
$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F56.3C37.F$776.F47.2C8.C
38.F$776.F48.C6.3C38.F$776.F45.3C48.F$776.F45.C50.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F55.C40.F$776.F54.C.C39.F$776.F55.C7.2C31.F$776.F63.C32.F$776.F61.C.C32.F$776.F61.2C33.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F48.3C45.F$776.F39.2C8.C
46.F$776.F40.C6.3C46.F$776.F37.3C56.F$776.F37.C58.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.
F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F 96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.
F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$776.F96.F$873.F$873.F$873.F$873.F$873.F$873.F$
873.F$873.F$873.F$873.F! Wow! I especially like the H-5G+block+boat. Is there any way to clean it up? praosylen#5847 (Discord) x₁=ηx V*_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ M. I. Wright Posts: 372 Joined: June 13th, 2015, 12:04 pm ### Re: Still-life 'factories' Hey, that's awesome, simsim. Thanks! Are there either (a) good edgy HF factories (the second one in your list works, but there isn't enough clearance for what I want to do with the HF), or (b) input conduits for Kazyan's? Code: Select all x = 10, y = 11, rule = B3/S23 3bo$b3o$o$2o$8b2o$8bo$6bobo$o5b2o$obo$3o$2bo! Edit: oops - conduit 1 works just fine, as it turns out. Last edited by M. I. Wright on September 28th, 2015, 7:37 pm, edited 1 time in total. gamer54657 wrote:God save us all. God save humanity. hgkhjfgh nutshelltlifeDiscord 'Conwaylife Lounge' simsim314 Posts: 1766 Joined: February 10th, 2014, 1:27 pm ### Re: Still-life 'factories' M. I. Wright wrote:Are there...good edgy HF factories I'm certain there are many very nice HF factories, but you will need to use some catalyst search utility to seek for them. I've just posted the most basic depth = 1 factories. Here is an interesting block factory: Code: Select all x = 30, y = 16, rule = LifeHistory 3$2.2C$3.C9.2C$3.C.C7.2C$4.2C13.3C$8.2C10.C$7.C.C8.3C$7.2C!
Scorbie
Posts: 1538
Joined: December 7th, 2013, 1:05 am
### Re: Still-life 'factories'
Not sure if this would ever going to be useful...
Code: Select all
x = 44, y = 18, rule = B3/S23
12b2o$12b2o5$bo15bobobobobobobobobobo5bo$obo36bo3bo$bo15bobobobobobobo
bobobo2bo$38bo4bo$17bobo3bo3bo3bo3bo2b5o2$2b2o16bobobobobobobobobo$3bo
$3o14b2o$o16b2o$10b2o$10b2o!
Best wishes to you! - Scorbie
A for awesome
Posts: 2292
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: Still-life 'factories'
Scorbie wrote:Not sure if this would ever going to be useful...
Code: Select all
x = 44, y = 18, rule = B3/S23
12b2o$12b2o5$bo15bobobobobobobobobobo5bo$obo36bo3bo$bo15bobobobobobobo
bobobo2bo$38bo4bo$17bobo3bo3bo3bo3bo2b5o2$2b2o16bobobobobobobobobo$3bo
$3o14b2o$o16b2o$10b2o$10b2o!
Longboat factories can be quite useful, due to this reaction:
Code: Select all
x = 19, y = 4, rule = B3/S23
4bo9bo$4bo9bo2bo$3bo9bo2bobo$3o7b3o4bo! Unfortunately does not work with your factory. praosylen#5847 (Discord) x₁=ηx V*_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ Kazyan Posts: 1062 Joined: February 6th, 2014, 11:02 pm ### Re: Still-life 'factories' Spartan glider-activated factory that makes a loaf and an inconvenient block: Code: Select all x = 25, y = 20, rule = LifeHistory .BC$CBCB$.2C2B$2.4B$3.4B6.2A$4.4B4.B2AB$5.4B3.4B$6.4B3.2B$7.3BD5B$8.B
DBD4B$8.D2BD2B2DB$8.B2D3B2D3B$9.10B$10.10B.2A$9.3B2A6B.A.A$10.2B2A6B
3.A$9.A4B2.2BA2B2.2A$8.ABAB5.A.A$7.A.A8.A$7.2A!
Yes, that's a catalytic longboat.
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook. Now on Amazon.
Scorbie
Posts: 1538
Joined: December 7th, 2013, 1:05 am
### Re: Still-life 'factories'
Kazyan wrote:Yes, that's a catalytic longboat.
Whoa, pretty cool! Did you add other spartan objects?
Best wishes to you! - Scorbie
Kazyan
Posts: 1062
Joined: February 6th, 2014, 11:02 pm
### Re: Still-life 'factories'
Scorbie wrote:Whoa, pretty cool! Did you add other spartan objects?
I've explored the block flare reaction, but there's still some reachable search space left. The catalytic longboat produces the second-most interesting perturbation after this one:
Code: Select all
x = 35, y = 32, rule = B3/S23
2bo$o$4bo$2bo$6bo$4bo$8bo$6bo$10bo$8bo$12bo$10bo$14bo$12bo$16bo$14bo$
18bo$16bobo$17b2o4$28bo4b2o$27bobo3b2o$22b2o3bobo$22b2o4bo3$31b2o$31bo
$32b3o$34bo!
I actually found the catalytic longboat a while back, then just recently found the tub+eater extension that restores the block for exactly one tick (via Bellman, surprisingly). That last block, at the top, preserves the restoration.
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook. Now on Amazon.
danieldb
Posts: 163
Joined: July 15th, 2015, 4:27 pm
Location: Right behind you holding a knife
Contact:
### Re: Still-life 'factories'
what does edgy mean
moved to drc
Extrementhusiast
Posts: 1870
Joined: June 16th, 2009, 11:24 pm
Location: USA
### Re: Still-life 'factories'
danieldb wrote:what does edgy mean
In this case, it means that the object emerges near the edge of the reaction envelope that produces it.
I Like My Heisenburps! (and others)
A for awesome
Posts: 2292
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: Still-life 'factories'
A R-to-beehive that I'm only posting because I find the 25-gen-long catalysis (manually found) interesting:
Code: Select all
x = 25, y = 17, rule = LifeHistory
20.A$18.3A$17.A$9.2DB5.2A$8.D2BDB.5B$7.2B2D6B$.2A4.11B$.A.A3.13B$3.A
3.13B$3.3A13B$.2A2.BA11B.B$A2.4A11B.2B$2A.A.3B2.11B.2B$3.A.2A4.5BC6B 2A$3.A.A5.4B3C5B2A$2.2A.A.A5.2BC5B.2B$6.2A6.6B!
praosylen#5847 (Discord)
x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
Kazyan
Posts: 1062
Joined: February 6th, 2014, 11:02 pm
### Re: Still-life 'factories'
Would anyone like to take a crack at completing this? I can't seem to perturb the top so that the fishhook on the right survives without canceling the beehive's restoration.
Code: Select all
x = 30, y = 23, rule = B3/S23
12bo$11bobo$bo9b2o$2bo25b2o$3o25bo$26bobo$26b2o3$24b2o$24b2o$15b2o$14b
o2bo$15b2o2$22b2o$22bobob2o$23b2obo2bo$26bob2o$20b2o4bo$21bo3b2o$18b3o
$18bo! Tanner Jacobi Coldlander, a novel, available in paperback and as an ebook. Now on Amazon. A for awesome Posts: 2292 Joined: September 13th, 2014, 5:36 pm Location: Pembina University, Home of the Gliders Contact: ### Re: Still-life 'factories' Kazyan wrote:Would anyone like to take a crack at completing this? I can't seem to perturb the top so that the fishhook on the right survives without canceling the beehive's restoration. Code: Select all rle Not without invoking a weird catalyst that only works in HighLife: Code: Select all x = 25, y = 36, rule = MixedMediumLife 16.B$15.B.B$16.B2$14.5B$14.B4.B$17.B2.B$17.2B.B2.B$14.B5.B.B.B$13.B.B 4.B2.B$14.B.B2.2B$15.B2$2.A$.A.A$.2A$18.2A$18.A$16.A.A$16.2A3$14.2A$
14.2A$5.2A$.A2.A2.A$2.A2.2A$3A$12.2A$12.A.A.2A$13.2A.A2.A$16.A.2A$10. 2A4.A$11.A3.2A$8.3A$8.A!
Even then, it's only a glider eater.
praosylen#5847 (Discord)
x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
A for awesome
Posts: 2292
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: Still-life 'factories'
A very edgy R-to-boat:
Code: Select all
x = 20, y = 15, rule = LifeHistory
6.2C$5.C.C$.2C2.C8.BD$.C.C.2C6.BDBD$3.C.4B.2B.2B2D$3.4C9B$.2C2.BC8B$C 2.3C9B$2C.C2.9B$3.C3.6B.2B$3.2C2.9B.2B$7.4BC6B2C$7.3B3C5B2C$8.2BC5B. 2B$9.6B!
If another R is sent through the same conduit, it is reset. I have no idea if this is useful, but the boat can be transformed into a number of different objects, including G, P, W, HF, and E.
Edit: Reduced catalysts.
praosylen#5847 (Discord)
x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
Scorbie
Posts: 1538
Joined: December 7th, 2013, 1:05 am
### Re: Still-life 'factories'
x = 27, y = 20, rule = B3/S23
11b2o6b2o$11b2o6bo$17bobo$17b2o$9b2o$3b2o3bo2bo$3bo4bobo$2obo5bo4b2o$o
2bob2o7bobo$2b2obo8bo$5bo12bo$5b2o9bo$20bo$18bo$22bo$20bo$24bo$22bo$
26bo\$24bo! | 70,728 | 138,455 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2021-04 | latest | en | 0.763074 |
https://too-meta.neocities.org/anki/analysis/1575415902581/front/?ref=footer | 1,679,658,501,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00753.warc.gz | 660,771,354 | 3,147 | Show Answer
Math and science::Analysis::Tao::03: Set theory
# Cardinality of sets
#### Equal cardinality
We say that two sets $$X$$ and $$Y$$ have equal cardinality iff [...].
#### Cardinality n
Let $$n$$ be a natural number. A set $$X$$ is said to have cardinality n if it has equal cardinality with the set [...]. We also say that such a set has $$n$$ elements.
#### Finite sets
A set is finite iff [...] for some natural number $$n$$; otherwise, the set is called infinite.
Notation: if $$X$$ is a finite set, we use $$\#(X)$$ to denote the cardinality of $$X$$. | 155 | 573 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2023-14 | latest | en | 0.890486 |
https://math.answers.com/Q/How_do_you_use_addition_and_subtraction_in_real_life | 1,718,690,038,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861747.46/warc/CC-MAIN-20240618042809-20240618072809-00559.warc.gz | 354,115,041 | 48,148 | 0
# How do you use addition and subtraction in real life?
Updated: 12/24/2022
Wiki User
11y ago
Adding up an amount on a deposit slip to give to your bank is one example. The possibilities are endless.
Wiki User
11y ago
Earn +20 pts
Q: How do you use addition and subtraction in real life?
Submit
Still have questions?
Related questions
### Are real numbers closed under addition and subtraction?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
### How will you use addition and subtraction in real life?
when u r adding prices it helps alot i am also in school learning addition and subtraction so i know how u feel but if u like to shop then it's very helpful
### When would you use a number line in life?
When you are starting to learn about numbers, their addition and subtraction.
### How do you use greatest common factor with addition and subtraction of fractions?
You don't. You use the GCF to reduce the answer once the addition or subtraction is complete.
### When do you use BIDMAS in real life?
When working out mathematical problems because BIDMAS is the order of arithmetical operations in step by step stages i.e. brackets, indices, division, multiplication, addition followed by subtraction.
### Explain how you know to use a variable in an addition or subtraction expression?
that we can use it
### In addition use in sentence?
In addition to his response I vote yes. or I like addition better than subtraction.
### Why would you use addition to solve a subtraction equation?
because you undo the operation in the equation= to undo subtraction you add | 355 | 1,682 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2024-26 | latest | en | 0.942952 |
https://solvedlib.com/n/quot-thc-erralcst-red-bccrexh-ithanineekra-icm-l-sxbtfore,21304718 | 1,659,923,912,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570741.21/warc/CC-MAIN-20220808001418-20220808031418-00330.warc.gz | 489,131,360 | 16,647 | # "thc Erralcst red bccrexh ithanineekra icm l Sxbtfore (utkc Uun kx bhth ou; ? 4wngr 221 Fast Fitch_ The H+
##### If two events, A and B,are such that P(A)= 1.3,P(B) = 0.7,and P(AnB) = 0.3,find the following:a)P (A / B),b)P (B | A);c)P (A | AUB),d)P (A AnB);e)P (AnB AUB):
If two events, A and B,are such that P(A)= 1.3,P(B) = 0.7,and P(AnB) = 0.3,find the following: a) P (A / B), b) P (B | A); c) P (A | AUB), d) P (A AnB); e) P (AnB AUB):...
##### 5) For the reaction 2 NO2 > 2 NO + 02 the rate equation is R...
5) For the reaction 2 NO2 > 2 NO + 02 the rate equation is R = k [NO2], where k = 1.4 x 10-10 L/mol-s at 25 C. If 3.00 moles of NO2 are initially present in a sealed 1.00 L vessel at 25 C a) What is the half-life of the reaction? b) What concentration and how many grams of NO2 remain after 150 ye...
##### Qpestion ?5 prsYou have full time job and are married to a stay-at-home spouse: You have two children. egcs 10 and L 8. Uslng the Non-working Spouse Method, how much Iife insurance would you need?S16o.000S100.000SBO,DOO8180,0605200,000
Qpestion ? 5 prs You have full time job and are married to a stay-at-home spouse: You have two children. egcs 10 and L 8. Uslng the Non-working Spouse Method, how much Iife insurance would you need? S16o.000 S100.000 SBO,DOO 8180,060 5200,000...
##### 6.00 bullet is fired horizontally into 1.00 kg wooden block resting on horizontal surface_ The coefficient of kinetic friction between block and surface is The bullet remains embedded in the block, which is bserved to slide 0.30 m along the surface before stopping_ What was the initial speed of the bullet? 222.661 mlsDetermine how much thermal energy was generated during the collision_ ATE6.7/10 pointsPrevious AnswersMy NotesAsk Your TeacherContentProblcmAs shown below; 870 kg car traveling east
6.00 bullet is fired horizontally into 1.00 kg wooden block resting on horizontal surface_ The coefficient of kinetic friction between block and surface is The bullet remains embedded in the block, which is bserved to slide 0.30 m along the surface before stopping_ What was the initial speed of the ...
##### Problem 3 Evaluate the following integral:sin(y? ) dydr(Hint: You can not evaluate the integral as wrilten. You need t0 rewrite the integral before evaluating it: Try drawing picture of the region you're integrating over:)Problem Compute the area enclosed by tle Polar graph r = 3sin(20).
Problem 3 Evaluate the following integral: sin(y? ) dydr (Hint: You can not evaluate the integral as wrilten. You need t0 rewrite the integral before evaluating it: Try drawing picture of the region you're integrating over:) Problem Compute the area enclosed by tle Polar graph r = 3sin(20)....
##### 12.2) What is the smallest horizontal force, P, that the person must exert on the top...
12.2) What is the smallest horizontal force, P, that the person must exert on the top box to initiate motion (slip or tip). Each box weighs 125 lb. The coefficient of static friction between the boxes is 0.5 and the coefficient of static friction between the box and the floor is 0.35....
##### A meterstick is balanced on a fulcrum at its center. Then a 400 N weight is...
A meterstick is balanced on a fulcrum at its center. Then a 400 N weight is placed 10 cm to the left of center. How many cm to the right of center would a 130 N weight need to be placed in order to balance the system?...
##### [8 pts] In the figure below; block m (of mass m-0.500 kg and moving at speed Vm) hits block M (of mass M-0.250 kg and initially at rest) in an elastic one-dimensional collision. Both blocks then continue on and up the loop-the-loop (which has radius R)_What is the minimum speed Vm so that block m is able to circle the loop-the-loop without falling off? b. What is the minimum speed Vm sO that block Mis able to circle the loop-the-loop without falling off?[M
[8 pts] In the figure below; block m (of mass m-0.500 kg and moving at speed Vm) hits block M (of mass M-0.250 kg and initially at rest) in an elastic one-dimensional collision. Both blocks then continue on and up the loop-the-loop (which has radius R)_ What is the minimum speed Vm so that block m i...
##### 1. Travel Company produces travel bags in a single pEOCESS WA The accounting and production records...
1. Travel Company produces travel bags in a single pEOCESS WA The accounting and production records for the cospany show for the month of June : HARE Beginning work in process (100% complete as to materials and 75% complete as to labor and overhead) Process manufacturing plant. pany show the followi...
##### Find the coefficient of the 1' term in the expansion o 2 (21 + 4'A 15B 30C G0D FVEE 2 I0
Find the coefficient of the 1' term in the expansion o 2 (21 + 4' A 15 B 30 C G0 D FV EE 2 I0...
##### 3. A neutral mutation occurs in a monomorphic population of size 5000, so that in the...
3. A neutral mutation occurs in a monomorphic population of size 5000, so that in the next generation there are 4999 wild-type individuals and one mutant. The efective population size of this population is 1000. Assuming that no other mutations occur in the near future, what is the probability that ...
##### 1. Have unions outlived their usefulness? (in America) 2. Does unionization among healthcare professionals compromise professional...
1. Have unions outlived their usefulness? (in America) 2. Does unionization among healthcare professionals compromise professional integrity? Please respond in opposition to your personal beliefs *both short 250 words...
##### Zira Co. reports the following production budget for the next four months. Production (units) April 584...
Zira Co. reports the following production budget for the next four months. Production (units) April 584 May 625 June 617 July 597 Each finished unit requires five pounds of raw materials and the company wants to end each month with raw materials inventory equal to 30% of next month's production ...
##### (1 point) solve the system 18-21 dx X dt 14-17 with the initial value -16 x(0)...
(1 point) solve the system 18-21 dx X dt 14-17 with the initial value -16 x(0) = ༈ ༈་ -12 xt) =...
##### S(e) (5 points) List the X-values on (a, b), where relative (local) extrema (min +max) occur:Answer(b) (2 points) At what x function on (a,b) has absolute minimum:Answer(p) 2 points) At what x function on (a,b) has absolute maximum:Answer
S (e) (5 points) List the X-values on (a, b), where relative (local) extrema (min +max) occur: Answer (b) (2 points) At what x function on (a,b) has absolute minimum: Answer (p) 2 points) At what x function on (a,b) has absolute maximum: Answer...
Part E Assume each battery has internal resistance 1.2 0 Express your answers using two significant figures Enter your answers numerically separated by commas_ AZd I1, Iz, Ig Submit Request Answer...
##### Give the expected product of the following reaction:compoundEtz0P-Ph,
Give the expected product of the following reaction: compound Etz0 P-Ph,...
##### When simipliified (2x10^3)(3x10^4)is equivalent 6x10^7
when simipliified (2x10^3)(3x10^4)is equivalent6x10^7...
##### Using AndroidStudio Create a mobile app UI that has the following labels and textboxes. Customer Name...
Using AndroidStudio Create a mobile app UI that has the following labels and textboxes. Customer Name Customer ID Customer Address The mobile app UI should also contain a Submit button. The following validation should be executed as soon as user clicks the Submit button. Customer ID should be bet...
##### HELLO! Please answer all the questions! don't leave any of them out! Thanks! Answer all the...
HELLO! Please answer all the questions! don't leave any of them out! Thanks! Answer all the questions asked please! om 8. A ball of silly putty hits and sticks to a bowling ball that was initially at rest. After the collision, the total kinetic energy of the bowling ball and silly! putty is O (A...
##### Find rhe critical points of f(r) and use the Second Derivativc Test (if possible) to detettine whether exch correspends to kcal minimum or (aximnum: Lerf(=)Crirical Polntwhut by the Sccond Dcrwvntive 'Test what by ch: Second Detivutive Tcv |Criricul Point
Find rhe critical points of f(r) and use the Second Derivativc Test (if possible) to detettine whether exch correspends to kcal minimum or (aximnum: Ler f(=) Crirical Polnt whut by the Sccond Dcrwvntive 'Test what by ch: Second Detivutive Tcv | Criricul Point...
##### Bandit Corporation Income Statement For the Year Ended December 31, 2019 Revenues - Part 5 Operating...
Bandit Corporation Income Statement For the Year Ended December 31, 2019 Revenues - Part 5 Operating Expenses Depreciation Expense 6.580,000 5.391.225 Loss on Sale of Machinery 315,000 Total Expenses 40.000 Income before Taxes 5.751.225 Income Tax Expense 621,775 Net Income 310,000 Bandit Corporatio...
##### At 25 %C,an aqueous solution has an equilibrium concentration of 0.00475 M for a generic cation; F(aq), and 0.00238 M for a generic anion, B?-(aq). What is the equilibrium constant, Ksp Of the generic salt A,B(s)?Ksp
At 25 %C,an aqueous solution has an equilibrium concentration of 0.00475 M for a generic cation; F(aq), and 0.00238 M for a generic anion, B?-(aq). What is the equilibrium constant, Ksp Of the generic salt A,B(s)? Ksp...
##### When switch in the iigure open; the volmeter of the battery reads 3.13 V When the switch closed; the volimeter reading drops to 2.94 and tho ammoter A roads 1.67 4 Assumo that Ine hvo Melers Are ideal; Ihey da nat allect Ihe circuit, (FigureExpress your answervoltsIree significant digits _E = 3.13SubrilPrevious AnswersCorrectPart BFind the internal resistance oi tne battery: Express your answer in ohms four signiticant digits_View Available Hint(s)Figureof 1AZpSubmitPrevious AnsiversIncorrect; T
When switch in the iigure open; the volmeter of the battery reads 3.13 V When the switch closed; the volimeter reading drops to 2.94 and tho ammoter A roads 1.67 4 Assumo that Ine hvo Melers Are ideal; Ihey da nat allect Ihe circuit, (Figure Express your answer volts Iree significant digits _ E = 3....
##### Dont post the results just send it to me because this is an asssignment 1. The...
dont post the results just send it to me because this is an asssignment 1. The traditional steam cycle used to produce electrical power contains 4 components, the boiler is labelled below. Label the remaining components in the blank provided. For each component, circle whether the component is asso...
##### The following data give the years of teaching experience for all five faculty members of a departmentLet x denote the years of teaching experience for a faculty member of this department Write the population distrdbynereiPGr)
The following data give the years of teaching experience for all five faculty members of a department Let x denote the years of teaching experience for a faculty member of this department Write the population distrdbynerei PGr)...
##### Fird tn8 &rea bounded b} Ihe graphs ol the indicated equations over the given interval: ~Xyeo; -2s*53 The area is square Lnits (Type an integer or decimal rounded to three decimal places as needed )
Fird tn8 &rea bounded b} Ihe graphs ol the indicated equations over the given interval: ~Xyeo; -2s*53 The area is square Lnits (Type an integer or decimal rounded to three decimal places as needed )...
##### Solve the following First Order Linear Differential Equations Iy' + y = Vi b. y + 2" 3 cos? (c)
Solve the following First Order Linear Differential Equations Iy' + y = Vi b. y + 2" 3 cos? (c)...
##### A Quclcvs Contains 39 tns Gnd 43 neutrons yhat 15 ctcs;ss 6 € i5 nuces
A Quclcvs Contains 39 tns Gnd 43 neutrons yhat 15 ctcs;ss 6 € i5 nuces... | 3,155 | 11,719 | {"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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2022-33 | latest | en | 0.88729 |
https://laserpointerforums.com/f44/lasers-prove-we-ve-been-moon-100780-6.html | 1,521,927,412,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257651007.67/warc/CC-MAIN-20180324210433-20180324230433-00547.warc.gz | 624,643,026 | 25,437 | Welcome to Laser Pointer Forums! If you are looking for a laser you may want to check out the Laser Company Top Sites List. The link will open in a new window for your convenience.
Laser Pointer Store
Laser Pointers Lasers prove we've been to the moon !
LPF Laser Pointer Company Database (link opens new window)
06-25-2017, 09:08 AM #81
Super Moderator Join Date: Jan 2014 Location: Qatar, land of the hot footed. Posts: 9,638 Rep Power: 1976820
Super Moderator
Join Date: Jan 2014
Location: Qatar, land of the hot footed.
Posts: 9,638
Rep Power: 1976820
Re: Lasers prove we've been to the moon !
I believe there are multiple big bangs, always have been, that our universe is much bigger than we think and the real universe includes trillions upon trillions of what we think of our lone universe, some tests have been done which have not given evidence whether such could be true, but science is trying! Maybe someday we will know.
__________________
Attention new brothers of the collimated light!
Newbie advice: Please take the time to first make an introduction in the Welcome section before posting questions: - https://laserpointerforums.com/f37
Divergence to spot size calc: - 1 mRad is about .057 degrees which expands to be very roughly ~10% the diameter of the moon or sun at their distances.
Divergence Calculator: pseudonomen137's JScript mRad Calculator - Measure your lasers beam dia. at 1 foot & then 20'.
Online calc. to determine spot intensity at different mRad's & powers: http://tinyurl.com/divergence-calculator
Laser Power Density Calculator: Laser Power Density Calculator - Ophir
Build a beam expander to reduce divergence: http://tinyurl.com/BeamExpander
University YAG Project The Professor's Homebuilt Lasers Site - YAG Lasers
YAG Power Calc. Laser Peak Power Calculator - Ophir
Angular Size Calculator; use with diode angle of radiation spec. for lens dia. at FL: Angular Size Calculator
RHD's Relative Brightness vs Wavelength Calc: https://tinyurl.com/RHD-brightness
High Current Pulse Diode Drivers: https://tinyurl.com/ya7whuk3
06-25-2017, 09:24 AM #82
Class 4 Laser Join Date: Feb 2008 Location: Yellowknife, NT, Canada Posts: 9,146 Rep Power: 1377502
diachi
Class 4 Laser
Join Date: Feb 2008
Posts: 9,146
Rep Power: 1377502
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by Alaskan I believe there are multiple big bangs, always have been, that our universe is much bigger than we think and the real universe includes trillions upon trillions of what we think of our lone universe, some tests have been done which have not given evidence whether such could be true, but science is trying! Maybe someday we will know.
Science is still missing a lot of the answers. Many of the basic laws of physics are readily observable and verifiable, even for the average person, but a lot of it is still unproven theory. Even some things that we can observe, test, verify etc., we can't explain. We can understand it, model it and calculate it, but we can't really explain the why or the how. Much of Quantum Physics being a prime example of that.
We've come a long way, but we've got much, much more to learn. I think it's wise to take a lot of science with a grain of salt, at least the things that we can't yet actually prove to be real. I.e. don't take theories as being solid fact or truth. We have been wrong many, many times before. We'll be wrong again. Although, sometimes it's good to be wrong.
Dark matter? We can't find any evidence that it exists, but in order for our models of the universe to actually work, it must be there. So either dark matter is out there, or our models are incorrect and our understanding of the universe from a Physics point of view is flawed.
Even then... the universe and the unending, awesome power of nature may always give us another challenge to overcome and another mystery to solve.
__________________
355nm | Bruker SmartBeam | Q-Switched Nd:YAG | Awaiting Arrival
405nm | Banggood LT-850 | 50mW Metered | Review Unit | >>Review<<
445nm | Sanwu Laser Pocket Series | 400mW Metered
445nm | NDB7242E Pen Build | 60mW Metered | >>Build Thread<<
450nm | LaserPointerStore - Thor H2 | 1.6W Metered | Review Unit | >>Review<<
473nm | B&W Tek BWB-10-OEM |
488nm | Spectra Physics 163 Argon | ~30mW Metered |
495nm | Laser66 Pen Build | WIP
515nm | PL515 Pen Build | 50mW | >>Build Thread<<
520nm | Laserlands 520 5mW | 3mW Metered | Review Unit | >>Review<<
532nm | Gearbest 303 Pointer | 50mW Metered
532nm | Gearbest JD-850 Pointer | 30mW Metered |
633nm | HeNe | 6mW
633nm | Spectra Physics 155 HeNe | <1mW >>Thread<<
650nm | Sanwu Laser Pocket Series | 200mW Metered
808nm | Melles Griot 532nm Lab Unit | No Crystals >10W
B&W Tek Spectrometer
LaserBee 2.5W USB LPM
Last edited by diachi; 06-25-2017 at 09:27 AM.
06-25-2017, 09:26 AM #83
Super Moderator Join Date: Jan 2014 Location: Qatar, land of the hot footed. Posts: 9,638 Rep Power: 1976820
Super Moderator
Join Date: Jan 2014
Location: Qatar, land of the hot footed.
Posts: 9,638
Rep Power: 1976820
Re: Lasers prove we've been to the moon !
Every generation so far has uncovered greater and greater understanding of what is really going on, but then the next one does it again to make their understanding obsolete, where this leap frogging it will end, could be many many generations from now, maybe never, maybe we are too limited to find the end of the rainbow.
__________________
Attention new brothers of the collimated light!
Newbie advice: Please take the time to first make an introduction in the Welcome section before posting questions: - https://laserpointerforums.com/f37
Divergence to spot size calc: - 1 mRad is about .057 degrees which expands to be very roughly ~10% the diameter of the moon or sun at their distances.
Divergence Calculator: pseudonomen137's JScript mRad Calculator - Measure your lasers beam dia. at 1 foot & then 20'.
Online calc. to determine spot intensity at different mRad's & powers: http://tinyurl.com/divergence-calculator
Laser Power Density Calculator: Laser Power Density Calculator - Ophir
Build a beam expander to reduce divergence: http://tinyurl.com/BeamExpander
University YAG Project The Professor's Homebuilt Lasers Site - YAG Lasers
YAG Power Calc. Laser Peak Power Calculator - Ophir
Angular Size Calculator; use with diode angle of radiation spec. for lens dia. at FL: Angular Size Calculator
RHD's Relative Brightness vs Wavelength Calc: https://tinyurl.com/RHD-brightness
High Current Pulse Diode Drivers: https://tinyurl.com/ya7whuk3
06-25-2017, 09:34 AM #84
Class 4 Laser Join Date: Feb 2008 Location: Yellowknife, NT, Canada Posts: 9,146 Rep Power: 1377502
diachi
Class 4 Laser
Join Date: Feb 2008
Posts: 9,146
Rep Power: 1377502
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by Alaskan Every generation so far has uncovered greater and greater understanding of what is really going on, but then the next one does it again to make their understanding obsolete, where this leap frogging it will end, could be many many generations from now, maybe never, maybe we are too limited to find the end of the rainbow.
Exactly.
"Everything revolves around the earth" - Nope.
"An atom is the smallest form of matter" - Nope.
There's many more, but those are the first that come to mind.
Quote:
Originally Posted by Alaskan where this leap frogging it will end, could be many many generations from now, maybe never, maybe we are too limited to find the end of the rainbow.
There is a theory that the more we learn about the universe, the more complex it gets. Resulting in us never being able to form a complete understanding of everything.
__________________
355nm | Bruker SmartBeam | Q-Switched Nd:YAG | Awaiting Arrival
405nm | Banggood LT-850 | 50mW Metered | Review Unit | >>Review<<
445nm | Sanwu Laser Pocket Series | 400mW Metered
445nm | NDB7242E Pen Build | 60mW Metered | >>Build Thread<<
450nm | LaserPointerStore - Thor H2 | 1.6W Metered | Review Unit | >>Review<<
473nm | B&W Tek BWB-10-OEM |
488nm | Spectra Physics 163 Argon | ~30mW Metered |
495nm | Laser66 Pen Build | WIP
515nm | PL515 Pen Build | 50mW | >>Build Thread<<
520nm | Laserlands 520 5mW | 3mW Metered | Review Unit | >>Review<<
532nm | Gearbest 303 Pointer | 50mW Metered
532nm | Gearbest JD-850 Pointer | 30mW Metered |
633nm | HeNe | 6mW
633nm | Spectra Physics 155 HeNe | <1mW >>Thread<<
650nm | Sanwu Laser Pocket Series | 200mW Metered
808nm | Melles Griot 532nm Lab Unit | No Crystals >10W
B&W Tek Spectrometer
LaserBee 2.5W USB LPM
06-25-2017, 08:04 PM #85
Class 4 Laser Join Date: Sep 2013 Location: Washington State Posts: 9,016 Rep Power: 1958433
paul1598419
Class 4 Laser
Join Date: Sep 2013
Location: Washington State
Posts: 9,016
Rep Power: 1958433
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by diachi It'd actually be relatively simple to calculate if it is indeed possible or not. As long as you know the output power of your transmitting laser and can calculate the signal attenuation from here to the Moon and back with a given aperture size/sensor efficiency. From there you can calculate the power received by the much smaller aperture of a human eye and figure out if it'd be visible or not. Keep in mind, the story on the FAQ is not from Steve Roberts (AKA "mixedgas" or "LSRFAQ"). It's from a different Steve.
I believe this whole controversy can be put to rest by going to Hakzaw1's post #58 and clicking on the link he has provided there. Look for post #5 by Zom-B and read the whole excerpt from Sam's Laser FAQs. Especially look at the last of excerpt by Sam Goldwasser and his take on this whole subject of seeing lasers with telescopes from earth that have been aimed at these reflectors. THAT is priceless.
__________________
405nm Laser Pointer 45mW
405nm C11 700mW
405nm Laser Shack Pointer 80mW
Thor H Dual Power 445nm, 438 mW & 1648 mW
445nm 3 watts MS-SSW-II
445nm 2.2 watts Nichia MS Envy
473nm 50 mW BWB-10-OEM DPSS
477nm 127 mW 501B
488nm Uniphase #2201-20SLAT argon laser head and power supply >40mW
493nm 120 mW 501B
520nm LaserLands pointer Measures 510nm
532nm LSR532H-1W Laser, LSR-PS-N1 Driver, RS-75-5 P.S. 1300 mW
532nm 200mW Thermostatically Controlled Fan Cooled (Besram) >230mW
532nm 189mW pocket lab laser
532nm lasers X6 100mW-200mW
532nm lasers X4 75mW- 140mW
632.8nm P210 New Laser Tube 0.57mW Melles Griot 05-LMP-827-037 PS
632.8nm Spectra- Physics He- Ne #102-2 4mW heads X2 and #236 power supply
632.8nm PMS He-Ne # 201P/ LPS-115 2mW
632.8nm Siemens HeNe LGK7630S 7.6mW
638nm 1 watt Cyprus II
635nm 5mW pointer
635nm 100mW pointer
650nm 65mW pointer
650nm 380mW 501B
808nm 1+W infrared laser
Ocean Optics USB2000 Spectrometer
B&W TEK BTC100 Spectrometers X3
Scientech Vector S310 with AC2500 10 Watt LPM/ Hyperion 6 Watt & 20 Watt LPM/ Radiant X4 3.7 Watt LPM
06-26-2017, 12:58 AM #86
Class 4 Laser Join Date: Aug 2007 Location: Netherlands Posts: 7,647 Rep Power: 296354
Benm
Class 4 Laser
Join Date: Aug 2007
Location: Netherlands
Posts: 7,647
Rep Power: 296354
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by diachi There is a theory that the more we learn about the universe, the more complex it gets. Resulting in us never being able to form a complete understanding of everything.
I think Feynman among others adhered to this 'onion theory' of things - you understand one layer, but that just presents the one below that needs to be understood.
Looking at dissecting atoms this is pretty clear. Discovering that the electrons come off under some circumstances did not take long. Figuring that the nucleus was not a single particle didn't take that long either, and now we are at the point of figuring out if the quarks that make up protons and neutrons are fundamental or not.
I'm not sure how far this can continue, nor about at what point we can say with certainty to have figured it all out.
Also we have some major things to figure out, mainly how gravity actually works. For electromagnetic, weak and strong forces we know the mediating (virtual) particles, but for gravity we still do not. Surely it has been named 'graviton', but it has never been observed to this day.
Surely we understand what gravity does, like keeping is on the ground or the moon in orbit, but we don't have much of an any on -how- that happens, while we do with all other interactions.
06-26-2017, 02:27 AM #87
Class 4 Laser Join Date: Sep 2013 Location: Washington State Posts: 9,016 Rep Power: 1958433
paul1598419
Class 4 Laser
Join Date: Sep 2013
Location: Washington State
Posts: 9,016
Rep Power: 1958433
Re: Lasers prove we've been to the moon !
Of all the things we understand in physics, gravity is the least understood of them all. Even when Newton was applying his laws of motion and gravity, he threw up his hands at the way he saw gravity pulling thing toward each other. It was counter intuitive to everything else he saw in nature as things push other things, such as each action has an equal but opposite reaction. Einstein was able to make things clearer with his law of special relativity and relativity and the photo electric effect. But, to this day, we still have no idea what gravity is or how it works.
__________________
405nm Laser Pointer 45mW
405nm C11 700mW
405nm Laser Shack Pointer 80mW
Thor H Dual Power 445nm, 438 mW & 1648 mW
445nm 3 watts MS-SSW-II
445nm 2.2 watts Nichia MS Envy
473nm 50 mW BWB-10-OEM DPSS
477nm 127 mW 501B
488nm Uniphase #2201-20SLAT argon laser head and power supply >40mW
493nm 120 mW 501B
520nm LaserLands pointer Measures 510nm
532nm LSR532H-1W Laser, LSR-PS-N1 Driver, RS-75-5 P.S. 1300 mW
532nm 200mW Thermostatically Controlled Fan Cooled (Besram) >230mW
532nm 189mW pocket lab laser
532nm lasers X6 100mW-200mW
532nm lasers X4 75mW- 140mW
632.8nm P210 New Laser Tube 0.57mW Melles Griot 05-LMP-827-037 PS
632.8nm Spectra- Physics He- Ne #102-2 4mW heads X2 and #236 power supply
632.8nm PMS He-Ne # 201P/ LPS-115 2mW
632.8nm Siemens HeNe LGK7630S 7.6mW
638nm 1 watt Cyprus II
635nm 5mW pointer
635nm 100mW pointer
650nm 65mW pointer
650nm 380mW 501B
808nm 1+W infrared laser
Ocean Optics USB2000 Spectrometer
B&W TEK BTC100 Spectrometers X3
Scientech Vector S310 with AC2500 10 Watt LPM/ Hyperion 6 Watt & 20 Watt LPM/ Radiant X4 3.7 Watt LPM
06-26-2017, 05:39 AM #88
Class 1M Laser Join Date: Jun 2017 Location: 209.50416699999997, -8.472361 Posts: 138 Rep Power: 65955
CE5
Class 1M Laser
Join Date: Jun 2017
Location: 209.50416699999997, -8.472361
Posts: 138
Rep Power: 65955
Re: Lasers prove we've been to the moon !
I would like to premise the following response with an apology to @Accutronitis, for my contribution to the continued tangential derailment of your Lunar Retroreflector, thread.
I'm still observing the behavioral patterns and norms, at play on this forum. And at present lack sufficient experiential observations to differentiate abnormalities.
To continue:
For those interested in Gravitational Physics, I have become quite enamored with Orlov's 'Foundation of Vortex Gravitation, Cosmology and Cosmogony' hypothesis.
Of special interest to me, is Section 3, starting on page #5 of the pdf.
The introduction set the hook, but Section 3 reeled me in.
Elegant observations, that lend themselves to be easily grasped and understood by casual laymen, and academics alike.
Here is the International Journal Of Sciences and Technology, link for those interested;
http://www.journalofsciences-technol...3813189874.pdf
06-26-2017, 03:48 PM #89
Class 3R Laser Join Date: Aug 2016 Location: European Union Posts: 1,305 Rep Power: 908617
Class 3R Laser
Join Date: Aug 2016
Location: European Union
Posts: 1,305
Rep Power: 908617
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by diachi ... There is a theory that the more we learn about the universe, the more complex it gets. Resulting in us never being able to form a complete understanding of everything.
Interesting. Do you have any source for that?
I had that crazy idea independently long time ago, but now I take it in some very reduced form now (more in terms of technology and our knowledge than Universe's essence). Still if that is the truth than there is no doubt the Universe is living organism playing a game with us and keeping us entertained. Still interesting is that Universe is basically exploring itself through us and considering tricky reality it makes me curious if there is something on this theory (or more accurately hypothesis?).
I really need to finish my philosophy article and publish it as I see such a discussions here. More explanation of the Surreal world and constructive critics is needed.
__________________
"Lasers are s3xy."
"That feeling when you see colours as their wavelengths."
"Laserpainting is a drug. Do not try it."
"If you do not feel and experience the magic, you cannot become the master of wizardry."
Current collection:
405 nm | 500 mW | Wicked Lasers Lunar
445 nm | 3.5 W | Wicked Lasers Arctic
473 nm | 100 mW | Jet Lasers PL-E Pro
520 nm | 1 W | Wicked Lasers Krypton
532 nm | 100 mW | Wicked Lasers Evo
532 nm | 800 mW | Sky Lasers PL
532 nm | 1.4+ W | Optotronics RPL-II
589 nm | 50 mW | Dragon Lasers Spartan
635 nm | 750 mW | Wicked Lasers Inferno
1 W RGB projector
(+ some pointers)
Wishlisted:
Sanwu's RGB Portable
Laserpainting art:
Latest artwork: The Pandora's Black Box
The Hologram Question has just been answered! (wazup post)
LPF social media hashtag: #laserpointerforums
Last edited by Radim; 06-26-2017 at 03:48 PM.
06-26-2017, 05:23 PM #90
Super Moderator Join Date: Jan 2014 Location: Qatar, land of the hot footed. Posts: 9,638 Rep Power: 1976820
Super Moderator
Join Date: Jan 2014
Location: Qatar, land of the hot footed.
Posts: 9,638
Rep Power: 1976820
Re: Lasers prove we've been to the moon !
Got to be right, look at our professions, getting more and more specialized.
__________________
Attention new brothers of the collimated light!
Newbie advice: Please take the time to first make an introduction in the Welcome section before posting questions: - https://laserpointerforums.com/f37
Divergence to spot size calc: - 1 mRad is about .057 degrees which expands to be very roughly ~10% the diameter of the moon or sun at their distances.
Divergence Calculator: pseudonomen137's JScript mRad Calculator - Measure your lasers beam dia. at 1 foot & then 20'.
Online calc. to determine spot intensity at different mRad's & powers: http://tinyurl.com/divergence-calculator
Laser Power Density Calculator: Laser Power Density Calculator - Ophir
Build a beam expander to reduce divergence: http://tinyurl.com/BeamExpander
University YAG Project The Professor's Homebuilt Lasers Site - YAG Lasers
YAG Power Calc. Laser Peak Power Calculator - Ophir
Angular Size Calculator; use with diode angle of radiation spec. for lens dia. at FL: Angular Size Calculator
RHD's Relative Brightness vs Wavelength Calc: https://tinyurl.com/RHD-brightness
High Current Pulse Diode Drivers: https://tinyurl.com/ya7whuk3
06-26-2017, 06:03 PM #91
Class 3R Laser Join Date: Aug 2016 Location: European Union Posts: 1,305 Rep Power: 908617
Class 3R Laser
Join Date: Aug 2016
Location: European Union
Posts: 1,305
Rep Power: 908617
Re: Lasers prove we've been to the moon !
True. Complexity is increasing, and the only way how to get everything, is to study the complexity itself and specialize on it. With this you have approach to any direction of science. Take stuff from it and build your image of the world. Unavoidable consequence of studying complexity is, you will go deeply specialized in at least several subjects to combine them in new direction.
__________________
"Lasers are s3xy."
"That feeling when you see colours as their wavelengths."
"Laserpainting is a drug. Do not try it."
"If you do not feel and experience the magic, you cannot become the master of wizardry."
Current collection:
405 nm | 500 mW | Wicked Lasers Lunar
445 nm | 3.5 W | Wicked Lasers Arctic
473 nm | 100 mW | Jet Lasers PL-E Pro
520 nm | 1 W | Wicked Lasers Krypton
532 nm | 100 mW | Wicked Lasers Evo
532 nm | 800 mW | Sky Lasers PL
532 nm | 1.4+ W | Optotronics RPL-II
589 nm | 50 mW | Dragon Lasers Spartan
635 nm | 750 mW | Wicked Lasers Inferno
1 W RGB projector
(+ some pointers)
Wishlisted:
Sanwu's RGB Portable
Laserpainting art:
Latest artwork: The Pandora's Black Box
The Hologram Question has just been answered! (wazup post)
LPF social media hashtag: #laserpointerforums
Last edited by Radim; 06-26-2017 at 06:04 PM.
06-27-2017, 02:23 AM #92
Class 4 Laser Join Date: Aug 2007 Location: Netherlands Posts: 7,647 Rep Power: 296354
Benm
Class 4 Laser
Join Date: Aug 2007
Location: Netherlands
Posts: 7,647
Rep Power: 296354
Re: Lasers prove we've been to the moon !
I guess we want to understand the thibgs we observe, and often do a good job at that.
We fundamentally understand how electrcical charges attract or repel anohter, even how atomic nucleii interact and all that. Yet we still do not know the fundamentals of how the earth stays in orbit around the sun, or what caused the apple to fall on newtons head.
Obviously we know what gravity does, but oddly we still have little idea on how it works. I find that a bit ironic since we've known about gravity long before we had any notion of things like electricty, magnetsm or such: tenthousand years ago men fell on their behinds after a wrong move, blissfully ignorant of why.
They discovered things like control of fire, electricty, nuclear fission and fusion since, but still have a very limited understanding of falling on their behinds under certain conditions
06-27-2017, 07:11 PM #93
Class 1M Laser Join Date: Jun 2017 Location: 209.50416699999997, -8.472361 Posts: 138 Rep Power: 65955
CE5
Class 1M Laser
Join Date: Jun 2017
Location: 209.50416699999997, -8.472361
Posts: 138
Rep Power: 65955
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by Accutronitis Dust On the Moon....
@Accutronitis, thanks for posting this clip. That was very informative and added to the thread not only as concerns the Lunar, conditions. But also included a brief overview that similar hostile conditions are present on the Martian, surface as well. You began this thread by drawing attention to the retrorelfectors, that were left on the Lunar surface during the Apollo, missions. This remains as you indicated, an interesting Laser related topic. However, like with most thought provoking subjects, the conversation soon diverged into other related areas such as the current, effusively charming cosmological spitballing. That should actually be viewed, as having achieved a certain level of validation for your original premise. But I digress.
To tiller the conversation back to the Lunar, questions- after exploring what the current status of the 'reflectors' may be due to the accumulation of Lunar dust on the surfaces, this also brings up another interesting aspect of some additional measuring equipment that was installed alongside the reflectors. That equipment consisting of Seismometers, which revealed other interesting aspects of the Lunar body.
https://en.wikipedia.org/wiki/Hollow_Moon
Now while this too lends itself as fertile fodder for other charming cosmological fantasies, it also provides another perspective that serves to reinforce the awe and wonder of creation. In that the Earth and Moon, relationship involves so many sublime nuances that, to coin a phrase from another recent post- layers of onion skins, really only tends to serve as a basic analogy for the current state of observational cosmological knowledge.
Also, I would like to suggest that your thread demonstrated some of the vital roles that Lasers have played.
And how they continue to provide support for Mankind's efforts towards exploring, and understand the universe that we live in.
06-28-2017, 12:25 AM #94
Class 4 Laser Join Date: Aug 2007 Location: Netherlands Posts: 7,647 Rep Power: 296354
Benm
Class 4 Laser
Join Date: Aug 2007
Location: Netherlands
Posts: 7,647
Rep Power: 296354
Re: Lasers prove we've been to the moon !
Well yeah, no hollow moon for me.
Earths moon Luna is actually quite large. In fact, it is so large that it would be considered to be a planet if it did not orbit earth. If earth was to somehow just disappear, luna would be the 3rd planet from the sun being not -that- much smaller than mercury.
As far as being dusty: both luna and mars probably are, very much so.
Even earth is pretty dusty in some areas, mostly those that see little to no rainfall, and if you travel there the find sand also gets into everything and is a major nuisance. Even with our gravity and dense atmosphere the stuff gets in everywhere and causes problems for equipment.
On the plus size we have explored the moon in person and mars by rovers so we know what to expect.
Back in the days leading up to the lunar missions there were serious concerns that the layer of dust on the moon would be so thick things like landers wound sink into it so deeply no exploration was possbile. We now know that the dust layer on either is not so thick a person or rover would simply fall through it never to be heard of again. We have not explored all of the surface though, and their could be parts that have 'quicksand' deep enough to get lost in... the quicksand being a mixture of dust and air anything dense would easily fall through.
06-28-2017, 01:51 AM #95
Class 4 Laser Join Date: Sep 2013 Location: Washington State Posts: 9,016 Rep Power: 1958433
paul1598419
Class 4 Laser
Join Date: Sep 2013
Location: Washington State
Posts: 9,016
Rep Power: 1958433
Re: Lasers prove we've been to the moon !
Quote:
Originally Posted by Benm We have not explored all of the surface though, and their could be parts that have 'quicksand' deep enough to get lost in... the quicksand being a mixture of dust and air anything dense would easily fall through.
Where is this "air" mixed with dust on the moon coming from? Last I heard there is NO atmosphere on the moon. Sounds great in theory, but without any air, highly improbable.
__________________
405nm Laser Pointer 45mW
405nm C11 700mW
405nm Laser Shack Pointer 80mW
Thor H Dual Power 445nm, 438 mW & 1648 mW
445nm 3 watts MS-SSW-II
445nm 2.2 watts Nichia MS Envy
473nm 50 mW BWB-10-OEM DPSS
477nm 127 mW 501B
488nm Uniphase #2201-20SLAT argon laser head and power supply >40mW
493nm 120 mW 501B
520nm LaserLands pointer Measures 510nm
532nm LSR532H-1W Laser, LSR-PS-N1 Driver, RS-75-5 P.S. 1300 mW
532nm 200mW Thermostatically Controlled Fan Cooled (Besram) >230mW
532nm 189mW pocket lab laser
532nm lasers X6 100mW-200mW
532nm lasers X4 75mW- 140mW
632.8nm P210 New Laser Tube 0.57mW Melles Griot 05-LMP-827-037 PS
632.8nm Spectra- Physics He- Ne #102-2 4mW heads X2 and #236 power supply
632.8nm PMS He-Ne # 201P/ LPS-115 2mW
632.8nm Siemens HeNe LGK7630S 7.6mW
638nm 1 watt Cyprus II
635nm 5mW pointer
635nm 100mW pointer
650nm 65mW pointer
650nm 380mW 501B
808nm 1+W infrared laser
Ocean Optics USB2000 Spectrometer
B&W TEK BTC100 Spectrometers X3
Scientech Vector S310 with AC2500 10 Watt LPM/ Hyperion 6 Watt & 20 Watt LPM/ Radiant X4 3.7 Watt LPM
06-29-2017, 12:44 AM #96
Class 4 Laser Join Date: Aug 2007 Location: Netherlands Posts: 7,647 Rep Power: 296354
Benm
Class 4 Laser
Join Date: Aug 2007
Location: Netherlands
Posts: 7,647
Rep Power: 296354
Re: Lasers prove we've been to the moon !
I should have worded that better indeed. Obviously it's not air in the sense of the stuff we breathe.
It's more of a very loosely stacked pocket of dust where the particles lean on eachother, with pretty much a vacuum between them. Such things need not collapse right away, but as soon as you set foot on them you'd sink in.
Let's say you got the dustbag out of your vacuum cleaner, not filled to the point where it stops working well, but where it's sort of "full of dust", and pile the contents of that onto a pile. You could put that in a vacuum chamber and then proceed to reduce pressure carefully to near zero.
The pile would not reduce to a 'pancake' under gravity, but most likely stay more or less the same since it an open structure all elements of which are much denser than hair anyway. If you were to step on such a pile it'd collapse under you immediately though.
Similarly you could shovel out a pit, fill it with something fluffy like cotton balls, put some leaves over it, and have a pretty good trap right here on earth: With the minimum load of the leaves it will keep its form, but as soon as you set foot in on it, down the hole you go.
Air is not really required for this at all, i just mistakenly mentioned it because that is what fills the gaps in such contraptions on earth
Thread Tools Display Modes Linear Mode
Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules
All times are GMT. The time now is 09:36 PM.
-- DarkShadows V5 -- Responsive LPF -2562016 -- Default Style Contact Us - Laser Pointers - Archive - Top | 7,971 | 29,283 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2018-13 | latest | en | 0.856027 |
https://copyassignment.com/python-increment-by-1/ | 1,726,694,835,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651941.8/warc/CC-MAIN-20240918201359-20240918231359-00455.warc.gz | 160,602,370 | 16,496 | # Python Increment By 1
## Introduction
In this post, we are going to learn all the methods for Python Increment By 1. We will see how to increase any variable by 1. This is really simple, we all know but we will still try to cover more and more examples to explain Python Increment By 1.
## Methods to Increment By 1 in Python
### 1. Python Increment By 1 with a simple + operator
Example:
``````x = 5
x = x + 1
print(x)
# Output
# 6``````
### 2. Python Increment By 1 with Increment Shorthand: Augmented Assignment Operator
Example:
``````x = 4
x += 1
print(x)
# Output
# 5``````
### 3. Python Increment By 1 inside while loop
Example:
``````x = 1
while x <= 5:
print(x)
x += 1
# Returns:
# 1
# 2
# 3
# 4
# 5``````
### 4. Python Increment By 1 inside for loop
Example:
``````x = 1
for i in range(5):
print(x)
x += 1
# Returns:
# 1
# 2
# 3
# 4
# 5``````
### 5. Python Increment By 1 with increment operator
Not possible, the increment operator does not exist in Python while it exists in other programming languages like C, C++, Java, etc.
Example:
``````x = 1
x++
print(x)``````
Output:
``````Traceback (most recent call last):
File "F:\thonny-python-programs\Run-python.py", line 2
x++
^
SyntaxError: invalid syntax``````
### 6. Python Increment operator for Strings
``````x = "copy"
y = "assignment"
c = x + y
print(c)
# Returns
# copyassignment``````
## Conclusion
We have learned how can we use Increment or we can say addition operator in Python. We can use this Increment operator in many ways like with other datatypes and built-in data structures like lists, dictionaries, etc. We also saw that we can use this Increment operator to add two strings easily. | 505 | 1,696 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-38 | latest | en | 0.818973 |
https://arms_en_ru.academic.ru/2501/design_load_factor | 1,701,659,895,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100523.4/warc/CC-MAIN-20231204020432-20231204050432-00232.warc.gz | 125,138,184 | 11,707 | статический коэффициент прочности
English-Russian arms dictionary. 2013.
### Смотреть что такое "design load factor" в других словарях:
• Load factor (aerodynamics) — Load factor is the ratio of the lift on an aircraft to the weight of the aircraft.Clancy, L.J., Aerodynamics , section 5.22] Hurt, H.H., Aerodynamics for Naval Aviators , page 37] The load factor is expressed in multiples of g where one g… … Wikipedia
• Load factor — may refer to:* Capacity factor, the ratio of the actual output of a power plant over a period of time and its output if it had operated a full capacity of that time period * Load factor (aerodynamics), n, is the vector expressed by the ratio of… … Wikipedia
• limit load factor — A specified load below which structural members or parts are designed not to fail. If the load factor is higher than the design load factor, either permanent deformation or failure may occur. Also called a design load factor. See gust envelope … Aviation dictionary
• Design load — In a general sense, the design load is the maximum amount of something a system is designed to handle or the maximum amount of something that the system can produce, which are very different meanings. For example, a crane with a design load of 20 … Wikipedia
• Factor of safety — See also: safety factor (plasma physics) Factor of safety (FoS), also known as safety factor (SF), is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is… … Wikipedia
• factor of safety — i. A design factor used to provide for the possibility of loads greater than those assumed, and for uncertainties in design and fabrication. (ICAO). In aircraft design, the margin of strength against loads greater than the limit load normally 1.5 … Aviation dictionary
• Limit state design — (LSD) refers to a design methodology used in structural engineering. The methodology is in fact a modernization and rationalization of engineering knowledge which was well established prior to the adoption of LSD. Beyond the concept of a limit… … Wikipedia
• Specified load — In civil engineering, specified loads are the best estimate of the actual loads a structure is expected to carry. These loads come in many different forms, such as people, equipment, vehicles, wind, rain, snow, earthquakes, the building materials … Wikipedia
• Structural load — Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.[1][2] Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of … Wikipedia
• Cooling load temperature difference calculation method — Contents 1 CLTD/CLF/SCL Cooling Load Calculation Method 2 History 3 Application 4 Explanation of Variables … Wikipedia
• Steel design — Steel design, or more specifically, structural steel design, is an area of knowledge of structural engineering used to design steel structures. The structures can range from schools to homes to bridges. There are currently two schools of thought… … Wikipedia
### Поделиться ссылкой на выделенное
##### Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку» | 704 | 3,269 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2023-50 | latest | en | 0.860723 |
https://www2.stetson.edu/~efriedma/mathmagic/0801.html | 1,561,616,639,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000894.72/warc/CC-MAIN-20190627055431-20190627081431-00120.warc.gz | 965,421,246 | 1,861 | # Problem of the Month (August 2001)
Consider the following operation on a positive integer: square it and then remove all occurences of any single digit. By repeating this operation, sometimes we can eliminate all the digits of a number. For example, 36 can be completely eliminated in 8 steps as follows: 36 ⇒ 129(6) ⇒ (1)664(1) ⇒ (44)0896 ⇒ (8)02(8)16 ⇒ 4(66)5(6) ⇒ (2)0(2)5 ⇒ 2(5) ⇒ (4).
Can every number be eliminated? If not, then which numbers apparently cannot be? What numbers take the longest to be eliminated?
Joseph DeVincentis conjectures that 37 is the first number that cannot be eliminated in this fashion. He notes that if this is true, then there are infinitely many numbers we can get from 37 that also cannot be eliminated.
Berend Jan van der Zwaag gave a conjectured list to those numbers less than 100 that cannot be eliminated: {37, 42, 44, 59, 61, 66, 67, 69, 72, 73, 82, 83, 86, 87, 89, 92, 93}. If anyone can eliminate any of these, let me know!
Here are two numbers that take a lot of steps to eliminate: Joseph DeVincentis gives this chain of 11 steps:
338 ⇒ 11(4)2(44) ⇒ 125(44) ⇒ 156(2)5 ⇒ (2)449(22)5 ⇒ (2)0(2)050(2)5 ⇒ 2(55)02(5) ⇒ (4)080(4) ⇒ (6)400 ⇒ 1(6)0000 ⇒ 1(00000000) ⇒ (1).
Berend Jan van der Zwaag gives this chain of 14 steps:
911 ⇒ 8(2)99(2)1 ⇒ (8)0(8)3(8)0(8)1 ⇒ (9)0601 ⇒ 36(1)20(1) ⇒ 1310(44)00 ⇒ (1)7(1)6(1)x106 ⇒ 5(77)6x1012
⇒ (3)1(3)6x1024 ⇒ 25(6)x1048 ⇒ 62(5)x1096 ⇒ 38(44)x10192 ⇒ 1(444)x10384 ⇒ 1(x10768) ⇒ (1).
I think I need to call 911 after that one! Can anyone eliminate 911 in fewer steps? Can you find a longer chain that is needed?
Joseph Babcock showed that all powers of 10 can be eliminated in two steps.
If you can extend any of these results, please e-mail me. Click here to go back to Math Magic. Last updated 8/31/01. | 632 | 1,796 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2019-26 | latest | en | 0.710716 |
https://trac.sagemath.org/attachment/ticket/9623/9623-reviewer2.patch | 1,619,121,448,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039604430.92/warc/CC-MAIN-20210422191215-20210422221215-00523.warc.gz | 665,691,242 | 3,954 | # Ticket #9623: 9623-reviewer2.patch
File 9623-reviewer2.patch, 1.4 KB (added by jason, 11 years ago)
apply on top of previous patches
• ## sage/interacts/library.py
```# HG changeset patch
# User Jason Grout <jason.grout@drake.edu>
# Date 1285685264 18000
# Node ID ee91ac281310eab90000fd15a85db6c098413ae5
# Parent 19a5a8d4139c72a9c53daaae2ac55c6ebbbd04e9
Fixed a typo and changed "<" to "\angle"
diff -r 19a5a8d4139c -r ee91ac281310 sage/interacts/library.py```
a labels = a_label + b_label + c_label show(unit_circle + triangle + triangle_points + labels, figsize=[5, 5], xmin=-1, xmax=1, ymin=-1, ymax=1) angl_txt = r"\$< A = {%s}^{\circ},\$ \$< B = {%s}^{\circ},\$ \$< C = {%s}^{\circ}\$" % ( angl_txt = r"\$\angle A = {%s}^{\circ},\$ \$\angle B = {%s}^{\circ},\$ \$\angle C = {%s}^{\circ}\$" % ( math.degrees(ak[0]), math.degrees(ak[1]), math.degrees(ak[2]) """ html('
Cube within a Hemisphere
') html('
A cube is placed within a hemisphere so that the corners ' +\ 'of the cube touch the surface of the hemisphere; Observe numerically' + \ 'of the cube touch the surface of the hemisphere; Observe numerically ' + \ 'the ratio of the volume of the cube and the volume of the hemisphere.
') x, y, z = SR.var("x,y,z") hemisphere_graph = implicit_plot3d(x**2+y**2+z**2==1, (x, -1, 1), (y, -1, 1), (z, 0, 1), color="green", opacity=0.4) | 492 | 1,349 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2021-17 | latest | en | 0.56724 |
https://teterfouband.firebaseapp.com/414.html | 1,669,674,746,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00113.warc.gz | 606,729,387 | 4,993 | # Theoreme de norton thevenin pdf file
It is a method for the reduction of a portion of a complex circuit into a simple one. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. Thevenins theorem introduction thevenins equivalent circuit illustration of thevenins theorem formal presentation of thevenins theorem proof of thevenins theorem worked example 2 worked example 3 worked example 4 summary introduction thevenins theorem is a popular theorem, used often for analysis of electronic circuits. Thevenins and nortons theorems illinois institute of. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel. Then, to find the norton current for the current source in the norton equivalent circuit, place a direct wire short connection between the load points and determine the resultant current. Now, we will find the equivalent circuit for two terminal resistive circuit with sources. Any two terminals of a network of any number of resistors, current sources andor voltage sources can be reduced to one current source in. Thevenins theorem and its dual, nortons theorem, are widely used to make. Thevenins theorem states that we can replace entire network by an equivalent circuit that. Pdf the equivalent circuit concept derives from the superposition principle and ohms law.
Thevenin and norton equivalents equivalent networks thevenin equivalent thevenin properties determining thevenin complicated circuits norton equivalent power transfer source transformation source rearrangement series rearrangement summary e1. Abstractthe full equivalence of the thevenin and norton. And it is clear that every circuit have both their thevenin and norton equivalent circuits for a. You are given a power supply in a black box with two terminals. Thevenin s theorem states that we can replace entire network by an equivalent circuit that contains only an independent voltage source in series with an impedance resistor such that the currentvoltage relationship at the load is unchanged. In circuit theory, thevenins theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors. Two forms of the equivalent circuit, the thevenin equivalent and the norton equivalent. It reduces the need for repeated solutions of the same sets of equations. The open circuit voltage, the voltage across the terminals when no current is being drawn.
Calculate the output voltage, v, when in open circuit condition no load resistormeaning infinite resistance. The nortons theorems reduce the networks equivalent to the circuit having one current source, parallel resistance and load. Norton thevenin pdf between v and i is exactly the same in each case. Cours circuit electrique thevenin norton pdf example requires further explanation. Lutilisation des seules lois des mailles et des noeuds nous. The voltage acr oss the load under open circ uit condition, also called as. Superposition, thevenin, norton, source transformation, network equivalence. Powerful pedagogical tools for treating special cases of electric circuits article pdf available in international journal of electrical engineering education 404. Any twoterminal network consisting of resistors, fixed voltagecurrent sources and linear dependent sources is externally equivalent to a circuit. Professor, department of electronics and communication engineering. Superposition, thevenin and norton mit opencourseware. Thevenins theorem greatly simplifies analysis of complex circuits by allowing us to replace all of the elements with a combination of just one voltage source and one resistor.
If there is not any independent source then both voc0 and isc0 so skip step 2. Pdf thevenins theorem and its applications researchgate. The thevenin equivalent circuit involves three parameters. As originally stated in terms of dc resistive circuits only, thevenins theorem aka. Thevenins and nortons equivalent circuits and superposition theorem thevenins and nortons theorems thevenins theorem as far as its appearance from outside is concerned, any two terminal network of resistors and energy s ources can be replaced by a series combination of an ideal voltage source voc and a resistor r, where. Just as with thevenins theorem, the qualification of linear is identical to that found in the superposition theorem. For a linear circuit n consisting of n inputs, namely. Pdf origins of the equivalent circuit concept researchgate. Equivalent thevenin and norton kirchhoff circuits of. Norton s thereom is identical to thevenin s theorem except that the equivalent circuit is an. Pdf the importance of thevenins and nortons theorems when. Rating is available when the video has been rented.
Thevenin s theorem and norton s theorem both are important dc network analysis techniques or theorem. Thevenins theorem is especially useful in analyzing power systems and other circuits where one particular resistor in the circuit called the load resistor is subject to change, and recalculation of the circuit is necessary with each trial value of load resistance, to determine the voltage across it and current through it. Thevenins and nortons theorems in the context of dc voltage. Nortons theorem, states that a complicated queueing system has an. Thevenins analysis o how to find equivalent thevenins voltage.
The helmholtztheveninnorton theorem is widely used in circuit. The thevenin and norton equivalent circuits are related by a source transformation. Thevenin equivalent circuit any twoterminal linear network, composed of. Norton thevenin pdf norton thevenin pdf norton thevenin pdf download.
A complex twoterminal circuit can be replaced by an equivalent circuit consisting of a voltage source. To understand the basic philosophy behind the thevenins theorem and its. Your browser does not currently recognize any of the video formats available. Anant agarwal and jeffrey lang, course materials for 6. Pdf thevenins theorem and its applications find, read and cite all the research you need on. L thevenin, made one of these quantum leaps in 1893. Nov 24, 2016 for more visit this feature is not available right now. | 1,272 | 6,262 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2022-49 | latest | en | 0.899313 |
https://boards.straightdope.com/t/so-what-exactly-is-the-problem-with-ms-excel-for-complex-mathematics-and-statistics/625365 | 1,611,295,771,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00409.warc.gz | 253,598,717 | 14,535 | # So, what exactly is the problem with MS Excel for complex mathematics and statistics?
This was a sub-topic inthis thread, but I would like to see it discussed more specifically as apparently MS Excel, which many professionals rely on every day to be an accurate calculation application is not considered an adequate tool for complex mathematics.
What is the issue with Excel when used for complex calculations? Is it coded wrong or what?
Complex calculations often require what is called symbolic computation; that is, working with variables, equations, and functions and so on as you would on pencil and paper, by solving equations, doing derivatives and integrals, etc. You can make computers do these kinds of things much faster than your caffeinated research assistant can. Symbolic computation packages include stuff like Mathematica, Matlab, and various code libraries for programming languages.
Excel doesn’t have any symbolic computation capabilities, though. (And it shouldn’t; that’s not what it’s for.) It is set up only for doing numeric computation (and some other stuff.) So it is a wholly inappropriate tool for doing all kinds of mathematical work.
Of course, there is plenty of fancy mathematics to be done in strictly numeric areas, as well. But that type of stuff tends to be done by writing your own program rather than relying on a spreadsheet model. You use it when it’s the right tool for the job, and use something else when it’s not.
I’d say that the biggest problem is that it’s proprietary and closed. Maybe it really does work correctly, but you have to take Microsoft’s word for that. Take the example of the 77.1*850 bug from the other thread: OK, so you’re not going to actually multiply those two particular numbers together by accident very often. But there was something funny in the code that made it do that, and you have no way of knowing what that something funny was, or if it might manifest in some other, completely different way. Most tools used by real researchers, though, if something like that cropped up, you (or anyone) could just take a look at the source code and see what was happening.
Another problem is that Excel, like most modern software, is a resource hog. That’s fine if you’re using something that used to be called a supercomputer, just to balance your checkbook. But when you’ve got a project that will take weeks to run, you want it to run as leanly and cleanly as possible.
To expand upon what friedo stated, the use of Excel (or any other spreadsheet type application) as an environment for creating and operating algorithms such as complex transforms, iterative solvers, and other complicated operations is tasking it to do something that it does very poorly. It is analogous to using Paintbrush to touch up photographs or AutoCad to perform cartography functions. It has neither the documentation features nor the debugging capability to be used as a programming tool; all of this is aside from some of the most notable bugs and memory limitations. Personally, the data I deal with is often millions of samples on multiple channels, which would completely overwhelm Excel if I tried to import an entire unfilitered dataset.
Excel, like other spreadsheet applicataions, is intended for bookkeeping type tasks and a limited set of visualization functions (of which most of the graph types are unnecessary, unclear, and provide poor formatting in their default configuration). Although the learning curve to start using it is shallower than, say, Matlab or R, and therefore preferred by professors and lab instructors to get students processing small sets of data, its functions are far more limited.
And yes, I’ve had many occasions in which statistical and DSP calculations performed in Excel did not match the (correct) results from R, Matlab, or Mathematica. Whether because this was some flaw in how the data was entered and formatted in Excel, or due to some inherent bug in a standard function I do not know, though in one particular case, I discovered that the Excel CHIINV function does not always provide correct or even consistent results.
The bottom line is if you are going to be performing complex numerical or statistical analysis, you should be using a dedicated tool or programming system that is both verified to function correctly in its internal operations and allows for documentation and debugging of your code. Using Excel as a jacked up algorithm solver is like trying to change your tire with a pastry spreader and a bendy straw.
Stranger
From my perspective, as a biologist, Excel’s built-in stats functions are very limited, and the graphing is plain lousy. Sure, you can do a T-test, or an ANOVA if you install some of the extra modules. And you can throw together a vaguely acceptable bar graph or scatter plot. Sometimes that’s enough, if you have simple experiments and small data sets. And I’ll do that if I just want to throw some preliminary numbers into a graph.
But it didn’t take me very long to out-grow Excel’s built in functions. Computationally speaking, my needs are trivial. But I do have to use some specialized (though not particularly complicated) statistical methods. If you understand the math, you can kludge your way through, but Excel makes it ugly and difficult.
Say you wanted to dice an onion, and you only had a hacksaw. Sure, you could do it, but you’ll make a huge mess, and everything will end in tears. It’s the wrong tool for the job.
According to the linked blog post in that other thread, Excel converts numbers into binary and a binary number needs to recur infinitely to properly represent the number 0.1. The consequences are supposedly infinitesimal except with that one particular type of number which you are very unlikely to come across.
I do find it ironic that binary can’t do the number 0.1 - I’d like to have seen Alanis Morrisette fit that one in to her song.
That’s not Excel, though. That’s just how arithmetic has to be done with the hardware we have.
In base b, the only fractions that have a terminating representation are those whose denominator is not divisible by any prime which doesn’t divide b. 0.1 = 1/(2 * 5), and 5 does not divide 2, so 0.1 doesn’t have a terminating representation. It’s exactly the same as representing 1/3 in decimal.
The visualization features are just shitty. There is no way to have two overlaid X-Y line plots, for instance.
Also–and this is a problem with any program that saves files as binary blobs–you cannot have proper source control. Any moderately complex project must save as human-readable text, because that is the only way for diff and other tools to work.
Here’s an essay on issues with spreadsheets in general and Excel in particular for statistics. Some of the info is a little old, but there’s more recent stuff as well.
If you want a more general discussion of this (like, if you actually want to learn what you need to know for doing extensive numerical computations), then this needs to be discussed on several levels.
The fundamental problem, discussed in this thread and several previous threads, and in that Joel Spolsky essay, always takes novice programmers by surprise when they first learn it (myself included – I was mortified). That is, the bedrock fractional units of our decimal numbers system, to-wit: 0.1, 0.01, 0.001, 0.0001, etc., CANNOT be represented precisely as binary numbers, which computers use. These, and nearly all multiples and combinations thereof, turn out to be infinitely repeating numbers in binary, just as 1/3 or 3/7 is when written as a decimal fraction.
So it doesn’t matter if your computer stores such numbers with 16 bits or 32 bits or 64 or 128 bits or 65536 bits or more. The number is always a finite number of bits long, and infinitely repeating numbers have to be chopped off there, and thus are always approximations.
There are several implications:
1. Your calculations will typically always be just approximations. Even if your starting data looks very precise (written in decimal), like 25.36743, its representation in the computer is an approximation.
2. Now, if you’re trying to compute how many gallons of paint you need to cover a tank with a circular floor, it might suffice to give all your data (including pi) with just 2 or 3 decimal places. If you’re trying to compute a rocket trajectory to the moon, it might take a few more places. If you’re trying to compute a rocket trajectory to Neptune, maybe even more places to get enough accuracy to actually hit the planet.
3. SO! You can always deal with this problem by just doing your calculations to more precision, as needed! (Not necessarily an option in a lot of languages or applications, like Excel. But possible in theory.) Right?
4. NO! Not necessarily. There are certain kinds of problems with this, where any amount of additional precision is impractical, or sometimes simply doesn’t solve the problem.
5. First, there is the case – common in heavy-duty scientific, engineering, and mathematical work, where you have really heavy-duty intensive, massive computations to be done. Things like computing functions and integrals using infinite series, or simulations of massive events (like nuclear explosions) at the atomic level where you are trying to track every atom. Stuff like that. The problem is (to over-simplify [del]somewhat[/del] a whole lot) is that, upon doing a WHOLE LOT of arithmetic, the round-off errors accumulate. Possibly to the point that your results have very little accuracy, or even none at all.
This can be improved, somewhat in some cases, by using Double Precision instead of Single Precision, or even more precision. Assuming your language or application offers the feature. Or you can write your own modules to do it, or use existing program libraries with such features.
But the MAJOR solution is to study and learn Numerical Analysis – typically, a FULL SEMESTER college class, offered either in Math or Computer Science department, in which you study mathematical techniques for doing extensive computations accurately. This is not a class for mathematical n00bs. It gets fairly heavy. You have to learn how to design computational algorithms for stuff like this.
1. Second, there is the case, which I have seen often, of trying to compare your computed values with some desired target. For example, if 0.1 is not really exactly 0.1, then what is:
0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1
If you compare that with 1.0, as in:
``````
if ( 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 == 1.0 ) {
print ("There is sanity in the world
") ;
}
else {
print ("The gods must be crazy!
") ;
}
``````
what outcome do you expect? Lots of programmers are surprised.
Here are some earlier threads where these problems were discussed:
http://boards.straightdope.com/sdmb/showthread.php?t=640830 (Starting at post #4, then #6, 13, 14, 16)
Especially in software that deals with money, where you expect dollars-and-cents computations to give you exact dollars-and-cents results, this bites often, and causes wrong results. You need to know techniques to do this “right” – First, you need to think about it and define exactly what the “right” results ought to be.
Note that no amount of precision solves this problem. You can’t fix it just by using Double Precision or 100-Fold Precision. Your floating point numbers will always have some small inaccuracy, and tests like the above will always be troublesome. It is possible that an applications like Excel will attempt to handle this by applying some sort of “fudge factor” in doing comparisons like that. Maybe. But somebody somewhere will argue that THAT isn’t even the right thing to do!
1. Above and beyond all the above, Excel apparently had a plain outright bug. A certain few numbers (which could result from inaccuracies like the above), when converted to a human-readable character string and displayed or printed, simply got converted wildly inaccurately. Thus the numbers that should have computed as (approximately) 65536 (correct to at least a dozen decimal fraction places), and displayed as 65536.0000 (or similar), got displayed at 100000 or something like that – That was just plain outright WAY wrong.
Senegoid gives a good overview of the issues. To expand upon a couple of the basic numerical analysis issues that we used to teach (typically in the first week of a one semester second year course.)
Machine epsilon - the number which estimates the rounding error in floating point arithmetic on a particular machine. It can vary depending upon your processor. All algorithm design for computational mathematics needs to understand this.
Ill conditioned systems. Some systems are intrinsically very very sensitive to even the smallest error in calculation. The favourite example is a 20 term polynomial that has roots of the integers -10 to +9 (or some such). An error in the least significant bit of any of the coefficients of the polynomial will result in a polynomial where half the roots become imaginary.
Expressions where there is a term that is the difference of two components that are often very very close to the same value. This leads to serious loss of precision, and often to simply wildly wrong results. As a paradigm spreadsheets make these sorts of error easy to commit because they isolate sub components of the calculation in difficult to track down ways.
Managing these issues is critical.
If you are a professional engineer of scientist doing computational mathematics I would say that near half of the work is still numerical solving of PDEs. (Signals processing and statistics probably make up a large slab of the remainder, although numerical sims are gaining ground.) This is real mathematics. Excel dosen’t do any of them. Well not for real. It is a tool for doing arithmetic and quick and dirty back of the envelope calculations (I will use it to calculate things that are a pain to do on a calculator, but no more complex.)
As has been pointed out above, one of the critical issues with Excel is that there is no way of expressing your spreadsheet in a source code form. So it is almost impossible to use Excel in any sort of real world software engineering process. No source code control, no easy way of reviewing code, and worst of all, essentially no way of testing the system in a systematic manner that would allow the system to be relied upon. Indeed Excel encourages some of the worst elements of poor engineering and science practice.
You are correct about floating point numbers, but in principle, you could store all numbers as algebraic expressions. This could require an arbitrarily high amount of memory, but it could be done.
I suspect that comparisons are in the general case a Very Hard Problem since they could require sophisticated transformations, though stuff like adding rationals together would be trivial.
Question – I know there was some experimental work in doing base 4 computing for a while (aside from DNA computing I mean), due to greater data density (more you can store in two 4-bits than two 2-bits). Though it didn’t really pan out (I recall the words “too much work for too little practical benefit”). Has any supercomputing company ever tried having a hardware subcomponent built for base-10 specifically for the finite representation problem with very common numbers like .1, or is it just not worth it compared to simpler workarounds even in incredibly mathematically sensitive scenarios?
This is a tangential point, but still worth some nitpicks.
(1) Once upon a time, most IBM business software used decimal arithmetic with a moveable decimal point. Decimal computations were exact.
(2) One has the option – though it is directly supported in few languages – of representing rational numbers exactly and doing rational number arithmetic. (This is what I do when I want to dazzle my users with exact answers. )
(3) Unless one is foolish enough to expect code like
x = 0.1 * 10;
if (x != 1) abort(“1 isn’t 1”);
to work as “expected”, the inability to represent exact fractions is only a minor part of more general imprecision problems. More significant are numeric issues like the summing problem addressed by Kahan’s summation algorithm.
Numerical computation is it’s own specialized sub-field of algorithms. Floating point can’t represent all numbers accurately. Normally, this is fine since the errors are small but certain arithmetic techniques can cause errors to compound in unpleasant ways.
For example, (1+1/x)^x trends towards e as x gets larger. The problem is, as x gets larger, 1/x gets tiny, making it hard to approximate using floating point and tiny errors in the representation get compounded through the exponation.
Using Wolfram Alpha which is a tool specially designed for numeric computation, I get:
1.001^1000 = 2.71692
1.000001^1000000 = 2.71828
1.000000001^1000000000 = 2.71828
1.000000000001^1000000000000 = 2.71828
1.000000000000001^1000000000000000 = 2.71828
1.000000000000000001^1000000000000000000 = 2.71828
Using Excel, I get:
1.001^1000 = 2.71692
1.000001^1000000 = 2.71828
1.000000001^1000000000 = 2.71828
1.000000000001^1000000000000 = 2.71852
1.000000000000001^1000000000000000 = 3.035
1.000000000000000001^1000000000000000000 = 1
Properly designed numeric computation algorithms like Wolfram Alpha carefully perform calculations in a way such that errors don’t compound exponentially like the example above. Certain common operations like operations involving matrix inversion are especially prone to such errors so great care needs to be taken in how they are coded. Usually, this is packaged into a library to use such as numpy so you don’t have to worry about the details.
This is why excel is unsuited to this sort of calculation.
Decimal point arithmetic is alive and still with us. The obvious language is COBOL. But the specific instruction sets in the core machines - in addition to the IBM business series, that converged into the single general purpose architecture of the 360 and 370, the DEC VAX had binary coded decimal instructions, and guess what? The x86 instruction set still has support for BCD. They can pack 18 decimal digits into an 80 bit FPU word. (You can either use four or eight bits per decimal digit, there are instructions for either.) These are integers only - no fractional part or fixed point arithmetic, although there is no reason it could not be trivially augmented to do this. One does however note that the majority of the instructions are not valid in the x64 instruction set. So they are finally dying. They are probably really slow.
The advent of RISC machines killed a lot of this nonsense off in new architectures. Even though x86 has won on the desktop.
I must be missing something here - but what exactly is this 77.1850 bug supposed to be? I typed =85077.1 into one cell, and =77.1*850 into another, and got 65535.0000000000 in each.
I then used my trusty old HP 32S RPN calculator to do the same thing, and got the same answer.
Then, just to be sure, I took a pencil to paper and did it by hand! Same answer.
What’s the bug?
Searching for “85077.1" gets me a link to a radio station. Searching on "77.1850” finds nothing.
I’m surprised you call it “nonsense”.
There are obviously a massive number of financial/business calcs being performed constantly - why wouldn’t the architecture be aligned with the types of calcs being performed.
IBM added one of these units to Power6 and moved this processing from firmware in the Z9 to hardware in the Z10.
When that calc was performed before the bug was fixed, excel would display “100,000”
"Q: Isn’t this really, really bad?
A: IMHO, no, the chance that you would see this in real life calculations is microscopic." | 4,345 | 19,805 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2021-04 | latest | en | 0.955968 |
https://forum.edugorilla.com/forums/topic/na-nb-nc-na-b-nb-c-nc-a-na-b-cap/ | 1,632,009,373,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056578.5/warc/CC-MAIN-20210918214805-20210919004805-00491.warc.gz | 311,671,676 | 23,403 | This topic contains 0 replies, has 0 voices, and was last updated by EduGorilla 2 years, 5 months ago.
• Author
Posts
EduGorilla
Keymaster
Select Question Language :
n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C) is equal to
### Options :-
1. n(A ∩ B ∪ C)
2. n(A ᴜ B ᴜ C)
3. n(A ∩ B ∩ C)
4. n(A ∩ B ∩ C) + n(A ᴜ B ᴜ C)
5. n(A ∪ B ∩ C)
Are You looking institutes / coaching center for
• IIT-JEE, NEET, CAT
• Bank PO, SSC, Railways
Select your Training / Study category
Reply To: n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B &cap….
Verify Yourself | 252 | 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} | 2.671875 | 3 | CC-MAIN-2021-39 | latest | en | 0.69721 |
http://room72math.blogspot.com/2009/03/scribe-post-for-march-13-2009.html?showComment=1237341000000 | 1,531,889,307,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590051.20/warc/CC-MAIN-20180718041450-20180718061450-00429.warc.gz | 317,741,663 | 12,617 | ## Saturday, March 14, 2009
### Scribe Post for March 13, 2009
Today at school we started with the Number of the day. For those who were away the number is 2468.135. Remeber number of the day is ALWAYS homework!
1. Half of the number of the day is:
2. Write the number of the day in expanded form:
3. Write the number of the day in written form:
4. Round the number of the day to the nearest 100:
5. What number is in the tenths place:
6. The number of the day doubled is:
7. Write the number of the day in expanded notation:
8. Write a power using the number in the 100th place as the base and the number in the 10s place as the exponent:
9. Write the above power in factored form:
10. Cube the number in the ones place:
11. Square the number in the hundreds place:
12. Divide the number by 3.55 and round to the nearest hundredth:
13. The product of all the numbers in the number of the day is:
14. List all the prime numbers in number of the day:
15. Write the number of the day in scientific notation:
16. The whole number is divisible by (circle): 2, 3, 4, 5, 6, 8, 9
17. Combine the numbers in the 1s place and the 10s place respectively to make a two digit number and write the prime factors:
20. Write a fraction using the 1000s place as the denominator and the tenths place as the numerator:
21. Use any two numbers to make an improper fraction:
22. Use any of the numbers to make a mixed fraction:
23. Write the answer to number 22 as a decimal:
24. Draw a picture to represent the answer to number 22:
25. Write the answer to number 21 as a percent:
We also took notes on Still More Probability.
Random- an event in which every outcome has an equal chance of occuring.
Experimental probability- the probability of an event occuring based on experiment results.
Theoretical probability- the expected probability of an event occuring.
e.g. flipping a coin
Theoretical probability Experimental probability
favourable over possible do the experiment
The larger or more trials in an experiment the closer experimental probability gets theoretical probability.
After that we took out our Maths links text book. We worked on page 180 and number 1 to 11.
Thank you for reading my scribepost.
I choose DEVIN to do the next blog.
Carla772 said...
Great Job Camille !
I liked how you put alot of color . Nice picture , links , and video. You did a great job!
Ronny 772 said...
Nice job camile, good video, nice use of color, and good photos.
But I think teacher guy said devin will do the blog later
argie772 said...
good job camille!
i liked how you used alot of colors, links pictures and a video.
well good job again
kevin772 said...
good job . lots and lots of colours
althea772 said...
good job!
you put lot's of information.you also put lot's of colour,picture,links,and vidio.
Ralph772 said...
Good Job! I liked how you put lots of colour, pictures, links and videos. Good Job!
devin772 said...
good job camille you put color,video and picture.
MaryJane772 said...
Awesome job Camille ! I liked the colours, video, and the picture. I also liked how you explained everything we did in class so well. It was a great job.
gilbert772 said...
Good job Camille I like how you put lots of color links and you even put a video! Anyways good job again.
Anonymous said...
This was good, i liked the color.
Elaine772 said...
Awesome job Camille! I liked how you put everything that we did and I also liked the video. Sorry my comment was late.
Telisa72 said...
Good job
Stephanie772 said...
Good Job Camille !
I like the colours ! nice picture and I like the video ! | 887 | 3,600 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2018-30 | latest | en | 0.915214 |
http://www.coderanch.com/t/208023/java-programmer-OCPJP/certification/ | 1,462,385,343,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860123840.94/warc/CC-MAIN-20160428161523-00078-ip-10-239-7-51.ec2.internal.warc.gz | 435,478,036 | 8,627 | Win a copy of Re-engineering Legacy Software this week in the Refactoring forum
or Docker in Action in the Cloud/Virtualization forum!
# b*=b1 vs b=b*b1
Jeremy Chan
Greenhorn
Posts: 12
As you can see
Will the following code compile ?
1. byte b=2;
2. byte b1=3;
3. b*=b1;
But
Will the following code compile ?
1. byte b=2;
2. byte b1=3;
3. b=b*b1;
The Answer is No , explicit cast from int to byte needed
Why?
b*=b1; does not equal to b=b*b1 ?
irisly
Greenhorn
Posts: 2
I want to know how to explain it. Who can tell us? thanks!
Ashik Uzzaman
Ranch Hand
Posts: 2373
Hi Chan,
byte b,b1=1; b *= b1;
Here b *= b1 means b = (byte)b*b1; implicit casting is happening here (in ur case-1), which is not happening in the second case.
------------------
azaman
[This message has been edited by Ashik uzzaman (edited August 20, 2001).]
Ragu Sivaraman
Ranch Hand
Posts: 464
Originally posted by Jeremy Chan:
As you can see
Will the following code compile ?
1. byte b=2;
2. byte b1=3;
3. b*=b1;
But
Will the following code compile ?
1. byte b=2;
2. byte b1=3;
3. b=b*b1;
The Answer is No , explicit cast from int to byte needed
Why?
b*=b1; does not equal to b=b*b1 ?
b*=b1;
It is Arithmetic Extended Assignment Operation
Implicit Casting is OK
b=b*b1;
Binary Operation with simple assignment
Implicit casting not applicable | 411 | 1,316 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-18 | longest | en | 0.810034 |
https://www.tristansonlinephysicsnotes.com/stacked-block | 1,721,902,924,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763857355.79/warc/CC-MAIN-20240725084035-20240725114035-00557.warc.gz | 870,759,829 | 86,594 | top of page
## Stacked and chained Blocks
A typical introduction to problems with multiple connected bodies accelerating is usually described with a tuck pulling a trailer with something stacked on top only held by friction, in physics land, it's 2 blocks stacked on one another with a tension attached to another that can transmit force, looking something like this. The main constraints of the system are that all 3 must have the same acceleration, and the static friction between A and B must be below the maximum.
The unknown variable could be the maximum force to slip, the minimum mass of block A, applied force, or several other variables. The free body diagrams and equations of motion are the same for any of these variations.
Because all the bocks have the same acceleration we can take the sum of external forces as equal to the total mass times acceleration. The green part shows that internal forces such as tension and static friction appear twice pointing in opposing directions, they cancel out.
f_AB is the static friction between A and B, and the slip condition is usually a constraint. f_B and f_C are kinetic friction forces between the blocks and the ground, both of these should usually be defined in terms of knowns (see eqn B2, B1, C1).
Plugging B2, B1, C1 into eqn 1 (external forces), a relation between "F_app" and "a" can be found.
The boxed answer can be rearranged to solve for any of these variables as long as the slip condition is assumed.
If the applied force is less than this, the static friction is not saturated, so use eqn 1 to solve for "a" and then substitute it into any of the other equations to find your unknown varible.
bottom of page | 361 | 1,689 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-30 | latest | en | 0.94815 |
https://www.car.chula.ac.th/display7.php?bib=b2094997 | 1,618,280,556,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038071212.27/warc/CC-MAIN-20210413000853-20210413030853-00037.warc.gz | 779,284,125 | 4,786 | Home / Help
Author Gut, Allan. author An Intermediate Course in Probability [electronic resource] / by Allan Gut New York, NY : Springer New York : Imprint: Springer, 1995 http://dx.doi.org/10.1007/978-1-4757-2431-8 XIII, 278 p. online resource
SUMMARY
The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theยญ ory before entering into more advanced courses (in probability and/or statistics). The presentation is fairly thorough and detailed with many solved examples. Several examples are solved with different methods in order to illustrate their different levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experiยญ ence has proved that the hard part in courses of this kind usually in the application of the results and methods; to know how, when, and where to apply what; and then, technically, to solve a given problem once one knows how to proceed. Exercises are spread out along the way, and every chapter ends with a large selection of problems. Chapters I through VI focus on some central areas of what might be called pure probability theory: multivariate random variables, condiยญ tioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process beยญ cause of its fundamental role in the theory of stochastic processes, but also because it provides an excellent application of the results and methยญ ods acquired earlier in the book. As an extra bonus, several facts about this process, which are frequently more or less taken for granted, are thereby properly verified
CONTENT
I. Multivariate Random Variables -- II. Conditioning -- III. Transforms -- IV. Order Statistics -- V. The Multivariate Normal Distribution -- VI. Convergence -- VII. The Poisson Process -- Appendixes -- 1. Suggestions for Further Reading -- 2. Some Distributions and Their Characteristics -- 3. Answers to Problems
Statistics Probabilities Statistics Statistical Theory and Methods Probability Theory and Stochastic Processes
Location
Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand | 469 | 2,257 | {"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} | 2.578125 | 3 | CC-MAIN-2021-17 | latest | en | 0.8971 |
https://help.scilab.org/docs/5.4.1/ru_RU/im_inv.html | 1,610,954,191,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703514423.60/warc/CC-MAIN-20210118061434-20210118091434-00598.warc.gz | 372,892,560 | 7,287 | Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Scilab 5.4.1
Change language to: English - Français - Português - 日本語 -
See the recommended documentation of this function
Scilab help >> Linear Algebra > Kernel > im_inv
# im_inv
inverse image
### Calling Sequence
```[X,dim]=im_inv(A,B [,tol])
[X,dim,Y]=im_inv(A,B, [,tol])```
### Arguments
A,B
two real or complex matrices with equal number of columns
X
orthogonal or unitary square matrix of order equal to the number of columns of `A`
dim
integer (dimension of subspace)
Y
orthogonal matrix of order equal to the number of rows of `A` and `B`.
### Description
`[X,dim]=im_inv(A,B)` computes `(A^-1)(B)` i.e vectors whose image through `A` are in range(`B`)
The `dim` first columns of `X` span `(A^-1)(B)`
`tol` is a threshold used to test if subspace inclusion; default value is `tol = 100*%eps`. If `Y` is returned, then `[Y*A*X,Y*B]` is partitioned as follows: `[A11,A12;0,A22]`,`[B1;0]`
where `B1` has full row rank (equals `rank(B)`) and `A22` has full column rank and has `dim` columns.
### Examples
```A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
W=rand(5,5);A=W*A;B=W*B;
[X,dim]=im_inv(A,B)
svd([A*X(:,1:dim),B]) //vectors A*X(:,1:dim) belong to range(B)
[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]``` | 442 | 1,338 | {"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} | 2.9375 | 3 | CC-MAIN-2021-04 | longest | en | 0.602936 |
http://mathhelpforum.com/calculus/168978-find-two-vectors-perpendicular-line.html | 1,496,126,666,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463613796.37/warc/CC-MAIN-20170530051312-20170530071312-00486.warc.gz | 307,294,816 | 10,721 | # Thread: Find two vectors perpendicular to a line
1. ## Find two vectors perpendicular to a line
This is a question from my calculus 3 class.
"Find two unit vectors in 2-space that are perpendicular to the line y = -5x + 1"
I have to do this without a dot product or any matrices. And so I'm lost as to what I have to do. Where do I begin is what I'm asking? I'm thinking I maybe have to make an initial vector along the line and then go from there? It's the rotation part that's tripping me up though.
2. Originally Posted by nautica17
"Find two unit vectors in 2-space that are perpendicular to the line y = -5x + 1"
You know that the slope of the line is $-5$ and the point $(0,1)$ is on the line.
The slope of the perpendicular is $\frac{1}{5}$.
Find two points one on each side of the line such that they and $(0,1)$ determine a slope of $\frac{1}{5}$.
Make unit vectors out of that.
3. Okay, thank-you, I'll work on that.
4. Edit: nevermind. | 259 | 955 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2017-22 | longest | en | 0.950013 |
https://www.hackmath.net/en/word-math-problems/grade?page_num=92 | 1,582,007,456,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875143635.54/warc/CC-MAIN-20200218055414-20200218085414-00021.warc.gz | 755,489,995 | 9,278 | # Grade - math word problems
1. Trapezoid MO-5-Z8
Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm2. What is the area of the trapezoid KLMN?
2. Earth and Sun
Earth is 150 million km away from the Sun, 300,000 km of sunlight travels in 1 second. How long will the light come from the Sun to the Earth?
3. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
4. School 6
Jirka lives 600m from the school, Honzík 1200m. How many kilometers a week does Honzik go over Jirka on his way to school and back? How many times more Honzík will go than Jirka?
5. Ratio - proportion
Reduce the number 16 in proportion 3:2 5:4 11:8
6. Sugar cubes
The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
7. Distance of numbers
Which number has the same distance from the numbers -5.65 and 7.25 on the numerical axis?
8. Steps
Walkway from the house to the school is 180 m long. How many more steps Michael makes than his father on the way to school, if the length of Michael's step is 60 cm and the length of his father's step is 90 cm.
9. Bronze medal
To produce 1 kg of bronze must be 0.95 kg copper, 0.04 kg of tin, 0.01 kg zinc. The bronze medal has a weight of 8.5 g. How much copper, tin and zinc does medal have?
10. Railway wagon
The railway wagon holds 75 m3 load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons?
11. In the orchard
In the orchard, they planted 25 apple trees, 20 pears, 15 plums and 40 marbles. A strong late frost, however, destroyed a fifth of all new trees. Unfortunately, it was all the trees of one kind of fruit. What is the probability that the plums have died ou
12. Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he
13. Syringe and patient
In 1 ampoule of 2 ml is 15 mg of Dipidol. The patient should receive 10 mg. How much ml do I draw into the syringe?
14. Electricity consumption cost
Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?
15. Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
16. Products
15 products are 48 € more expensive than 12 products. How many euros will it cost five same products?
17. Steamer
At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer?
18. Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
19. Isosceles right triangle
Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
20. Trapezoid thirds
The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.
To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.
Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc... | 1,029 | 3,795 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2020-10 | latest | en | 0.939382 |
https://www.gamedev.net/forums/topic/93021-function-recursion/ | 1,527,020,095,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864872.17/warc/CC-MAIN-20180522190147-20180522210109-00017.warc.gz | 759,190,945 | 25,815 | Public Group
#### Archived
This topic is now archived and is closed to further replies.
# Function Recursion
This topic is 5865 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Going through my tutorial book on C++ I was reading about Function Recursion. It went in-depth explaining it, giving a couple of examples that were slightly confusing. It ended up saying that while it is a tool that''s available it''s not widely used in C++ for the most part My question is this: I don''t really understand exactly how it works except that the function calls itself or another function that in turn calls the original again. The syntax in the example didn''t make a lot of sense to me. Is this something that I should attempt to find more information on, or is it used so rarely that it''s something I can ignore until I get more proficient with the basics? Thanks for any help, Anaton Flying Tigers CFSG
##### Share on other sites
Recursion is a useful tool, and is the basis of a number of algorithm (though there is usually a way to express them in non-recursive form).
How it works. As you figured out, you write a function that calls itself, until some condition is fulfilled.
For example n! = 1*2*3*...n thus n!=n*(n-1)! with 0!=1
Therefore, if you know the value of (n-1)!, you can compute the value of n!. So, we are going to write the function in a way that, when asked to compute n!, it will first compute n-1 (by calling itself), and multiply the result by n
unsigned int Fact( unsigned int n ) // Note: this code is wrong !{ return n*Fact(n-1)}
The problem with the code above is that the recursion never ends : we need to add a case where Factorial doesn't call itself. Well, for the factorial, the basic case is 0!=1, so we add a test for it.
unsigned int Fact( unsigned int n ) // Note: this code is wrong !{ if( n == 0 ) return 1; return n*Fact(n-1)}
Now, if I call Fact(3), what happens is as follow
Fact(3)| if( 3 == 0 ) return 1; // ignore| return 3*Fact(2) | if( 2 == 0 ) return 1; // ignore | return 2*Fact(1); | if( 1 == 0 ) return 1; // ignore | return 1*Fact(0); | if( 0 == 0 ) return 1 // 1 | <----- 1*1 // 1 | <----- 2*1 // 2| <----- 3*2 // 6
Factorial is a trivial examples, but there are algorithms that are more easily expressed in recursive form than in non-recursive form.
Example : tree traversal. A tree is composed of nodes which hold a value and two pointers (left and right) to the children of the node. A (in-order) tree traversal would be (pseudo code):
Visit( Node* n ){ if ( n == NULL ) return; Visit( n->left ); Print( n->data ); Visit( n->right);}
Similarly, sorting routines, binary search ... all kind of Divide and Conquer algorithms (do a search on that) are easy to express (and code, even if it can be inefficient) in recursive form.
Hope it helped a bit.
[Questions (STFW) | GDNet Start Here | GDNet Search | Forum FAQ | Google | Asking Smart Questions ]
[Docs (RTFM) | MSDN | SGI's STL | OpenGL | File formats]
[C++ Must Haves (RTFS) | MinGW | Boost | Loki | FLTK | SDL ]
Stolen from Magmai Kai Holmlor, who held it from Oluseyi, who was inspired by Kylotan...
[edited by - Fruny on May 1, 2002 9:06:48 PM]
##### Share on other sites
Ok your diagram helps make some sense of recursion. In the book (C++ in 21 days) they used a bunch of boxes with interconnecting arrows that made as much sense as mud to the uninitiated (me!).
Am I correct in understanding that recursions are useful in algorithms? What about normal programming (ie making a MOD that does NOT change the AI in a game)?
#include <iostream>int fib (int n);int main(){ int n, answer; std::cout << "Enter a number to find: "; std::cin >> n; std::cout << "\n\n"; answer = fib(n); std::cout << answer << " is the " << n; std::cout << "th Fibonacci number\n"; return 0;}int fib (int n){ std::cout << "Processing fib(" << n << ")..."; if (n < 3 ) { std::cout << "Return 1\n"; return (1); } else { std::cout << "Call fib(" << n-2 << ") "; std::cout << "and fib(" << n-1 << ").\n"; return( fib(n-2) + fib(n-1)); }}
This is the Example in the book. I see where you are testing to see if n is less than 3 and if so, return 1. If not, then it goes through the else portion of the code. I guess what I don't understand here is why should n < 3? Why not 4 or 7 or any number? Also am I correct in interpreting that in the else block it's taking the input number and subtracting 2 from it then 1 from it, the adding the result together, testing it again to see if it is < 3, if not repeat, if so return 1?
Thanks for your help Fruny, I do appreciate it.
Anaton
Flying Tigers CFSG
[edited by - Anaton on May 1, 2002 11:06:03 PM]
##### Share on other sites
Recursion is just one technique you have to be aware of. Mods are all just programming (just like anything else! They have nothing special). It is up to you, when designing your program, to decide whether you need recursive routines or not. There is no hard and fast rule, it is a matter of experience.
In the Fibonacci example, the special case is n<3 because the Fibonacci sequence is defined by Fib(1)=Fib(2)=1 and Fib(n)=Fib(n-1)+Fib(n-2) for n>=3.
[Questions (STFW) | GDNet Start Here | GDNet Search | Forum FAQ | Google | Asking Smart Questions ]
[Docs (RTFM) | MSDN | SGI''s STL | OpenGL | File formats]
[C++ Must Haves (RTFS) | MinGW | Boost | Loki | FLTK | SDL ]
Stolen from Magmai Kai Holmlor, who held it from Oluseyi, who was inspired by Kylotan...
##### Share on other sites
Thanks again Fruny. I have a better idea about it now but I think for the immediate I won''t use it unless it''s the only solution to my problem at hand.
• 23
• 10
• 19
• 15
• 14 | 1,619 | 5,893 | {"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} | 3.578125 | 4 | CC-MAIN-2018-22 | latest | en | 0.92915 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.