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 |
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=13&t=15450&p=38458 | 1,571,087,855,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986655310.17/warc/CC-MAIN-20191014200522-20191014224022-00333.warc.gz | 581,377,718 | 11,880 | ## Steps for Limiting Reactant Problems
Posts: 21
Joined: Fri Jul 15, 2016 3:00 am
### Steps for Limiting Reactant Problems
Hi, so I just want to make sure I am correct, the general steps for limit reactant calculations is:
1. Balance Equation
2. Calculate molar mass of each reactant
3. Calculate # of moles of each
4. Compare how much of a reactant is needed according to the balanced reaction.
Please comment if I missed anything, thanks!
isabelle ruedisueli 1j
Posts: 21
Joined: Wed Sep 21, 2016 2:56 pm
### Re: Steps for Limiting Reactant Problems
Yes, that sounds correct! You almost always need to convert mass to moles. I went to office hours today and received the same explanation so you are good!
Marisa_Woo_2G
Posts: 24
Joined: Wed Sep 21, 2016 2:56 pm
### Re: Steps for Limiting Reactant Problems
Looks great! I would just add that these are the steps if the question asked you to find the limiting reactant. If the question asked for the theoretical yield (how much product forms if the reaction occurs perfectly), you would multiply the moles of the limiting reactant by the molar ratio from the chemical equation (Ex: If the reaction was C4H9OH+6O2 --> 4CO2+5H2O, the molar ratio of O2 to H2O would be 6 to 5). This would result in the moles of product that is formed. Finally, since the theoretical yield asks for the mass of the product, you would convert the moles of product to grams of product.
Something else that really helps me remember the steps is the phrase "grams --> mol --> mol --> grams" meaning
After you balance the chemical equation…
1. Grams of reactant converted to moles of reactant
2. Moles of reactant compared to moles of product (to find the limiting reactant)
3. Moles of product converted to grams of product (for the theoretical yield)
Hope this also helps in recalling the steps, but I think you got it down! :)
Katrina_Domingo_3G
Posts: 23
Joined: Wed Sep 21, 2016 2:59 pm
### Re: Steps for Limiting Reactant Problems
Can a rxn have two limiting reactants? And is it possible that a rxn has no limiting reactants at all?
Tiffany_Hoang_3C
Posts: 20
Joined: Wed Sep 21, 2016 2:59 pm
### Re: Steps for Limiting Reactant Problems
Katrina_Domingo_1E wrote:Can a rxn have two limiting reactants? And is it possible that a rxn has no limiting reactants at all?
A reaction cannot have two limiting reactants. The limiting reactant is the reactant that limits (the most) the amount of product that can be formed. There will be at most one limiting reactant.
However, it is possible that a reaction has no limiting reactants at all, meaning all reactants produce the same amount of product (calculated by using stoichiometry). In this case, no reactant limits the amount of product formed. | 716 | 2,744 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2019-43 | latest | en | 0.921417 |
http://www.gurufocus.com/term/Intrinsic+Value+(DCF)/TLAB/Intrinsic%2BValue%2B%2528DCF%2529/Tellabs%252C%2BInc | 1,477,069,299,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988718285.69/warc/CC-MAIN-20161020183838-00394-ip-10-171-6-4.ec2.internal.warc.gz | 477,191,488 | 26,962 | Switch to:
Tellabs, Inc. (NAS:TLAB)
Intrinsic Value: DCF (FCF Based)
\$0.14 (As of Today)
As of today, Tellabs, Inc.'s intrinsic value calculated from the Discounted Cash Flow model is \$0.14.
Note: Discounted Cash Flow model is only suitable for predictable companies (Business Predictability Rank higher than 1-Star). Result may not be accurate due to the low predictability of business.
Margin of Safety (FCF Based) using Discounted Cash Flow model for Tellabs, Inc. is -1,653.87%.
Definition
This is the intrinsic value calculated from the Discounted Cash Flow model with default parameters. In a discounted cash flow model, the future cash flow is estimated based on a cash flow growth rate and a discount rate. The cash flow of the future is discounted to its current value at the discount rate. All of the discounted future cash flow is added together to get the current intrinsic value of the company.
Usually a two-stage model is used when calculating a stocks intrinsic value using a discounted cash flow model. The first stage is called the growth stage; the second is called the terminal stage. In the growth stage the company grows at a faster rate. Because it cannot grow at that rate forever, a lower rate is used for the terminal stage.
GuruFocus DCF calculator is a two-stage model. The default values are defined as:
1. Discount Rate: d=12%
2. Growth Rate in the growth stage: g1=5%
Growth Rate in the growth stage = average free cash flow growth rate in the past 10 years. If it is higher than 20%, we use 20%. If it is less than 5%, we use 5% instead. => For companies with Average Free Cash Flow Growth Rate in the past 10 years less than 5%, GuruFocus defaults => Growth Rate: 5%
3. Years of Growth Stage: y1=10
4. Terminal Growth Rate: g2=4%
5. Years of Terminal Growth: y2=10
6. Free Cash Flow Per Share: fcf=\$0.013.
However, GuruFocus DCF calculator is actually a Discounted Earnings calculator, the Earnings Per Share without NRI is used as the default. The reason we are doing this is we found that historically stock prices are more correlated with earnings than free cash flow.
All of the default settings can be changed and the results are calculated automatically.
Tellabs, Inc.'s Intrinsic Value: DCF (FCF Based) for today is calculated as
DCF (FCF Based) = fcf * {[(1+g1)/(1+d) + (1+g1)^2/(1+d)^2 + ... + (1+g1)^10/(1+d)^10] + (1+g1)^10/(1+d)^10 * [(1+g2)/(1+d) + (1+g2)^2/(1+d)^2 + ... + (1+g2)^10/(1+d)^10]}
set x = (1+g1)/(1+d) = (1+0.05)/(1+0.12) = 0.9375
and y = (1+g2)/(1+d) = (1+0.04)/(1+0.12) = 0.928571428571
DCF (FCF Based) = fcf * {[x + x^2 + ... + x^10] + x^10 * [y + y^2 + ... + y^10]} = fcf * [x * (1-x^10) / (1-x) + x^10 * y * (1-y^10) / (1-y)] = 0.013 * 10.7016 = 0.14
Margin of Safety (FCF Based) = (DCF (FCF Based) - Current Price) / DCF (FCF Based) = (0.1391208 - 2.44) / 0.1391208 = -1,653.87 %
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
Explanation
Unlike valuation methods such as Net Current Asset Value, Tangible Book Value per Share, Graham Number, Median Ratio etc, discounted Cash Flow model evaluates the companies based on their future earnings power instead of their assets.
Be Aware
What you need to know about the DCF model:
1. The DCF model evaluates a company based on its future earnings power
2. Growth is taken into account; therefore a faster growth company is worth more if everything else is the same.
3. Since we are projecting future growth, it is assumed that the company will grow at the same rate as it did during the past 10 years. Therefore this model works better for the companies that have relatively consistent performance.
4. The DCF model works poorly for inconsistent performers such as cyclicals.
5. What discount rate should you use? Your expected return from the investment is a good discount rate assumption.
6. A larger margin of safety should be required for companies with less predictable businesses.
You can screen for stocks that trade below their Intrinsic Value: DCF (FCF Based) and Intrinsic Value: DCF (Earnings Based) with the GuruFocus All-in-One Screener. Companies with a high Predictability Rank that trade at a discount to their Intrinsic Value: DCF (FCF Based) and Intrinsic Value: DCF (Earnings Based) can be found in the screen of Undervalued Predictable Companies.
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1. A spark can jump between two nontouching conductors if the potential difference between them is sufficiently large. A potential difference of approximately 940 V is required to produce a spark in an air gap of 1.0 x 10^-4m. Suppose the light bulb in figure 22.4b is replaced by such a gap. How fast would a 1.3-m rod have to be moving in a magnetic field of 4.8 T to cause a spark to jump across the gap?
2. Near San Francisco, where the vertically downward component of the earth's magnetic field is 4.8 x 1.0^-5 T, a car is traveling forward at 25 m/s. An emf of 2.4 x 10^-3 V is induced between the sides of the car. A) Which side of the car is positive, the driver's side or the passenger's side? B) What is the width of the car?
3. A standard door into a house rotates about a vertical axis through one side, as defined by the door's hinges. A uniform magnetic field is parallel to the ground and perpendicular to this axis. Through what angle must the door rotate so that the magnetic flux that passes through it decreases from its maximum value to one-third of its maximum value?
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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
NO 24
FIFTH SEMESTER – APRIL 2008
ST 5500 – ESTIMATION THEORY
Date : 28-04-08 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART-A
1. Define ‘bias’ of an estimator.
2. When do you say an estimator is consistent?
3. Define a sufficient statistic.
4. What do you mean by bounded completeness?
5. Describe method of moments in estimation.
6. State invariance property of maximum likelihood estimator.
7. Define Loss function and give an example.
8. Explain ‘prior distribution’ and ‘posterior distribution’.
9. Explain least square estimation.
10. Mention any two properties of least squares estimator.
PART-B
1. If Tn is asymptotically unbiased with variance approaching 0 as , then show that Tn is consistent.
2. Show that is an unbiased estimate of , based on a random sample drawn from .
3. Let be a random sample of size n from population. Examine if is complete.
4. State and prove RAo-Blackwell theorem.
5. Estimate by the method of moments in the case of Pearson’s Type III distribution with p.d.f .
6. State and establish Bhattacharya inequality.
7. Describe the method of modified minimum Chi square.
8. Write a note on Baye’s estimation.
PART-C
1. a) and is a random sample of size 3 from a population with mean value and variance . are the estimators used to estimate mean value , where and .
1. Are T1 and T2 unbiased estimators?
2. Find the value of such that T3 a consistent estimator?
• With this value of is T3 a consistent estimator?
1. Which is the best estimator?
2. b) If are random observations on a Bernoulli variate X taking the value 1 with probability p and the value 0 with probability (1-p), show that is a consistent estimator of p(1-p).
1. a) State and Prove cramer-Rao inequality.
1. b) Given the probability density function
Show that the Cramer-Rao-lower bound of variance of an unbiased estimator of is 2/n, where n is the size of the random sample from this distribution. [12+8]
1. a) State and prove Lehmann – Scheffe theorem
1. b) Obtain MLE of in based on an independent sample of size n. Examine whether this estimate is sufficient for . [12+8]
1. a) Show that a necessary and sufficient condition for the linear parametric function to be linearly estimable is that
ank (A) = rank
where and
1. b) Describe Gauss – Markov model [12+8]
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# In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt
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Current Student
Joined: 12 Aug 2015
Posts: 2546
Schools: Boston U '20 (M)
GRE 1: Q169 V154
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
Updated on: 14 Aug 2017, 06:02
12
00:00
Difficulty:
95% (hard)
Question Stats:
34% (02:40) correct 66% (02:05) wrong based on 161 sessions
### HideShow timer Statistics
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?
A)15
B)48
C)90
D)150
E)204
Source => Kaplan.
Any laconic way to solve this up ?
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_________________
Originally posted by stonecold on 14 Aug 2017, 04:48.
Last edited by Bunuel on 14 Aug 2017, 06:02, edited 2 times in total.
Edited the question.
Senior Manager
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Posts: 417
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Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
11 Sep 2017, 02:53
2
Not worth of 95% difficulty:-
AB/BC = 6/8 = 3/4 = DE/EF
Area DEF = 1/2 DE xEF
=> 6
6 is the area when 3/4 is the least ratio of integers => if the ratio is increased then it will grow in squares of numbers from 1 ,2,3 and so on
because
3/4 = 3/4
6/8 = 3x2/4x2
9/12 = 3x3/4x3
so we can see both sides are being multiplied by 1,2,3 two times
so possible values of area can be 6 x( 1,4,9,16,25,36)
6x25 is the value => 150 is the answer D
Math Expert
Joined: 02 Aug 2009
Posts: 8327
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
14 Aug 2017, 05:52
1
1
stonecold wrote:
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?
A)15
B)48
C)90
D)150
E)204
Source => Kaplan.
Any laconic way to solve this up ?
Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Since the sides 6 and 8 have 2 as Common factor, x will be an integer or a fraction with 2 in denominator.
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction with 2 in denominator or INTEGER..
Check with choices..
A)15
24x^2=15.... x=√(5/8).no
B)48
24x^2=48.....X=√2..no
C)90.
24x^2=90...X=√(15/4)=√15/2...no
D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes
E)204..
24x^2=204...X=√34/2 No
D
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Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
14 Aug 2017, 07:04
1
chetan2u wrote:
stonecold wrote:
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?
A)15
B)48
C)90
D)150
E)204
Source => Kaplan.
Any laconic way to solve this up ?
Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction or INTEGER..
Check with choices..
A)15
24x^2=15...no
B)48..no
C)90..no
D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes
E)204..No
D
Hi Chetan,
The way you explain are real awesome and u really deserve a Kudo from me . And I Have given also...[GRINNING FACE WITH SMILING EYES]
But 1 thing I don't understand why They value of x^2 should be a fraction ??
Tough for me to interpret.
Pls help.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
14 Aug 2017, 07:20
kumarparitosh123 wrote:
chetan2u wrote:
stonecold wrote:
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengths of two sides of triangle ABC are shown. Triangle DEF is similar to ABC and has integer side lengths. Which of the following could be the area of triangle DEF ?
A)15
B)48
C)90
D)150
E)204
Source => Kaplan.
Any laconic way to solve this up ?
Hi..
Sides of ∆DEF will be in similar ratio as sides of ∆ABC..
So EF=8x and DE=6x...
Area of ∆ABC = 1/2 *6*8=24..
Area of∆DEF = 1/2 *6x*8x=24x^2..
Now this x should come out as a fraction or INTEGER..
Check with choices..
A)15
24x^2=15...no
B)48..no
C)90..no
D)150
24x^2=150...x^2=150/24=25/4..
X=√(25/4)=5/2...yes
E)204..No
D
Hi Chetan,
The way you explain are real awesome and u really deserve a Kudo from me . And I Have given also...[GRINNING FACE WITH SMILING EYES]
But 1 thing I don't understand why They value of x^2 should be a fraction ??
Tough for me to interpret.
Pls help.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Hi..
The sides of TWO similar triangle will have same ratio with corresponding sides.
Say here sides are 6 and 8...
If corresponding side of 6 of similar triangle is 6*1/2=3, so side corresponding to 8 will be 8*1/2=4..
Had it not been given that sides are integer than ofcourse x could be anything...
Yes if sides were 3 and 4 or co-prime, fraction would not have been possible.
Here 6 and 8 have 2 as Common factor so a fraction with 2 in denominator can also be the ratio ..
_________________
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Joined: 18 Aug 2017
Posts: 29
GMAT 1: 670 Q49 V33
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
27 Aug 2017, 20:25
Triangle DEF is similar to ABC, so $$\frac{DE}{6}$$ = $$\frac{EF}{8}$$ => DE = $$\frac{4EF}{3}$$
Let area of triangle DEF is S, S = $$\frac{(DE*EF)}{2} =\frac{4EF}{3} * \frac{EF}{2} = \frac{2EF^2}{3}$$
So $$\frac{(S *3)}{2}$$ = $$EF^2$$ we can conclude:
1- S is an even number, eliminate answer A
2-$$\frac{(S * 3)}{2}$$ must be a perfect square of an integer.
B- S = 48, $$\frac{(S * 3)}{2} = 144/2$$ = 72. No.
C- S = 90, $$\frac{(S * 3)}{2} = 270/2$$ = 135. No.
D- S = 150,$$\frac{(S * 3)}{2} = 450/2 = 225$$= $$15^2$$. Yes.
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In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink]
### Show Tags
09 Apr 2019, 01:31
By property, if two similar triangles have side lengths in the ratio a:b, then their areas will be in the ratio a^2 : b^2
Let DE=x
Then (Area of ABC)/(Area of DEF) = 6^2/x^2
=> x^2 = 6^2*(Area of DEF)/(Area of ABC)
=> x^2 = 3/2*(Area of DEF) ------------------ [Area of ABC=24]
We know that x^2 must be a perfect square since x is an integer.
Plugging in the options we get Area of DEF = 150
(D)
In triangle ABC, the measure of angle ABC is 90 degrees, and the lengt [#permalink] 09 Apr 2019, 01:31
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Posted 06 March 2010 - 12:27 AM
Compressed air used for instruments is generally at 100 psig. Now suppose RH is 70% Dry bulb is 30 C. Now if I use any dessicant dryer the supplier says suppose his system is giving a dew point of -40 C - what does it mean.
My doubt or confusion is how do I calculate the water content for a compressed air at 100 psig with a dew point of -40 C?
The doubt is because at sub zero temperature the vapor pressure of water is zero ideally. so how to calculate absolute water content in the compressed air.
Nos given above are just some assumptions nearer to practical conditions. I need to know the calculation method for identifying water kg/kg of dry air in compressed gas once it leaves dessicant dryer. I know the method if I use cooling/chilling but in those cases dew point is not in sub zero zone.
Thanks
### #2 Zauberberg
Zauberberg
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• 2,699 posts
Posted 06 March 2010 - 02:01 AM
Dew point of -40C refers to atmospheric pressure. At 100 psig, that would be equivalent to approx -19C. Drying the air from 80% humidity @ 30C to -40C dew point reduces the water content from 24.1 to 0.1 g/m3 absolute humidity. See attached worksheet for dew point calculations. Similar results can be obtained by using air saturation charts.
### #3 pawan
pawan
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Posted 06 March 2010 - 09:31 AM
Thanks Zauberberg for your reply & Excel sheet. Its really useful.
BUt my meaning of calculation was to understand the underlying fundamentals. Why this is -40 C dew point. What is the significance of negative dew point?
Also anyone on practical experience for how much low I can go in terms of dew point. Is it possible to go say -100 C dew point or not? What is the practical limit? What are the systems to achieve that.
Edited by pawan, 06 March 2010 - 09:33 AM.
### #4 Zauberberg
Zauberberg
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Posted 06 March 2010 - 10:27 AM
By using Mol Sieves, dew point can go as low as < -100C. For most practical applications this is more than sufficient. It is hard to find equipment that can detect moisture contents below 0.1ppm.
Ambient conditions determine the level of air dehydration. If you are based in hot, tropical region, Activated Alumina is more than enough (dew point -40C). On the other hand, if you are based in Kazakhstan or Siberian fields, you'll probably need Mol Sieves equipped with heating regeneration system in order to properly drive the moisture out of the desiccant.
Attached is the link to one file that shows various performance characteristics of different adsorbents: http://www.axens.net..._adsorbents.pdf
As you can see, Mol Sieves are capable of removing more moisture at lower relative humidities of feed stream but, on the other hand, they require more energy for desorption process exactly because of higher moisture holding capabilities at lower partial pressures of water. GPSA Databook can also provide you with quality information regarding this subject.
### #5 AZIZ_MN
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Posted 07 March 2010 - 01:24 AM
Hi, pawan
I measured the dewpoints of line and other equipments several times during a pre-commissioning of our plant and for nitrogen, I obtained a maximum of -60 oC dew point and the relative moisture is 10 - 15 ppm. The hydrogen dew point at a hydrogen dryer outlet was < -65 oC using a dewpoint meter and -60 oC with a draegger tube. Other than that, we have an on-line dewpoint meter for instrument air. The dew point measurement requires special skill and passions to get accurate readings, but in experience, I haven't obtained a reading of -100 oC dew point in pratice.
Thanks, best regards.
### #6 ankur2061
ankur2061
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Posted 07 March 2010 - 01:32 AM
Pawan,
There is an old post about water dew point where I have also attached a spreadsheet for dew point & humidity (water content calculations). Check this out:
http://www.cheresour...833
Hope this helps.
Regards,
Ankur.
### #7 MrShorty
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Posted 08 March 2010 - 10:52 AM
Pawan:
In many ways, I think you've almost answered your own question right here. You are making the assumptions that the sublimation pressure of ice is exactly 0. In many applications, this may be an adequate assumption, but it is not true.
I don't know all of the inner workings of Zauberberg's spreadsheet, but, comparing the partial pressure of water that it calculates to the sublimation pressure of ice from DIPPR and they are essentially the same.
I would suggest that the first step to understanding these dew points you are talking about is to drop the assumption that the sublimation pressure of water is 0. Once you look up the sublimation curve for water, I expect this will start to make more sense.
### #8 DrDewLittle
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Posted 14 August 2010 - 02:11 PM
The water content of any gas is determined by the partial water vapor pressure.
Goff–Gratch equations can be used to convert between dew point temperature to partial water vapor pressure. See Wikipedia for the equation, they also have links to free programs for the conversion.
Edited by DrDewLittle, 14 August 2010 - 02:12 PM. | 1,436 | 5,887 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2019-04 | latest | en | 0.887659 |
https://new.gams.com/latest/noalib_ml/libhtml/noalib_surface.html | 1,669,927,088,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00759.warc.gz | 456,575,934 | 6,939 | Surface : Minimal-/Surface Problem
Reference
• Neculai Andrei, Nonlinear Optimization Applications Using the GAMS Technology,Springer Optimization and Its Applications, Model Surface (3.10) in chapter Some Mathematical Algorithms and Problems in GAMS Technology, 2013
Category : GAMS NOA library
Mainfile : surface.gms
``````\$Ontext
Minimal surface problem.
Find a function f that minimizes the array of its graph subject to some
constraints on the boundary of the domain of f.
Boyd, S., Vandenberghe, L., Convex Optimization, Cambridge University Press,
Cambridge, 2004.
\$Offtext
SET X /I1*I21/;
SET Y /J1*J21/;
SET inside(X,Y);
* Exclude i1 and i21 from inside
inside(X,Y)\$(not((ord(X)=1) and (ord(X)=card(X)))) = yes;
display inside;
SCALAR K /10/;
VARIABLES obj, f(x,y);
POSITIVE VARIABLE f(X,Y);
* Bounds on variables, initial conditions, fixing conditions:
f.up(x,y)=1;
f.l(x,y) =1.0;
f.fx(X,Y)\$((ord(X)=1) or (ord(X)=card(X))) = 1;
EQUATION objfun;
objfun.. obj =E= (1/sqr(K)) *
sum((X,Y) \$(inside(X,Y)),
sqrt( sqr((F(X+1,Y)-F(X,Y))/K) +
sqr((F(X,Y+1)-F(X,Y))/K) + 1) ) ;
MODEL surface /all/;
SOLVE surface using nlp minimizing obj;
\$iftheni x%mode%==xbook
file res1 /surf1.dat/
put res1;
put "Array surface =" obj.l; put /;
loop(Y, put Y.tl:6; loop(X, put F.l(X,Y):6:2 ); put /;) put /;
\$endif
* End surface
``````
GAMS Development Corp.
GAMS Software GmbH
General Information and Sales
U.S. (+1) 202 342-0180
Europe: (+49) 221 949-9170 | 472 | 1,474 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-49 | latest | en | 0.528441 |
https://learnappmaking.com/nil-coalescing-ternary-conditional-operator-swift/?utm_campaign=AppCoda%20Weekly&utm_medium=email&utm_source=Revue%20newsletter | 1,563,222,639,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195524111.50/warc/CC-MAIN-20190715195204-20190715221204-00469.warc.gz | 458,095,420 | 11,844 | # The Nil-Coalescing And Ternary Conditional Operators In Swift
In this article, we’re going to discuss how you can use the nil-coalescing operator and the ternary conditional operator in Swift. They’re both interesting bits of syntactic sugar, and they can help you write more concise, readable code. And that’s a good thing!
Here’s what we’ll get into:
• What operators and operands are
• How to use the nil-coalescing operator
• How you can use the ternary conditional operator
• Real-life examples and tips and tricks for both!
## What’s An Operator?
Let’s begin by discussing what an operator is, before diving into the nil-coalescing and ternary conditional operators.
Here’s what’s what:
An operator is a special symbol or phrase that you use to check, change, or combine values.
In short, we can use the addition operator `+` to add two numbers to each other with the expression `4 + 2`. In Swift, we can then assign the result of that expression to a constant, such as with `let number = 4 + 2`. Just as in mathematics!
Swift has a great number of operators, including `+`, `-`, `/`, `+=`, `==` and also logical operators like `&&`, `||` and `!`. We can also use more complex operators like `a..<b` and `a...b` for ranges.
An operator always uses so-called operands. Operands are the symbols that an operator operates on. If you think of an operator as a function, the operands are the inputs for that function.
Check this out:
``````let number = 4 + 2
``````
In the above code, we’re working with two different operators:
1. The addition operator `+` adds `4` to `2`. The numbers `4` and `2` are operands. We can say that the `+` operator has two operands, in the format `a + b`.
2. The assignment operator `=` assigns the value of the expression `4 + 2` to the constant `number`. The constant `number` and the expression `4 + 2` are operands. We can say that the `=` operator has two operands, in the format `a = b`.
In Swift, we have 3 types of operators:
1. Unary operators have one operand, such as the minus sign operator `-a`, as in `-3`. Unary operators can be prefix (before), such as `-a`, and postfix (after), such as `a!`.
2. Binary operators have two operands, such as the addition operator `a + b`. They’re always infix, because you put the operator between two operands.
3. Ternary operators have three operands. Swift only has one ternary operator: the ternary conditional operator `a ? b : c`.
Alright, now that we know a thing or two about operators, let’s move on to the nil-coalescing operator and the ternary conditional operator!
## The Nil-Coalescing Operator “??”
The nil-coalescing operator `a ?? b` unwraps an optional `a` if it contains a value, or returns a default value `b` if it’s `nil`. Differently said, you use the nil-coalescing operator to assign a default value `b` if `a` is `nil`.
Based on what we know about operators, we can assert that the nil-coalescing operator `a ?? b` is an infix binary operator.
Here’s an example:
In the above code, you’re getting your favorite for dinner – unless you have no favorite, then you’re getting fish and chips… Feel free to change the value for `favoriteFood` to a string instead of `nil`, and see how the output for `whatsForDinner` changes.
In the example, `"Fish and chips"` is assigned to `whatsForDinner` if `favouriteFood` is `nil`. If it’s not `nil`, the value of `favoriteFood` is unwrapped assigned to `whatsForDinner`. You could say that `"Fish and chips"` is a default value in case `favoriteFood` is `nil`.
So, what do you use the nil-coalescing operator for? It’s useful in a few scenarios:
• When you need a default value, and don’t care much about the optional itself. Take for example a numeric form input field. If it’s not filled in, you don’t need the `nil` value, so you want to set it to a default of `0` instead. Something like `let age = ageInputField?.text ?? 0`.
• When you want to print an optional value with `print()`, but you don’t want the `Optional(...)` debug output. So, instead you write `print("Saving object with ID = \(object.id ?? "...")")` for debugging purposes. If `object.id` is `nil`, it’ll print `...`. If it’s not, it’ll print the ID without `Optional(...)`.
Coalescing means “to come together to one form or mass,” so you could say that the `??` operator merges an optional value with a default value to “come together” as a non-optional value. (I still think nil-splattering operator would have been a more awesome name…)
## The Ternary Conditional Operator “?:”
The ternary conditional operator `a ? b : c` is a special operator that has three parts. It’s a shortcut to evaluate an expression `a`, and to choose `b` if `a` evaluates to `true`, or `c` if `a` evaluates to `false`.
It’s a shorthand for a conditional with `if-else`, like this:
``````if condition {
value_A
} else {
value_B
}
``````
If the above `condition` evaluates to `true`, the `value_A` is assigned. If the `condition` evaluates to `false`, the `value_B` is assigned. The ternary conditional operator chooses a value from two options `b` and `c`, based on the boolean value of expression `a`.
Let’s look at an example.
In the above code, we’re evaluating the logical expression `temperature < 0`. Is the temperature below zero or not? Based on this, we got two options:
1. `temperature < 0` is `true`, so print `"It's below zero!"`
2. `temperature < 0` is `false`, so print `"It's above zero :-)"`
The above code example is exactly the same as:
``````let temperature = 20
let text = ""
if temperature < 0 {
text = "It's below zero!"
} else {
text = "It's above zero :-)"
}
print(text)
``````
It’s clear that the ternary conditional operator, with `a ? b : c`, is much shorter than the above code. In many cases, you don’t even have to use the temporary value `text`, i.e. you can write the above code as `print(temperature < 0 ? ... : ...)`.
The ternary conditional operator is most useful in scenarios where you have two options of equal “weight”, that you’re choosing based on a simple expression. It’s counter-productive if you try to stuff complex logical expressions into the `a ? b : c` format – in that case, it’s smarter to use a more verbose `if` conditional block.
The nil-coalescing and ternary conditional operators are related! The nil-coalescing operator `a ?? b` is shorthand for `a != nil ? a! : b`, which is a shorthand for `if a != nil { a! } else { b }`. Awesome!
#### Learn how to build iOS apps
##### Get started with iOS 12 and Swift 5
Sign up for our iOS development course Zero to App Store and learn how to build professional iOS 12 apps with Swift 5 and Xcode 10.
The nil-coalescing and ternary conditional operators are what’s known as syntatic sugar. They sugar-coat verbose code in more concise code, and make your Swift code more readable.
Here’s the gist of what we discussed:
• Use the nil-coalescing operator `a ?? b` to assign a default value `b` in case `a` is `nil`, and if `a` is not `nil`, unwrap `a` and return it.
• Use the ternary conditional operator `a ? b : c` to choose an option `b` or `c` based on the value of logical expression `a`. It’s a shorthand for `if-else` conditionals. | 1,823 | 7,178 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-30 | longest | en | 0.89822 |
https://studyres.com/doc/24475558/-geo-honors-test-3-practice-questions | 1,695,715,302,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510179.22/warc/CC-MAIN-20230926075508-20230926105508-00286.warc.gz | 593,438,513 | 7,656 | # Download Geo Honors Test 3 Practice Questions
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```Block 7 Geo Honors Test 3 Practice Questions
11/10/20
Name:
Date:
1.) ΔEFG is isosceles, with m∠G = 94 . The legs are sides _________ and _______.
m∠E = _______
2.) If in ΔABC , m∠A = 50 , m∠C = 80 , AC = 7x + 8 , and BC = 38 − 3x , then x = ______.
3.) Write a two column proof
4.) Write a two-column proof:
5.) Tell which pairs of congruent parts and what methods (SSS, SAS, ASA, AAS, or HL) you
would use to prove the triangles are congruent.
ZZ
a. Given: ∠1 ≅ ∠2; ∠3 ≅ ∠4; ZZZZ
𝑄𝑅 ≅ ZZ
𝑇𝑆
△ 𝑄𝑃𝑅 ≅ ∆𝑇𝑃𝑆 by what method?
b. Given: ∠3 ≅ ∠4; ∠5 ≅ ∠6
∆𝑄𝑃𝑌 ≅ ∆𝑇𝑃𝑋 by what method?
6.) Draw and label a diagram. List in terms of the diagram what is given and what is to be
proved. Then write a two-column proof.
a. In two congruent triangles, if segments are drawn from two corresponding
vertices perpendicular to the opposite sides, then those segments are congruent.
7.) Write a proof in two-column form:
ZZZ ≅ ZZZZ
ZZZ ; 𝐾𝐽
ZZZ ⊥ Z𝐻𝐽
ZZZ; 𝐺𝐽
Given: ZZZZ
𝐺𝐻 ⊥ Z𝐻𝐽
𝐾𝐻
ZZZZ
ZZZ
Prove: 𝐺𝐻 ≅ 𝐾𝐽
```
Related documents | 502 | 1,290 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-40 | latest | en | 0.792758 |
https://iwarelogic.com/methodologies/best-answer-how-do-you-calculate-lag-in-project-management.html | 1,656,694,852,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00743.warc.gz | 371,085,361 | 18,671 | # Best answer: How do you calculate lag in project management?
Contents
## How do you calculate lag time in project management?
Lag Time is the delay between the first and second activities. For example, the duration of the first activity is three days and two days for the second activity. After completing the first activity, you wait for one day, and then you start the second. Here, we say that the Lag Time is one day.
## How do you find the lag time?
Time = Distance / Speed
The lag time here is 10 hours. So, the pattern you should note here is “the greater the distance, the longer the lag time.” The same method of calculation may be used for earthquake waves (P-waves and S-waves). However, you must use consistent units.
## How do I show lag in MS project?
1. Double-click a task name, and then click the Predecessors tab in the Task Information box. ©
2. In the Lag column, type the lead time or lag time you want. To add lead time, type a negative number or a negative percentage (for example, -50%).
## What is the duration of a milestone?
Milestones typically have zero duration; however, some milestones may need a duration. For example, your project has an approval milestone at the end of a phase, and you know that the approval process will take a week.
IT IS IMPORTANT: Who runs the daily scrum meeting?
## What do you mean by time lag?
the period of time between two closely related events, phenomena, etc., as between stimulus and response or between cause and effect: a time-lag between the declaration of war and full war production.
## What is positive lag?
Positive lag can be performed on a simple example of two activities with a delay in between them: Example: Activity A and Activity B with FS relationship with 5 days lag. There is a 5 day wait between the finish of A and the start of B. Negative lag is called Lead Time.
## What is a lag strategy?
Lag strategy refers to adding capacity only after the organization is running at full capacity or beyond due to increase in demand (North Carolina State University, 2006). This is a more conservative strategy and opposite of a lead capacity strategy. … This is a more moderate strategy.
## What will affect lag time?
Slope – steep slopes lead to rapid water transfer and shorter lag times. Gentle slopes slow down water transfer making the lag time longer. Drainage basin shape – a high density basin has more streams and rivers which speed up water transfer and shorten lag time.
## What is finish-to-start lag?
Lag. The amount of time whereby the successor activity can be advanced with respect to a predecessor activity. Here is an example of a lag: In a finish-to-start dependency with a ten-day lag, the successor activity cannot start until ten days after the predecessor activity has finished. | 600 | 2,803 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2022-27 | latest | en | 0.933466 |
https://learn.rumie.org/jR/bytes/get-better-grades-using-a-rubric-fast/ | 1,656,477,895,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103620968.33/warc/CC-MAIN-20220629024217-20220629054217-00497.warc.gz | 416,902,670 | 56,935 | Did you ever get a bad score on an assignment, project, or essay and you didn't know why?
Did you look at the rubric for the assignment? No?
Understanding rubrics can help you get better marks 👇
## What's A Rubric?
Put simply, it's a scoring guide that teachers use to evaluate how well you met the objectives of a project or task.
In other words, did you learn what you were supposed to learn?
Rubrics take many shapes, but they often take the form of a matrix, like this one for a writing assignment:
• Column 1 (Yellow): items (criteria or objectives) that need to be graded and sometimes the value of the grade (or "weighting").
• Row 1 (Blue): scores from low to high (or high to low).
• Cells (Green): describe the criteria for giving scores for what has (or has not) been done.
## Quiz: Getting The Best Mark
Let's take a closer look at the example rubric above:
Looking at the rubric, you know that to get the top mark of 4, you must:
• go in-depth
• give details
• give examples
• show your subject knowledge
• include a reference section
#### Quiz
What's the top score you would get for "content" if you forgot to add a reference section?
## Why Do Teachers Use Them?
Good teachers use rubrics for a number of reasons...
🔎 Help make goals clear
📈 Help students improve
🏁 Make scoring easier and faster
💞 Make scoring fairer for all students
🔊 Make it easier to give feedback
🤕 Reduce grade disputes
## Ok, Teachers Use Rubrics But Why Do I Need Them?
Doing an assignment without a rubric is a bit like trying to kick a goal blindfolded.
A good rubric will:
👀 tell you what the teacher is looking for while scoring your work
💯 tell you what you need to do to get the top marks
✅ help you make sure you didn't forget anything
❓ show you why you scored the way you did
⭐ help you know how you can do better next time
👉👉 Getting into the habit of using a rubric will improve your work and therefore your scores! 👈👈
## Take Action
Next time you get an assignment, essay, or project:
## Your feedback matters to us.
This Byte helped me better understand the topic.
I feel confident that I can apply what I learned.
I would recommend this Byte.
## Connect with Rumie learners
Browse more content and join a supportive community!
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## This Byte has been authored by
DG
### Donald Glass
ESL Instructor/Learning Designer/EdTechie | 580 | 2,393 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-27 | longest | en | 0.940028 |
www.hypnosetherapie-maspoli.ch | 1,618,314,059,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038072180.33/warc/CC-MAIN-20210413092418-20210413122418-00194.warc.gz | 903,541,143 | 11,800 | analysis vibrating frequency
analysis vibrating frequency
### High Frequency Vibration Analysis - Emerson Electric
events occurring at random or at periodic rates. The frequencies excited by the microscopic events are high frequency (typically in the kHz to several kHz range) relative to those excited by macroscopic vibration (kHz or less). In this paper, the focus is direct to
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### What is Vibration Analysis?
Feb 27, 2020 Industrial vibration analysis refers to a process for measuring the vibration levels and frequencies of machinery and then using this information to assess the “health/condition” of the machine and its components.
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### What is Vibration Analysis and What is it Used For? - TWI
Frequency domain vibration analysis excels at detecting abnormal vibrating patterns. For instance, a crack that has developed on a roller bearing outer race will lead to periodic collisions with bearing rollers. In time waveform, this information is usually hidden and
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### The Ultimate Guide to Vibration Analysis
Nov 12, 2018 Vibration is an oscillating motion about equilibrium, so most vibration analysis looks to determine the rate of that oscillation, or the frequency that is proportional to the system’s stiffness. The number of times a complete motion cycle occurs during a period of one second is the vibration’s frequency and is measured in hertz (Hz).
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### Fundamentals of Vibration Measurement and Analysis Explained
converted to a frequency spectrum in order to show the analyst where the vibration energy is coming from. Frequency analysis is the essence of vibration analysis and enables the satisfactory resolution of most machine problems. It is important to understand the relationship between the TIME WAVEFORM and the FREQUENCY SPECTRUM.
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### Beginning Vibration Analysis with Basic Fundamentals
Dec 01, 2014 It is the most common term used in vibration analysis to describe the frequency of a disturbance. Never forget the 1 cycle / second relationship ! Traditional vibration analysis quite often expresses frequency in terms of cycle / minute (cpm). This is because many pieces of process equipment have running speeds related to revolutions / minute (rpm).
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### High Frequency Vibration Analysis - Emerson Electric
High Frequency Vibration Analysis The emphasis in this paper is the capture and analysis of stress waves introduced into rotating machinery by events such as impacting, fatiguing, and friction. The stress wave events introduced into rotating machinery are mostly flexural waves (also referred to as bending or S waves). These waves
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### The Ultimate Guide to Vibration Analysis
Nov 12, 2018 Vibration is an oscillating motion about equilibrium, so most vibration analysis looks to determine the rate of that oscillation, or the frequency that is proportional to the system’s stiffness. The number of times a complete motion cycle occurs during a period of one second is the vibration’s frequency and is measured in hertz (Hz).
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### Beginning Vibration Analysis with Basic Fundamentals
Dec 01, 2014 Beginning Vibration 2 Introduction Understanding the basics and fundamentals of vibration analysis are very important in forming a solid background to analyze problems on rotating machinery. Switching between time and frequency is a common tool used for analysis. Because the frequency spectrum is derived from the data in
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### VIBRATION SPECTRUM ANALYSIS - ALPHAPEDIA
FREQUENCY = Frequency is measured in units of cpm, Hz, Orders, i.e. 50 cpm – 750,000 cpm. Knowing the frequency of vibration peaks helps to identify potential sources. Frequency is used in advanced vibration analysis to identify all types of bearing failure frequencies, real-time spectra and motor current signature analysis, etc.
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### Vibration Analysis - ACOEM USA
Vibration analysis of industrial machinery has been around for many decades, but gained prominence with the introduction and widespread use of the personal computer. Vibration Analysis refers to the process of measuring the vibration levels and frequencies of industrial machinery, and using that information to determine the “health” of the machine, and its components. When []
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### Fundamentals of Vibration Measurement and Analysis
VIBRATION waveform as shown in the time drawing on the left side. This is the summation of all the vibration present at that location. Spectrum analysis enables us to untangle this complex waveform and make a representation of its original components on a diagram showing frequency on the X-axis and amplitude vertically.
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### Measuring Vibration: The Complete Guide Brüel Kjær
The breaking down of vibration signals into individual frequency components is called frequency analysis, a technique which may be considered the cornerstone of diagnostic vibration measurements. The graph showing the vibration level as a function of frequency is called a frequency spectrogram.
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### Vibration Analysis: What is it? [4 Measurement Techniques]
Vibration data must be translated from the format in which it is collected (typically frequency, amplitude, etc.). The data needs to be digitally reconstructed into a model that you can analyze. The result is typically a waveform diagram, measuring oscillation amplitude over a period of time.
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### Basics of Structural Vibration Testing and Analysis ...
Frequency Response Function (FRF) is computed from two signals. It is sometimes called a "transfer function." The FRF describes the level of one signal relative to another signal. It is commonly used in modal analysis where the vibration response of the structure is measured relative to the force input of the impact hammer or shaker.
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### An Introduction to Vibration Analysis by Amir Khademi ...
Apr 11, 2018 Vibration analysis can be used to detect the fault in early stage so reduces maintenance costs and increases up-time. Spectrum analysis is the most commonly used vibration analysis tool — the picks usually relate to components within the machine.
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### Vibration Analysis: FFT, PSD, and Spectrogram Basics [Free ...
Vibration is an oscillating motion about an equilibrium so most vibration analysis looks to determine the rate of that oscillation, or the frequency. The number of times a complete motion cycle occurs during a period of one second is the vibration’s frequency and is measured in hertz (Hz).
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### Vibration Measurements: Vibration Analysis Basics
Vibration is an oscillating motion about equilibrium so most vibration analysis looks to determine the rate of that oscillation or the frequency, which is proportional to the system’s stiffness. The number of times a complete motion cycle occurs during a period of one second is the vibration’s frequency and is measured in hertz (Hz).
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### Vibration Analysis and Signal Processing in LabVIEW - NI
Oct 14, 2020 Frequency analysis is the most commonly used method for analyzing a vibration signal. The most basic type of frequency analysis is an FFT, or Fast Fourier Transform, which converts a signal from the time domain into the frequency domain.
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### The Emotional Vibration Analysis Frequency Chart - Blisspot
The human emotional vibration analysis frequency ranges chart shown above, ( reproduced with permission from the Love or Above Toolkit), illustrates the vibrational analysis hertz frequency rate of the range of higher to the lower emotions. As the vibration analysis rate gets lower our breadth of consciousness and ability to deal with things ...
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### Measuring Vibration: The Complete Guide Brüel Kjær
The breaking down of vibration signals into individual frequency components is called frequency analysis, a technique which may be considered the cornerstone of diagnostic vibration measurements. The graph showing the vibration level as a function of frequency is called a frequency
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### The Ultimate Guide to Vibration Analysis
Nov 12, 2018 Vibration is an oscillating motion about equilibrium, so most vibration analysis looks to determine the rate of that oscillation, or the frequency that is proportional to the system’s stiffness. The number of times a complete motion cycle occurs during a period of one second is the vibration’s frequency
More
### VIBRATION SPECTRUM ANALYSIS - ALPHAPEDIA
FREQUENCY = Frequency is measured in units of cpm, Hz, Orders, i.e. 50 cpm – 750,000 cpm. Knowing the frequency of vibration peaks helps to identify potential sources. Frequency is used in advanced vibration analysis to identify all types of bearing failure frequencies, real-time spectra and motor current signature analysis
More
### Fundamentals of Vibration Measurement and Analysis
VIBRATION waveform as shown in the time drawing on the left side. This is the summation of all the vibration present at that location. Spectrum analysis enables us to untangle this complex waveform and make a representation of its original components on a diagram showing frequency
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### Vibration Analysis: What is it? [4 Measurement Techniques]
Vibration data must be translated from the format in which it is collected (typically frequency, amplitude, etc.). The data needs to be digitally reconstructed into a model that you can analyze. The result is
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### Vibration Analysis and Signal Processing in LabVIEW - NI
Oct 14, 2020 Frequency analysis is the most commonly used method for analyzing a vibration signal. The most basic type of frequency analysis is an FFT, or Fast Fourier Transform, which converts a signal from the time domain into the frequency
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### Basics of Structural Vibration Testing and Analysis ...
Frequency Response Function (FRF) is computed from two signals. It is sometimes called a "transfer function." The FRF describes the level of one signal relative to another signal. It is commonly used in modal analysis where the vibration
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### Analysis Vibration Analysis Of A System With 3 Mas ...
Analysis Vibration analysis of a system with 3 masses and springs under base excitation within a frequency range 2. Dynamics of analysis of a rotating mechanism 1. Vibration analysis of a system
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### Molecular vibration - Wikipedia
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from
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### Vibration Analysis in Gearboxes Power-MI
Jul 29, 2020 Basic Terms for the Vibration Analysis in Gearboxes. The design and manufacture of gears are specialized activities of very high precision. There is an extensive number of concepts associated with the design, geometry and construction of these machine elements. ... The ISO 10816-21 establishes some acceptance limits based on frequency
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### The Emotional Vibration Analysis Frequency Chart - Blisspot
The human emotional vibration analysis frequency ranges chart shown above, ( reproduced with permission from the Love or Above Toolkit), illustrates the vibrational analysis hertz frequency rate of the range of higher to the lower emotions. As the vibration analysis
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### GLOSSARY OF TERMS: Vibration Analysis PI Process ...
AVERAGE: In vibration analysis, an average usually refers to the process whereby the vibration software will, after converting waveforms into spectrums via FFT, add the resultant spectrums
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### myFrequency - Vibration Analysis - Apps on Google Play
It's time to conduct vibration measurements with the easiest smartphone application for vibration analysis and measurements - made in Germany. You can use this userfriendly and mighty app as an
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### Library Tools - Vibration Analysis Case Studies ...
Most detailed analysis of machinery vibration data is done in the frequency domain, but certain information is more easily interpreted in the time domain. Frequency Response The frequency
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### Vibration Analysis: What is it? [4 Measurement Techniques]
Vibration data must be translated from the format in which it is collected (typically frequency, amplitude, etc.). The data needs to be digitally reconstructed into a model
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### Beginning Vibration Analysis - CTC
Frequency Span / Number of Analyzer Lines The frequency span is calculated as the ending frequency minus the starting frequency. The number of analyzer lines depends on the analyzer and how the
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### Vibration Diagnostic Guide - EDGE
vibration signal, its amplitude and its frequency. • Frequency is the number of times an event occurs in a given time period (the event being one vibration cycle). The frequency at which the vibration
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### Basics of Structural Vibration Testing and Analysis ...
Frequency Response Function (FRF) is computed from two signals. It is sometimes called a "transfer function." The FRF describes the level of one signal relative to another signal. It is commonly used in modal analysis where the vibration
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### Library Tools - Vibration Analysis Case Studies ...
Most detailed analysis of machinery vibration data is done in the frequency domain, but certain information is more easily interpreted in the time domain. Frequency Response The frequency
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### Dimensional analysis vibration frequency of a star
I'm doing a classical mechanics course of the MIT on my own. In a problem set there is the following problem to be solved using dimensional analysis: "Derive an expression for the vibration frequency of a star of mass M and radius R, if that vibration
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Analysis Vibration analysis of a system with 3 masses and springs under base excitation within a frequency range 2. Dynamics of analysis of a rotating mechanism 1. Vibration analysis of a system
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### SIGNAL PROCESSING FOR EFFECTIVE VIBRATION ANALYSIS
Effective vibration analysis first begins with acquiring an accurate time-varying signal from an industry standard vibration transducer, such as an accelerometer. The raw analog signal is typically brought into a portable, digital instrument that processes it for a variety of user functions. Depending on user requirements for analysis
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### Molecular vibration - Wikipedia
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from
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### Vibration Analysis in Gearboxes Power-MI
Jul 29, 2020 Basic Terms for the Vibration Analysis in Gearboxes. The design and manufacture of gears are specialized activities of very high precision. There is an extensive number of concepts associated with the design, geometry and construction of these machine elements. ... The ISO 10816-21 establishes some acceptance limits based on frequency
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The Four Principles of Vibration Analysis. Essentially, vibration (data gathered using sensors and accelerometers) is converted into electrical charge and measured as a signal. Vibration analysis compares and provides insights based on measurements of vibration frequency
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An order is a frequency where the number is a multiple of a reference rotational speed. Order Analysis captures a reference RPM signal and correlates it with the measured vibration on the rotational
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### How to Model Gearbox Vibration and Noise in COMSOL ...
May 23, 2017 The frequency band in which the housing vibration is dominant is 1000–3000 Hz. Time history and frequency spectrum of the normal acceleration at one of the points on the gearbox housing. Performing an Analysis
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### Vibration Analysis, for Designers Machine Design
The common types of vibration analysis based on results of the modal-superposition method are time response and frequency response. A vibration problem can be presented by the following equation:
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https://raymiller5050.com/hwqyr/53032b-baseline-hazard-function-interpretation | 1,627,481,259,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153729.44/warc/CC-MAIN-20210728123318-20210728153318-00501.warc.gz | 482,528,858 | 15,547 | # baseline hazard function interpretation
hazard function. That is, the intercept term serves to scale the baseline hazard. exp is the exponential function … Bayesian information criterion for censored survival models. It corresponds to the value of the hazard if all the x i are equal to zero (the quantity exp (0) equals 1). These cookies do not store any personal information. What do we mean by validating a prognostic model? Lecture 32: Survivor and Hazard Functions (Text Section 10.2) Let Y denote survival time, and let fY (y) be its probability density function.The cdf of Y is then FY (y) = P(Y • y) = Z y 0 fY (t)dt: Hence, FY (y) represents the probability of failure by time y. As the hazard function $$h(t)$$ is the derivative of the cumulative hazard function $$H(t)$$, we can roughly estimate the rate of change in $$H(t)$$ by taking successive differences in $$\hat H(t)$$ between adjacent time points, $$\Delta \hat H(t) = \hat H(t_j) – \hat H(t_{j-1})$$. The assumption is that the baseline hazard function … But where do these hazards come from? This routine is provided in most statistical software. For example if the baseline … h (t) is the hazard function determined by a set of p covariates (x 1, x 2,..., x p) the coefficients (b 1, b 2,..., b p) measure the impact (i.e., the effect size) of covariates. The baseline hazard function ‚ 0(t) in model (6.1) can take any shape as a function of t.The only requirement is that ‚ 0(t) > 0. PROC PHREG performs a stratified analysis to adjust for such subpopulation differences. Member Training: Discrete Time Event History Analysis, Getting Started with R (and Why You Might Want to), Poisson and Negative Binomial Regression for Count Data, Introduction to R: A Step-by-Step Approach to the Fundamentals (Jan 2021), Analyzing Count Data: Poisson, Negative Binomial, and Other Essential Models (Jan 2021), Effect Size Statistics, Power, and Sample Size Calculations, Principal Component Analysis and Factor Analysis, Survival Analysis and Event History Analysis. Briefly, the hazard function can be interpreted as the risk of dying at time t. ... the term $$h_0$$ is called the baseline hazard. is usually called a scale parameter. Since it’s so important, though, let’s take a look. Thus, a one unit increase in prio means the the baseline hazard … To estimate , Cox (1972, 1975) introduced the partial likelihood function, which eliminates the unknown baseline hazard … the hazard function associated with a set of possibly time-varying covariates is the sum of, rather than the product of, the baseline hazard function and the regression function of covariates. The model assumes that the hazard function is composed of two non-negative functions: a baseline hazard function, λ 0 (t), and a risk score, r(x)=e h(x), defined as the effect of an individual’s observed covariates on the baseline hazard . The first of these, $$h_0(t)$$, is called the baseline hazard function or the hazard for a reference individual with covariate values 0. That’s the hazard. In interval k, given by [τ k−1,τ k), the hazard function for a given subject is assumed to be constant and is related to the baseline hazard function by the function , where λ k is the baseline hazard function … If you omit the OUT= option, the data set is created and given a default name by using the DATA n convention. The model works such that the log-hazard of an individual subject is a linear function of their static covariates and a population-level baseline hazard function that changes over time. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. if TRUE baseline_hazard will smooth the estimated baseline hazard using Friedman's super smoother supsmu. Adjust D above by "Variance Inflation Factor" 1 2 1 R VIF − = where R2 = variance of X explained by Z But like a lot of concepts in Survival Analysis, the concept of “hazard” is similar, but not exactly the same as, its meaning in everyday English. Simple transformations can be applied to the Bre- slow estimator to provide estimation of the baseline and conditional survival functions. The Cox model is expressed by the hazard function denoted by h(t). The aim of fitting a Cox model to time-to-event data is to estimate the effect of covariates on the baseline hazard function. Thus, the predictors have a multiplicative or proportional effect on the predicted hazard. This date will be time 0 for each student. The accelerated failure-time form of the hazard function … So a probability of the event was called “hazard.”. The hazard function is the nonparametric part of the Cox proportional hazards regression function, whereas the impact of the predictor variables is a loglinear regression. In fact we can plot it. The hazard ratio is the ratio of the hazard functions between two population groups. This formulation describes a different aspect of the association between covari- Different kinds of proportional hazard models may be obtained by making different assumptions about the baseline survival function, or equivalently, the baseline hazard function. Estimate the initial hazard function of a system, h in (t), using historical failure … PH generator Generates data from proportional hazard model with piecewised baseline hazard function. We can then calculate the probability that any given student will finish in each year that they’re eligible. Tagged With: Cox Regression, discrete, Event History Analysis, hazard function, Survival Analysis, Data Analysis with SPSS The BASELINE statement creates a new SAS data set that contains the baseline function estimates at the event times of each stratum for every set of covariates given in the COVARIATES= data set.If the COVARIATES= data set is not specified, a reference set of covariates consisting of the reference levels for the CLASS variables and the average values for the continuous variables is used. Hazard Function The formula for the hazard function of the Weibull distribution is $$h(x) = \gamma x^{(\gamma - 1)} \hspace{.3in} x \ge 0; \gamma > 0$$ The following is the plot of the Weibull hazard function with the same values of γ as the pdf plots above. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. I am only looking at 21… Parameter θ 1 has a hazard ratio (HR) interpretation for subject-matter audience. Thus, the predictors have a multiplicative or proportional effect on the predicted hazard. the predicted values of the regression model on the log hazard scale. Notice that the predicted hazard (i.e., h(t)), or the rate of suffering the event of interest in the next instant, is the product of the baseline hazard (h 0 (t)) and the exponential function of the linear combination of the predictors. The concept is the same when time is continuous, but the math isn’t. Censoring Censoring is present when we … The baseline hazard function, not itself estimated within the model, is the hazard function obtained when all covariate are set to zero. The BASELINE statement creates a new SAS data set that contains the baseline function estimates at the event times of each stratum for every set of covariates given in the COVARIATES= data set.If the … The hazard function … The output is … Survival analysis is used for modeling and analyzing survival rate (likely to survive) and hazard rate (likely to die). In survival analysis, the hazard function is a useful way to describe the distribution of survival times. the term h 0 is called the baseline hazard. (4th Edition) The problem was that what was returned by the old basehazard() option was not (and what is returned by the new basehc() option is not) the baseline hazard; it is the numerator of the baseline hazard, called the hazard contribution by Kalbfleisch and Prentice (2002, p. 115, eq. So for each student, we mark whether they’ve experienced the event in each of the 7 years after advancing to candidacy. Some features of the site may not work correctly. eval_times. The hazard ratio is the ratio of the hazard functions between two population groups. The second year hazard is 23/485 = .048. Necessary cookies are absolutely essential for the website to function properly. This is a short course on survival analysis applied to the financial field. For example, perhaps the trajectory of hazards is different depending on whether the student is in the sciences or humanities. OUT= SAS-data-set names the output BASELINE data set. The dot product of X and β is taken in the exponent just like in standard linear regression. Hazard function: h(t) def= lim h#0 P[t T te. where h(t; x) is the hazard function at time t for a subject with covariate values x 1, … x k, h 0(t) is the baseline hazard function, i.e., the hazard function when all covariates equal zero. Practically they’re the same since the student will still graduate in that year. if TRUE the cumulative survival function … ), in the Cox … Step 1. Notice that the predicted hazard (i.e., h(t)), or the rate of suffering the event of interest in the next instant, is the product of the baseline hazard (h 0 (t)) and the exponential function of the linear combination of the predictors. We also use third-party cookies that help us analyze and understand how you use this website. If the hazard ratio estimate is less than one, this means that the hazard function … Estimate the initial hazard function of a system, h in (t), using historical failure times and surviving times if the data are censored. If you’re not familiar with Survival Analysis, it’s a set of statistical methods for modelling the time until an event occurs. The Cox partial likelihood, shown below, is obtained by using Breslow's estimate of the baseline hazard function, plugging it into the full likelihood and then observing that the result is a product of two factors. Since the hazard is a function of time, the hazard ratio, say, for exposed versus unexposed, is also a function of time; it may be different at different times of follow up. cumulative. For a baseline … The aim of fitting a Cox model to time-to-event data is to estimate the effect of covariates on the baseline hazard function. Step 2. Yeah, it’s a relic of the fact that in early applications, the event was often death. The constant hazard function is a consequence of thememoryless propertyof the exponential distribution: the distribution of the subject’s remaining survival timegiventhat s/he has survived till timetdoes not depend ont. the predicted values of the regression model on the log hazard scale. One of the key concepts in Survival Analysis is the Hazard Function. It is mandatory to procure user consent prior to running these cookies on your website. Let’s say we have 500 graduate students in our sample and (amazingly), 15 of them (3%) manage to finish their dissertation in the first year after advancing. We used these data in our simulation study. Medical decision making : an international journal of the Society for Medical Decision Making, View 6 excerpts, references background and methods, By clicking accept or continuing to use the site, you agree to the terms outlined in our. So Cox’s proportional hazards model is a semiparametric model. In survival analysis, the hazard ratio is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory variable. The accelerated failure-time form of the hazard function … Epidemiology: non-binary exposure X (say, amount of smoking) Adjust for confounders Z (age, sex, etc. Where, xs are the predictors; bs are the coefficients of the predictors which indicate the measure of the impact of their respective predictors; h0 is the baseline hazard. In several applications, it is important to have an explicit, preferably smooth, estimate of the baseline hazard function, or more generally the baseline distribution function. Taking a look at these coefficients for a moment, prio (the number of prior arrests) has a coefficient of about 0.09. Otherwise, let te = the largest censored time. That is the number who finished (the event occurred)/the number who were eligible to finish (the number at risk). T ) = 1 for t < t1 be stored in your browser only with your.... Model D in Table 14.1 s say that in the Nelson-Aalen estimate \! Below, in a drug study, the probability that any given student will in... While you navigate through the website to function properly so let ’ s use an example you ’ the! A one unit increase in prio means the the baseline hazard function hazards is different depending on the!, they are no longer included in the second year 23 more students manage to finish the. A single instant that in the sample of candidates the data set is created and given a default by. Understand how you use this website predictors have a multiplicative or proportional effect on the hazard! Slow estimator to provide estimation of the key Concepts in survival Analysis Basic Concepts, the predictors have a or... You consent to receive cookies on your website about 0.09 we can then fit models to predict these.... An interval of time in discrete years often death ’ s say that for whatever reason, makes. Stored in your browser only with your consent ’ t treated population die... Get a bit more complicated values of the hazard function is a short on. We give you the best experience of our website in a drug,! Equations get a bit more complicated re eligible some of these cookies affect... Assumption is violated for some covariate is.03 coefficients for a moment, prio ( the number of sample,... Transformations can be applied to the Bre- slow estimator to provide estimation of the event occurring any... Survive ) and hazard rate ( likely to die ) ≥ tm ’ re familiar with — the until. Best experience of our website Institute for AI a bit more complicated the second year more... Two population groups s use an example you ’ re probably familiar with calculus, you use... Is a useful way to describe the distribution of survival times occur we. Linear regression, perhaps the trajectory of hazards is different depending on whether the student is in data... Of death from the lifelines package called the baseline hazard will be evaluated a one unit in... S take a look at these coefficients for a moment, prio ( number... Describe the distribution of survival Analysis is used for modeling and analyzing survival rate ( likely survive. These hazards during any given time point within the model, is the partial likelihood shown,! \ ( h ( X ) as the control population we have know!, once a student finishes 2 or 2.25 years after advancing, not itself estimated within the model, the! Unit increase in prio means the the baseline hazard function, it makes sense to think of in. S a relic of the hazard function is 's super smoother supsmu a dataset from the treatment data is estimate. Ratios in … Interpretation¶ Aid and economic evaluation whether they ’ re probably familiar with — time. Taking a look at these coefficients for a moment, prio ( the event occurred /the... Approach, the intercept term serves to scale the baseline hazard, is the same for covariates. A free, AI-powered research tool for scientific literature, based at the Allen Institute for AI let te the. A one unit increase in prio means the the baseline hazard function.. The model baseline hazard function interpretation is the probability of the hazard function is estimated using historical failure data condition! The same since the student is in the sample of candidates assumption violated! To zero called the baseline hazard function for model D in Table 14.1 likely to ). With — the time until a PhD candidate completes their dissertation increase in prio means the the hazard! At which the baseline hazard function for model D in Table 14.1 unit change in X that. Were eligible to finish ( the event occurring during any given student will still graduate in that.. Facilitated the use of the event in each year that they ’ re probably familiar with,. Interval of time rather than at a single instant know where i ’ m going with this calculate the of. Regression coefficients are assumed to be the same for all covariates set equal zero! Rate ( likely to die ) ( likely to survive ) and hazard rate ( likely to survive and. After advancing will smooth the estimated baseline hazard function and we must have multiplicative... Website uses cookies to improve your experience while you navigate through the website to properly! Practically they ’ re eligible term h 0 is called the baseline hazard will be computed where,, the. Probability of the event was often death describe the distribution of survival Basic., adjustments are made based on the baseline hazard function is performs a stratified Analysis Adjust... Survival Analysis, the hazard of a positive outcome, like finishing your dissertation te! So let ’ s so important, though, let ’ s start there Membership... The website to function properly semantic Scholar is a useful way to describe the distribution of survival.! Finish in each year that they ’ re the same when time is continuous, but the math ’! Data n convention likelihood shown below, in a drug study, the baseline is for covariates... Depending on whether the student is in the sciences or humanities, AI-powered research tool for scientific literature, at. Your experience while you navigate through the website wider '' X gives power. And zTfl is the hazard changes as a function of time, the hazard changes with time multiplicative proportional... Statistical software packages, but the math isn ’ t the partial likelihood below. Us analyze and understand how you use this website uses cookies to improve your experience while navigate. In Learning them \ ( h ( t ) = 1 for t < t1 given a default name using. Time until a PhD candidate completes their dissertation must have a multiplicative proportional. The concept is the probability of the model, is the same when time measured! More power, as it should each student the website the term h 0 is called the baseline hazard.! The first year, that ’ s say that for whatever reason, it sense. Way to describe the distribution of survival Analysis is used for modeling analyzing. Exponent just like in standard linear regression baseline hazard function interpretation is called the \baseline '' hazard, is! Whether they ’ re familiar with — the time until a PhD completes... Models to predict these hazards for covariates, number of instants, the predictors have clear. Are an baseline hazard function interpretation number of sample size, and the baseline hazard function the predictors have multiplicative! Functions between two population groups tool for scientific literature, based at Allen... And security features of the 500 who were eligible to finish same since the student is in the second 23... Consulting, Resources, and the baseline hazard using Friedman 's super smoother supsmu all statistical. ) interpretation for subject-matter audience for such subpopulation differences subject-matter audience the value of model! In early applications, the predictors have a multiplicative or proportional effect on the predicted hazard 21… Consulting! Such subpopulation differences baseline survivor function and cumulative hazard function is if there are an infinite number of prior )... In the sciences or humanities imple- mented in all major statistical software packages a dataset the... For scientific literature, based at the Allen Institute for AI to scale the baseline.. Lifelines package and it … in this approach, the probability of finishing within one year of,... A PhD candidate completes their dissertation aneurysm repair improves survival for individual patients development. Given student will still graduate in that year, as it should time is measured discretely so! Proportional hazards model is a short course on survival Analysis, the intercept serves. Prognostic survival models as a function of time, the baseline hazard … where,, and the baseline conditional. ’ ve experienced the event to occur and we must have a multiplicative or proportional effect on the hazard! Included in the sciences or humanities hazards is different depending on whether the student will still in... Yeah, it may not be important if a student finishes, they are no included! That in the sciences or humanities X0 ) describes how the hazard is parametric. Was called “ hazard. ” for Researchers covariate are set to zero the option to opt-out of these cookies be... Is survival Analysis and Challenges in Learning them the baseline hazard … where, and. To plot the cumulative hazard function, not itself estimated within the model, is the same hazard! Important, though baseline hazard function interpretation let ’ s why in Cox regression models, the treated population die. Standard linear regression a semiparametric model mean by validating a prognostic model of some of cookies... Makes sense to think of the regression model on the covariates and survival! The 500 who were eligible understand how you use this website 0 is called the \baseline '' hazard which! Let te = the largest censored time s 15/500, revision and combination of prognostic survival models graduate that! These cookies will be computed where,, and the baseline hazard using 's... Predictors have a multiplicative or proportional effect on the predicted values of the hazard changes with time given will... This date will be stored in your browser only with your consent the number of sample size, and Workshops! Higher hazard of a positive outcome, like finishing your dissertation, they are longer. … Interpretation¶ Factor uses cookies to improve your experience while you navigate the. | 4,527 | 21,801 | {"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} | 3.171875 | 3 | CC-MAIN-2021-31 | latest | en | 0.798697 |
http://conversion.org/length/x-unit-siegbahn/nautical-mile-us-pre-1954 | 1,721,870,623,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518532.61/warc/CC-MAIN-20240724232540-20240725022540-00801.warc.gz | 6,952,798 | 7,495 | # x unit; siegbahn to nautical mile (US pre 1954) conversion
Conversion number between x unit; siegbahn [xu] and nautical mile (US pre 1954) is 5.4072633560106 × 10-17. This means, that x unit; siegbahn is smaller unit than nautical mile (US pre 1954).
### Contents [show][hide]
Switch to reverse conversion:
from nautical mile (US pre 1954) to x unit; siegbahn conversion
### Enter the number in x unit; siegbahn:
Decimal Fraction Exponential Expression
[xu]
eg.: 10.12345 or 1.123e5
Result in nautical mile (US pre 1954)
?
precision 0 1 2 3 4 5 6 7 8 9 [info] Decimal: Exponential:
### Calculation process of conversion value
• 1 x unit; siegbahn = (1.0021*10^-13) / (1853.248) = 5.4072633560106 × 10-17 nautical mile (US pre 1954)
• 1 nautical mile (US pre 1954) = (1853.248) / (1.0021*10^-13) = 1.8493643348967 × 10+16 x unit; siegbahn
• ? x unit; siegbahn × (1.0021*10^-13 ("m"/"x unit; siegbahn")) / (1853.248 ("m"/"nautical mile (US pre 1954)")) = ? nautical mile (US pre 1954)
### High precision conversion
If conversion between x unit; siegbahn to metre and metre to nautical mile (US pre 1954) is exactly definied, high precision conversion from x unit; siegbahn to nautical mile (US pre 1954) is enabled.
Since definition contain rounded number(s) too, there is no sense for high precision calculation, but if you want, you can enable it. Keep in mind, that converted number will be inaccurate due this rounding error!
### x unit; siegbahn to nautical mile (US pre 1954) conversion chart
Start value: [x unit; siegbahn] Step size [x unit; siegbahn] How many lines? (max 100)
visual:
x unit; siegbahnnautical mile (US pre 1954)
00
105.4072633560106 × 10-16
201.0814526712021 × 10-15
301.6221790068032 × 10-15
402.1629053424043 × 10-15
502.7036316780053 × 10-15
603.2443580136064 × 10-15
703.7850843492074 × 10-15
804.3258106848085 × 10-15
904.8665370204096 × 10-15
1005.4072633560106 × 10-15
1105.9479896916117 × 10-15
Copy to Excel
## Multiple conversion
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## Details about x unit; siegbahn and nautical mile (US pre 1954) units:
Convert X unit; siegbahn to other unit:
### x unit; siegbahn
Definition of x unit; siegbahn unit: ≈ 1.0021x10-13.
Convert Nautical mile (US pre 1954) to other unit:
### nautical mile (US pre 1954)
Definition of nautical mile (US pre 1954) unit: ≡ 1853.248 m .
← Back to Length units | 847 | 2,503 | {"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} | 3.21875 | 3 | CC-MAIN-2024-30 | latest | en | 0.507552 |
http://nrich.maths.org/public/leg.php?code=-68&cl=1&cldcmpid=10057 | 1,506,165,415,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689624.87/warc/CC-MAIN-20170923104407-20170923124407-00200.warc.gz | 235,407,890 | 10,018 | # Search by Topic
#### Resources tagged with Visualising similar to Peg and Pin Boards:
Filter by: Content type:
Stage:
Challenge level:
### There are 187 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising
### Nine-pin Triangles
##### Stage: 2 Challenge Level:
How many different triangles can you make on a circular pegboard that has nine pegs?
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What is the best way to shunt these carriages so that each train can continue its journey?
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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
### Tetrafit
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A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
### Painting Possibilities
##### Stage: 2 Challenge Level:
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
### Red Even
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You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
### Routes 1 and 5
##### Stage: 1 Challenge Level:
Find your way through the grid starting at 2 and following these operations. What number do you end on?
### Shunting Puzzle
##### Stage: 2 Challenge Level:
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
### Counters
##### Stage: 2 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
### A City of Towers
##### Stage: 1 Challenge Level:
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
### Counting Cards
##### Stage: 2 Challenge Level:
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
### Four Triangles Puzzle
##### Stage: 1 and 2 Challenge Level:
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
### Paw Prints
##### Stage: 2 Challenge Level:
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
### Hexpentas
##### Stage: 1 and 2 Challenge Level:
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
### Dodecamagic
##### Stage: 2 Challenge Level:
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
### Teddy Bear Line-up
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If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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##### Stage: 1 Challenge Level:
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##### Stage: 1 Challenge Level:
Can you cover the camel with these pieces?
### Waiting for Blast Off
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### Map Folding
##### Stage: 2 Challenge Level:
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
### 28 and It's Upward and Onward
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Can you find ways of joining cubes together so that 28 faces are visible?
### Paper Patchwork 1
##### Stage: 1 Challenge Level:
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
### Cubes Cut Into Four Pieces
##### Stage: 1 Challenge Level:
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
### Paper Patchwork 2
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Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
### More Pebbles
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Have a go at this 3D extension to the Pebbles problem.
### Triple Cubes
##### Stage: 1 and 2 Challenge Level:
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### Overlaps
##### Stage: 1 Challenge Level:
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
### Diagrams
##### Stage: 2 Challenge Level:
A group activity using visualisation of squares and triangles.
### Happy Halving
##### Stage: 1 Challenge Level:
Can you split each of the shapes below in half so that the two parts are exactly the same?
### Thinking Through, and By, Visualising
##### Stage: 2, 3 and 4
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
### Paper Partners
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Can you describe a piece of paper clearly enough for your partner to know which piece it is?
### One Big Triangle
##### Stage: 1 Challenge Level:
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
### Tetrahedron Faces
##### Stage: 2 Challenge Level:
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
### Redblue
##### Stage: 2 Challenge Level:
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
### Neighbours
##### Stage: 2 Challenge Level:
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
### Rearrange the Square
##### Stage: 1 Challenge Level:
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
### Start Cube Drilling
##### Stage: 1 Challenge Level:
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
### Two Squared
##### Stage: 2 Challenge Level:
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
### Move a Match
##### Stage: 2 Challenge Level:
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement? | 2,206 | 9,699 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-39 | latest | en | 0.88961 |
https://gamedev.stackexchange.com/questions/109635/neural-network-ai-evolution | 1,582,737,348,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146414.42/warc/CC-MAIN-20200226150200-20200226180200-00528.warc.gz | 370,338,628 | 32,009 | Neural Network ai evolution?
I've created a small simulation game and I have a basic neural network in place, each "creature" in my game has random weights on it's nodes and they all behave differently.
Their goal is to stay inside a circular "safe zone" that moves around the center of the game world. After 1000 generations of evolution not a single one of them makes any attempt to follow the circle around, so I was thinking I either..
1. Don't know how to train them properly
2. Don't know how to find who should live/ die.
3. Using the wrong input/ outputs.
Here is the diagram of the brain (ignore the numbers)
Can anyone shed any light on what my issue is here? I'm sorry if this is vague I've only been using these for a couple of hours. But to elaborate on my question, what kind of inputs/ outputs should I be using with my neural network and what is the general procedure (in respect to my evolution approach) to train them to do the correct thing?? Could the error be caused by the number of nodes in the hidden layer or something?
• are you using normalized (0..1) values for input? – dnk drone.vs.drones Oct 13 '15 at 14:40
• No. should that be a thing I should change? How can I normalize a distance when there is no "max distance" ? – Shaun Wild Oct 13 '15 at 14:41
• As far as I know NN require normalized values in input and returns normalized values as output. I suggest you to define a max distance – dnk drone.vs.drones Oct 13 '15 at 14:43
• I normalized the angle to be 0...1 instead of 0...360 and did dist sq from 0...1 instead of 0...100^3, they still seem to just move around aimlessly generation after generation. – Shaun Wild Oct 13 '15 at 14:47
• I don't know much about neural networks. In generational algorithms, you have a stage where you assess "fitness" (or "how good are we?"). Do you have that stage, and are you using the appropriate mechanism to tell how "good" the creature did (distance to the center?) – ashes999 Oct 13 '15 at 16:12 | 495 | 1,983 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2020-10 | latest | en | 0.938017 |
https://www.jiskha.com/display.cgi?id=1264458448 | 1,516,596,692,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890991.69/warc/CC-MAIN-20180122034327-20180122054327-00695.warc.gz | 974,625,209 | 3,748 | # Algebra
posted by .
Find the next two numbers in the geometric sequence:
1, 1/3, 1/9
• Algebra -
Each number is 1/3 of the one before it.
1/3 * 1/9 = 1/27
1/27 * 1/3 = ?
• Algebra -
Thank You Ms, Sue
• Algebra -
You're welcome.
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w =xSyz) + Xy _ 4yz...
##### The temperature at point (x,y) Tlx, Y) _ measured in degrees Celsius bug crawls so that its position after seconds given by x = V 2 + t,y = 9 25 wnere and are measured in centimeters. The temperature function satisfies 7x(2, 10) and T,(2, 10) 8. How fast is the temperature rising on the bug s path after seconds? (Round your answer to two decimal places.} 'Cls
The temperature at point (x,y) Tlx, Y) _ measured in degrees Celsius bug crawls so that its position after seconds given by x = V 2 + t,y = 9 25 wnere and are measured in centimeters. The temperature function satisfies 7x(2, 10) and T,(2, 10) 8. How fast is the temperature rising on the bug s path a... | 1,458 | 5,356 | {"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} | 2.59375 | 3 | CC-MAIN-2022-33 | latest | en | 0.891857 |
http://www.popularmechanics.com/science/math/a26477/riddle-of-the-week-26/ | 1,511,233,371,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806310.85/warc/CC-MAIN-20171121021058-20171121041058-00457.warc.gz | 493,949,613 | 57,202 | # Riddle of the Week #26: Riddles in the Dark
## Difficulty level: Moderate
Michael Stillwell
This week we decided to change it up a bit and revisit some classic riddles that you may have heard in your childhood. These are wordplay riddles, each its own little ditty, unlike our normal logic puzzles. Here are the Riddles in the Dark.
### Problems
1. Gollum: What has roots as nobody sees, is taller than trees, up, up, up it goes, and yet, never grows?
2. Bilbo: Thirty white horses on a red hill. First they champ, then they stamp, then they stand still.
3. Gollum: Voiceless it cries, wingless flutters, toothless bites, mouthless mutters.
4. Bilbo: An eye in a blue face saw an eye in a green face. "That eye is like to this eye," said the first eye. "But in low place, not in high place."
5. Gollum: It cannot be seen, cannot be felt, cannot be heard, cannot be smelt. It lies behind stars and under hills, and empty holes it fills. It comes first and follows after, ends life, kills laughter.
6. Bilbo: A box without hinges, key or lid, yet golden treasure inside is hid.
7. Gollum: Alive without breath, as cold as death, never thirsty, ever drinking, all in mail never clinking.
8. Bilbo: No-legs lay on one-leg, two legs sat near on three legs, four legs got some.
9. Gollum: This thing all things devours: birds, beasts, trees, flowers; gnaws iron, bites steel; grinds hard stones to meal; slays king, ruins town, and beats high mountain down.
10. Bilbo: What have I got in my pocket?
### Hint
Read The Hobbit, or There and Back Again.
### Solutions
Once you have figured out these tricksy riddles, you can check the answers here.
*See all of our riddles here. | 441 | 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} | 2.84375 | 3 | CC-MAIN-2017-47 | longest | en | 0.919666 |
https://www.jiskha.com/display.cgi?id=1160244401 | 1,516,681,730,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891706.88/warc/CC-MAIN-20180123032443-20180123052443-00564.warc.gz | 927,035,628 | 3,988 | # math
posted by .
100 people set up a phone call system so that the initial contact person call three persons, each of whom calla three persons,and so on until all have been contacted. The maximum people who do not need to make calls is?
Very Simple Question
How would you solve it:
(1+x^2)(1-x^3)
(1+x^2)(1-x^3)
This is the same as
1*(1-x^3) + (x^2)*(1-x^3) = 1 - x^3 + x^2 - x^5
We have
1 who call 3
1+3 who call 3
1+3+9 who call 3
1+3+9+27 who call the remaining 60 who don't need to call anyone.
So it looks like 40 will need to call someone and 60 won't need to call anyone. If I understand the question correctly.
Check that, of the last 27 who need to call, not everyone made a call. There were 60 people remaining to be called and only 20 of the 27 needed to call someone. 7 of the 27 didn't need to call anyone, so 67 people total did not need to call anyone. Check this too.
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More Similar Questions | 727 | 2,842 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2018-05 | latest | en | 0.958523 |
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Focal Point Focal Point Forums Performance Management Framework (PMF) % of total measure - help with denominator
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% of total measure - help with denominator
Guru
posted March 30, 2011 01:32 PM
Hi Team,
Currently we have some measures that are defined by age, meaning there are dollars owed that are between 0 to 30 days old, some that are 31 to 60 days old, and so on. These are discrete measures, like this:
A/R \$ 0-30 days
A/R \$ 31-60 days
We have some companion measures that show similar information, but as a % of total. So, the dollars from 0-30 days are divided by the total dollars to show what percent of all outstanding dollars are 0-30 days old. On the measure loader screen for these % of total measures, the numerator and denominator looks something like this:
NUMERATOR=IF <0-30> then AMOUNT else 0;
DENOMINATOR=AMOUNT;
Now we would like to turn all the dollar measures into one measure and all the percentage measures into one measure, and use a dimension to provide the aging breakout. I am very clear on how this will work for the dollar measures; the data needs to look like this:
```AGING_DIM_KEY AMOUNT
0_30 100
31_60 100
61_90 100
91_180 100
181_365 100
366_PLUS 100
```
So, in this case the total AR will be 600, and I would like to use that for the denominator of the percent of total measures. However, I cannot quite see how I would make that happen with an aging dimension. The closest that I've been able to come to designing this is to make it data driven:
```AGING_DIM_KEY NUMERATOR DENOMINATOR
0_30 100 600
31_60 100 600
61_90 100 600
91_180 100 600
181_365 100 600
366_PLUS 100 600
```
The measure loader screen would look like this:
NUMERATOR=NUMERATOR;
DENOMINATOR=DENOMINATOR;
The obvious problem is that the NUMERATOR can aggregate at a higher dimension level, but the DENOMINATOR cannot. At the top level of the aging dimension, the NUMERATOR and DENOMINATOR should equal each other, but in this case it would be 600 / 3600.
I wonder if this would work:
NUMERATOR=NUMERATOR;
DENOMINATOR=MIN.DENOMINATOR;
Cheers,
Joey
-WebFOCUS 8.2.01 on Windows
Posts: 319 | Location: Los Angeles, CA | Registered: November 15, 2005 IP
Guru
posted April 04, 2011 07:28 PM Hide Post
Hi Team,
I've been thinking about this a lot, and have come to realize that my idea of putting using DENOMINATOR=MIN.AMOUNT won't work. This is on the measure loader screen, so it would only kick in during measure load, not during query run-time like I need.
So, that leaves me to wonder about the alternate aggregation features of PMF. I found one mention in the pmf_doc.pdf file about something called External Aggregation. This is what it says:
```
External Aggregation: Select whether to allow aggregate measure values using external tables
with pre-populated rollup values. Choose one of the following: Y (Yes) N (No). The default is N (No).
External Aggregation MFD: Type the name of the Master File to use for external aggregation.
```
So, this sounds like it might be a viable path, but I need to know more about this. The name and feature description implies to me that I can load a table with values at every level of a dimension versus loading values at the lowest level and relying on summarized aggregation. If so, this is likely a viable solution for what I'm trying to do here.
Is there anywhere I can read a little more about this? I searched the pmf manual, the install guide and the developer's guide, but could only find the above entry. The New Features (5.2) document spoke of pre-aggregated cubes, and I wonder if that is something similar to External Aggregation:
```Integration with Pre-Aggregated Cubes
To further support extra large and complex metric pools, PMF 5.2 has been enhanced to
support external pre-aggregated cubes. This allows PMF to merge externally aggregated
metrics with normal PMF managed metrics in a way that allows them to fully
participate in PMF capabilities and remains transparent to the consumer.
```
I wonder if it's possible to pre-aggregate values along one dimension and allow straight roll-up along the others? I suspect not. If not, then that means I need to calculate the % of total value for each and every dimension intercession point, and store it in a table. I suppose I will need high level roll-up values, but how would I key the dimension values? PMF dimension source tables are keyed at the lowest level and then PMF generates internal keys for the higher levels.
Would appreciate your help figuring this out.
Cheers,
Joey
-WebFOCUS 8.2.01 on Windows
Posts: 319 | Location: Los Angeles, CA | Registered: November 15, 2005 IP
Platinum Member
posted April 06, 2011 10:15 AM Hide Post
Hi Joey,
We have not been ignoring you
Let me deal first with the nature of this "Aging" dimension. If I am following you, the Aging dimension is a one level dimension. Next we have a Measure (or Measures) which use this dimension. These Measure(s) are percentage Measures along the Aging dimension, but they do not appear to add up properly when we remove this dimension from the sort (i.e, if we sum up along all values of this dimension). What I am not following is why you would ever remove this dimension from the sort. By definition, if you add up all values along this dimension, then you you always get 100%. This 100% applies across any additional dimensional sorts you might want. So if you are adding up all Aging values for Location EAST, Department XYZ, for 2011Q2, you will still get 100%.
Am I understanding this correctly? If so, then you might be able to handle this as a customization. Check the sorts - if the Aging dimension is not one of the sorts, then the Actual is 100% (I assume the Targets would also have to add up to 100% as well).
Next, you are asking about External Aggregation - which means your data is stored in a pre-aggregated cube that is not maintained by PMF. Your suspicions are correct in that you need to store the value of every dimensional intersection in the external data store including all higher level aggregations. However, you do not need to use PMF's internal key values. Instead your external store must have the same dimensions and dimensional values that you are using inside PMF. In other words, the external data store must be a cube that mirrors the PMF_CUBE_VW inside of PMF. So if you are doing a report and you just want information for location 'EAST', PMF passes a "WHERE LOCATION_LEVEL01_VALUE EQ 'EAST'" to the external data store.
Eric
Posts: 164 | Registered: March 26, 2003 IP | 1,638 | 6,737 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-40 | longest | en | 0.90514 |
http://www.reddit.com/user/KalladAmos?sort=hot | 1,409,268,102,000,000,000 | text/html | crawl-data/CC-MAIN-2014-35/segments/1408500831098.94/warc/CC-MAIN-20140820021351-00306-ip-10-180-136-8.ec2.internal.warc.gz | 570,560,378 | 11,641 | # reddit's stories are created by its users
[–][S] 2 points3 points (0 children)
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In relation to gravity, momentum, friction and drag of cause!
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You should freeze in mid-air due to the fact that the space is turning back in time while you are friezed in a separate temporary timeframe during the travel. :)
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In relation to gravity of cause! Like when you jump regularly you don't travel several miles due to the fact of gravity, similar (I believe) it is with the time turner, so as long as you are affected by gravity you will stay in relation to the point on the earth's crust directly below you. For the other part about standing still there is a hypothesis that the interfering matter would react as the same way as antimatter in contact with regular matter (instantly killing you and anyone in the surrounding area). The big question is what will happen if you are in an moving object in relation to the earth, due to the fact that the space is reversing and not you who is in an alter time reality. This makes 2 possible hypothesises, take the train for example: one hypothesis being you would appear on the tracks while the former you is heading towards you in a train. The other hypothesis is that you will appear in the train due to your relation to it, and that the same time your former self is in an exact version of that train heading towards you, making it possible not only to send yourself but also sending mass in a system related to you in the same relation to the earth gravitational pull as you but not in the the same relation to you in different times.
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So if the subject would stand on a train for an hour and then used the time turner, then your former self wound be travelling towards you and at the same time stand beside you?
your question is a revered version of question 2 ;)
The concept of Time turners. by in HPMOR
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New to reddit btw :)
The concept of Time turners. by in HPMOR
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I am currently trying to create a new post with the same name and with my spelling being correct.
The concept of Time turners. by in HPMOR
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If i have understand this corectly a timeturner bent the space around the carakter so he stand on the same place but in a differnet time, while the another you is there it shoud be in the given time. So i wonder what will happen If:
1.That happens if u stand still for an hour and then turned the time turner? 2.If someone removed an objekt earlier where you are standing 3.If you turn the time in an moving objekt, for example a train. | 739 | 3,142 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2014-35 | latest | en | 0.974568 |
https://ceramhyd.com/math-593 | 1,669,720,684,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710691.77/warc/CC-MAIN-20221129100233-20221129130233-00671.warc.gz | 201,416,955 | 6,659 | # Intergral solver
One tool that can be used is Intergral solver. We can help me with math work.
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Expanded form is the usual way you might see it in an equation: To solve an exponential equation, expand both sides and then factor out a common factor. Each side will have one number multiplied by another specific number raised to a power. Then take that power and multiply it by itself (to get one number squared). That’s your answer! Base form is used for when we’re given just the base (or “base-rate”) value of something: To solve a base-rate problem, first find the base rate (number of events per unit time), then subtract that from 1. Finally, multiply the result by the event rate (also called “per unit time”).
Any mathematician worth their salt knows how to solve logarithmic functions. For the rest of us, it may not be so obvious. Let's take a step-by-step approach to solving these equations. Logarithmic functions are ones where the variable (usually x) is the exponent of some other number, called the base. The most common bases you'll see are 10 and e (which is approximately 2.71828). To solve a logarithmic function, you want to set the equation equal to y and solve for x. For example, consider the equation log _10 (x)=2. This can be rewritten as 10^2=x, which should look familiar - we're just raising 10 to the second power and setting it equal to x. So in this case, x=100. Easy enough, right? What if we have a more complex equation, like log_e (x)=3? We can use properties of logs to simplify this equation. First, we can rewrite it as ln(x)=3. This is just another way of writing a logarithmic equation with base e - ln(x) is read as "the natural log of x." Now we can use a property of logs that says ln(ab)=ln(a)+ln(b). So in our equation, we have ln(x^3)=ln(x)+ln(x)+ln(x). If we take the natural logs of both sides of our equation, we get 3ln(x)=ln(x^3). And finally, we can use another property of logs that says ln(a^b)=bln(a), so 3ln(x)=3ln(x), and therefore x=1. So there you have it! Two equations solved using some basic properties of logs. With a little practice, you'll be solving these equations like a pro.
Algebra is a subject that covers the study of mathematics, one of the most important subjects in school. In algebra, students learn to solve equations and perform operations by manipulating numbers and symbols. Students can use algebra to solve everyday problems like adding a column of numbers or calculating the cost of an item. Algebra equation solver software is software that helps students practice algebra equations. It can be used by students at all levels, from beginners to experienced algebra students. The software generally includes tools for solving equations and graphing. Because it is so useful, there are plenty of options available for the best algebra equation solver. Here are some features to consider: Online vs On-device vs Software vs Website . There are different ways you can use algebra equation solver software: on a computer, on your smartphone, or on a website. You should pick the one that works best for you. Online and on-device options are better for students who want to practice with other people online or around the world, while software and website options work best when you’re working alone. In all cases, it’s important to have an easy-to-use interface that allows you to focus on your problem solving skills instead of learning how to use the software. Cost . There are many different types of algebra equation solver software out there, but they can cost anywhere from free
Solving exponential functions can be a bit tricky because of the tricky constant that appears at the end of the equation. But don’t worry! There are a few ways to solve exponential functions. Let’s start with the easiest way: plugging in values. When your function has a non-zero constant at the end, you can use that constant to find your answer. For example, let’s say our function is y = 2x^3 + 2 and we want to solve for x using this method. First, plug in 2 for x by putting x=2 into our function. Then, multiply both sides by 3 on the left to get x=6. Finally, add 2 to both sides to get x=8. If you were able to do this, then your answer is 8! When you can’t use this method, there are two other ways to solve an exponential equation: tangent or logarithmic. Tangent means “slope”, and it is used when you know the slope of your graph at one point in time (such as when it starts) and want to find out where it ends up at another point in time (such as when it ends). Logarithmic means “log base number”, and it is used when you want to find out how quickly something grows over
## Help with math
It helps me with everyday math and the fact that there’s barely any ads make it even better. Not only that it gives you math problem answers it explains how to get the solution so you also learn. This app is definitely better than math way, the old app I used for math answers. | 1,245 | 5,413 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-49 | longest | en | 0.943379 |
https://bigideasmathanswers.com/hexadecimal-addition-and-subtraction/ | 1,709,122,663,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474715.58/warc/CC-MAIN-20240228112121-20240228142121-00057.warc.gz | 139,287,405 | 41,221 | # Hexadecimal Addition and Subtraction | How to Add & Subtract Hexadecimal Numbers? | Hexadecimal Arithmetic Examples
In the hexadecimal number system, the numbers are expressed with the base 16. Hexadecimal is also called as Hex. It is like decimal, binary or octal numbers. The list of 16 hexadecimal numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Here, we are going to learn how to perform addition, subtraction operations in between two hexadecimal numbers with the examples for the better understanding of the concept. So, interested people can check out this complete page.
## What is Hexadecimal Number System?
A hexadecimal number is a number having a base of 16. These numbers are also called the 16 number system. It has 16 different symbols, 0 to 9 represent the binary values, A, B, C, D, E, F represent 10 to 15 values respectively. Each position in the hexadecimal number represents 0 power of the base 16. The last position in the number represents an x power of base 16.
Examples of Hexadecimal Numbers:
1. B84F
The decimal value of B84F is 11 x 16 + 8 x 16 + 4 x 16 + 16 x 16
= 176 + 128 + 64 + 256
= 624
2. Convert 857 to hexadecimal
857 ÷ 16 = 53.5625
0.5625 x 16 = 9 (Remainder 9)
53 ÷ 16 = 3.3125
0.3125 x 16 = 5 (Remainder 5)
3 ÷ 16 = 0.1875
0.1875 x 16 = 3 (Remainder 3)
Read remainders from bottom to top
So, 857 = (359)16
Also, Read: Binary Subtraction
### Procedure for Adding & Subtracting in Hexadecimal
Below provided are the simple steps that are helpful to compute the addtion and subtraction of two hexadecimal numbers.
1. Hexadecimal Numbers Addition
• Write two hexadecimal numbers one after another in two different lines
• Begin adding from the rightmost digits.
• If the digit is in the form of an alphabet then convert it to the respective decimal number to make the process easy
• Add those digits and convert the sum to the hexadecimal
• If you got the carry, then represent it on the top of the first number next digit and result on the bottom of the second number added digit.
• Continue the process until you left nothing on the left side.
We can also add two hexadecimal numbers by following this table.
For Example:
926 + 1A2
9 2 6
(+) 1 A 2
= A C 8
So, 926 + 1A2 = AC8
2. Hexadecimal Numbers Subtraction
• Write two hexadecimal numbers in different lines
• Subtraction starts from the rightmost digits of the numbers.
• Convert the alphabets into decimals and subtract two digits and again convert the difference value as hexadecimal.
• In case the first number digit is smaller than the second number digit, then barrow from the left side digit.
• The borrowed value is always 16 as its base is 16. Then add borrowed value and first number digit and subtract.
• Don’t forget to mention the borrowed value on the top of the first number digit.
• After borrowing, the left side digit decreased by 1.
• Repeat the process till you have nothing remaining on the left side.
For Example:
938 – 1A2
8 – 2 = 6
3 – A(10) = (16 + 3) – 10 = 19 – 10 = 9
(9 – 1) – 1 = 8 – 1 = 7
So, 938 – 1A2 = 796.
### Hexadecimal Addition and Subtraction Examples
Example 1:
Evaluate (1AB2)16 + (2198)16
Solution:
Given expression is (1AB2)16 + (2198)16
From the table,
2 + 8 = A
B + 9 = 4 and 1 is carry
1 + A + 1 = C
1 + 2 = 3
Therefore, (1AB2)16 + (2198)16 = 3C4A
Example 2:
Find subtraction of (B84F)16 and (A53)16.
Solution:
F means 15. F – 3 = 15 – 3 = 12 = C
4 + 16 = 20 – 5 = 15 = F
8 – 1 = 7
7 + 16 = 23 – A = 23 – 10 = 13 = D
8 – 1 = 7
23
10 7 20
B 8 4 F
(-) 0 A 5 3
= 7 D F C
So, (B84F)16 – (A53)16 = (7DFC)16
Example 3:
Find the addition, subtraction of (AB53)16, (155)16
Solution:
The addition of numbers is (AB53)16 + (155)16
3 + 5 = 8
5 + 5 = 10 = A
B + 1 = 11 + 1 = 12 = C
A + 0 = 10 + 0 = 10 = A
So, (AB53)16 + (155)16 = (ACA8)16
Subtraction of numbers is (AB53)16 – (155)16
(3 + 16) – 5 = 19 – 5 = 14 = E
(5 – 1) – 5 = 4 – 5
(4 + 16) – 5 = 20 – 5 = 15 = F
(B – 1) – 1 = (11 – 1) – 1 = 10 – 1 = 9
A – 0 = A
A B 5 3
(-) 0 1 5 5
= A 9 F E
So, (AB53)16 – (155)16 = (A9FE)16
Example 4:
(i) Calculate (9AB)16 + (12C)16
(ii) Compute (CB5)16 – (223)16
Solution:
(i) (9AB)16 + (12C)16
B + C = 11 + 12 = 23 = 7 and 1 is carry
1 + A + 2 = 3 + 10 = 13 = D
9 + 1 = 10 = A
So, (9AB)16 + (12C)16 = (AD7)16
(ii) (CB5)16 – (223)16
5 – 3 = 2
B – 2 = 11 – 2 = 9
C – 2 = 12 – 2 = A
So, (CB5)16 – (223)16 = (A92)16 | 1,556 | 4,441 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.625 | 5 | CC-MAIN-2024-10 | longest | en | 0.807129 |
http://judaism.stackexchange.com/questions/16883/is-the-passage-describing-an-approximation-of-pi-or-is-it-one-of-the-miracles-of/29995 | 1,469,272,209,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257822172.7/warc/CC-MAIN-20160723071022-00012-ip-10-185-27-174.ec2.internal.warc.gz | 136,755,733 | 24,524 | # Is the passage describing an approximation of pi or is it one of the miracles of Bais Hamikdash?
In Sepher M'lakhim we read how different measurement was taken. I wonder if this passage (Ⅰ M'lakhim 7:23) is describing an approximation of PI (3.1415...), or was this one of the hidden miracles?
וַיַּעַשׂ אֶת־הַיָּם מוּצָק עֶשֶׂר בָּאַמָּה מִשְּׂפָתֹו עַד־שְׂפָתֹו עָגֹל ׀ סָבִיב וְחָמֵשׁ בָּאַמָּה קֹומָתֹו [וּקְוֵה כ] (וְקָו ק) שְׁלֹשִׁים בָּאַמָּה יָסֹב אֹתֹו סָבִיב׃
Now he made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference.
-
can you define what you mean "one of the hidden miracles"? are you saying that it was a miracle that it was only 30 cubits, instead of the true value it should have been mathematically? – Menachem Jun 6 '12 at 22:48
I'm no believer in biblical literacy, but I've never seen the problem here. It doesn't say "10 cubits to infinity decimal places", it says "5, 10 and 30 cubits" That, to me, suggests that I probably rounded up from nine and a half -- why is that a problem? – Jack V. Jun 12 '12 at 14:30
Thank you all for taking your time answering my questions. It is greatly appreciated. – Ben Jun 17 '12 at 15:40
Inner diameter; outer circumference? Or a curved in lip on the bowl with the circumference measured around the middle of the bowl, and the diameter across the top? Frankly, I've never seen the problem here. – TRiG Jul 17 '12 at 18:05
Related: judaism.stackexchange.com/q/18903. – msh210 Sep 4 '12 at 3:32
It's approximating π, as is clear from the g'mara (Eruvin 14:1).
The problem is that that g'mara seems to be saying that it's a pretty precise approximation, and we know it's not. (Tosafos there raise this question and offer no answer.)
But to answer your question, whether it's an approximation of π or a miracle, it's the former.
-
Thank you very much. I had hope for a definite answer. I'm satisfied to know that is is non. I'm satisfied with the explanation you gave. I hope that I can learn form g'mara my self some day. – Ben Jun 6 '12 at 16:41
To your question, whether the verse is approximating π or describing (no pun intended) a miracle, I think there is a definite answer: it's approximating π. – msh210 Jun 6 '12 at 18:46
IIRC, one of the other tosafos, (Tosafos HaRosh, I think, but I can't find a copy online) rereads the gemara so that it makes more sense. I don't really remember how, though. – jake Jun 6 '12 at 19:32
Wikipedia has a set of answers in their article on Approximations of pi. That links to a terrific article on rabbinic approximations of π by Boaz Tsaban and David Garber. Tsaban and Garber summarize as follows (pp. 10-11):
1. The rational-religious approach of Maimonides holds that, since we cannot know the exact values, the Bible tells us that we do not have to worry about this and that is suffices to use the value 3.
2. The mystical approach of [Matityahu Hacohen] Munk contends that 3 was indeed the ration of the circumference to the diameter in King Solomon's temple: This value is used in order to bridge the gap between our world and the "world of truth." For the sake of consistence, the halachic conditions are applied to the suitable regular polygons.
3. The practical approach of R' Shimon Ben Tsemah [who learns from other places in Talmud that they used a more precise version of π] asserts the the rough approximations are used when teaching the students, but, when it comes to practice, the calculations are to be done by the experts.
So to answer your question, if you hold by Munk (I don't know who he is), then it's a miracle. If you hold by Rambam or R' Shimon ben Tsemah, it's an approximation
((Aside: two different psaks come out of this for practical reasons like sukkot - either you use the best mathematical approximation (R' Shimon ben Tsemah) or you use 3 (Rambam and Munk). In order to use 3 as π, you can just measure the perimeter of the interior inscribed regular hexagon.))
-
Rabbi Max Munk "three geometry problems in tanach and talmud" (Hebrew), SINAI, 51: 218-227 (Harav Kook Institution, 5722) -- one of the sources used in books.google.co.cr/… -- looks like it's the same – Menachem Jun 6 '12 at 23:17
The GR"A points out the following:
The word circumference (kav) is spelled קוה but pronounced קו. The gematria of the former is 111 and the latter is 106. The ratio of 111 to 106, multiplied by the approximation of 3, gives you:
(111 / 106) * 3 = 3.1415
Perhaps pi to five digits is a better approximation than 3?
-
So you're taking the approximation side, not the miracle side. – Double AA Jun 6 '12 at 19:06
At what point is pi ever not an approximation? I think five places is pretty good. – yoel Jun 6 '12 at 19:08
Indeed pi is a transcendental number. I'm only pointing out how you try to answer the question, because it wasn't very clear from your post. – Double AA Jun 6 '12 at 19:10
I plead ignore: why do you take the ratio? And then why use the ratio to scale the approximation? Is there any methodology for this? And is there any suggestion that the value 3.1415 should be used in place of 3? Where does the Gra say this? Does he explain it? – Curiouser Jun 6 '12 at 19:23
@Curiouser, Early authorities had already proposed that the reason the "ה" is not extant in the kri is to hint to the fact that the measurement is in fact an approximation and is actually "missing" some length. The Gr"a is merely showing that there is a neat remez that can show how the number was approximated, that is the approximation is essentially a scaling by the ratio of the kri with the ksiv. There is no "methodology". If it would have been easier to hint to e.g. the difference instead of the scaling factor, perhaps it would have. – jake Jun 6 '12 at 19:48
I think that the point is being missed here.
There are not that many places where there is a difference between the written word (k'siv) and the way the word is pronounced (kri). This is especially true where the written word would be pronounced the same way. The reason is generally that neither is quite correct. The "real" word should be some combination.
In this case, the gematria of the written word קוה is 111, while the gematria of the spoken word קו is 106. As the Gra shows, this provides a value of 3.1415.
Everyone seems to be impressed that Archimedes placed pi between 3 1/7 and 3 10/71 around 300 BCE, but that is between 3.1408 and 3.1429. The book of Kings was written about 600 BCE. Mathematics was not advance enough at this time to any person to provide this accuracy. It seems to me to less credulous to believe that there is a divine aspect than to say that it is a coincidence.
-
Nice false dichotomy. – Double AA Jul 17 '13 at 21:00
This dichotomy is what I am presented with in discussion with those who do not accept Torah. They tend to attribute most things to coincidences. Your alternative explanation is....? – Steven Schulman Jul 17 '13 at 21:49
@StevenSchulman The problem with this answer is that it seems to go against the Gemara. – Shmuel Brin Jul 17 '13 at 22:44
Hi @StevenSchulman and welcome to mi.yodeya! The idea that the true meaning of words with a different k'ri than k'siv is an interesting one. Does it have a written source? – WAF Jul 18 '13 at 14:34
How does the Gr"a get 3.1315 from 111 and 106? Please reply with @Daniel in the comment so I get notified. – Daniel Jul 18 '13 at 18:38
There is a very, very full and wonderful essay on this topic (in English, translated from the Ruusian original) which can be found here, but I will quote two paragraphs which will significantly add to what has been discussed here already:
It appears to me that the correction קו/קוה (qava/qav) has not merely numerical meaning. The word קוה (qava) is feminine (in Hebrew the feminine words almost always end with ה) while קו (qav) is masculine. The way the word is spelled is called "masoret"-מסורת and is feminine, the way it is pronounced is called "mickra"- מקרא and is masculine. On the other side, in the pair circle-diameter, the circle represents a feminine, material notion (e.g. the mother Earth) while the straight line represents the masculine, spiritual notion (e.g. the rain that fertilizes the earth). Hence the word קוה (qava) is related to the circle while קו (qav) to the diameter. With this correspondence the verse 7:23 reads "קו (qav) ten cubits from the one brim to the other … and a קוה (qava) of thirty cubits did circle it round about". Thus the ratio of a circle to diameter becomes (30xqava)/(10xqav)=333/106.
Notice that that all objects in the tabernacle where straight. May be this is the reason why Rambam draw the Menorah with straight branches? If in the "heavens", in the spiritual world, there are no curved lines, the circle is perhaps represented there by a polygon. In case of the perimeter of the circle, the hexagon could serve as a model. In case of the area, the dodecagon could be the model. In the first case the perimeter is equal 2∙3∙radius of the surrounding circle; in the second case the area equals 3∙square of the radius, as if π=3. That is why the Sages considered the equality π=3 not as an acceptable approximation but as a reflection of a certain spiritual truth.
There is a lot more material there and it is well worth a look, especially if you are mathematically inclined.
-
I think we already have two such answers – Shmuel Brin Nov 21 '13 at 7:12
@ShmuelBrin - Read it again. – user4523 Oct 7 '14 at 8:31 | 2,742 | 9,499 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2016-30 | latest | en | 0.921877 |
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# Bite-sized knowledgeto upgradeyour career
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# Superposition
In Brief,
Superposition is essentially when a qubit is in a state somewhere in between 0 and 1 that then becomes either 0 or 1 when observed. A very common example is one of a spinning coin. When you flip a coin, there is a mixture of heads and tails (like a qubit being in the states of 0 and 1) but when it stops, it is either heads or tails (this is what happens when we observe the qubit to get the result of our calculation).
Calculations can be performed while the qubit is in a superposition, which is what makes quantum computers so powerful.
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If you know a bit about computers, you may know that computers use bits, which can either be on or off, usually referred to as 1 and 0 respectively. The states of these bits can be modified using logic gates like
These three gates correspond to rotations around the z-axis by different amounts, with T being a 45-degree rotation, S being a 90-degree rotation and Pauli-Z being a 180-degree rotation.
Qubits can be represented using an equation, which is what we will do.
The Hadamard gate is very important because it puts the qubit into a state of superposition. It corresponds to a 90-degree rotation around the x and the z axes.
Qubits are the quantum equivalent of bits, but they work very differently from classical bits (the bits used in our computers). Qubits, like classical bits, can be in states of 0 and 1, also known as spin up and spin down, but what makes qubits useful is the concept of quantum superposition.
First we will look at the Pauli-X gate,also known as the NOT gate,and works very similarly to the NOT gate in classical computer science.All it does is switch the probabilities of |0>and |1>. So if we start the qubit with a 100%possibility of being0,then this gate will change it to a 100% possibi...
For this article, you won’t need to worry too much about these. Just know that they are important when representing the states of the qubit because a lot of quantum mechanics uses imaginary numbers.The theta and phi symbols are used to describe a vector on the Bloch sphere. In quantum mechanics, ...
You’ve heard a bunch about this Bloch sphere throughout this article and it is just a sphere that is used to visualize the state of a qubit. So how does any of this relate to qubit logic gates? Well, logic gates correspond to rotations on the Bloch sphere, which modify the equation previously men...
This is the Bloch sphere in the 0 state. Both theta and phi are at 0 right now.
One important thing to remember when it comes to the Bloch sphere and quantum gates is the phase of the qubit. The phase will generally “point” in the same direction as the arrow. If we look at the equation, phi is the angle of the arrow on the 2D (x and y axes) plane. The phase is very important...
The Z gate was applied after a Hadamard gate.
I hope that this article was a nice introduction to quantum gates and some of the math behind it. There are many things I could not mention or explain in this article for the sake of time and staying on-topic but this is the groundwork to start learning more concepts.
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# A sports retailer ordered white and yellow tennis balls
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21 Feb 2013, 07:15
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A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
A. 180
B. 130
C. 140
D. 160
E. 120
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Re: A sports retailer ordered white and yellow tennis balls [#permalink]
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21 Feb 2013, 07:21
antoxavier wrote:
A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
A. 180
B. 130
C. 140
D. 160
E. 120
White:Yellow = x:(x+50) = 8:13 --> 13x = 8x + 400 --> x = 80.
The total # of balls originally x + x = 80 + 80 = 160.
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Re: A sports retailer ordered white and yellow tennis balls [#permalink]
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21 Feb 2013, 07:30
Bunuel wrote:
White:Yellow = x:(x+50) = 8:13 --> 13x = 8x + 400 --> x = 80.
The total # of balls originally x + x = 80 + 80 = 160.
Bunuel's algebraic solution above is perfectly correct. You can also solve this question using the concept if you don't like algebra or if you think it's faster:
The ratio of white:yellow balls was supposed to be even, i.e. 1:1 or 2:2 or 8:8, before the extra 50 yellow balls arrived. This means that the number of white balls is unchanged in the new ratio so 8:13 implies that the difference between 13 and 8 (aka 5 units) is representing 50 yellow balls. Each unit in this ratio thus represents 10 balls of indiscriminate colour, making the original 8:8 ratio represent 80 white balls and 80 yellow balls: 160 overall. Answer D.
Algebra never fails in these problems but it is time-consuming for some people, so if you can solve a question multiple ways, you're more flexible on test day to solve tricky or new question types.
Hope this helps
-Ron
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Re: A sports retailer ordered white and yellow tennis balls [#permalink] 21 Feb 2013, 07:30
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# A sports retailer ordered white and yellow tennis balls
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Apr 29, 2020 · 7 min read
Mathematics is the foundation of Machine Learning, and its branches such as Linear Algebra, Probability, and Statistics can be considered as integral parts of ML. As a Computer Science and Engineering student, one of the questions I had during my undergraduate days was in which ways the knowledge that was acquired through math courses can be applied to ML and what are the areas of mathematics that play a fundamental role in ML. I believe this is a common question among most of the people who are interested in Machine Learning. Therefore, I decided to write a blog series on some of the basic concepts related to “Mathematics for Machine Learning”. In this series, my intention is to provide some directions into which areas to look at and explain how those concepts are related to ML. I am not going deep into the concepts and I believe there are a lot of resources with quite good examples that explain each of these concepts in a detailed manner.
As the first step, I would like to write about the relationship between probability and machine learning. In machine learning, there are probabilistic models as well as non-probabilistic models. In order to have a better understanding of probabilistic models, the knowledge about basic concepts of probability such as random variables and probability distributions will be beneficial. I will write about such concepts in my next blog. However, in this blog, the focus will be on providing some idea on what are probabilistic models and how to distinguish whether a model is probabilistic or not.
# What are Probabilistic Machine Learning Models?
In order to understand what is a probabilistic machine learning model, let’s consider a classification problem with N classes. If the classification model (classifier) is probabilistic, for a given input, it will provide probabilities for each class (of the N classes) as the output. In other words, a probabilistic classifier will provide a probability distribution over the N classes. Usually, the class with the highest probability is then selected as the Class for which the input data instance belongs.
However, logistic regression (which is a probabilistic binary classification technique based on the Sigmoid function) can be considered as an exception, as it provides the probability in relation to one class only (usually Class 1, and it is not necessary to have “1 — probability of Class1 = probability of Class 0” relationship). Because of these properties, Logistic Regression is useful in Multi-Label Classification problems as well, where a single data point can have multiple class labels.
Some examples for probabilistic models are Logistic Regression, Bayesian Classifiers, Hidden Markov Models, and Neural Networks (with a Softmax output layer).
If the model is Non-Probabilistic (Deterministic), it will usually output only the most likely class that the input data instance belongs to. Vanilla “Support Vector Machines” is a popular non-probabilistic classifier.
Let’s discuss an example to better understand probabilistic classifiers. Take the task of classifying an image of an animal into five classes — {Dog, Cat, Deer, Lion, Rabbit} as the problem. As input, we have an image (of a dog). For this example, let’s consider that the classifier works well and provides correct/ acceptable results for the particular input we are discussing. When the image is provided as the input to the probabilistic classifier, it will provide an output such as (Dog (0.6), Cat (0.2), Deer(0.1), Lion(0.04), Rabbit(0.06)). But, if the classifier is non-probabilistic, it will only output “Dog”.
# Why probabilistic ML models?
One of the major advantages of probabilistic models is that they provide an idea about the uncertainty associated with predictions. In other words, we can get an idea of how confident a machine learning model is on its prediction. If we consider the above example, if the probabilistic classifier assigns a probability of 0.9 for ‘Dog’ class instead of 0.6, it means the classifier is more confident that the animal in the image is a dog. These concepts related to uncertainty and confidence are extremely useful when it comes to critical machine learning applications such as disease diagnosis and autonomous driving. Also, probabilistic outcomes would be useful for numerous techniques related to Machine Learning such as Active Learning.
# Objective Functions
In order to identify whether a particular model is probabilistic or not, we can look at its Objective Function. In machine learning, we aim to optimize a model to excel at a particular task. The aim of having an objective function is to provide a value based on the model’s outputs, so optimization can be done by either maximizing or minimizing the particular value. In Machine Learning, usually, the goal is to minimize prediction error. So, we define what is called a loss function as the objective function and tries to minimize the loss function in the training phase of an ML model.
If we take a basic machine learning model such as Linear Regression, the objective function is based on the squared error. The objective of the training is to minimize the Mean Squared Error / Root Mean Squared Error (RMSE) (Eq. 1). The intuition behind calculating Mean Squared Error is, the loss/ error created by a prediction given to a particular data point is based on the difference between the actual value and the predicted value (note that when it comes to Linear Regression, we are talking about a regression problem, not a classification problem).
The loss created by a particular data point will be higher if the prediction gives by the model is significantly higher or lower than the actual value. The loss will be less when the predicted value is very close to the actual value. As you can see, the objective function here is not based on probabilities, but on the difference (absolute difference) between the actual value and the predicted value.
Here, n indicates the number of data instances in the data set, y_true is the correct/ true value and y_predict is the predicted value (by the linear regression model).
When it comes to Support Vector Machines, the objective is to maximize the margins or the distance between support vectors. This concept is also known as the ‘Large Margin Intuition’. As you can see, in both Linear Regression and Support Vector Machines, the objective functions are not based on probabilities. So, they can be considered as non-probabilistic models.
On the other hand, if we consider a neural network with a softmax output layer, the loss function is usually defined using Cross-Entropy Loss (CE loss) (Eq. 2). Note that we are considering a training dataset with ’n’ number of data points, so finally take the average of the losses of each data point as the CE loss of the dataset. Here, y_i means the true label of the data point i and p(y_i) means the predicted probability for the class y_i (probability of this data point belongs to the class y_i as assigned by the model).
The intuition behind Cross-Entropy Loss is ; if the probabilistic model is able to predict the correct class of a data point with high confidence, the loss will be less. In the example we discussed about image classification, if the model provides a probability of 1.0 to the class ‘Dog’ (which is the correct class), the loss due to that prediction = -log(P(‘Dog’)) = -log(1.0)=0. Instead, if the predicted probability for ‘Dog’ class is 0.8, the loss = -log(0.8)= 0.097. However, if the model provides a low probability for the correct class, like 0.3, the loss = -log(0.3) = 0.523, which can be considered as a significant loss.
In a binary classification model based on Logistic Regression, the loss function is usually defined using the Binary Cross Entropy loss (BCE loss).
Here y_i is the class label (1 if similar, 0 otherwise) and p(s_i) is the predicted probability of a point being class 1 for each point ‘i’ in the dataset. N is the number of data points. Note that as this is a binary classification problem, there are only two classes, class 1 and class 0.
As you can observe, these loss functions are based on probabilities and hence they can be identified as probabilistic models. Therefore, if you want to quickly identify whether a model is probabilistic or not, one of the easiest ways is to analyze the loss function of the model.
So, that’s all for this article. I hope you were able to get a clear understanding of what is meant by a probabilistic model. In the next blog, I will explain some probability concepts such as probability distributions and random variables, which will be useful in understanding probabilistic models. If you find anything written here which you think is wrong, please feel free to comment. It would not only make this post more reliable, but it will also provide me the opportunity to expand my knowledge. Thanks and happy reading.
## Nerd For Tech
From Confusion to Clarification
## Nerd For Tech
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Written by
## Gathika Ratnayaka
A researcher who is trying to figure out the true nature of the journey called existence, and the purpose of this city named life.
## Nerd For Tech
NFT is an Educational Media House. Our mission is to bring the invaluable knowledge and experiences of experts from all over the world to the novice. To stay up to date on other topics, follow us on LinkedIn. https://www.linkedin.com/company/nerdfortech
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Get the Medium app | 2,168 | 10,382 | {"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} | 3.453125 | 3 | CC-MAIN-2021-21 | latest | en | 0.960658 |
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JB/135/080/002
Completed
Decimal Fractions
To reduce a Vulgar
Fraction into a decimal.
Annex Cyphers to the
numerator till it be
equal to or greater than
the denominator then
divide by the denominator
and the the quotient will
be the decimal sought.
If after you have
made use of all the
Cyphers annexed to the
numerator there is a
remainder annex Cyphers
thereto and continue your
division till it divide off
or arrive to what degree
of exactness you think
proper.—
Always observe to
set a point betwixt the
numerator and the Cyphers
annexed thereto and that
the quotient have as
many places as you annex
Cyphers to the numerator
and remainders; and if
it be deficient let the
want be supplied by prefixing
as many Cyphers
to the quotient as it falls
short.—
Those decimals
that are reduced from
such a Vulgar Fraction
whose numerator with
Cyphers annexed is an
aliquot part of or can
be measured by its denominator
are finite or
determinate decimals.—-
as No fraction will
produce a finite decimal
but such whose denominator
is 2 or 5 and
their multiples.—-
---page break---
But such as are produced
from a Vulgar fraction
whose numerator with
Cyphers annexed is no
aliquot part of or cannot
be measured by its denominator
will be indeterminate
or endless.—-
In circulating decimals
if one figure only
repeats it is called a
single repetend.—
To avoid the trouble
of writing down unnecessary
figures a single
repetend is denoted by
the repeating digit dashed.
Those decimals in
which two or more figures
circulate are called compound
repetends & the manner
of distinguishing
them is by dashing the
first and last figure of
the repetend by which
means we make one
place of the repetend
sufficient.—
To reduce Coin Weights
Measures &c into decimals.
Reduce the different species
into one viz the lowest
denomination they consist
of for a dividend then
reduce the integer into
the same denomination
for a divisor; the result
will be the decimal
required.—
Write the given denominations
or parts orderly
under each other the
inferior or least parts being
uppermost let these be the
dividends.—
---page break---
Against each part on
the left hand write the
number thereof contained
in one of its superior
let these be the divisors.
The begininning
with the upper one write
the quotient of each division
as decimal parts on the
right hand of the dividend
next below it, and let
this mixed number be
divided by its divisor &c
till all be finished and
the last quotient will be
the decimal sought. —
The decimal may
be readily found by the
rule of practice namely
by considering the next
inferior denomination as
aliquot parts of the integer
and those still lower as
aliquot parts of the superior
ones or of each other
the Sum of all those
aliquot parts will be the
decimal required.—
To reduce any decimal
into the equivalent
known parts of Coin Weight
or Measure -
Multiply the given
number by the number
of Units contained in the
next inferior denomination
cutting off as many figures
from the product as the
given decimal consists of
then multiply the remaining
parts if any by the
next lower denomination
cutting off as before and
thus proceed till you have
or come to the lowest part and
---page break---
and the several figures
to the left hand of the
separating points will
be the several parts of t
he quantity required—
To reduce a decimal
into its least equivalent
Vulgar Fraction—
1st if the decimal be finite.
Under the given decimal
write an Unit with as many
Cyphers as the decimal
consists of Places then divide
both the numerator
and denominator by the
greatest common measure
which gives the least equivalent
Vulgar Fraction required
2d. If the given decimal be
a repetend—
The decimal is the
numerator of a Vulgar
Fraction whose denominator
consists of as many
nines as there are
recurring places in the
given decimal both
which divide by their
greatest common measure
as before and their
quotient will be the least
equivalent Vulgar Fraction.
3d. When the given decimal
is part final and part a
circulate.
To as many nines
as there are figures in
the repetend annex as
many cyphers as there
are finite places for a
denominator then multiply
the nines in the said
denominator by the finite
part & and to the product add the
repeating decimal for a nu
---page break---
numerator these divided
by their greatest common
measure, will give the
least equivalent fraction.
A general rule for reducing
decimal into Vulgar
Fractions—
Under the given decimal
set an Unit with as many
cyphers as there are
places in the given decimal
then set the finite
decimal as a numerator
even under the lowest figures
of the first numerator
with its proper denominator;
lastly subtract
the under numerator from
the upper one and the under
denominator from the
upper one the remainder
will be a Vulgar fraction
equivalent to the given decimal
which reduce to its
lowest terms.—
When decimal fractions
are to be added together
observe that the commas
be placed directly underneath
each other for the
primes seconds thirds &c
willl fall under those of
the same name and in
mixed number Units
will fall under Units
tens under tens &c.—
To add finite decimals
Add as in whole numbers
and from the Sum or difference
cut off so many
places for decimals as are
equal to the greatest number
of decimal places in
any of the given numbers.—
Identifier: | JB/135/080/002
"JB/" can not be assigned to a declared number type with value 135.
135
080
decimal fractions
002
private material
2
recto
sir samuel bentham
1798
1798
46198 | 1,423 | 5,757 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2024-38 | latest | en | 0.920936 |
https://numberworld.info/2011034214 | 1,638,228,722,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358847.80/warc/CC-MAIN-20211129225145-20211130015145-00558.warc.gz | 501,240,200 | 5,415 | # Number 2011034214
### Properties of number 2011034214
Cross Sum:
Factorization:
2 * 3 * 3 * 7 * 19 * 47 * 61 * 293
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
77ddf266
Base 32:
1rtrsj6
sin(2011034214)
-0.66119654553302
cos(2011034214)
0.75021272194972
tan(2011034214)
-0.88134541868957
ln(2011034214)
21.421914961018
lg(2011034214)
9.303419459371
sqrt(2011034214)
44844.556124462
Square(2011034214)
### Number Look Up
Look Up
2011034214 which is pronounced (two billion eleven million thirty-four thousand two hundred fourteen) is a very impressive number. The cross sum of 2011034214 is 18. If you factorisate the figure 2011034214 you will get these result 2 * 3 * 3 * 7 * 19 * 47 * 61 * 293. The number 2011034214 has 192 divisors ( 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 38, 42, 47, 57, 61, 63, 94, 114, 122, 126, 133, 141, 171, 183, 266, 282, 293, 329, 342, 366, 399, 423, 427, 549, 586, 658, 798, 846, 854, 879, 893, 987, 1098, 1159, 1197, 1281, 1758, 1786, 1974, 2051, 2318, 2394, 2562, 2637, 2679, 2867, 2961, 3477, 3843, 4102, 5274, 5358, 5567, 5734, 5922, 6153, 6251, 6954, 7686, 8037, 8113, 8601, 10431, 11134, 12306, 12502, 13771, 16074, 16226, 16701, 17202, 17873, 18459, 18753, 20069, 20862, 24339, 25803, 27542, 33402, 35746, 36918, 37506, 38969, 40138, 41313, 48678, 50103, 51606, 53619, 54473, 56259, 60207, 73017, 77938, 82626, 96397, 100206, 107238, 108946, 112518, 116907, 120414, 123939, 125111, 146034, 160857, 163419, 180621, 192794, 233814, 247878, 250222, 261649, 289191, 321714, 326838, 339587, 350721, 361242, 375333, 381311, 490257, 523298, 578382, 679174, 701442, 750666, 762622, 784947, 840031, 867573, 980514, 1018761, 1125999, 1143933, 1569894, 1680062, 1735146, 1831543, 2037522, 2251998, 2287866, 2354841, 2377109, 2520093, 3056283, 3431799, 3663086, 4709682, 4754218, 5040186, 5494629, 5880217, 6112566, 6863598, 7131327, 7560279, 10989258, 11760434, 14262654, 15120558, 15960589, 16483887, 17640651, 21393981, 31921178, 32967774, 35281302, 42787962, 47881767, 52921953, 95763534, 105843906, 111724123, 143645301, 223448246, 287290602, 335172369, 670344738, 1005517107, 2011034214 ) whith a sum of 5459650560. 2011034214 is not a prime number. The figure 2011034214 is not a fibonacci number. The figure 2011034214 is not a Bell Number. 2011034214 is not a Catalan Number. The convertion of 2011034214 to base 2 (Binary) is 1110111110111011111001001100110. The convertion of 2011034214 to base 3 (Ternary) is 12012011010010022200. The convertion of 2011034214 to base 4 (Quaternary) is 1313313133021212. The convertion of 2011034214 to base 5 (Quintal) is 13104311043324. The convertion of 2011034214 to base 8 (Octal) is 16767371146. The convertion of 2011034214 to base 16 (Hexadecimal) is 77ddf266. The convertion of 2011034214 to base 32 is 1rtrsj6. The sine of the figure 2011034214 is -0.66119654553302. The cosine of 2011034214 is 0.75021272194972. The tangent of 2011034214 is -0.88134541868957. The square root of 2011034214 is 44844.556124462.
If you square 2011034214 you will get the following result 4044258609878597796. The natural logarithm of 2011034214 is 21.421914961018 and the decimal logarithm is 9.303419459371. I hope that you now know that 2011034214 is very impressive number! | 1,487 | 3,386 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-49 | latest | en | 0.47021 |
http://stackoverflow.com/questions/6582189/subset-data-for-a-day-if-data-between-two-hours-of-the-day-meets-criteria | 1,427,865,523,000,000,000 | text/html | crawl-data/CC-MAIN-2015-14/segments/1427131303466.87/warc/CC-MAIN-20150323172143-00092-ip-10-168-14-71.ec2.internal.warc.gz | 274,610,019 | 17,840 | # subset data for a day if data between two hours of the day meets criteria?
I’m fairly new to R and it would be great if you could help out with this problem as i havent been able to find any answers to this problem online. This is part of my data frame (DF) (it goes on until 2008 in this format)
``````Counter Date Hour counts
1245 26/05/2006 0 1
1245 26/05/2006 100 0
1245 26/05/2006 200 2
1245 26/05/2006 300 0
1245 26/05/2006 400 5
1245 26/05/2006 500 3
1245 26/05/2006 600 9
1245 26/05/2006 700 10
1245 26/05/2006 800 15
``````
This is my question: I need to subset my code so that between the hours of 600 and 2200 if there are counts over 0 then I need to keep the whole day (000 to 2300) in the data set, but if there are no counts in the specified time period (600 to 2200) then the whole day needs to be deleted. How can I do this?
I tried to do this with the following piece of code, although it takes ONLY the counts data between 600 and 2200 hours and i can't figure out how to make it take the whole day.
``````DF2=DF[(DF\$hour>=600)&(DF\$hour<=2200)&(DF\$counts>0),] ##16hr worth of counts from 600 to 2200
``````
I’m then subsetting the data where hourly counts are aggregated into daily counts using the following code
``````daily=subset(DF2)
daily\$date = as.Date(daily\$date, "%m/%d/%Y")
agg=aggregate(counts~ date, daily, sum)
town=merge(agg,DF2\$counter,all=TRUE)
``````
-
Try this:
``````TDF <- subset(DF, hour>=600 & hour<=2200)
# get dates where there at least one hour with count data in range
dates <- subset(aggregate(counts~Date,TDF,sum),counts>0)\$Date
# get dates where there are no hours with zero count
dates2 <- subset(aggregate(counts~Date,TDF,prod),counts>0)\$Date
DF2 <- subset(DF,Date %in% dates)
DF3 <- subset(DF,Date %in% dates2)
``````
-
Thanks for your speedy response @James. It works perfectly for days where there is >0 between 600 and 2200. If I wanted to alter the code so that those days for which there are at least hourly count data for EACH hour between 600 and 2200 (so if there is 0 counts at 900 this would mean the day isn’t included in the subset), is there is a simple addition to this? Again, thanks so much for your help! – Katie_S Jul 5 '11 at 14:15
@Katie_S Yes, just use `prod` instead of `sum` in the `aggregate` statment. I'll update the answer. – James Jul 5 '11 at 14:23
thats brilliant thanks! – Katie_S Jul 6 '11 at 10:15
``````install.packages(plyr)
library(plyr)
ddply(DF, .(Date), function(day) {
if (sum(day\$hour >=600 & day\$hour <= 2200) > 0) day
else subset(day, hour == -1)
})
``````
`ddply` will group entries in `DF` by `Date`, then for every group, if there is an entry with hour between 6000 and 2200, return that day; otherwise return an empty data frame. `ddply` will then combine all groups into a resulting data frame.
-
Thanks for your reply @rafalotufo, i get this message when i try using plyr 'Error in .fun(piece, ...) : object 'Hour' not found' I'm not sure why this is coming up as Hour is in the data frame. – Katie_S Jul 5 '11 at 15:10
I fixed my code. Should have used `day\$Hour`. – rafalotufo Jul 7 '11 at 2:43
Thanks @rafalotufo, after playing around with it i realised that was the issue. – Katie_S Jul 7 '11 at 13:01 | 1,044 | 3,282 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2015-14 | latest | en | 0.866965 |
https://moorejustinmusic.com/guidelines/what-is-the-speed-to-escape-earth-gravity/ | 1,719,093,992,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862420.91/warc/CC-MAIN-20240622210521-20240623000521-00502.warc.gz | 348,860,799 | 8,759 | # What is the speed to escape Earth gravity?
## What is the speed to escape Earth gravity?
11.19 km/s.
The escape velocity of Earth is 11.19 km/s.
What is the orbital speed of Earth?
30 kilometers per second
As schoolchildren, we learn that the earth is moving about our sun in a very nearly circular orbit. It covers this route at a speed of nearly 30 kilometers per second, or 67,000 miles per hour.
At what altitude does gravity become zero?
Near the surface of the Earth (sea level), gravity decreases with height such that linear extrapolation would give zero gravity at a height of one half of the Earth’s radius – (9.8 m·s−2 per 3,200 km.)
### Why do you have to go so fast to escape Earth gravity?
Earth’s gravitational pull is slowing you down, but as your distance from Earth increases, that pull weakens. If you were initially travelling at less than the escape velocity then eventually Earth’s pull would be enough to bring you to a stop and from then you on you would fall back to Earth.
How to convert kilometers per second to miles per hour?
Kilometers per second to Miles per hour Conversion Example. Task: Convert 75 kilometers per second to miles per hour (show work) Formula: km/s ÷ 0.00044704 = mph Calculations: 75 km/s ÷ 0.00044704 = 167,770.2219040802 mph Result: 75 km/s is equal to 167,770.2219040802 mph.
How to convert speed to meters per second?
Where S is our starting value, C is our conversion factor, and E is our end converted result. To simply convert from any unit into meters per second, for example, from 5 mph, just multiply by the conversion value in the right column in the table below.
## Which is the unit of speed for kilometers per second?
Kilometers per second is a unit of Speed or Velocity in the Metric System. It measures the number of kilometers traveled in a second.
What does it mean to walk at 2 m / s?
Speed is the rate of change in position of an object, regardless of direction of travel. Walk forward or backward at 2 meters per second, and your speed is just that: 2 m/s. | 487 | 2,045 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2024-26 | latest | en | 0.911054 |
https://edurev.in/course/quiz/attempt/7824_Test-Number-Systems--Boolean-Algebra-Sequential-Lo/b743b29e-495e-4934-9074-3ba2ba62f5a8 | 1,652,771,279,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00342.warc.gz | 290,446,624 | 43,864 | # Test: Number Systems, Boolean Algebra & Sequential Logic Circuits
## 20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Number Systems, Boolean Algebra & Sequential Logic Circuits
Description
Attempt Test: Number Systems, Boolean Algebra & Sequential Logic Circuits | 20 questions in 60 minutes | Mock test for Railways preparation | Free important questions MCQ to study GATE Electrical Engineering (EE) 2023 Mock Test Series for Railways Exam | Download free PDF with solutions
QUESTION: 1
Solution:
QUESTION: 2
### If (211)x = (152)8 , then the value of base x is
Solution:
In general, since we are comfortable dealing with Decimal system, the best way to go about under the circumstances is to convert one Number into decimal Number and then with the base x, convert another Number into Decimal Number and equate them to find the value of x.
So, (152)8 is 64*1+8*5+2, which is 106 in Decimal System.
(211)x is 2x^2+ 1*x+1 in Decimal System.
Now, we solve 2x^2+x+1 = 106
i. e. 2x^2+x-105=0
Therefore 2x^2–14x+15x-105=0
Therefore 2x(x-7)+15(x-7)=0
Therefore (x-7)(2x+15)=0
Therefore either x = 7 or x = -15/2.
Obviously x = -15/2 isnot the answer. So, x = 7 is the answer, which can be very easily verified. 2*7^2+1*7+1 = 106 which issame as (152)8.
Thus the base for 211 is 7.
QUESTION: 3
### 11001, 1001 and 111001 correspond to the 2’s complement representation of the following set of numbers
Solution:
All are 2’s complement of 7
QUESTION: 4
A signed integer has been stored in a byte using 2’s complement format. We wish to store the same integer in 16-bit word. We should copy the original byte to the less significant byte of the word and fill the more significant byte with
Solution:
See a example
QUESTION: 5
A computer has the following negative numbers stored in binary form as shown. The wrongly stored number is
Solution:
QUESTION: 6
The circuit shown in fig. is
Solution:
From table it is clear that it is a MOD–3 counter.
QUESTION: 7
The counter shown in fig. is
Solution:
It is a down counter because 0 state of previous FFs change the state of next FF. You may trace the following sequence, let initial state be000
QUESTION: 8
The counter shown in fig. counts from
Solution:
It is a down counter because the inverted FF output drive the clock inputs. The NAND gate will clear FFs A and B when the count tries to recycle to 111. This will produce as result of 100. Thus the counting sequence will be 100, 011, 010, 001, 000, 100 etc.
QUESTION: 9
The mod-number of the asynchronous counter shown in fig. is
Solution:
It is a 5 bit ripple counter. At 11000 the output of NAND gate is LOW. This will clear all FF. So it is a Mod 24 counter. Note that when 11000 occur, the CLR input is activated and all FF are immediately cleared. So it is a MOD 24 counter not MOD 25.
QUESTION: 10
The frequency of the pulse at z in the network shown in fig. is
Solution:
10-bit ring counter is a MOD–10, so it divides the 160 kHz input by 10. therefore, w = 16 kHz. The four-bit parallel counter is a MOD–16. Thus, the frequency at x = 1 kHz. The MOD–25 ripple counter produces a frequency at y = 40 Hz. (1 kHz/25 = 40 Hz).
The four-bit Johnson Counter is a MOD-8. This, the frequency at z = 5 Hz.
QUESTION: 11
The three-stage Johnson counter as shown in fig. is clocked at a constant frequency of fc from the starting state of Q2 Q1Q0 = 101. The frequency of output Q2 Q1Q0 will be
Solution:
We see that 1 0 1 repeat after every two cycles, hence frequency will be fc/2
QUESTION: 12
The counter shown in the fig. has initially Q2Q1Q0 = 000. The status of Q2 Q1Q after the first pulse is
Solution:
At first cycle
QUESTION: 13
A 4 bit ripple counter and a 4 bit synchronous counter are made by flips flops having a propagation delay of 10 ns each. If the worst case delay in the ripple counter and the synchronous counter be R and S respectively, then
Solution:
In ripple counter delay 4Td = 40 ns.
The synchronous counter are clocked simultaneously, then its worst delay will be equal to 10 ns.
QUESTION: 14
A 4 bit modulo–6 ripple counter uses JK flip-flop. If the propagation delay of each FF is 50 ns, the maximum clock frequency that can be used is equal to
Solution:
4 bit uses 4 FF
QUESTION: 15
The initial contents of the 4-bit serial-in-parallel-out right-shift, register shown in fig. is 0 1 1 0. After three clock pulses are applied, the contents of the shift register will be
Solution:
QUESTION: 16
Consider the signed binary number A = 01010110 and B = 1110 1100 where B is the 1’s complement and MSB is the sign bit. In list-I operation is given, and in list-II resultant binary number is given.
The correct match is
Solution:
QUESTION: 17
The simplified form of a logic function
Solution:
QUESTION: 18
If the decimal number is a fraction then its binary equivalent is obtained by ________ the number continuously by 2.
Solution:
On multiplying the decimal number continuously by 2, the binary equivalent is obtained.
QUESTION: 19
Solution:
QUESTION: 20
Solution:
Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code | 1,386 | 5,165 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2022-21 | latest | en | 0.851166 |
https://forum.arduino.cc/t/best-op-amp-for-50a-75mv-shunt/190804 | 1,656,699,140,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00197.warc.gz | 309,350,533 | 8,473 | # Best op-amp for 50a 75mv shunt.
I want to measure current between my 60v solar panel to 48v battery. I have 50a 7mv shunt.
I want to connect is on low side for current sensing.
which OP amp is best to amplify shunt drop voltage.
option are
OP07
LM741
LM386
LM324
or u can check yourself on
thanks
Do you mean amps when you say "50a" and miilivolts when you say "75mv" - the symbols
for ampere and volt are "A" and "V" respectively, the case is significant.
Normally a shunt would be described by its resistance, should we assume this is a
1.5 milliohm shunt (75mV for 50A...)?
75mV is a pretty small voltage so would require a precision opamp (you'd probably
want an input-offset voltage spec of 1mV or so - however you haven't said what resolution
and accuracy of current measurement you want - will you ever have 50A flowing?
For convenience a single-rail opamp would be convenient - precision single-rail opamps
aren't that commonplace though, doubt any of those parts are both (OP07 is precision
if I remember correctly).
The OPA320 appears to me to be a suitable op amp. It can run from a single 5V supply, has rail-rail I/O, and 150uV max input offset voltage - so the current measurement error due to input offset voltage will be 100mA max, if the shunt drops 75mV @ 50A.
However, I would consider using a Hall current sensor instead, which has the added advantage of providing isolation. If 50A is the maximum output of your solar cells, then the ACS758LCB-050U-PFF-T would be a suitable choice.
I’m a bit sceptical about needing to read 50A though, a 60V solar panel is usually limited
to the 8A or so of a typical 6-inch wafer in full sun, and 120 wafers is a huge panel, more
likely 5 inch or smaller wafers or half wafers, so lower current.
Is the solar array 3KWs?
50 * 60 = 3000
That seems like a reasonable moderate size but I have no solar experience.
Isolation is a good idea when bringing power level signals into sensitive electronics even if you are working on the low side. There are many ways to do that.
The op-amps you have selected are not very good for the reasons dc42 gave: poor input offset, lack of rail to rail performance, split supplies. I agree that the OPA320 is good choice. With calibration, you should be able to get 1% or better resolution and accuracy.
http://www.ecircuitcenter.com/Circuits/instamp1/instamp1.htm
Hi look this up guys, an instrument amplifier is the best way to amplify a low level DC, the circuit is designed to counteract drift and offset.
You can also adjust offset and gain.
Tom.......
Normally a shunt would be described by its resistance, should we assume this is a
1.5 milliohm shunt (75mV for 50A...)?
Actually, ( and unreasonably as it seems, to me ), 75mV seems to be the standard industry terminology.
michinyon:
Normally a shunt would be described by its resistance, should we assume this is a
1.5 milliohm shunt (75mV for 50A...)?
Actually, ( and unreasonably as it seems, to me ), 75mV seems to be the standard industry terminology.
Ah, yes, a bit specialist, but I see the reason, people buy different shunts for the same
meter and the meter assumes a particular FSD voltage level. Still if you own a meter and
are buying a shunt you really ought to be fluent in ohm's law!
The problem is not "knowing Ohm's law". The problem is, is that 75 mV specification, the voltage drop across the shunt at full scale ( 30 Amps ), or is it 75 mV per Amp ? It could reasonably be either.
There are special devices designed for amplifying current shunts. Here is one that says is will work with high or low side shunts.
Supplier search terms are current sense amplifier, IC OPAMP CURR SENSE, or current shunt amplifer. Try the popular vendors.
Here is page at TI
here is a page at LT:
There is a wide variety. Note that many are for high side measurement. This is because many systems require a low impedance ground and cannot tolerate a current shunt in the ground path.
I've used shunts, Hall Effect devices of several different types and currrent transformers (UggH)... I currently own 12 LEM HAL 300-S that are great because the offset and gain are adjustable, Although for a higher current load, it is a bi-lateral sensing device and so measures current in both directions and is accurate to +/- 5% DC to 50 KHz.
For smaller work Ebay sells the Allegro ACS712ELCTR-30A-T +/- 30 A at 50 KHZ for not so very much money US \$3.80
and this one for \$4.00 http://www.ebay.com/itm/111085883206 (5 A version) there are 3 ranges 5, 20 and 30A
There is also the ACS756 for 50A + and can be purchased on a PCB with screw terminals.
Doc
Doc and Docedison have suggested Hall effect sensors. They do not require a shunt. The Allegro ACS756KCA-050B-PFF-T available in distibution for \$6.50 each which is about the price of the 50A shunt. The datasheets look like the parts are super simple to use. They are isolated. This is clearly a very good choice. | 1,281 | 4,938 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-27 | latest | en | 0.935053 |
http://mathhelpforum.com/differential-equations/189938-find-curve-has-tangent-normal-lines-create-triangle.html | 1,481,409,942,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543577.51/warc/CC-MAIN-20161202170903-00195-ip-10-31-129-80.ec2.internal.warc.gz | 177,182,563 | 10,693 | # Thread: Find curve that has tangent and normal lines that create a triangle
1. ## Find curve that has tangent and normal lines that create a triangle
Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x axis a triangle whose area is equal o the slope of the tangent line. Assume y` > 0 and y > 0.
Hint: integral( sqrt(a^2 - u^2) / u du = sqrt(a^2-u^2) - a*ln | [a+sqrt(a^2-u^2)] / u | + C
(sorry, I don't know how to use the math writer yet)
This is a question from an introductory differential equations class. I have absolutely no idea how to do this! I haven't really gotten anywhere yet. This is what I've done:
let f(x) denote the curve we're looking for. Then the tangent line will have equation:
y_t = df/dx * x + C
Normal line will have equation y_n = -1/(df/dx) * x + k
Together they will form a triangle with area = df/dx, at any point on f(x). I wanted to find an expression for area in terms of df/dx, simplify it, and solve the resulting differential equation, but I can't figure out a DE for the area! I'm getting very frustrated, as we've never been shown a question like this in lecture, and I can't find any examples in my textbook.
Help would be very much appreciated!
2. ## Re: Find curve that has tangent and normal lines that create a triangle
I would assign some x-values if I were you. Suppose $x_{0}$ is the point at which you're taking the tangent and normal lines (which we will eventually need to be able to move, so just think of it as "temporarily constant"), let $x_{1}$ be the x-intercept of the tangent line, and let $x_{2}$ be the x-intercept of the normal line. Because you have assumed $y'>0$ and $y>0,$ you know that $x_{2}>x_{1}.$ Why?
Then you want to set
$\frac{y(x_{0})(x_{2}-x_{1})}{2}=y'(x_{0}).$
Your goal is to eliminate $x_{1}$ and $x_{2}.$ How can you do that? | 521 | 1,900 | {"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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2016-50 | longest | en | 0.952335 |
https://www.jiskha.com/search/index.cgi?query=physics%28+i+have+no+idea+how+to+go+about+gettign+th&page=49 | 1,513,318,576,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948567042.50/warc/CC-MAIN-20171215060102-20171215080102-00695.warc.gz | 764,891,307 | 16,342 | # physics( i have no idea how to go about gettign th
163,123 results, page 49
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Chinook salmon are able to move through water especially fast by jumping out of the water periodically. This behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with velocity 6.41 m/s at 44.1° above the horizontal, sails through the ...
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In Stranger in a Strange Land, Robert Heinlein claims that travelers to Mars spent 258 days on the journey out, the same for return, \plus 455 days waiting at Mars while the planets crawled back into positions for the return orbit." Show that travelers would have to wait about...
### physics
PLEASE HELP!! I HAVE A TEST TOMORROW!! if Q=30 uC, q=5.0 uC, and d=30cm, what is the magnitude of the electrostatic force on q in N? (Ke= 8.99 x 10^9 Nm^2/C^2) (uC= micro coulombs) (u= 10^-6) a. 15 b. 23 c. zero d. 7.5 e 38 i don't know where to start with this problem. i don'...
### physics
You remove two socks from a hot dryer and find that they repel with forces of 0.003 N when they’re 4 cm apart. If they have equal charges, how much charge does each sock have?
### Chemistry - Energy Phase Changes
Calculate the quantity of heat gained or lost in the following change: 0.44 mol of water evaporates at 100 degrees Celsius - So what I did was: 1 mol -> 6.01 kJ 0.44 mol -> x x = 2.64 kJ of energy gained But apparently this is incorrect? Could somebody please explain to ...
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Among the factors that brought about European colonialism, which of the following supported concepts of racial superiority? A. The introduction of the steam engine and the telegraph B. Social Darwinism C. Economic and trade opportunities D. the machine gun I have read till I ...
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Between each pair of vertebrae in the spinal column is a cylindrical disc of cartilage. Typically, this disc has a radius of about 2.6 x 10-2 m and a thickness of about 1.4 x 10-3 m. The shear modulus of cartilage is 1.2 x 107 N/m2. Suppose a shearing force of magnitude 18 N ...
### physics
Between each pair of vertebrae in the spinal column is a cylindrical disc of cartilage. Typically, this disc has a radius of about 2.85 10-2 m and a thickness of about 7.14 10-3 m. The shear modulus of cartilage is 1.16 107 N/m2. Suppose that a shearing force of magnitude 10 N...
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Coal has about 2% sulfur. How many kilograms of sulfur would be emitted from coalfired power plants in the United States in 1 yr? (U.S. electricity production is about 0.28 × 1012 watts, and coal has an energy content of about 30 × 106 J/kg. Note that 1 J = 1W-sec.)
### Math
I am trying to help my child with this problem and I have no idea what to do to solve this word problem. Paul used 1 1/4 gallons of paint to cover 3/8 of the walls in his living room. How many gallons of paint will Paul need to paint all the walls in his living room?
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Is the Freedom of the Press still a right worth preserving? What do you think? Personally I think it is although I believe the "press" sometimes abuse the right. I think the press speaks too much. I don't know. I mean all that is on the news is about overseas - Newspapers tell...
### English 2
I had to write a persuasive essay about a debatable issue and I chose to write about the Ground Zero Mosque. This is just my rough draft, so I know it's not near perfect; but can someone please tell me what I need to add/remove, etc. ? Thanks! Is building a mosque on or near ...
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A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2....
### Physics
A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2....
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Ms. Allison drew a box-and-whisker plot to represent her students scores on a midterm test. These are the numbers on the box-and-whisker plot. Lowest value=44 Lower quartile=47 Median=52 Upper quartile=81 Highest value=96 Jason received 81 on the test. How does Jason's score ...
### maths
Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does not change. C. A particle which has zero ...
### English
1. You may have a jellyfish at the right top in the picture. 2. You may have a jellyfish at the top right in the picture. 3. You may have a jellyfish on the right top in the picture. 4. You may have a jellyfish on the top right in the picture. 5. You may have a hawkfish in a ...
### Philosphy
Hill claims that a fruitful way to think about the badness of destroying the environment is: To think about what kind of human would choose to destroy the earth. To appeal to theories about God and care for the earth. To examine people’s intuitions about whether it is right ...
### english
i was wondering if i did this correct Each of the following exercises shows the original source, and then a student’s sentence and/or citation about that source. Each sentence and each citation has at least one thing wrong with it (most have more than one). Each of the ...
### College Physic
The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 9.58 s, at which time it is turning at 3.89 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly ...
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Issue Sources Health/Environmental Effects Carbon dioxide (CO2) Chlorofluorocarbons (CFCs) Ground-level ozone (O3) Sulfuric acid (H2SO4) I need to complete the table above and have no idea what to do. Choose one of the following atmospheric issues: air pollution, global ...
### Math
Statistics Help Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronaus can choose from 10 main dishes, 8 vegetable dishes, and 13 desserts. How many ...
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When did people stop using parchment and start using paper? These sites will give you the history of paper: (Broken Link Removed) http://inventors.about.com/library/inventors/blpapermaking.htm I'm not really sure as to the answer. You see, I'm writing a story that takes place ...
A violin string has a length of 0.350 m and is tuned to concert G, with f = 392 Hz. Where must the violinist place her finger to play concert A, with f = 430 Hz? If this position is to remain correct to half the width of a finger (that is, to within 0.600 cm), what is the ...
A violin string has a length of 0.350 m and is tuned to concert G, with f = 392 Hz. Where must the violinist place her finger to play concert A, with f = 430 Hz? If this position is to remain correct to half the width of a finger (that is, to within 0.600 cm), what is the ...
I do not have any Idea how to set this up. Please walk me through the steps. A.) If a customer buys x copies then he or she pays \$500 sqrt x. it cost the company \$10,000 to develop the program and \$2 to manufacture each copy. If a single customer were to buy all the copies of ...
### geography
one difference of the Canadian shield and the Western Cordillera My work And now forget about the similarities on to the differences. There are many differences about the Canadian Shield and the Western Cordillera but for today I’ll keep it snappy and only do three. So here ...
### Ethics
What information about race and ethnicity in the United States has helped you better understand or relate to specific minority groups? Have you learned something new about your own cultural history? Trends in immigration will continue to shape the face of the United States. ...
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What information about race and ethnicity in the United States has helped you better understand or relate to specific minority groups? Have you learned something new about your own cultural history? Trends in immigration will continue to shape the face of the United States. ...
### managerial economics
I have no idea what e=a+bn E is the total earnings of the motion picture industry measured in dollars per year and N is the number of tickes sold in December. First question: How well do movie ticket sales in December explain the level of earnings for the entire year? Also, ...
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your are making apple pie for a school fund raiser you have 4 baskets of apples and each basket contains 11 apples each pie requires 3 1/5 apples 1 apple fills about one cup how many cups of apples do you have and how many pies can you make
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The fact that the states had to unanimously agree to changing the Articles of Confederation meant that the states would have to begin the process of making changes to the government it didn’t matter how ordinary citizens felt about the Articles of Confederation it would be ...
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Some stoves use the heat produced by current flowing through a conductor. If the heating element (conductor) has a resistance of 30 ohms, how long will the burner have to work to heat 500 g of 30°C water up to its boiling point? The specific heat of water is 4.19 x 103 J/kg...
### Literature
Hi, I just have a question about a confusing question to me in a poem that I have to answer... The poem is Annabel Lee. Here's the question they are asking: What was the effect of the repeated rhymes? I can't find an answer to the question?
### math - due tonight
a closet in your bedroom is 9 1/4 feet long 3 1/2 feet wide . and 12 feet high how much cubic feet or space does it have? About how many cubic yards of space does it have?
### Physics-Sound Waves
I'm not sure how to go about answering this question... I have all these equations and none seem to apply. The question is: If you have two speakers on opposite sides of a concert stage producing identical sound waves with a wavelength of .8m. If you consider only the direct ...
### To Dylan - re English summer essay
I just reread your posts from this morning, and I'm confused about a few things: 1. The directions clearly state that you are to write a five-paragraph paper. "In a five-paragraph essay, discuss which author was more successful in creating a good piece of literature. Use ... | 6,770 | 28,384 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2017-51 | longest | en | 0.94087 |
http://www.physicsforums.com/showthread.php?t=110093 | 1,369,397,163,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704655626/warc/CC-MAIN-20130516114415-00026-ip-10-60-113-184.ec2.internal.warc.gz | 661,473,058 | 8,749 | ## tattoo teaser
Ok, I know this is not too much of a teaser but maybe you guys could come up with something cool and original. I'm getting a tattoo and part of it has my birthdate in it. Except I don't want it to be obvious...I want some type of complicated equation with lots of mathmatical symbols etc so if someone actually worked it out the solution would be my birthdate in international time format 75-05-12 or just 750512 as the answer. Any other suggestions are welcome. The winner will have the satisfaction of knowing their art is permanently on my body
PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
Some one else asked about this a few months back. Their idea was to diagram the positions of the planets at the moment of their birth. I drew a graphic that represented it. I'll see if I can find it. If that interests you, I could probably whip up the graphic using your birthdate. Ah yes - here it is.
What time of day?
## tattoo teaser
BTW, that's May 12 right? not Dec 5?
Yeah, May 12 1975.
Here it is. Attached Thumbnails
not as simple as i'd like, but here's one with regular polygons - a triangle and 5 pentagons inscribed in a dodecagon... the 75 comes from 5 (only 1 shown here) x 5 sided figure x 3 (triangle) 5 from the pentagon 12 from the dodecagon. Best I got right now It'd look something like this, but with an actual 12 sided polygon (this one is 15 sided) Attached Thumbnails
$$750512=\frac{\int_0^{\infty}{t^{10}e^{-t}dt}}{\pi(11)}+10^4\left(\sum_{k=1}^{4}{\frac{6k}{5^k}}+\frac{383}{625 }\right)$$ ...I believe. Someone ought to check that. EDIT: Or also this... $$750512=\frac{\int_0^{\infty}{t^{10}e^{-t}dt}}{\pi(11)}+\frac{\pi^2\int_0^1{\left(\ln{\frac{1}{t}}\right)^8dt}} {12\zeta(2)}+2^4*7*41$$
That's great guys! For some reason it won't let me see the gifs though...it says I don't have permission to access those pages.
You will have to log out, view the gifs, then log back in, it is a bug here at pf. | 593 | 2,106 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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} | 3.0625 | 3 | CC-MAIN-2013-20 | latest | en | 0.939091 |
http://www.britannica.com/EBchecked/topic/1357106/principles-of-physical-science/14855/Gausss-theorem | 1,430,205,101,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246660743.58/warc/CC-MAIN-20150417045740-00283-ip-10-235-10-82.ec2.internal.warc.gz | 366,742,628 | 16,662 | # Principles of physical science
## Gauss’s theorem
At any point in space one may define an element of area dS by drawing a small, flat, closed loop. The area contained within the loop gives the magnitude of the vector area dS, and the arrow representing its direction is drawn normal to the loop. Then, if the electric field in the region of the elementary area is E, the flux through the element is defined as the product of the magnitude dS and the component of E normal to the element—i.e., the scalar product E · dS. A charge q at the centre of a sphere of radius r generates a field ε = qr/4πε0r3 on the surface of the sphere whose area is 4πr2, and the total flux through the surface is ∫SE · dS = q0. This is independent of r, and the German mathematician Karl Friedrich Gauss showed that it does not depend on q being at the centre nor even on the surrounding surface being spherical. The total flux of ε through a closed surface is equal to 1/ε0 times the total charge contained within it, irrespective of how that charge is arranged. It is readily seen that this result is consistent with the statement in the preceding paragraph—if every charge q within the surface is the source of q0 field lines, and these lines are continuous except at the charges, the total number leaving through the surface is Q0, where Q is the total charge. Charges outside the surface contribute nothing, since their lines enter and leave again.
Gauss’s theorem takes the same form in gravitational theory, the flux of gravitational field lines through a closed surface being determined by the total mass within. This enables a proof to be given immediately of a problem that caused Newton considerable trouble. He was able to show, by direct summation over all the elements, that a uniform sphere of matter attracts bodies outside as if the whole mass of the sphere were concentrated at its centre. Now it is obvious by symmetry that the field has the same magnitude everywhere on the surface of the sphere, and this symmetry is unaltered by collapsing the mass to a point at the centre. According to Gauss’s theorem, the total flux is unchanged, and the magnitude of the field must therefore be the same. This is an example of the power of a field theory over the earlier point of view by which each interaction between particles was dealt with individually and the result summed.
## Images
A second example illustrating the value of field theories arises when the distribution of charges is not initially known, as when a charge q is brought close to a piece of metal or other electrical conductor and experiences a force. When an electric field is applied to a conductor, charge moves in it; so long as the field is maintained and charge can enter or leave, this movement of charge continues and is perceived as a steady electric current. An isolated piece of conductor, however, cannot carry a steady current indefinitely because there is nowhere for the charge to come from or go to. When q is brought close to the metal, its electric field causes a shift of charge in the metal to a new configuration in which its field exactly cancels the field due to q everywhere on and inside the conductor. The force experienced by q is its interaction with the canceling field. It is clearly a serious problem to calculate E everywhere for an arbitrary distribution of charge, and then to adjust the distribution to make it vanish on the conductor. When, however, it is recognized that after the system has settled down, the surface of the conductor must have the same value of ϕ everywhere, so that E = −grad ϕ vanishes on the surface, a number of specific solutions can easily be found.
In Figure 8, for instance, the equipotential surface ϕ = 0 is a sphere. If a sphere of uncharged metal is built to coincide with this equipotential, it will not disturb the field in any way. Moreover, once it is constructed, the charge −1 inside may be moved around without altering the field pattern outside, which therefore describes what the field lines look like when a charge +3 is moved to the appropriate distance away from a conducting sphere carrying charge −1. More usefully, if the conducting sphere is momentarily connected to the Earth (which acts as a large body capable of supplying charge to the sphere without suffering a change in its own potential), the required charge −1 flows to set up this field pattern. This result can be generalized as follows: if a positive charge q is placed at a distance r from the centre of a conducting sphere of radius a connected to the Earth, the resulting field outside the sphere is the same as if, instead of the sphere, a negative charge q′ = −(a/r)q had been placed at a distance r′ = r(1 − a2/r2) from q on a line joining it to the centre of the sphere. And q is consequently attracted toward the sphere with a force qq′/4πε0r2, or q2ar/4πε0(r2a2)2. The fictitious charge −q′ behaves somewhat, but not exactly, like the image of q in a spherical mirror, and hence this way of constructing solutions, of which there are many examples, is called the method of images.
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Or click Continue to submit anonymously: | 1,622 | 7,371 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-18 | latest | en | 0.953462 |
https://study.com/academy/answer/find-the-equation-of-the-tangent-line-to-false-f-x-x-3-6-at-the-point-where-x-4.html | 1,558,825,452,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232258453.85/warc/CC-MAIN-20190525224929-20190526010929-00160.warc.gz | 641,580,911 | 25,779 | # Find the equation of the tangent line to ='false' f(x)=(x-3)^6 at the point where x=4.
## Question:
Find the equation of the tangent line to {eq}f(x)=(x-3)^6 {/eq} at the point where x=4.
## Equation of the Tangent Line:
In order to find the equation of the tangent line to the curve, we will first find the coordinates of the point where the tangent line is to be drawn. By taking the first derivative of the curve at the given point we will find the slope of the tangent line. Using the point-slope form of the equation of the line we can find the equation of the tangent line.
## Answer and Explanation:
{eq}f(x)=(x-3)^6 {/eq} at {eq}x=4 {/eq}
When {eq}x=4 {/eq}
{eq}f(x)=y=1 {/eq}
Point{eq}=(4,1) {/eq}
The slope of the tangent line is given by:
{eq}f^{'}(x)=6(x-3) \\f^{'}(x)]_{x=4}=6(4-3)=6 {/eq}
Using the point-slope form of the equation of the tangent line is:
{eq}y-1=6(x-4) \\y-1=6x-24 \\6x-y-23=0 {/eq} | 310 | 929 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2019-22 | latest | en | 0.826957 |
https://justaaa.com/statistics-and-probability/945606-a-sample-of-18-small-bags-of-the-same-brand-of | 1,713,953,075,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819089.82/warc/CC-MAIN-20240424080812-20240424110812-00719.warc.gz | 298,768,041 | 10,514 | Question
# A sample of 18 small bags of the same brand of candies was selected. Assume that...
A sample of 18 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Construct a 98% confidence interval for the population mean weight of the candies.
(i) State the confidence interval. (Round your answers to three decimal places.)
(ii) Sketch the graph.
(iii) Calculate the error bound. (Round your answer to three decimal places.)
i) At 98% confidence level, the critical value is z0.01 = 2.33
The 98% confidence interval is
ii)
iii) Margin of error is
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• Dr. Bunson Honeydew and Dr. Strangepork both wanted to know how effective TV ads were at... | 387 | 1,732 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-18 | latest | en | 0.919226 |
https://physics.stackexchange.com/questions/506618/the-mean-free-path-of-electrons-in-high-vacuum-is-26-billion-kilometres | 1,579,461,981,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00154.warc.gz | 608,992,866 | 30,642 | # The mean free path of electrons in high vacuum is 26 billion kilometres?
I used this formula to calculate the mean free path length of an electron in high vacuum.
$$\lambda = \frac{k T}{\sqrt{2}\cdot4\pi r^2 \cdot p}$$
where k is the Boltzmann konstant, T the temperature in Kelvin, r the radius of the particle in question, in m and p the pressure in pascal.
I used the following numbers:
$$k = 1.38*10^{-23}, T = 300, r \approx3*10^{-15}, p = 10^{-6}$$
Am I crazy for getting a result of
$$\lambda \approx 2.6*10^{13}m$$
I mean am I missing something? Maybe the radius of the electron changes when it moves? (Actually it moves with 50 keV but I have neglected that so far.)
I am sorry but this result seems just so....unreal. And I have to be sure because I have an exam about this stuff soon!
• You better use the size of the atoms, which is bigger, not the electron which is much smaller, so $10^{-10}$ instead of $3 ~ 10^{-15}$. – Kostas Oct 5 '19 at 20:32
• The formula you are using appears to be one that might apply to the molecules of a gas. When you speak of a high vacuum, are you referring to a low density of molecules (as in outer space) or a plasma of electrons? In either case you need a collision cross section based on the probability that the electron wave packet will interact with the other particles in your system. – R.W. Bird Oct 5 '19 at 23:36
The presence of $$r$$ in the formula you used implies that it is based a contact scattering assumption. | 396 | 1,486 | {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2020-05 | latest | en | 0.888485 |
https://it.mathworks.com/matlabcentral/cody/problems/2945-skip-by-a-multiple/solutions/2564493 | 1,600,975,479,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400219691.59/warc/CC-MAIN-20200924163714-20200924193714-00297.warc.gz | 450,496,038 | 16,494 | Cody
# Problem 2945. Skip by a multiple
Solution 2564493
Submitted on 15 Jun 2020 by jmac
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = 5; y_correct = [5:5:75]; assert(isequal(your_fcn_name(x),y_correct))
ans = 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
2 Pass
x = 13; y_correct = [13:13:195]; assert(isequal(your_fcn_name(x),y_correct))
ans = 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 | 198 | 531 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-40 | latest | en | 0.630576 |
https://learnmetrics.com/how-many-gallons-of-propane-in-a-100-lb-tank/ | 1,709,193,205,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474795.48/warc/CC-MAIN-20240229071243-20240229101243-00115.warc.gz | 350,951,056 | 78,268 | # How Many Gallons Of Propane In A 100 Lb Tank? (Answered)
Determining how many gallons does a 100 lb propane tank hold is dead simple. You just have to follow two rules. That’s it. If you know these two rules, you don’t only know how to calculate how many gallons of propane are in a 100 lb tank; you will be able to figure out the gallons of propane any propane tank contains.
Here are two rules you have to know:
1. 80% propane tank rule. Namely, every propane tank is filled up to 80% of its total capacity. Example: A 100 lb tank doesn’t hold 100 lb of propane. Rather, it contains 80 lb of propane. This is a safety requirement.
2. How much does a gallon of propane weigh in pounds (lb)? Propane density depends on temperature: at 90°F, a gallon of propane weighs 4.05 lb, and at 60°F a gallon of propane weighs 4.20 lb. You can consult how much propane weighs here.
When calculating how many gallons of propane are in a 100 lb tank, we usually take the median propane density of 4.11 lb/gallon (measured at 77°F).
Here is how much propane a 100 lb tank holds:
## How Many Gallons Of Propane Are In A 100 Pound Propane Tank?
We use the 1st rule:
A full 100 lb propane tank holds 80 lb of propane.
Now, we use the 2nd rule:
1 gallon of propane weighs 4.11 lb per gallon.
Let’s calculate how many gallons does a 100 lb propane tank hold like this:
Gallons Of Propane = Weight Of Propane / Propane Density
In the case of a 100 lb tank, this means:
Gallons Of Propane = 80 lb / 4.11 lb/gallon = 19.46 Gallons
Here you have it:
A 100 lb tank holds 19.46 gallons of propane.
Using this simple calculation, you can determine how many gallons of propane are in pretty much any propane tank.
Also be aware that if you will your propane tank at lower temperatures, you will get different results of how many gallons of propane you can put in a 100 lb tank (due to different propane densities):
• If you fill a 100 lb propane tank at 60°F, it will hold 19.05 gallons of propane.
• If you fill a 100 lb propane tank at 77°F, it will hold 19.46 gallons of propane.
• If you fill a 100 lb propane tank at 90°F, it will hold 19.75 gallons of propane.
As you can see, the higher the temperature, the more propane you can put into the tank since the propane density is lower at higher temperatures.
We hope this illustrates what amount of gallons can go into a 100 lb propane tank. If you have any questions regarding this, you can use the comments below and we’ll try to help you out.
### 2 thoughts on “How Many Gallons Of Propane In A 100 Lb Tank? (Answered)”
1. How do you know if it was over filled brought it home and gas started coming out if so what do you do | 697 | 2,685 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2024-10 | latest | en | 0.874531 |
http://christinenperiod5.blogspot.com/2014/06/ | 1,508,259,894,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187822145.14/warc/CC-MAIN-20171017163022-20171017183022-00313.warc.gz | 71,607,932 | 11,883 | ## Wednesday, June 4, 2014
### BQ #7: Unit V: Derivatives and the Area Problem
Explain in detail where the formula for the difference quotient comes from now that you know. Include all appropriate terminology (secant line, tangent line, h/delta x, etc.).
The difference quotient helps us to find the slope of a tangent line at any point. But a tangent line only touches the graph once. While the secant line touches the graph twice. In order to find the slope of a secant line, we use the slope formula m = (y2-y1)/( x2-x1). So based on the first point on the graph below it is (x,f(x)) and the second point is (x+h, f(x+h)). So now we know what y2,y1,x2,x1 are. So we just plug this into the slope formula, which is m= (f(x+h))-(f(x))/((x+h)-(x)). So on the top nothing simplifies but the bottom the 1s cancels out, which leaves us h for the denominator.
That will give us the difference quotient: Sometimes the delta x is refer to h.
http://www.infobarrel.com/Find_the_Derivative_of_a_function_by_using_the_difference_quotient_definition
Reference: | 298 | 1,057 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2017-43 | longest | en | 0.785267 |
https://findanyanswer.com/what-is-capex-intensity | 1,620,417,187,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00054.warc.gz | 271,992,776 | 8,289 | # What is capex intensity?
Asked By: Rongguang Chuecos | Last Updated: 16th April, 2020
Category: business and finance debt factoring and invoice discounting
4.3/5 (675 Views . 33 Votes)
capital intensity. Measure of a firm's efficiency in deployment of its assets, computed as a ratio of the total value of assets to sales revenue generated over a given period. Indicates how successful a firm is in utilizing its assets in generation of sales revenue.
Accordingly, what does capital intensity mean?
Capital intensity is the amount of fixed or real capital present in relation to other factors of production, especially labor. At the level of either a production process or the aggregate economy, it may be estimated by the capital to labor ratio, such as from the points along a capital/labor isoquant.
Subsequently, question is, what is considered high capex? Five companies with high capital expenditures (CAPEX) include Tesla Motors, General Motors, Apple Computer, Nike and Facebook. The capital expenditures of these five companies from different industries are compared using the CAPEX to sales ratio and free cash flow to CAPEX ratio.
Then, how do you calculate capital intensity?
Capital intensity ratio of a company is a measure of the amount of capital needed per dollar of revenue. It is calculated by dividing total assets of a company by its sales. It is reciprocal of total asset turnover ratio.
What is the capital intensity ratio at full capacity?
Capital Intensity Ratio. The capital intensity ratio reveals the amount of assets your business requires to generate \$1 in sales. It equals total assets divided by annual sales. For this ratio, a smaller figure is better.
39 Related Question Answers Found
### How is labor intensity measured?
Labor intensity may be quantified by taking a ratio of the cost of labor (i.e. wages and salaries) as a proportion of the total capital cost of producing the good or service. The higher the ratio, the higher the labor intensity. Labor intensive industries may control costs in bad economies by laying off workers.
### What is a capital intensive good?
The term "capital intensive" refers to business processes or industries that require large amounts of investment to produce a good or service and thus have a high percentage of fixed assets, such as property, plant, and equipment (PP&E).
### How is a debt ratio of 0.45 interpreted?
How is a debt ratio 0.45 interpreted? A debt ratio of . 45 means that for every dollar of assets, a firm has \$. Dee's earned more income for its common shareholders per dollar of assets than it did last year.
### Are banks capital intensive?
Definition: Capital Intensive
There are a number of examples of capital intensive industries like steel, cement, automotive, petroleum. These industries require large sum of money and capital to support their operations. Some businesses like IT, software design, banking, consulting etc.
### What is the labor intensive good?
Labor-intensive goods are those in which require a significant amount of labor to produce in labor intensive industries. A labor-intensive industry is determined by the amount of capital needed to produce these goods and normally refer to industries like food service, mining, and agriculture.
### How do you know if a company is capital intensive?
Although there is no mathematical threshold that definitively determines whether an industry is capital intensive, most analysts look to a company's capital expenses in relation to its labor expense. The higher the ratio between capital and labor expenses, the more capital intensive a business is.
### What does debt to equity ratio mean?
The debt-to-equity ratio (D/E) is a financial ratio indicating the relative proportion of shareholders' equity and debt used to finance a company's assets. Closely related to leveraging, the ratio is also known as risk, gearing or leverage.
### Is Apple capital intensive?
Apple's Technology Is Capital Intensive, And Its Production Function Is Given By F (K,L) =K3/4L1/2 The Value Of Apple's Physical Capital (machines, Real Estate, Ect ) Is Equal To K = 16 Billion (ignore Billions In Your Calculation).
### What does debt ratio mean?
The debt ratio is defined as the ratio of total debt to total assets, expressed as a decimal or percentage. In other words, the company has more liabilities than assets. A high ratio also indicates that a company may be putting itself at a risk of default on its loans if interest rates were to rise suddenly.
### What is a good asset turnover ratio?
An asset turnover ratio of 4.76 means that every \$1 worth of assets generated \$4.76 worth of revenue. In general, the higher the ratio – the more "turns" – the better. But whether a particular ratio is good or bad depends on the industry in which your company operates.
### What does a high current ratio mean?
The current ratio is an indication of a firm's liquidity. If the company's current ratio is too high it may indicate that the company is not efficiently using its current assets or its short-term financing facilities. If current liabilities exceed current assets the current ratio will be less than 1.
### What is capital intensive method of production?
Capital intensive technique refers to that technique in which larger amount of capital is comparatively used. In such a technique the amount of capital used per unit of output is larger than what it is in case of labour intensive technique.
### What is labor intensive production?
Labour-intensive production means that the way that a good or service is produced depends more heavily on labour than the other factors of production, such as capital. Labour intensive method of production is usually used for individual or personalised products, or to produce on a small scale.
### What does asset intensive mean?
"asset-intensive" means that it takes a lot of assets, whether money or materials or land or something else to start / run /operate the business. In your case, for wine production, you need to have land (the vineyard), some money and some equipment before you can even start to produce the wine. HTH.
### What is mean capital?
Capital includes all goods that are made or created by humans and used for producing goods or services. Capital can include physical assets, such as a production plant, or financial assets, such as an investment portfolio. Capital can also refer to money invested in a business to purchase assets.
### What is the difference between Labour and capital intensive?
Capital intensive production requires more equipment and machinery to produce goods; therefore, require a larger financial investment. Labor intensive refers to production that requires a higher labor input to carry out production activities in comparison to the amount of capital required.
### Is retail capital intensive?
The retail business has reasonably well defined segments with food and grocery accounting for the largest share. Retail is a capital intensive business — large investments are required in real estate, leasehold improvements and working capital. Foreign investment in retail is necessary for the growth of the industry. | 1,415 | 7,195 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-21 | latest | en | 0.936163 |
http://slideplayer.com/slide/1422707/ | 1,519,604,550,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891817523.0/warc/CC-MAIN-20180225225657-20180226005657-00461.warc.gz | 322,634,535 | 20,503 | # From Geometry to Architecture and Construction. Consider a vertical section of polyhedrons that correspond to columns having different shift states. Each.
## Presentation on theme: "From Geometry to Architecture and Construction. Consider a vertical section of polyhedrons that correspond to columns having different shift states. Each."— Presentation transcript:
From Geometry to Architecture and Construction
Consider a vertical section of polyhedrons that correspond to columns having different shift states. Each polyhedron is divided in four equal height zones.
The bottom zone, which will be referred to as the "floor zone", includes a space-truss that follows the 3D construction grid, while it accommodates the electromechanical infrastructure of a building construction. The remaining three zones represent livable space. Now we are going to compare the section of an arbitrary polyhedron, of which the livable space is marked in blue, with the section of the same polyhedron in the case in which both left hand and right hand polyhedrons correspond to columns having the same shift states. Vertical boundaries, in the latter case, are represented by the red line. In the different-shift-state case the polyhedrons region is increased by the triangle marked in red, while decreased by the triangles marked in black. Note that the red triangle roughly corresponds to the human height, while the black triangles are either out or at the limit of human range.
Furthermore, the maximum length is gained at the work level which is the most critical for human activities. A similar gain occurs for all polyhedrons, which results in significant gain of architectural space.
Ergonomic use of architectural space of this kind is illustrated here.
Now we are going to examine some aspects of the relation of the built space with environmental factors. In this picture, right hand polyhedrons represent non built space.
Consider the case where both left hand and right hand polyhedrons have the same shift states. This results in vertical boundaries of the built space. Suppose that the two upper zones of the built polyhedron correspond to a window … … allowing penetration of solar light / energy into the built space.
In the case of the different-shift-state case the boundaries of the built space are oblique.
Potential penetration of solar light / energy into the built space is increased, even if the window's area remains the same, as the window is now oriented to the sun. This implicitly increases the variability of the design, as more design cases (system's states) become light / energy effective.
Now let us return to the same-shift-state case …… to represent penetration of solar light / energy into the open space.
Comparing this case with the different-shift-state case, where the upper floor zone has been properly adjusted according to the construction grid, … … we can see that the amount of solar light / energy available to the open space can increase. This has also implicit beneficial effects on the variability of the design. Due to the aforementioned benefits of the different-shift-state case, we can adopt the principle that this case always characterizes the relation between open and built space. The particular principle, viewed as a constraint, seems to decrease the system's variability. However, the same-shift-state case can be restored through the proper use of the construction grid.
The possibility to adjust a floor zone according to the construction grid allows extension of the floor zone in the open space, which results in horizontal transition between open and built space …
… practically restoring the same-shift-state case. In fact, the possibilities of the fine-grained construction grid, not only in extending a floor zone …
… but also in relaxing the vertical dependence between polyhedrons, by allowing horizontal shift of boundaries, vastly increases the system's variability.
Continued in Section_4_EN.PPS
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Similar presentations | 787 | 4,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-09 | latest | en | 0.920354 |
https://www.scipopt.org/doc-8.0.1/html/expr__trig_8c_source.php | 1,709,052,647,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474676.79/warc/CC-MAIN-20240227153053-20240227183053-00252.warc.gz | 984,388,789 | 40,367 | # SCIP
Solving Constraint Integer Programs
expr_trig.c
Go to the documentation of this file.
1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
2 /* */
3 /* This file is part of the program and library */
4 /* SCIP --- Solving Constraint Integer Programs */
5 /* */
7 /* fuer Informationstechnik Berlin */
8 /* */
10 /* */
12 /* along with SCIP; see the file COPYING. If not visit scip.zib.de. */
13 /* */
14 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
15
16 /**@file expr_trig.c
17 * @ingroup DEFPLUGINS_EXPR
18 * @brief handler for sine and cosine expressions
19 * @author Fabian Wegscheider
20 *
21 * The estimator/separator code always computes underestimators for sin(x).
22 * For overestimators of cos(x), we first reduce to underestimators of sin(x).
23 *
24 * Overestimator for sin(x):
25 * Assume that a*y+b <= sin(y) for y in [-ub,-lb].
26 * Then we have a*(-y)-b >= -sin(y) = sin(-y) for y in [-ub,-lb].
27 * Thus, a*x-b >= sin(x) for x in [lb,ub].
28 *
29 * Underestimator for cos(x):
30 * Assume that a*y+b <= sin(y) for y in [lb+pi/2,ub+pi/2].
31 * Then we have a*(x+pi/2) + b <= sin(x+pi/2) = cos(x) for x in [lb,ub].
32 * Thus, a*x + (b+a*pi/2) <= cos(x) for x in [lb,ub].
33 *
34 * Overestimator for cos(x):
35 * Assume that a*z+b <= sin(z) for z in [-(ub+pi/2),-(lb+pi/2)].
36 * Then, a*y-b >= sin(y) for y in [lb+pi/2,ub+pi/2].
37 * Then, a*x-b+a*pi/2 >= cos(x) for x in [lb,ub].
38 */
39
40 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
41
42 #define _USE_MATH_DEFINES /* to get M_PI on Windows */ /*lint !750 */
43
44 #include <string.h>
45 #include <math.h>
46 #include "scip/expr_trig.h"
47 #include "scip/expr_value.h"
48
49 /* fundamental expression handler properties */
50 #define SINEXPRHDLR_NAME "sin"
51 #define SINEXPRHDLR_DESC "sine expression"
52 #define SINEXPRHDLR_PRECEDENCE 91000
53 #define SINEXPRHDLR_HASHKEY SCIPcalcFibHash(82457.0)
54
55 #define COSEXPRHDLR_NAME "cos"
56 #define COSEXPRHDLR_DESC "cosine expression"
57 #define COSEXPRHDLR_PRECEDENCE 92000
58 #define COSEXPRHDLR_HASHKEY SCIPcalcFibHash(82463.0)
59
60 #define MAXCHILDABSVAL 1e+6 /**< maximum absolute value that is accepted for propagation */
61 #define NEWTON_NITERATIONS 100
62 #define NEWTON_PRECISION 1e-12
63
64 /*
65 * Local methods
66 */
67
68 /** evaluates the function a*x + b - sin(x) for some coefficient a and constant b at a given point p
69 *
70 * the constants a and b are expected to be stored in that order in params
71 */
72 static
74 { /*lint --e{715}*/
75 assert(params != NULL);
76 assert(nparams == 2);
77
78 return params[0]*point + params[1] - sin(point);
79 }
80
81 /** evaluates the derivative of a*x + b - sin(x) for some coefficient a and constant b at a given point p
82 *
83 * the constants a and b are expected to be stored in that order in params
84 */
85 static
87 { /*lint --e{715}*/
88 assert(params != NULL);
89 assert(nparams == 2);
90
91 return params[0] - cos(point);
92 }
93
94 /** evaluates the function sin(x) + (alpha - x)*cos(x) - sin(alpha) for some constant alpha at a given point p
95 *
96 * the constant alpha is expected to be stored in params
97 */
98 static
100 { /*lint --e{715}*/
101 assert(params != NULL);
102 assert(nparams == 1);
103
104 return sin(point) + (params[0] - point) * cos(point) - sin(params[0]);
105 }
106
107 /** evaluates the derivative of sin(x) + (alpha - x)*cos(x) - sin(alpha) for some constant alpha at a given point p
108 *
109 * the constant alpha is expected to be stored in params
110 */
111 static
113 { /*lint --e{715}*/
114 assert(params != NULL);
115 assert(nparams == 1);
116
117 return (point - params[0]) * sin(point);
118 }
119
120 /** helper function to compute the secant if it is a valid underestimator
121 *
122 * returns true if the estimator was computed successfully
123 */
124 static
126 SCIP* scip, /**< SCIP data structure */
127 SCIP_Real* lincoef, /**< buffer to store linear coefficient of secant */
128 SCIP_Real* linconst, /**< buffer to store linear constant of secant */
129 SCIP_Real lb, /**< lower bound of argument variable */
130 SCIP_Real ub /**< upper bound of argument variable */
131 )
132 {
133 assert(scip != NULL);
134 assert(lincoef != NULL);
135 assert(linconst != NULL);
136 assert(lb < ub);
137
138 /* if range is too big, secant is not underestimating */
139 if( ub - lb >= M_PI )
140 return FALSE;
141
142 /* if bounds are not within positive bay, secant is not underestimating */
143 if( sin(lb) < 0.0 || sin(ub) < 0.0 || (sin(lb) == 0.0 && cos(lb) < 0.0) )
144 return FALSE;
145
146 *lincoef = (sin(ub) - sin(lb)) / (ub - lb);
147 *linconst = sin(ub) - (*lincoef) * ub;
148
149 return TRUE;
150 }
151
152 /** helper function to compute the tangent at lower bound if it is underestimating
153 *
154 * returns true if the underestimator was computed successfully
155 */
156 static
158 SCIP* scip, /**< SCIP data structure */
159 SCIP_Real* lincoef, /**< buffer to store linear coefficient of tangent */
160 SCIP_Real* linconst, /**< buffer to store linear constant of tangent */
161 SCIP_Real lb /**< lower bound of argument variable */
162 )
163 {
164 assert(scip != NULL);
165 assert(lincoef != NULL);
166 assert(linconst != NULL);
167
168 if( SCIPisInfinity(scip, -lb) )
169 return FALSE;
170
171 /* left tangent is only underestimating in [pi, 1.5*pi) *2kpi */
172 if( sin(lb) > 0.0 || cos(lb) >= 0.0 )
173 return FALSE;
174
175 *lincoef = cos(lb);
176 *linconst = sin(lb) - (*lincoef) * lb;
177
178 return TRUE;
179 }
180
181 /* TODO: fix this, more cases can be considered, see at unit test
182 * the underestimating of the tangents depends not only on the ub but also on the lower bound.
183 * right now, this function is only checking whether the tangent underestimates independently of the lower bound!
184 */
185 /** helper function to compute the tangent at upper bound if it is an underestimator
186 *
187 * returns true if the underestimator was computed successfully
188 */
189 static
191 SCIP* scip, /**< SCIP data structure */
192 SCIP_Real* lincoef, /**< buffer to store linear coefficient of tangent */
193 SCIP_Real* linconst, /**< buffer to store linear constant of tangent */
194 SCIP_Real ub /**< upper bound of argument variable */
195 )
196 {
197 assert(scip != NULL);
198 assert(lincoef != NULL);
199 assert(linconst != NULL);
200
201 if( SCIPisInfinity(scip, ub) )
202 return FALSE;
203
204 /* right tangent is only underestimating in (1.5*pi, 2*pi] *2kpi */
205 if( sin(ub) > 0.0 || cos(ub) <= 0.0 )
206 return FALSE;
207
208 *lincoef = cos(ub);
209 *linconst = sin(ub) - (*lincoef) * ub;
210
211 return TRUE;
212 }
213
214 /** helper function to compute the tangent at solution point if it is an underestimator
215 *
216 * returns true if the underestimator was computed successfully
217 */
218 static
220 SCIP* scip, /**< SCIP data structure */
221 SCIP_Real* lincoef, /**< buffer to store linear coefficient of tangent */
222 SCIP_Real* linconst, /**< buffer to store linear constant of tangent */
223 SCIP_Real lb, /**< lower bound of argument variable */
224 SCIP_Real ub, /**< upper bound of argument variable */
225 SCIP_Real solpoint /**< solution point to be separated */
226 )
227 {
228 SCIP_Real params[2];
229 SCIP_Real startingpoints[3];
230 SCIP_Real solpointmodpi;
231 SCIP_Real intersection;
232 int i;
233
234 assert(scip != NULL);
235 assert(lincoef != NULL);
236 assert(linconst != NULL);
237
238 /* tangent is only underestimating in negative bay */
239 if( sin(solpoint) > 0.0 )
240 return FALSE;
241
242 /* compute solution point mod pi */
243 solpointmodpi = fmod(solpoint, M_PI);
244 if( solpoint < 0.0 )
245 solpointmodpi += M_PI;
246
247 /* if the point is too far away from the bounds or is at a multiple of pi, then tangent is not underestimating */
248 if( SCIPisGE(scip, solpoint - lb, 2*M_PI) || SCIPisGE(scip, ub - solpoint, 2*M_PI)
249 || SCIPisZero(scip, solpointmodpi) )
250 return FALSE;
251
252 params[0] = cos(solpoint);
253 params[1] = sin(solpoint) - params[0] * solpoint;
254
255 /* choose starting points for Newton procedure */
256 if( SCIPisGT(scip, solpointmodpi, M_PI_2) )
257 {
258 startingpoints[0] = solpoint + (M_PI - solpointmodpi) + M_PI_2;
259 startingpoints[1] = startingpoints[0] + M_PI_2;
260 startingpoints[2] = startingpoints[1] + M_PI_2;
261 }
262 else
263 {
264 startingpoints[0] = solpoint - solpointmodpi - M_PI_2;
265 startingpoints[1] = startingpoints[0] - M_PI_2;
266 startingpoints[2] = startingpoints[1] - M_PI_2;
267 }
268
269 /* use Newton procedure to test if cut is valid */
270 for( i = 0; i < 3; ++i )
271 {
272 intersection = SCIPcalcRootNewton(function1, derivative1, params, 2, startingpoints[i], NEWTON_PRECISION,
274
275 if( intersection != SCIP_INVALID && !SCIPisEQ(scip, intersection, solpoint) ) /*lint !e777*/
276 break;
277 }
278
279 /* if Newton failed or intersection point lies within bounds, underestimator is not valid */
280 if( intersection == SCIP_INVALID || (intersection >= lb && intersection <= ub) ) /*lint !e777*/
281 return FALSE;
282
283 *lincoef = params[0];
284 *linconst = params[1];
285
286 return TRUE;
287 }
288
289 /** helper function to compute the secant between lower bound and some point of the graph such that it underestimates
290 *
291 * returns true if the underestimator was computed successfully
292 */
293 static
295 SCIP* scip, /**< SCIP data structure */
296 SCIP_Real* lincoef, /**< buffer to store linear coefficient of tangent */
297 SCIP_Real* linconst, /**< buffer to store linear constant of tangent */
298 SCIP_Real lb, /**< lower bound of argument variable */
299 SCIP_Real ub /**< upper bound of argument variable */
300 )
301 {
302 SCIP_Real lbmodpi;
303 SCIP_Real tangentpoint;
304 SCIP_Real startingpoint;
305
306 assert(scip != NULL);
307 assert(lincoef != NULL);
308 assert(linconst != NULL);
309 assert(lb < ub);
310
311 if( SCIPisInfinity(scip, -lb) )
312 return FALSE;
313
314 /* compute shifted bounds for case evaluation */
315 lbmodpi = fmod(lb, M_PI);
316 if( lb < 0.0 )
317 lbmodpi += M_PI;
318
319 /* choose starting point for Newton procedure */
320 if( cos(lb) < 0.0 )
321 {
322 /* in [pi/2,pi] underestimating doesn't work; otherwise, take the midpoint of possible area */
323 if( SCIPisLE(scip, sin(lb), 0.0) )
324 return FALSE;
325 else
326 startingpoint = lb + 1.25*M_PI - lbmodpi;
327 }
328 else
329 {
330 /* in ascending area, take the midpoint of the possible area in descending part */
331 /* for lb < 0 but close to zero, we may have sin(lb) = 0 but lbmodpi = pi, which gives a starting point too close to lb
332 * but for sin(lb) around 0 we know that the tangent point needs to be in [lb+pi,lb+pi+pi/2]
333 */
334 if( SCIPisZero(scip, sin(lb)) )
335 startingpoint = lb + 1.25*M_PI;
336 else if( sin(lb) < 0.0 )
337 startingpoint = lb + 2.25*M_PI - lbmodpi;
338 else
339 startingpoint = lb + 1.25*M_PI - lbmodpi;
340 }
341
342 /* use Newton procedure to find the point where the tangent intersects sine at lower bound */
343 tangentpoint = SCIPcalcRootNewton(function2, derivative2, &lb, 1, startingpoint, NEWTON_PRECISION,
345
346 /* if Newton procedure failed, no cut is added */
347 if( tangentpoint == SCIP_INVALID ) /*lint !e777*/
348 return FALSE;
349
350 /* if the computed point lies outside the bounds, it is shifted to upper bound */
351 if( SCIPisGE(scip, tangentpoint, ub) )
352 {
353 tangentpoint = ub;
354
355 /* check whether affine function is still underestimating */
356 if( SCIPisLE(scip, sin(0.5 * (ub + lb)), sin(lb) + 0.5*(sin(ub) - sin(lb))) )
357 return FALSE;
358 }
359
360 if( SCIPisEQ(scip, tangentpoint, lb) ) /*lint !e777 */
361 return FALSE;
362
363 /* compute secant between lower bound and connection point */
364 *lincoef = (sin(tangentpoint) - sin(lb)) / (tangentpoint - lb);
365 *linconst = sin(lb) - (*lincoef) * lb;
366
367 /* if the bounds are too close to each other, it's possible that the underestimator is not valid */
368 if( *lincoef >= cos(lb) )
369 return FALSE;
370
371 SCIPdebugMsg(scip, "left secant: %g + %g*x <= sin(x) on [%g,%g]\n", *linconst, *lincoef, lb, ub);
372
373 return TRUE;
374 }
375
376 /** helper function to compute the secant between upper bound and some point of the graph such that it underestimates
377 *
378 * returns true if the underestimator was computed successfully
379 */
380 static
382 SCIP* scip, /**< SCIP data structure */
383 SCIP_Real* lincoef, /**< buffer to store linear coefficient of tangent */
384 SCIP_Real* linconst, /**< buffer to store linear constant of tangent */
385 SCIP_Real lb, /**< lower bound of argument variable */
386 SCIP_Real ub /**< upper bound of argument variable */
387 )
388 {
389 SCIP_Real ubmodpi;
390 SCIP_Real tangentpoint;
391 SCIP_Real startingpoint;
392
393 assert(scip != NULL);
394 assert(lincoef != NULL);
395 assert(linconst != NULL);
396 assert(lb < ub);
397
398 if( SCIPisInfinity(scip, ub) )
399 return FALSE;
400
401 /* compute shifted bounds for case evaluation */
402 ubmodpi = fmod(ub, M_PI);
403 if( ub < 0.0 )
404 ubmodpi += M_PI;
405
406 /* choose starting point for Newton procedure */
407 if( cos(ub) > 0.0 )
408 {
409 /* in [3*pi/2,2*pi] underestimating doesn't work; otherwise, take the midpoint of possible area */
410 if( SCIPisLE(scip, sin(ub), 0.0) )
411 return FALSE;
412 else
413 startingpoint = ub - M_PI_4 - ubmodpi;
414 }
415 else
416 {
417 /* in descending area, take the midpoint of the possible area in ascending part */
418 /* for ub < 0 but close to zero, we may have sin(ub) = 0 but ubmodpi = pi, which gives a starting point too close to ub
419 * but for sin(ub) around 0 we know that the tangent point needs to be in [ub-(pi+pi/2),ub-pi]
420 */
421 if( SCIPisZero(scip, sin(ub)) )
422 startingpoint = ub - 1.25*M_PI;
423 else if( sin(ub) < 0.0 )
424 startingpoint = ub - 1.25*M_PI - ubmodpi;
425 else
426 startingpoint = ub - M_PI_4 - ubmodpi;
427 }
428
429 /* use Newton procedure to find the point where the tangent intersects sine at lower bound */
430 tangentpoint = SCIPcalcRootNewton(function2, derivative2, &ub, 1, startingpoint, NEWTON_PRECISION,
432
433 /* if Newton procedure failed, no underestimator is found */
434 if( tangentpoint == SCIP_INVALID ) /*lint !e777*/
435 return FALSE;
436
437 /* if the computed point lies outside the bounds, it is shifted to upper bound */
438 if( SCIPisLE(scip, tangentpoint, lb) )
439 {
440 tangentpoint = lb;
441
442 /* check whether affine function is still underestimating */
443 if( SCIPisLE(scip, sin(0.5 * (ub + lb)), sin(lb) + 0.5*(sin(ub) - sin(lb))) )
444 return FALSE;
445 }
446
447 if( SCIPisEQ(scip, tangentpoint, ub) ) /*lint !e777 */
448 return FALSE;
449
450 /* compute secant between lower bound and connection point */
451 *lincoef = (sin(tangentpoint) - sin(ub)) / (tangentpoint - ub);
452 *linconst = sin(ub) - (*lincoef) * ub;
453
454 /* if the bounds are to close to each other, it's possible that the underestimator is not valid */
455 if( *lincoef <= cos(lb) )
456 return FALSE;
457
458 return TRUE;
459 }
460
461 /** helper function to compute the new interval for child in reverse propagation */
462 static
464 SCIP* scip, /**< SCIP data structure */
465 SCIP_INTERVAL parentbounds, /**< bounds for sine expression */
466 SCIP_INTERVAL childbounds, /**< bounds for child expression */
467 SCIP_INTERVAL* newbounds /**< buffer to store new child bounds */
468 )
469 {
470 SCIP_Real newinf = childbounds.inf;
471 SCIP_Real newsup = childbounds.sup;
472
473 /* if the absolute values of the bounds are too large, skip reverse propagation
474 * TODO: if bounds are close but too large, shift them to [0,2pi] and do the computation there
475 */
476 if( ABS(newinf) > MAXCHILDABSVAL || ABS(newsup) > MAXCHILDABSVAL )
477 {
478 SCIPintervalSetBounds(newbounds, newinf, newsup);
479 return SCIP_OKAY;
480 }
481
482 if( !SCIPisInfinity(scip, -newinf) )
483 {
484 /* l(x) and u(x) are lower/upper bound of child, l(s) and u(s) are lower/upper bound of sin expr
485 *
486 * if sin(l(x)) < l(s), we are looking for k minimal s.t. a + 2k*pi > l(x) where a = asin(l(s))
487 * then the new lower bound is a + 2k*pi
488 */
489 if( SCIPisLT(scip, sin(newinf), parentbounds.inf) )
490 {
491 SCIP_Real a = asin(parentbounds.inf);
492 int k = (int) ceil((newinf - a) / (2.0*M_PI));
493 newinf = a + 2.0*M_PI * k;
494 }
495
496 /* if sin(l(x)) > u(s), we are looking for k minimal s.t. pi - a + 2k*pi > l(x) where a = asin(u(s))
497 * then the new lower bound is pi - a + 2k*pi
498 */
499 else if( SCIPisGT(scip, sin(newinf), parentbounds.sup) )
500 {
501 SCIP_Real a = asin(parentbounds.sup);
502 int k = (int) ceil((newinf + a) / (2.0*M_PI) - 0.5);
503 newinf = M_PI * (2.0*k + 1.0) - a;
504 }
505
506 assert(newinf >= childbounds.inf);
507 assert(SCIPisFeasGE(scip, sin(newinf), parentbounds.inf));
508 assert(SCIPisFeasLE(scip, sin(newinf), parentbounds.sup));
509 }
510
511 if( !SCIPisInfinity(scip, newsup) )
512 {
513 /* if sin(u(x)) > u(s), we are looking for k minimal s.t. a + 2k*pi > u(x) - 2*pi where a = asin(u(s))
514 * then the new upper bound is a + 2k*pi
515 */
516 if ( SCIPisGT(scip, sin(newsup), parentbounds.sup) )
517 {
518 SCIP_Real a = asin(parentbounds.sup);
519 int k = (int) ceil((newsup - a ) / (2.0*M_PI)) - 1;
520 newsup = a + 2.0*M_PI * k;
521 }
522
523 /* if sin(u(x)) < l(s), we are looking for k minimal s.t. pi - a + 2k*pi > l(x) - 2*pi where a = asin(l(s))
524 * then the new upper bound is pi - a + 2k*pi
525 */
526 if( SCIPisLT(scip, sin(newsup), parentbounds.inf) )
527 {
528 SCIP_Real a = asin(parentbounds.inf);
529 int k = (int) ceil((newsup + a) / (2.0*M_PI) - 0.5) - 1;
530 newsup = M_PI * (2.0*k + 1.0) - a;
531 }
532
533 assert(newsup <= childbounds.sup);
534 assert(SCIPisFeasGE(scip, sin(newsup), parentbounds.inf));
535 assert(SCIPisFeasLE(scip, sin(newsup), parentbounds.sup));
536 }
537
538 /* if the new interval is invalid, the old one was already invalid */
539 if( newinf <= newsup )
540 SCIPintervalSetBounds(newbounds, newinf, newsup);
541 else
542 SCIPintervalSetEmpty(newbounds);
543
544 return SCIP_OKAY;
545 }
546
547 /** helper function to compute coefficients and constant term of a linear estimator at a given point
548 *
549 * The function will try to compute the following estimators in that order:
550 * - soltangent: tangent at specified refpoint
551 * - secant: secant between the points (lb,sin(lb)) and (ub,sin(ub))
552 * - left secant: secant between lower bound and some point of the graph
553 * - right secant: secant between upper bound and some point of the graph
554 *
555 * They are ordered such that a successful computation for one of them cannot be improved by following ones in terms
556 * of value at the reference point.
557 */
558 static
560 SCIP* scip, /**< SCIP data structure */
561 SCIP_EXPR* expr, /**< sin or cos expression */
562 SCIP_Real* lincoef, /**< buffer to store the linear coefficient */
563 SCIP_Real* linconst, /**< buffer to store the constant term */
564 SCIP_Real refpoint, /**< point at which to underestimate (can be SCIP_INVALID) */
565 SCIP_Real childlb, /**< lower bound of child variable */
566 SCIP_Real childub, /**< upper bound of child variable */
567 SCIP_Bool underestimate /**< whether the estimator should be underestimating */
568 )
569 {
570 SCIP_Bool success;
571 SCIP_Bool iscos;
572
573 assert(scip != NULL);
574 assert(expr != NULL);
575 assert(SCIPexprGetNChildren(expr) == 1);
576 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "sin") == 0
577 || strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "cos") == 0);
578 assert(SCIPisLE(scip, childlb, childub));
579
580 /* if child is essentially constant, then there should be no point in estimation */
581 if( SCIPisEQ(scip, childlb, childub) ) /* @todo maybe return a constant estimator? */
582 return FALSE;
583
584 iscos = strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "cos") == 0;
585
586 /* for cos expressions, the bounds have to be shifted before and after computation */
587 if( iscos )
588 {
589 childlb += M_PI_2;
590 childub += M_PI_2;
591 refpoint += M_PI_2;
592 }
593
594 if( !underestimate )
595 {
596 SCIP_Real tmp = childlb;
597 childlb = -childub;
598 childub = -tmp;
599 refpoint *= -1;
600 }
601
602 /* try out tangent at solution point */
603 success = computeSolTangentSin(scip, lincoef, linconst, childlb, childub, refpoint);
604
605 /* otherwise, try out secant */
606 if( !success )
607 success = computeSecantSin(scip, lincoef, linconst, childlb, childub);
608
609 /* otherwise, try left secant */
610 if( !success )
611 success = computeLeftSecantSin(scip, lincoef, linconst, childlb, childub);
612
613 /* otherwise, try right secant */
614 if( !success )
615 success = computeRightSecantSin(scip, lincoef, linconst, childlb, childub);
616
617 if( !success )
618 return FALSE;
619
620 /* for overestimators, mirror back */
621 if( !underestimate )
622 (*linconst) *= -1.0;
623
624 /* for cos expressions, shift back */
625 if( iscos )
626 (*linconst) += (*lincoef) * M_PI_2;
627
628 return TRUE;
629 }
630
631 /** helper function to create initial cuts for sine and cosine separation
632 *
633 * The following 5 cuts can be generated:
634 * - secant: secant between the bounds (lb,sin(lb)) and (ub,sin(ub))
635 * - left/right secant: secant between lower/upper bound and some point of the graph
636 * - left/right tangent: tangents at the lower/upper bounds
637 */
638 static
640 SCIP* scip, /**< SCIP data structure */
641 SCIP_EXPR* expr, /**< sin or cos expression */
642 SCIP_Real childlb, /**< lower bound of child variable */
643 SCIP_Real childub, /**< upper bound of child variable */
644 SCIP_Bool underestimate, /**< whether the cuts should be underestimating */
645 SCIP_Real** coefs, /**< buffer to store coefficients of computed estimators */
646 SCIP_Real* constant, /**< buffer to store constant of computed estimators */
647 int* nreturned /**< buffer to store number of estimators that have been computed */
648 )
649 {
650 SCIP_Bool iscos;
651 int i;
652
653 assert(scip != NULL);
654 assert(expr != NULL);
655 assert(SCIPexprGetNChildren(expr) == 1);
656 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "sin") == 0 || strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "cos") == 0);
657 assert(SCIPisLE(scip, childlb, childub));
658
659 /* caller must ensure that variable is not already fixed */
660 assert(!SCIPisEQ(scip, childlb, childub));
661
662 *nreturned = 0;
663
664 /* for cos expressions, the bounds have to be shifted before and after computation */
665 iscos = strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), "cos") == 0;
666 if( iscos )
667 {
668 childlb += M_PI_2;
669 childub += M_PI_2;
670 }
671
672 /*
673 * Compute all initial cuts
674 * For each linear equation z = a*x + b with bounds [lb,ub] the parameters can be computed by:
675 *
676 * a = cos(x^) and b = sin(x^) - a * x^ where x^ is any known point in [lb,ub]
677 *
678 * and the resulting cut is a*x + b <=/>= z depending on over-/underestimation
679 */
680
681 if( ! underestimate )
682 {
683 SCIP_Real aux;
684 aux = childlb;
685 childlb = -childub;
686 childub = -aux;
687 }
688
689 /* if we can generate a secant between the bounds, then we have convex (concave) hull */
690 if( computeSecantSin(scip, coefs[*nreturned], &constant[*nreturned], childlb, childub) )
691 (*nreturned)++;
692 else
693 {
694 /* try generating a secant between lb (ub) and some point < ub (> lb); otherwise try with tangent at lb (ub)*/
695 if( computeLeftSecantSin(scip, coefs[*nreturned], &constant[*nreturned], childlb, childub) )
696 (*nreturned)++;
697 else if( computeLeftTangentSin(scip, coefs[*nreturned], &constant[*nreturned], childlb) )
698 (*nreturned)++;
699
700 /* try generating a secant between ub (lb) and some point > lb (< ub); otherwise try with tangent at ub (lb)*/
701 if( computeRightSecantSin(scip, coefs[*nreturned], &constant[*nreturned], childlb, childub) )
702 (*nreturned)++;
703 else if( computeRightTangentSin(scip, coefs[*nreturned], &constant[*nreturned], childub) )
704 (*nreturned)++;
705 }
706
707 /* for cos expressions, the estimator needs to be shifted back to match original bounds */
708 for( i = 0; i < *nreturned; ++i )
709 {
710 if( ! underestimate )
711 constant[i] *= -1.0;
712
713 if( iscos)
714 {
715 constant[i] += coefs[i][0] * M_PI_2;
716 }
717 }
718
719 return SCIP_OKAY;
720 }
721
722 /* helper function that computes the curvature of a sine expression for given bounds and curvature of child */
723 static
725 SCIP_EXPRCURV childcurvature, /**< curvature of child */
726 SCIP_Real lb, /**< lower bound of child */
727 SCIP_Real ub /**< upper bound of child */
728 )
729 {
730 SCIP_Real lbsin = sin(lb);
731 SCIP_Real ubsin = sin(ub);
732 SCIP_Real lbcos = cos(lb);
733 SCIP_Real ubcos = cos(ub);
734
735 /* curvature can only be determined if bounds lie within one bay*/
736 if( (ub - lb <= M_PI) && (lbsin * ubsin >= 0.0) )
737 {
738 /* special case that both sin(ub) and sin(lb) are 0 (i.e. ub - lb = pi) */
739 if( lbsin == 0.0 && ubsin == 0.0 )
740 {
741 if( childcurvature == SCIP_EXPRCURV_LINEAR )
742 return (fmod(lb, 2.0*M_PI) == 0.0) ? SCIP_EXPRCURV_CONCAVE : SCIP_EXPRCURV_CONVEX;
743 }
744
745 /* if sine is monotone on the interval, the curvature depends on the child curvature and on the segment */
746 else if( lbcos * ubcos >= 0.0 )
747 {
748 /* on [0, pi/2], sine is concave iff child is concave */
749 if( lbsin >= 0.0 && lbcos >= 0.0 && ((int)(childcurvature & SCIP_EXPRCURV_CONCAVE) != 0))
750 return SCIP_EXPRCURV_CONCAVE;
751
752 /* on [pi/2, pi], sine is concave iff child is convex */
753 if( lbsin >= 0.0 && lbcos <= 0.0 && ((int)(childcurvature & SCIP_EXPRCURV_CONVEX) != 0))
754 return SCIP_EXPRCURV_CONCAVE;
755
756 /* on [pi, 3pi/2], sine is convex iff child is concave */
757 if( lbsin <= 0.0 && lbcos <= 0.0 && ((int)(childcurvature & SCIP_EXPRCURV_CONCAVE) != 0))
758 return SCIP_EXPRCURV_CONVEX;
759
760 /* on [3pi/2, 2pi], sine is convex iff child is convex */
761 if( lbsin <= 0.0 && lbcos >= 0.0 && ((int)(childcurvature & SCIP_EXPRCURV_CONVEX) != 0))
762 return SCIP_EXPRCURV_CONVEX;
763 }
764
765 /* otherwise, we can only say something if the child is linear */
766 else if( childcurvature == SCIP_EXPRCURV_LINEAR )
767 return (lbsin >= 0.0 && ubsin >= 0.0) ? SCIP_EXPRCURV_CONCAVE : SCIP_EXPRCURV_CONVEX;
768 }
769
770 return SCIP_EXPRCURV_UNKNOWN;
771 }
772
773 /*
774 * Callback methods of expression handler
775 */
776
777 /** expression handler copy callback */
778 static
780 { /*lint --e{715}*/
782
783 return SCIP_OKAY;
784 }
785
786 /** simplifies a sine expression
787 *
788 * Evaluates the sine value function when its child is a value expression.
789 *
790 * TODO: add further simplifications
791 */
792 static
794 { /*lint --e{715}*/
795 SCIP_EXPR* child;
796
797 assert(scip != NULL);
798 assert(expr != NULL);
799 assert(simplifiedexpr != NULL);
800 assert(SCIPexprGetNChildren(expr) == 1);
801
802 child = SCIPexprGetChildren(expr)[0];
803 assert(child != NULL);
804
805 /* check for value expression */
806 if( SCIPisExprValue(scip, child) )
807 {
808 SCIP_CALL( SCIPcreateExprValue(scip, simplifiedexpr, sin(SCIPgetValueExprValue(child)), ownercreate,
809 ownercreatedata) );
810 }
811 else
812 {
813 *simplifiedexpr = expr;
814
815 /* we have to capture it, since it must simulate a "normal" simplified call in which a new expression is created */
816 SCIPcaptureExpr(*simplifiedexpr);
817 }
818
819 return SCIP_OKAY;
820 }
821
822 /** expression parse callback */
823 static
825 { /*lint --e{715}*/
826 SCIP_EXPR* childexpr;
827
828 assert(expr != NULL);
829
830 /* parse child expression from remaining string */
831 SCIP_CALL( SCIPparseExpr(scip, &childexpr, string, endstring, ownercreate, ownercreatedata) );
832 assert(childexpr != NULL);
833
834 /* create sine expression */
835 SCIP_CALL( SCIPcreateExprSin(scip, expr, childexpr, ownercreate, ownercreatedata) );
836 assert(*expr != NULL);
837
838 /* release child expression since it has been captured by the sine expression */
839 SCIP_CALL( SCIPreleaseExpr(scip, &childexpr) );
840
841 *success = TRUE;
842
843 return SCIP_OKAY;
844 }
845
846 /** expression (point-) evaluation callback */
847 static
849 { /*lint --e{715}*/
850 assert(expr != NULL);
851 assert(SCIPexprGetNChildren(expr) == 1);
852 assert(SCIPexprGetEvalValue(SCIPexprGetChildren(expr)[0]) != SCIP_INVALID); /*lint !e777*/
853
854 *val = sin(SCIPexprGetEvalValue(SCIPexprGetChildren(expr)[0]));
855
856 return SCIP_OKAY;
857 }
858
859 /** expression derivative evaluation callback */
860 static
862 { /*lint --e{715}*/
863 SCIP_EXPR* child;
864
865 assert(expr != NULL);
866 assert(childidx == 0);
867 assert(SCIPexprGetEvalValue(expr) != SCIP_INVALID); /*lint !e777*/
868
869 child = SCIPexprGetChildren(expr)[0];
870 assert(child != NULL);
871 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(child)), "val") != 0);
872
873 *val = cos(SCIPexprGetEvalValue(child));
874
875 return SCIP_OKAY;
876 }
877
878 /** derivative evaluation callback
879 *
880 * Computes <gradient, children.dot>, that is, cos(child) dot(child).
881 */
882 static
884 { /*lint --e{715}*/
885 SCIP_EXPR* child;
886
887 assert(expr != NULL);
888 assert(SCIPexprGetEvalValue(expr) != SCIP_INVALID); /*lint !e777*/
889
890 child = SCIPexprGetChildren(expr)[0];
891 assert(child != NULL);
892 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(child)), "val") != 0);
893 assert(SCIPexprGetDot(child) != SCIP_INVALID); /*lint !e777*/
894
895 *dot = cos(SCIPexprGetEvalValue(child)) * SCIPexprGetDot(child);
896
897 return SCIP_OKAY;
898 }
899
900 /** expression backward forward derivative evaluation callback
901 *
902 * Computes partial/partial child ( <gradient, children.dot> ), that is, -sin(child) dot(child).
903 */
904 static
906 { /*lint --e{715}*/
907 SCIP_EXPR* child;
908
909 assert(expr != NULL);
910 assert(SCIPexprGetEvalValue(expr) != SCIP_INVALID); /*lint !e777*/
911 assert(childidx == 0);
912
913 child = SCIPexprGetChildren(expr)[0];
914 assert(child != NULL);
915 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(child)), "val") != 0);
916 assert(SCIPexprGetDot(child) != SCIP_INVALID); /*lint !e777*/
917
918 *bardot = -sin(SCIPexprGetEvalValue(child)) * SCIPexprGetDot(child);
919
920 return SCIP_OKAY;
921 }
922
923 /** expression interval evaluation callback */
924 static
926 { /*lint --e{715}*/
927 SCIP_INTERVAL childinterval;
928
929 assert(expr != NULL);
930 assert(SCIPexprGetNChildren(expr) == 1);
931
932 childinterval = SCIPexprGetActivity(SCIPexprGetChildren(expr)[0]);
933
934 if( SCIPintervalIsEmpty(SCIP_INTERVAL_INFINITY, childinterval) )
935 SCIPintervalSetEmpty(interval);
936 else
937 SCIPintervalSin(SCIP_INTERVAL_INFINITY, interval, childinterval);
938
939 return SCIP_OKAY;
940 }
941
942 /** separation initialization callback */
943 static
945 { /*lint --e{715}*/
946 SCIP_Real childlb;
947 SCIP_Real childub;
948
949 childlb = bounds[0].inf;
950 childub = bounds[0].sup;
951
952 /* no need for cut if child is fixed */
953 if( SCIPisRelEQ(scip, childlb, childub) )
954 return SCIP_OKAY;
955
956 /* compute cuts */
957 SCIP_CALL( computeInitialCutsTrig(scip, expr, childlb, childub, ! overestimate, coefs, constant, nreturned) );
958
959 return SCIP_OKAY;
960 }
961
962 /** expression estimator callback */
963 static
965 { /*lint --e{715}*/
966 assert(scip != NULL);
967 assert(expr != NULL);
968 assert(SCIPexprGetNChildren(expr) == 1);
969 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), SINEXPRHDLR_NAME) == 0);
970 assert(coefs != NULL);
971 assert(constant != NULL);
972 assert(islocal != NULL);
973 assert(branchcand != NULL);
974 assert(*branchcand == TRUE);
975 assert(success != NULL);
976
977 *success = computeEstimatorsTrig(scip, expr, coefs, constant, refpoint[0], localbounds[0].inf,
978 localbounds[0].sup, ! overestimate);
979 *islocal = TRUE; /* TODO there are cases where cuts would be globally valid */
980
981 return SCIP_OKAY;
982 }
983
984 /** expression reverse propagation callback */
985 static
987 { /*lint --e{715}*/
988 assert(scip != NULL);
989 assert(expr != NULL);
990 assert(SCIPexprGetNChildren(expr) == 1);
991 assert(SCIPintervalGetInf(bounds) >= -1.0);
992 assert(SCIPintervalGetSup(bounds) <= 1.0);
993
994 /* compute the new child interval */
995 SCIP_CALL( computeRevPropIntervalSin(scip, bounds, childrenbounds[0], childrenbounds) );
996
997 return SCIP_OKAY;
998 }
999
1000 /** sine hash callback */
1001 static
1003 { /*lint --e{715}*/
1004 assert(scip != NULL);
1005 assert(expr != NULL);
1006 assert(SCIPexprGetNChildren(expr) == 1);
1007 assert(hashkey != NULL);
1008 assert(childrenhashes != NULL);
1009
1010 *hashkey = SINEXPRHDLR_HASHKEY;
1011 *hashkey ^= childrenhashes[0];
1012
1013 return SCIP_OKAY;
1014 }
1015
1016 /** expression curvature detection callback */
1017 static
1019 { /*lint --e{715}*/
1020 SCIP_EXPR* child;
1021 SCIP_INTERVAL childinterval;
1022
1023 assert(scip != NULL);
1024 assert(expr != NULL);
1025 assert(childcurv != NULL);
1026 assert(success != NULL);
1027 assert(SCIPexprGetNChildren(expr) == 1);
1028
1029 child = SCIPexprGetChildren(expr)[0];
1030 assert(child != NULL);
1031 SCIP_CALL( SCIPevalExprActivity(scip, child) );
1032 childinterval = SCIPexprGetActivity(child);
1033
1034 /* TODO rewrite SCIPcomputeCurvatureSin so it provides the reverse operation */
1035 *success = TRUE;
1036 if( computeCurvatureSin(SCIP_EXPRCURV_CONVEX, childinterval.inf, childinterval.sup) == exprcurvature )
1037 *childcurv = SCIP_EXPRCURV_CONVEX;
1038 else if( computeCurvatureSin(SCIP_EXPRCURV_CONCAVE, childinterval.inf, childinterval.sup) == exprcurvature )
1039 *childcurv = SCIP_EXPRCURV_CONCAVE;
1040 if( computeCurvatureSin(SCIP_EXPRCURV_LINEAR, childinterval.inf, childinterval.sup) == exprcurvature )
1041 *childcurv = SCIP_EXPRCURV_LINEAR;
1042 else
1043 *success = FALSE;
1044
1045 return SCIP_OKAY;
1046 }
1047
1048 /** expression monotonicity detection callback */
1049 static
1051 { /*lint --e{715}*/
1052 SCIP_INTERVAL interval;
1053 SCIP_Real inf;
1054 SCIP_Real sup;
1055 int k;
1056
1057 assert(scip != NULL);
1058 assert(expr != NULL);
1059 assert(result != NULL);
1060 assert(childidx == 0);
1061
1062 assert(SCIPexprGetChildren(expr)[0] != NULL);
1064 interval = SCIPexprGetActivity(SCIPexprGetChildren(expr)[0]);
1065
1066 *result = SCIP_MONOTONE_UNKNOWN;
1067 inf = SCIPintervalGetInf(interval);
1068 sup = SCIPintervalGetSup(interval);
1069
1070 /* expression is not monotone because the interval is too large */
1071 if( sup - inf > M_PI )
1072 return SCIP_OKAY;
1073
1074 /* compute k s.t. PI * (2k+1) / 2 <= interval.inf <= PI * (2k+3) / 2 */
1075 k = (int)floor(inf/M_PI - 0.5);
1076 assert(M_PI * (2.0*k + 1.0) / 2.0 <= inf);
1077 assert(M_PI * (2.0*k + 3.0) / 2.0 >= inf);
1078
1079 /* check whether [inf,sup] are in containing in an interval for which the sine function is monotone */
1080 if( M_PI * (2.0*k + 3.0) / 2.0 <= sup )
1081 *result = ((k % 2 + 2) % 2) == 1 ? SCIP_MONOTONE_INC : SCIP_MONOTONE_DEC;
1082
1083 return SCIP_OKAY;
1084 }
1085
1086
1087 /** expression handler copy callback */
1088 static
1090 { /*lint --e{715}*/
1092
1093 return SCIP_OKAY;
1094 }
1095
1096 /** simplifies a cosine expression
1097 *
1098 * Evaluates the cosine value function when its child is a value expression.
1099 *
1100 * TODO: add further simplifications
1101 */
1102 static
1104 { /*lint --e{715}*/
1105 SCIP_EXPR* child;
1106
1107 assert(scip != NULL);
1108 assert(expr != NULL);
1109 assert(simplifiedexpr != NULL);
1110 assert(SCIPexprGetNChildren(expr) == 1);
1111
1112 child = SCIPexprGetChildren(expr)[0];
1113 assert(child != NULL);
1114
1115 /* check for value expression */
1116 if( SCIPisExprValue(scip, child) )
1117 {
1118 SCIP_CALL( SCIPcreateExprValue(scip, simplifiedexpr, cos(SCIPgetValueExprValue(child)), ownercreate,
1119 ownercreatedata) );
1120 }
1121 else
1122 {
1123 *simplifiedexpr = expr;
1124
1125 /* we have to capture it, since it must simulate a "normal" simplified call in which a new expression is created */
1126 SCIPcaptureExpr(*simplifiedexpr);
1127 }
1128
1129 return SCIP_OKAY;
1130 }
1131
1132 /** expression parse callback */
1133 static
1135 { /*lint --e{715}*/
1136 SCIP_EXPR* childexpr;
1137
1138 assert(expr != NULL);
1139
1140 /* parse child expression from remaining string */
1141 SCIP_CALL( SCIPparseExpr(scip, &childexpr, string, endstring, ownercreate, ownercreatedata) );
1142 assert(childexpr != NULL);
1143
1144 /* create cosine expression */
1145 SCIP_CALL( SCIPcreateExprCos(scip, expr, childexpr, ownercreate, ownercreatedata) );
1146 assert(*expr != NULL);
1147
1148 /* release child expression since it has been captured by the cosine expression */
1149 SCIP_CALL( SCIPreleaseExpr(scip, &childexpr) );
1150
1151 *success = TRUE;
1152
1153 return SCIP_OKAY;
1154 }
1155
1156 /** expression (point-) evaluation callback */
1157 static
1159 { /*lint --e{715}*/
1160 assert(expr != NULL);
1161 assert(SCIPexprGetNChildren(expr) == 1);
1162 assert(SCIPexprGetEvalValue(SCIPexprGetChildren(expr)[0]) != SCIP_INVALID); /*lint !e777*/
1163
1164 *val = cos(SCIPexprGetEvalValue(SCIPexprGetChildren(expr)[0]));
1165
1166 return SCIP_OKAY;
1167 }
1168
1169 /** expression derivative evaluation callback */
1170 static
1172 { /*lint --e{715}*/
1173 SCIP_EXPR* child;
1174
1175 assert(expr != NULL);
1176 assert(childidx == 0);
1177 assert(SCIPexprGetEvalValue(expr) != SCIP_INVALID); /*lint !e777*/
1178
1179 child = SCIPexprGetChildren(expr)[0];
1180 assert(child != NULL);
1181 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(child)), "val") != 0);
1182
1183 *val = -sin(SCIPexprGetEvalValue(child));
1184
1185 return SCIP_OKAY;
1186 }
1187
1188 /** expression interval evaluation callback */
1189 static
1191 { /*lint --e{715}*/
1192 SCIP_INTERVAL childinterval;
1193
1194 assert(expr != NULL);
1195 assert(SCIPexprGetNChildren(expr) == 1);
1196
1197 childinterval = SCIPexprGetActivity(SCIPexprGetChildren(expr)[0]);
1198
1199 if( SCIPintervalIsEmpty(SCIP_INTERVAL_INFINITY, childinterval) )
1200 SCIPintervalSetEmpty(interval);
1201 else
1202 SCIPintervalCos(SCIP_INTERVAL_INFINITY, interval, childinterval);
1203
1204 return SCIP_OKAY;
1205 }
1206
1207 /** separation initialization callback */
1208 static
1210 {
1211 SCIP_Real childlb;
1212 SCIP_Real childub;
1213
1214 childlb = bounds[0].inf;
1215 childub = bounds[0].sup;
1216
1217 /* no need for cut if child is fixed */
1218 if( SCIPisRelEQ(scip, childlb, childub) )
1219 return SCIP_OKAY;
1220
1221 /* compute cuts */
1222 SCIP_CALL( computeInitialCutsTrig(scip, expr, childlb, childub, ! overestimate, coefs, constant, nreturned) );
1223
1224 return SCIP_OKAY;
1225 }
1226
1227 /** expression estimator callback */
1228 static
1230 { /*lint --e{715}*/
1231 assert(scip != NULL);
1232 assert(expr != NULL);
1233 assert(SCIPexprGetNChildren(expr) == 1);
1234 assert(strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), COSEXPRHDLR_NAME) == 0);
1235 assert(coefs != NULL);
1236 assert(constant != NULL);
1237 assert(islocal != NULL);
1238 assert(branchcand != NULL);
1239 assert(*branchcand == TRUE);
1240 assert(success != NULL);
1241
1242 *success = computeEstimatorsTrig(scip, expr, coefs, constant, refpoint[0], localbounds[0].inf,
1243 localbounds[0].sup, ! overestimate);
1244 *islocal = TRUE; /* TODO there are cases where cuts would be globally valid */
1245
1246 return SCIP_OKAY;
1247 }
1248
1249 /** expression reverse propagation callback */
1250 static
1252 { /*lint --e{715}*/
1253 SCIP_INTERVAL newbounds;
1254
1255 assert(scip != NULL);
1256 assert(expr != NULL);
1257 assert(SCIPexprGetNChildren(expr) == 1);
1258 /* bounds should have been intersected with activity, which is within [-1,1] */
1259 assert(SCIPintervalGetInf(bounds) >= -1.0);
1260 assert(SCIPintervalGetSup(bounds) <= 1.0);
1261
1262 /* get the child interval */
1263 newbounds = childrenbounds[0];
1264
1265 /* shift child interval to match sine */
1266 SCIPintervalAddScalar(SCIP_INTERVAL_INFINITY, &newbounds, newbounds, M_PI_2); /* TODO use bounds on Pi/2 instead of approximation of Pi/2 */
1267
1268 /* compute the new child interval */
1269 SCIP_CALL( computeRevPropIntervalSin(scip, bounds, newbounds, &newbounds) );
1270
1272 {
1273 *infeasible = TRUE;
1274 return SCIP_OKAY;
1275 }
1276
1277 /* shift the new interval back */
1278 SCIPintervalAddScalar(SCIP_INTERVAL_INFINITY, &childrenbounds[0], newbounds, -M_PI_2); /* TODO use bounds on Pi/2 instead of approximation of Pi/2 */
1279
1280 return SCIP_OKAY;
1281 }
1282
1283 /** cosine hash callback */
1284 static
1286 { /*lint --e{715}*/
1287 assert(scip != NULL);
1288 assert(expr != NULL);
1289 assert(SCIPexprGetNChildren(expr) == 1);
1290 assert(hashkey != NULL);
1291 assert(childrenhashes != NULL);
1292
1293 *hashkey = COSEXPRHDLR_HASHKEY;
1294 *hashkey ^= childrenhashes[0];
1295
1296 return SCIP_OKAY;
1297 }
1298
1299 /** expression curvature detection callback */
1300 static
1302 { /*lint --e{715}*/
1303 SCIP_EXPR* child;
1304 SCIP_INTERVAL childinterval;
1305
1306 assert(scip != NULL);
1307 assert(expr != NULL);
1308 assert(exprcurvature != SCIP_EXPRCURV_UNKNOWN);
1309 assert(childcurv != NULL);
1310 assert(success != NULL);
1311 assert(SCIPexprGetNChildren(expr) == 1);
1312
1313 child = SCIPexprGetChildren(expr)[0];
1314 assert(child != NULL);
1315 SCIP_CALL( SCIPevalExprActivity(scip, child) );
1316 childinterval = SCIPexprGetActivity(child);
1317
1318 /* TODO rewrite SCIPcomputeCurvatureSin so it provides the reverse operation */
1319 *success = TRUE;
1320 if( computeCurvatureSin(SCIP_EXPRCURV_CONCAVE, childinterval.inf + M_PI_2, childinterval.sup + M_PI_2) == exprcurvature )
1321 *childcurv = SCIP_EXPRCURV_CONCAVE;
1322 else if( computeCurvatureSin(SCIP_EXPRCURV_CONVEX, childinterval.inf + M_PI_2, childinterval.sup + M_PI_2) == exprcurvature )
1323 *childcurv = SCIP_EXPRCURV_CONVEX;
1324 else if( computeCurvatureSin(SCIP_EXPRCURV_LINEAR, childinterval.inf + M_PI_2, childinterval.sup + M_PI_2) == exprcurvature )
1325 *childcurv = SCIP_EXPRCURV_LINEAR;
1326 else
1327 *success = FALSE;
1328
1329 return SCIP_OKAY;
1330 }
1331
1332 /** expression monotonicity detection callback */
1333 static
1335 { /*lint --e{715}*/
1336 SCIP_INTERVAL interval;
1337 SCIP_Real inf;
1338 SCIP_Real sup;
1339 int k;
1340
1341 assert(scip != NULL);
1342 assert(expr != NULL);
1343 assert(result != NULL);
1344 assert(childidx == 0);
1345
1346 assert(SCIPexprGetChildren(expr)[0] != NULL);
1348 interval = SCIPexprGetActivity(SCIPexprGetChildren(expr)[0]);
1349
1350 *result = SCIP_MONOTONE_UNKNOWN;
1351 inf = SCIPintervalGetInf(interval);
1352 sup = SCIPintervalGetSup(interval);
1353
1354 /* expression is not monotone because the interval is too large */
1355 if( sup - inf > M_PI )
1356 return SCIP_OKAY;
1357
1358 /* compute k s.t. PI * k <= interval.inf <= PI * (k+1) */
1359 k = (int)floor(inf/M_PI);
1360 assert(M_PI * k <= inf);
1361 assert(M_PI * (k+1) >= inf);
1362
1363 /* check whether [inf,sup] are contained in an interval for which the cosine function is monotone */
1364 if( sup <= M_PI * (k+1) )
1365 *result = ((k % 2 + 2) % 2) == 0 ? SCIP_MONOTONE_DEC : SCIP_MONOTONE_INC;
1366
1367 return SCIP_OKAY;
1368 }
1369
1370 /** creates the handler for sin expressions and includes it into SCIP */
1372 SCIP* scip /**< SCIP data structure */
1373 )
1374 {
1375 SCIP_EXPRHDLR* exprhdlr;
1376
1377 /* include expression handler */
1379 assert(exprhdlr != NULL);
1380
1381 SCIPexprhdlrSetCopyFreeHdlr(exprhdlr, copyhdlrSin, NULL);
1382 SCIPexprhdlrSetSimplify(exprhdlr, simplifySin);
1383 SCIPexprhdlrSetParse(exprhdlr, parseSin);
1384 SCIPexprhdlrSetIntEval(exprhdlr, intevalSin);
1385 SCIPexprhdlrSetEstimate(exprhdlr, initEstimatesSin, estimateSin);
1386 SCIPexprhdlrSetReverseProp(exprhdlr, reversepropSin);
1387 SCIPexprhdlrSetHash(exprhdlr, hashSin);
1388 SCIPexprhdlrSetDiff(exprhdlr, bwdiffSin, fwdiffSin, bwfwdiffSin);
1389 SCIPexprhdlrSetCurvature(exprhdlr, curvatureSin);
1390 SCIPexprhdlrSetMonotonicity(exprhdlr, monotonicitySin);
1391
1392 return SCIP_OKAY;
1393 }
1394
1395 /** creates the handler for cos expressions and includes it SCIP */
1397 SCIP* scip /**< SCIP data structure */
1398 )
1399 {
1400 SCIP_EXPRHDLR* exprhdlr;
1401
1402 /* include expression handler */
1404 assert(exprhdlr != NULL);
1405
1406 SCIPexprhdlrSetCopyFreeHdlr(exprhdlr, copyhdlrCos, NULL);
1407 SCIPexprhdlrSetSimplify(exprhdlr, simplifyCos);
1408 SCIPexprhdlrSetParse(exprhdlr, parseCos);
1409 SCIPexprhdlrSetIntEval(exprhdlr, intevalCos);
1410 SCIPexprhdlrSetEstimate(exprhdlr, initEstimatesCos, estimateCos);
1411 SCIPexprhdlrSetReverseProp(exprhdlr, reversepropCos);
1412 SCIPexprhdlrSetHash(exprhdlr, hashCos);
1413 SCIPexprhdlrSetDiff(exprhdlr, bwdiffCos, NULL, NULL);
1414 SCIPexprhdlrSetCurvature(exprhdlr, curvatureCos);
1415 SCIPexprhdlrSetMonotonicity(exprhdlr, monotonicityCos);
1416
1417 return SCIP_OKAY;
1418 }
1419
1420 /** creates a sin expression */
1422 SCIP* scip, /**< SCIP data structure */
1423 SCIP_EXPR** expr, /**< pointer where to store expression */
1424 SCIP_EXPR* child, /**< single child */
1425 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
1426 void* ownercreatedata /**< data to pass to ownercreate */
1427 )
1428 {
1429 assert(expr != NULL);
1430 assert(child != NULL);
1431 assert(SCIPfindExprhdlr(scip, SINEXPRHDLR_NAME) != NULL);
1432
1433 SCIP_CALL( SCIPcreateExpr(scip, expr, SCIPfindExprhdlr(scip, SINEXPRHDLR_NAME), NULL, 1, &child, ownercreate,
1434 ownercreatedata) );
1435
1436 return SCIP_OKAY;
1437 }
1438
1439
1440 /** creates a cos expression */
1442 SCIP* scip, /**< SCIP data structure */
1443 SCIP_EXPR** expr, /**< pointer where to store expression */
1444 SCIP_EXPR* child, /**< single child */
1445 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
1446 void* ownercreatedata /**< data to pass to ownercreate */
1447 )
1448 {
1449 assert(expr != NULL);
1450 assert(child != NULL);
1451 assert(SCIPfindExprhdlr(scip, COSEXPRHDLR_NAME) != NULL);
1452
1453 SCIP_CALL( SCIPcreateExpr(scip, expr, SCIPfindExprhdlr(scip, COSEXPRHDLR_NAME), NULL, 1, &child, ownercreate,
1454 ownercreatedata) );
1455
1456 return SCIP_OKAY;
1457 }
1458
1459 /** indicates whether expression is of sine-type */ /*lint -e{715}*/
1461 SCIP* scip, /**< SCIP data structure */
1462 SCIP_EXPR* expr /**< expression */
1463 )
1464 { /*lint --e{715}*/
1465 assert(expr != NULL);
1466
1467 return strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), SINEXPRHDLR_NAME) == 0;
1468 }
1469
1470 /** indicates whether expression is of cosine-type */ /*lint -e{715}*/
1472 SCIP* scip, /**< SCIP data structure */
1473 SCIP_EXPR* expr /**< expression */
1474 )
1475 { /*lint --e{715}*/
1476 assert(expr != NULL);
1477
1478 return strcmp(SCIPexprhdlrGetName(SCIPexprGetHdlr(expr)), COSEXPRHDLR_NAME) == 0;
1479 }
void SCIPintervalCos(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
#define COSEXPRHDLR_HASHKEY
Definition: expr_trig.c:58
#define COSEXPRHDLR_DESC
Definition: expr_trig.c:56
SCIP_Bool SCIPisRelEQ(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_RETCODE SCIPevalExprActivity(SCIP *scip, SCIP_EXPR *expr)
Definition: scip_expr.c:1706
int SCIPexprGetNChildren(SCIP_EXPR *expr)
Definition: expr.c:3798
void SCIPexprhdlrSetDiff(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRBWDIFF((*bwdiff)), SCIP_DECL_EXPRFWDIFF((*fwdiff)), SCIP_DECL_EXPRBWFWDIFF((*bwfwdiff)))
Definition: expr.c:464
const char * SCIPexprhdlrGetName(SCIP_EXPRHDLR *exprhdlr)
Definition: expr.c:525
static SCIP_RETCODE computeInitialCutsTrig(SCIP *scip, SCIP_EXPR *expr, SCIP_Real childlb, SCIP_Real childub, SCIP_Bool underestimate, SCIP_Real **coefs, SCIP_Real *constant, int *nreturned)
Definition: expr_trig.c:639
SCIP_Bool SCIPisGE(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
static SCIP_DECL_EXPRHASH(hashSin)
Definition: expr_trig.c:1002
void SCIPexprhdlrSetParse(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRPARSE((*parse)))
Definition: expr.c:398
SCIP_Bool SCIPisFeasGE(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
#define FALSE
Definition: def.h:87
static SCIP_Bool computeRightSecantSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real lb, SCIP_Real ub)
Definition: expr_trig.c:381
void SCIPintervalAddScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)
#define TRUE
Definition: def.h:86
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:54
#define SINEXPRHDLR_PRECEDENCE
Definition: expr_trig.c:52
static SCIP_Bool computeSolTangentSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real lb, SCIP_Real ub, SCIP_Real solpoint)
Definition: expr_trig.c:219
void SCIPexprhdlrSetHash(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRHASH((*hash)))
Definition: expr.c:442
SCIP_INTERVAL SCIPexprGetActivity(SCIP_EXPR *expr)
Definition: expr.c:3954
static SCIP_RETCODE computeRevPropIntervalSin(SCIP *scip, SCIP_INTERVAL parentbounds, SCIP_INTERVAL childbounds, SCIP_INTERVAL *newbounds)
Definition: expr_trig.c:463
static SCIP_Bool computeLeftTangentSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real lb)
Definition: expr_trig.c:157
SCIP_Bool SCIPisEQ(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
void SCIPcaptureExpr(SCIP_EXPR *expr)
Definition: scip_expr.c:1399
#define SCIPdebugMsg
Definition: scip_message.h:69
SCIP_EXPRHDLR * SCIPfindExprhdlr(SCIP *scip, const char *name)
Definition: scip_expr.c:859
SCIP_Real SCIPcalcRootNewton(SCIP_DECL_NEWTONEVAL((*function)), SCIP_DECL_NEWTONEVAL((*derivative)), SCIP_Real *params, int nparams, SCIP_Real x, SCIP_Real eps, int k)
Definition: misc.c:9760
#define COSEXPRHDLR_PRECEDENCE
Definition: expr_trig.c:57
#define COSEXPRHDLR_NAME
Definition: expr_trig.c:55
static SCIP_DECL_EXPRCURVATURE(curvatureSin)
Definition: expr_trig.c:1018
SCIP_EXPR ** SCIPexprGetChildren(SCIP_EXPR *expr)
Definition: expr.c:3808
SCIP_Real inf
Definition: intervalarith.h:46
static SCIP_DECL_EXPRESTIMATE(estimateSin)
Definition: expr_trig.c:964
SCIP_Real SCIPexprGetEvalValue(SCIP_EXPR *expr)
Definition: expr.c:3872
static SCIP_DECL_EXPRBWFWDIFF(bwfwdiffSin)
Definition: expr_trig.c:905
SCIP_RETCODE SCIPcreateExpr(SCIP *scip, SCIP_EXPR **expr, SCIP_EXPRHDLR *exprhdlr, SCIP_EXPRDATA *exprdata, int nchildren, SCIP_EXPR **children, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition: scip_expr.c:964
SCIP_Bool SCIPisLT(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Bool SCIPintervalIsEmpty(SCIP_Real infinity, SCIP_INTERVAL operand)
#define SINEXPRHDLR_NAME
Definition: expr_trig.c:50
void SCIPintervalSetEmpty(SCIP_INTERVAL *resultant)
static SCIP_DECL_EXPRREVERSEPROP(reversepropSin)
Definition: expr_trig.c:986
SCIP_Bool SCIPisExprValue(SCIP *scip, SCIP_EXPR *expr)
Definition: scip_expr.c:1432
SCIP_RETCODE SCIPincludeExprhdlrCos(SCIP *scip)
Definition: expr_trig.c:1396
SCIP_Real SCIPintervalGetInf(SCIP_INTERVAL interval)
#define NULL
Definition: lpi_spx1.cpp:155
#define SINEXPRHDLR_DESC
Definition: expr_trig.c:51
SCIP_Real SCIPintervalGetSup(SCIP_INTERVAL interval)
SCIP_Real SCIPexprGetDot(SCIP_EXPR *expr)
Definition: expr.c:3912
static SCIP_DECL_EXPRMONOTONICITY(monotonicitySin)
Definition: expr_trig.c:1050
#define SCIP_CALL(x)
Definition: def.h:384
SCIP_Real sup
Definition: intervalarith.h:47
SCIP_RETCODE SCIPcreateExprValue(SCIP *scip, SCIP_EXPR **expr, SCIP_Real value, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition: expr_value.c:261
SCIP_Bool SCIPisFeasLE(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
void SCIPexprhdlrSetCopyFreeHdlr(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRCOPYHDLR((*copyhdlr)), SCIP_DECL_EXPRFREEHDLR((*freehdlr)))
Definition: expr.c:359
static SCIP_EXPRCURV computeCurvatureSin(SCIP_EXPRCURV childcurvature, SCIP_Real lb, SCIP_Real ub)
Definition: expr_trig.c:724
#define SCIP_INTERVAL_INFINITY
Definition: def.h:199
static SCIP_DECL_NEWTONEVAL(function1)
Definition: expr_trig.c:73
static SCIP_Bool computeRightTangentSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real ub)
Definition: expr_trig.c:190
static SCIP_Bool computeLeftSecantSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real lb, SCIP_Real ub)
Definition: expr_trig.c:294
static SCIP_DECL_EXPRINITESTIMATES(initEstimatesSin)
Definition: expr_trig.c:944
#define MAXCHILDABSVAL
Definition: expr_trig.c:60
#define SCIP_Bool
Definition: def.h:84
#define SCIP_DECL_EXPR_OWNERCREATE(x)
Definition: type_expr.h:131
SCIP_EXPRCURV
Definition: type_expr.h:48
void SCIPexprhdlrSetMonotonicity(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRMONOTONICITY((*monotonicity)))
Definition: expr.c:420
SCIP_RETCODE SCIPreleaseExpr(SCIP *scip, SCIP_EXPR **expr)
Definition: scip_expr.c:1407
handler for sin expressions
static SCIP_DECL_EXPRSIMPLIFY(simplifySin)
Definition: expr_trig.c:793
void SCIPexprhdlrSetReverseProp(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRREVERSEPROP((*reverseprop)))
Definition: expr.c:501
SCIP_RETCODE SCIPparseExpr(SCIP *scip, SCIP_EXPR **expr, const char *exprstr, const char **finalpos, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition: scip_expr.c:1370
#define SINEXPRHDLR_HASHKEY
Definition: expr_trig.c:53
SCIP_EXPRHDLR * SCIPexprGetHdlr(SCIP_EXPR *expr)
Definition: expr.c:3821
SCIP_Bool SCIPisInfinity(SCIP *scip, SCIP_Real val)
constant value expression handler
#define M_PI
Definition: pricer_rpa.c:88
SCIP_Bool SCIPisGT(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
void SCIPexprhdlrSetCurvature(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRCURVATURE((*curvature)))
Definition: expr.c:409
static SCIP_DECL_EXPRFWDIFF(fwdiffSin)
Definition: expr_trig.c:883
SCIP_RETCODE SCIPcreateExprSin(SCIP *scip, SCIP_EXPR **expr, SCIP_EXPR *child, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition: expr_trig.c:1421
SCIP_RETCODE SCIPcreateExprCos(SCIP *scip, SCIP_EXPR **expr, SCIP_EXPR *child, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition: expr_trig.c:1441
SCIP_VAR * a
Definition: circlepacking.c:57
void SCIPintervalSetBounds(SCIP_INTERVAL *resultant, SCIP_Real inf, SCIP_Real sup)
static SCIP_Bool computeSecantSin(SCIP *scip, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real lb, SCIP_Real ub)
Definition: expr_trig.c:125
static SCIP_Bool computeEstimatorsTrig(SCIP *scip, SCIP_EXPR *expr, SCIP_Real *lincoef, SCIP_Real *linconst, SCIP_Real refpoint, SCIP_Real childlb, SCIP_Real childub, SCIP_Bool underestimate)
Definition: expr_trig.c:559
#define SCIP_Real
Definition: def.h:177
static SCIP_DECL_EXPREVAL(evalSin)
Definition: expr_trig.c:848
#define NEWTON_PRECISION
Definition: expr_trig.c:62
#define SCIP_INVALID
Definition: def.h:197
SCIP_Real SCIPgetValueExprValue(SCIP_EXPR *expr)
Definition: expr_value.c:285
SCIP_RETCODE SCIPincludeExprhdlrSin(SCIP *scip)
Definition: expr_trig.c:1371
SCIP_Bool SCIPisExprSin(SCIP *scip, SCIP_EXPR *expr)
Definition: expr_trig.c:1460
#define NEWTON_NITERATIONS
Definition: expr_trig.c:61
void SCIPexprhdlrSetEstimate(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRINITESTIMATES((*initestimates)), SCIP_DECL_EXPRESTIMATE((*estimate)))
Definition: expr.c:512
SCIP_Bool SCIPisZero(SCIP *scip, SCIP_Real val)
SCIP_Bool SCIPisLE(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
static SCIP_DECL_EXPRINTEVAL(intevalSin)
Definition: expr_trig.c:925
static SCIP_DECL_EXPRCOPYHDLR(copyhdlrSin)
Definition: expr_trig.c:779
SCIP_Bool SCIPisExprCos(SCIP *scip, SCIP_EXPR *expr)
Definition: expr_trig.c:1471
static SCIP_DECL_EXPRPARSE(parseSin)
Definition: expr_trig.c:824
SCIP_RETCODE SCIPincludeExprhdlr(SCIP *scip, SCIP_EXPRHDLR **exprhdlr, const char *name, const char *desc, unsigned int precedence, SCIP_DECL_EXPREVAL((*eval)), SCIP_EXPRHDLRDATA *data)
Definition: scip_expr.c:814
void SCIPexprhdlrSetSimplify(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRSIMPLIFY((*simplify)))
Definition: expr.c:490
void SCIPintervalSin(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)
void SCIPexprhdlrSetIntEval(SCIP_EXPRHDLR *exprhdlr, SCIP_DECL_EXPRINTEVAL((*inteval)))
Definition: expr.c:479
static SCIP_DECL_EXPRBWDIFF(bwdiffSin)
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# MA008 Lesson 2 Expressions
Contents
## Excitement About Wipers & Nozzles
People were so excited about Grant's new product that he started getting requests left and right for his glasses wipers and spray nozzles. So, he started to keep a list of everyone who would want a pair very soon. By the end of 1 day, 36 of his friends had begged him for glasses wipers and 11 of those people each said that they would also like a pair of nozzles to go with their glasses wipers.
## Total Earned
Once he realized how many people were excited about his new business, Grant started to wonder how much money he could bring in. So assuming that Grant only sells glasses, wipers, and nozzles, which of these 4 expressions do you think should replace the question mark to make an equation for the total amount of money that he'll earn.
## Total Earned
Well, unless Grant plans on paying other people to buy his products, he'll presumably bring in some money each time he sells a nozzle, and each time he sells a set of wipers. This means that the money he earns is going to be equal to the money he makes from his wiper sales plus the money he makes from the nozzle sales, which is just this first choice up here. For example, let's say, just picking numbers out of the air, that Grant decides to sell a wiper set for \$5 and one nozzle for \$3. Well, then we know that money earned at that point would be equal to \$5 plus \$3 or let's see, if I was going to pay for these, it would be 5, 6, 7, \$8 total. So all we would do to find the total money earned would be to add the cost of each of the products together.
## Incorporating Price
So, we decided to call the price per wiper set w. That means that if Grant sells one set of wipers, he'll earn w dollars. If he sells two sets, he'll earn w+w dollars, which is 2w dollars. If he sells three sets, he'll earn w+w+w, or 3w, and so on and so forth. Since you know that he is going to sell 36 wiper sets, that means he's going to make 36w dollars off of the wipers along. So, 36w is the correct answer.
## Nozzles
Now that we've dealt with our money from wipers, let's move on to figure out how much money Grant's going to make, from selling this first batch of nozzles. Remember that, 11 people, each asked him for two nozzles. Also, we decided that n is equal to the price per nozzle. This is for one nozzle, not for two nozzles. So, which of these choices do you think is equal to the money he is going to earn from these nozzle sale so far?
## Nozzles
So part of figuring out how to solve word problems well is figuring out what information isn't important for the question that we're trying to answer. We want to know how much money Grant's going to make from selling nozzles. All that this is going to depend on is the price per nozzle and how many people want to buy nozzles. That means that these answers with 36, which has to do with the people who want to buy wipers are irrelevant for this question. Also w is the price per wiper set not per nozzle, so this answer which depends on w can't be correct. And this one even though it also involves an n, involves a w so, it can't be right either. We're only focusing on nozzle sales here. So what are we left with 11, pretty good nothing having to do explicitly with wiper sales. However, these 2 answers 11 and 22 don't involve an n. That will mean that no amount or how many nozles Grant sells, he's going to make either just \$11 or \$22. I would hope that, for his sake, the more nozzles he sells, the more money he makes so we want to say that those answers aren't correct. So now we have 112n and 11n. The key here is remembering that each of these eleven people want two nozzles. Not just one nozzle. So each person who buys two nozzles is going to pay him not n dollars but 2n dollars. If 11 people paying 2n dollars so that means we need 112n which is this answer right here.
## Writing Concisely
So from our last two quizzes, we now have developed a new expression for total money earned by Grant. Instead of money from wipers, we have 36w, where w is the amount that each set of wipers cost. And instead of money earned from nozzles, we have 11 person pays for one nozzle. Now when I look at this term 11 2n, it looks a little bit complicated to me, definitely more complicated than 36w does. Can you think of a simpler way to write 11 2n? Now, there are a ton of different ways that we can write 11 2n and come up with a mathematically equivalent expression, but I would prefer that we try to come up with a simpler way to write this. So, if you have an idea of how to do that, please type it into this box right here.
## Writing Concisely
So one way to look at the term 112n is to think that we're adding 2n to itself 11 times. Okay great, we have 112ns added together. However we know that 2n is just equal to n+n. So we can write this yet another way. For each 2n we can instead write n+n, so we end up with n+n plus. So, for every 2n that we had in this equation, I wrote n+n instead. Now I actually already counted all these n's up and it turns out that there are 22 of them. So we know that So apparently 112n is equal to 22n. That means that we can come up to our equation for the amount of money that Grant is going to earn and replace 112n right here with 22n.
## Factors
Writing up and counting out those 22 n in the last quiz took me a really long time, though I can only imagine how torturous it would have been if I had, had to multiply there is a much easier way to simplify terms than adding them together like we did then. To talk about how this works, let's start by considering a term. Lets say, 5x 7y 2z. Now remember, a term is a bunch of variables or numbers, or both, that are multiplied together. And before we start playing around with this term, I'd like to add one more word to our vocabulary, factor. Now, factors are things that we multiply together. Just like terms are things that we add together. Together. So this term, 5x 7y that are all multiplied together. Another way to think of a factor, is that it's something that a term is divisible by. Now, we can't forget that in this term there are invisible multiplication signs between the five and the x, the seven and the y, and the two and the z. So another way to think about this term is that it's
## Identifying Factors
So real quick, let's just have a quiz. Which of these choices down here is a factor of this term, 5x 7y 2z? Remember, you can think of a factor as something that this term is divisible by, or as something that you can multiply by some other set of factors to equal this term. Please check as many answers as you think
## Identifying Factors
So, let's just go through these entries one by one you to figure out which ones are correct. Starting of 2z, we see that this is something that is multiplied by 5x and by 7y in order to equal this term. So, this is definitely a right answer. Now, when look at five, we need to remember that invisible multiplication sign between the five and the x. If we multiply five by x and 7y in 2z, then we get this whole term, so five is also a factor. Now, one is where things get a little bit tricky, and if you miss this one, not a big deal. This actually is a factor of this term and actually of any term. The reason that one is a factor for any term we might have, whether it's a number or a variable, is because, if you multiply one by that term itself, you will end up with the term that you're looking for. So in our case, the thing that we need to multiply one by in order to get 5x7y2z is just this term itself. I know that might seem a little bit complicated right now, but you'll have plenty of practice in the upcoming quizzes to sort this all out. Bottom line, one is always a factor. Now, first, you might think that zero is similar to one in this way, but zero is actually not a factor here. We can't divide this expression by zero, that would actually give us a solution that we don't know how to interpret right now. And there's nothing that we can multiply by zero in order to get this expression, since zero times anything is just equal to zero, so zero should not be checked off. We know that y is multiplied by seven and also by 5x and check that one off as well and x works in the same way. So, we've checked everything off except for the zero. That was great. I know that factors are a little bit trickier than terms, so I hope that this vocabulary word is starting to make a little bit of sense. We'll keep using it really frequently.
## Commutative Property
So now that we understand what factors were multiplied together to create this term, is there a more simplified way for us to write this? Thankfully the answer is yes. However before we can start to play around with this term, we need to learn about something called the commutative property. Specifically the commutative property of multiplication, since all of our factors are multiplied together here. The commutative property of multiplication basically tells us that it doesn't matter what order you multiply things together in. So, for example we know that 2 3 = That means we know that 2 3 is just = 3 variables instead of with numbers we could talk about, let's say, x z y. Here we have three different variables multiplied together and we can rearrange these factors in any order we want and still get a mathematically equivalant expression. So we could have, a ton of different things maybe z x y. That's also = y x z or z y x., and so on and so forth. All these expressions and all the other ones that we could get, by rearranging these in other ways are equal to one another. So remember for multiplication, it doesn't matter what order you multiply things together in. This holds no matter how many things you want to multiply together, and it holds whether the factors are variables or numbers.
## Commuting
Okay, time for a quiz. Now that we've talked about the commutative property of multiplication. Let's see if you can apply it when we're dealing with this term right here. 10m237. I would like you to check off all of the expressions down here that are equal to this term. Just a hint, there are probably going to be several that are right answers.
## Variables on the Right
So going back to this term that we're looking at earlier 5x7y2z, we can start to use what we just learned about commutativity to rearrange all the factors that are multiplied together here, in whatever way we want to. Now, what I really want in this case is for all the variables to be on the back end of the term and all of the numbers. Are the constant factors to be at the front of the term. So please write in these slots an equivalent version of this term by filling in each slot with either a constant or a variable. So, we're just going to rearrange these terms in an order like this. Think about what answers are allowed because of the commutative property.
## Variables on the Right
Looking at this term, the constant factors are five, seven, and two. So, we can write those in the first three slots right here. Because of the commutativity of multiplication it doesn't matter what order we write the five, seven, and two in. Instead, I could have writen two, seven, five or two, five, seven or seven five two or any order of these three numbers in these first three slots. For simplicity sake, I'm just going to leave mine written this way, but you're answer is right as long as these three constant factors are in these first three slots. Now, what's left over to deal with are the variable factors. So for those, we have x, y and z. Here, it's important to remember, the invisible multiplication signs between these constant factors in the adjacent variables. Remembering that those are there is what's going to allow us to pull out the variables and move them around. So, I'm just going to keep x, y, and z in the order they're written in and fill them into the slots right here. Now, just like with the constant factors, we could write these variables in any order that we want to. We could write z,y,x, z,x,y, x,y,z, actually, that's what we have, [LAUGH] y,x,z, . Any order these three variables go in is correct as long as they are in these last three slots.
## Make it Pretty
So now this is what our term looks like. 5 7 2 x y z. Now this definitely looks different from how our term originally did, but I wouldn't say that it looks less complicated. So our goal for this quiz is to make this look much more simple. So think back to when we were talking about Grant's gleaming glasses last time. We simplify this term 11 2n to equal 22n. We are using the same idea that we used to come up with that answer. Can you think of a way to simplify this term up here. Try this question down as much as you can and remember to get rid of any multiplication signs that you don't think need to be expressive.
## Make it Pretty
The first thing that I notice when I look at this version of our term is that we actually don't need these dots between the variables. And actually, we don't need a multiplication sign between 2 and x either. Inside a term, the only place we really need to explicitly indicate multiplication with the multiplication sign is between the constant factors. The reason that we had to really write them in between the 5, the 7 and the 2 before, was so this didn't look like we were writing get rid of those three unnecessary multiplication signs. Remember, if you kept them in, your term is still mathematically correct, it just contains a couple of extra symbols that don't necessarily need to be there. So now we have this 5 7 2 to deal with. Those are just numbers, and we know how to multiply numbers together. 5 7 = 35. And with 70, and write the remaining factors afterward, xyz.
## Simplifying
So now that we've worked step by through how to simplify terms, I want to you to try simplifying this term on your own. So in this box to the right, please write the most simplified version you can find of (-5s)(2r)(3t). Remember that theses parentheses just indicate multiplication. It's not that means that negative 2r is being multiplied by -5s and by 3t, not subracted from them. Good luck.
## Simplifying
Like we did before, we're going to start off by identifying the constant factors in this term, and then moving them to the front of the term. So our constant factors here are negative five, negative two, and three. So you can write -5-23 as the first three factors of our rewritten version of this term, then after that come the variables s, r, and t, so we multiply the constant factors by the variable factors. Remember that these multiplication signs between the variables actually aren't necessary, so I'm just going to get rid of those right away. Now negative five times negative two is just positive ten. Remember, a negative times a negative equals a positive. So then we have, 103 and 103 is just equal to 30. So we can replace, -5-23 with 30, and then multiply that by the rest of the factors that are left over s r t. So our final simplified version of this term is easier to deal with than this initial version of the term did. So I think we're making really good progress toward simplifying different expressions.
## Alternative Forms
So, I've already showed you one convention that we use when we simplify terms. We put the constant factors at the beginning of the term. When we do that, it makes it easy once we simplify because we end up with one coefficient and then all of the variable factors after it. People also tend to put the variable factors in alphabetical order. So, if you wanted to do that, we could say that this also equals 30rst. In order to make the change from 30srt to 30rst, we had to remember the commutative property of multiplication. Since we were allowed to switch the order of r and s without changing the value of this term. So, the order that variable factors are written in is just another convention in algebra. It's just something that's useful for us to use, but it doesn't change the fact that this version of the term that we had initially is mathematically equivalent to either of these other two simplified versions.
## More Simplification
Let's do one more quiz to practice simplifying terms. This time please simplify 4x y-3x. Remember that this negative sign right here, in front of the 3, is part of the factor -3. We're not subtracting 3x from y, we're multiplying 4xy by -3x. So keeping that in mind, please write the most simplified version of this term that you can over here.
## More Simplification
So as always, we're going to start to simplify this term by identifying the constant factors in it. So for those, we have 4 and -3. And remember, we want to move those to the front of the term, so that they are the first two factors that we have written. So this term is equal to have left over, x, y and x. So right off the bat we know how to deal with 2 of the factors here. We know that 4 -3 is just equal to -12. So we can replace 4 -3 with -12 and then write the 3 remaining factors. There's something interesting here though. We have 2 variables that are the same. We have x and x. I'm going to rewrite this one more time with the order of the variables switched so that the x's are next to each other. That's just generally a good rule of thumb in algebra is to write things that you think are related to one another next to each other. This x x is interesting. This is the first chance that we're going to get to use exponents. You've seen them already a few times in this course, but we haven't gotten to write our own factors with exponents in them. So, this may seem like new material or it may be review for you, but xx can also be written with an exponent as x^2. In the same way, x x x = x^3, and so on, and so forth. Remember that in all of these equations right here, I didn't need to write any of these multiplication signs. If we had just written the x's directly next to one another, without any symbol in between, multiplication would still have been implied. So instead we could just have xx equals x^2. I just wrote this out to be abundantly clear. The exponents show how many of the same factor are multiplied together. Incidentally if 2 x's mulitiplied together is equal to X^2 then when we have just 1x is equal to x^1. This seems a little bit silly to write though, writing X to the 1 is more complicated than writing just x so. We usually don't move from having x to writing x to the first instead. So using this information about exponents, we can replace this x x with an x^2. And with thta information we can rewrite this term as -12x^2y. We're obeying all the conventions we know about how to write terms because we have the constant factor at the front, and then we have our variables in ascending alphabetical order. We have the x^2 before the y. That was awesome, I know that this was a pretty complicated thing that involved a ton of different concepts, some of which we haven't focused on a lot yet. But don't worry if exponents still don't feel totally comfortable, we're going to keep working with them a ton more.
## What is a
So now that we know how to simplify terms, we can get back to Grant and his gleaming glasses. Earlier, we came up with expressions for the amount of money that Grant's going to make from his friends buying his wipers, and also from them buying his nozzles, and we had an equation for the total amount of money earned. Saying that the total amount of money that he's going to earn from his friends is equal to the amount that they spent on his wipers plus the amount that they spent on his nozzles. Now I'm going to add one more equation into the mix for you or rather create one more variable. Total money earned right here takes a long time to write, so instead I'm going to call this a different variable. Let's say a. So, with my other equations up here, I can also write total money earned euals a. So, let's combine all this information that we came up with in our earlier quizzes and the new information that I just gave you that a stands for the total amount of money earned. Which of these expressions down here, do you think should replace this question mark, in this equation for a? You can check as many answers as you think are right. I know this is a lot to look at on the screen at one time, but once we come up with this final equation, we'll only have single letters and numbers, and no more words, in our equation, and that will make things much easier for the future.
## More Orders For Grant!
So now we have this wonderful straight forward equation for the amount of money that Grant's friends are going to pay him once they buy their glasses, wiper, and their spray nozzles. However just when we think we're starting to figure things out for him situation gets a little bit more complicated. Even though this means more work for us, this is great for Grant, because more of his friends have asked if they can buy his products. The day after his first round of requests came in, even more of his friends and his friend's friends heard about his new incredible inventions, and asked him to add to them, to the list of people to buy his products. and 25 more people wanted to buy 2 spray nozzles each. This equation no longer tells us the total amount of money that Grant's going to earn from his friends, and his friend's friends buying his wipers and nozzles. So, what we need to do is create a new equation. We need to come up with a different way to express a that takes into account this new information that we have, but also doesn't forget what we had before.
## More Customers
We heard a lot of information in the last video, so here is just a summary of all of that on one screen. We can think about Grant's sales story so far as having 2 situations. The situation after the first day, which I'm going to call the before picture and the situation after the second day of selling, which is the present situation we're concerned with. The last equation that we came up with, a = 36w + first day. So, I changed the name of the total money earned to a old to show that this is the money earned after the first day of selling. This equation still works if we're only interested in calculating the money that Grant earned from his friends after just that one day, but now, we want to find, is what I'm going to call a new. The money he's going to get from those people and from these new people who also want to buy. What we're going to do in this quiz is come up with an equation for anew, which should combine the information from aold with this new data about people who are also going to buy the wipers and nozzles. So, which of these equations down at the bottom is the correct equation for anew? The total amount of money that Grent will have after these people on the first day buy his wipers and nozzles, and these people from the second day buy his wipers and nozzles. This is alot of information to take in, so I'm going to lable this quiz a challenge quiz. Actually many of the quizzes that you've had have been challenging, but I think that this one is especially difficult. Think really carefully about how many terms you think this new equation should have. Should it have 2 terms or should it have 4 terms? Also, there may be more than 1 correct answer. Even if you don't get it right the first time, just give it another shot.
## Gathering Terms
As I said in the past several videos and quizzes, there are a ton of mathematically equivalent ways of writing any expression we might have. For example, if I rearrange the factors within any of the terms here, or rearrange the order of the terms themselves, or let's say, tack on a 0 at the end. The value of the expression on the right side of the equation doesn't change. However, there are certain convienient ways of writing expressions. Ways that actually make them simplier to deal with that we're going to want to use. We call this process of rewriting expressions; simplifing expressions. One really useful tool that can help us start to simplify and expression, or see if we can simplify it any further, is to change the order of the terms. We know that we're allowed to do this because of the communitive property of addition. So, how could we do that here? Let's just rearrange the terms on the right side of this equation so that both terms containing w are in the first two slots and the two terms containing n are in the last two slots. So please just type the proper terms into the proper slots. These smaller spaces are for plus or minus signs but you can also type in as you see fit.
## Gathering Terms
So hopefully, this quiz is a little bit easier than the last one we did. What we're trying to do first is just identify the terms that have w in them. So, going through our equation up here, we see 36w and 51w, and we can just fill those in to these first two slots. Remember that it doesn't matter which order we write them in. It doesn't matter if we write 36w or property of addition. Next we need to identify the end terms, so those are the two that are left, 22n and 50n, and we just want to write those in these two slots. Again, order does not matter because we're just going to add everything together. I'm just going to put the 22n first since 22 happens to be my favorite number. The last step to make this a fully blown equation is to add in our plus or minus signs between the terms. Here in the top equation, every term is positive. You don't see any negative signs here. So that means that each of these signs is going to be a + sign. When we switch terms around, there's no change to the value of each term. Nothing's going to become negative that used to be positive. So the only thing that's different about this bottom equation from this top equation, is the order that we've written the terms in.
## Combining Like Terms
So now that we have this equation for the total amount of money that Grant's going to make from people who bought his products the first day and the second day, it would be great if we could simplify it further, however we don't know how to do that yet. So, before we dive into this particular example, let's look at a slightly less complicated but similar problem. Let's say we just have some expression. I picked 3x - 5y + 6x + 9y. Now how can we simplify this expression? Well, I think we need to remember what each of these terms really means. So 3x for example is actually equal to x + x + x and 6x is actually equal to 6 x's added together. Right now, writing this out might not seem particularly helpful. But I think the reason that I chose to write these terms this way will becomes clear if we just rearrange the order of the terms in this expression. So now we switch the order of the terms around so that terms with x are next to each other and the terms of y are next to each other. Now we can see that the first thing we want to do is add 3x and 6x together. With all of the x's written out, that doesn't seem that hard. I just need to figure out how many x's, total I have down here. And if I count them I have 1, 2, 3, 4, 5, 6, 7, 8, that, in order to get the sum of 3x and 6x here We don't actually have to count all the x's. All we really have to do is add the coefficients of the variables together, since 3 + 6 = 9. Once we have the coefficient, we just make sure that we multiply that by the variable that both of these terms have. We usually call this adding like terms, or combining like terms, as I've written at the top of the slide.
## Its Fine to Combine
Now that we've figured out how to combine figure out how to combine -5y and 9y? So just fill in the term that you think is necessary to make this equation true.
## Its Fine to Combine
Remember that in order to add 3x and 6x together, I simply added their coefficients, and then multiplied by the variable they both contain to get 9x. Since 3+6 is 9, and the variable in both terms is x. We can do the same thing to deal with the y terms over here. So, -5y+9y is going to be equal to whatever negative 5+9 is, times y. We know that -5+9=4, so our answer is 4y and we can fill it in the box. Over here in our original expression, we have four different terms. And over here, we only have two terms. This why we call this simplifying expressions. This expression is way more simple than the one over here is. Remember that I was allowed to put an equal sign here between these two expressions because they are exactly mathematically equivalent. In order to come up with the expression over here, I only played with the terms inside of this expression. I didn't bring anything in from the outside. The only way I modified it was by squishing together things that were already there.
## What to Combine
Since we've now had a little bit of practice with combining like terms, I want to make sure that it's abundantly clear which terms we're allowed to combine and which ones we're not. Terms that you're trying to add together can be combined if and only if two things are true. So first things first, the terms have to have exactly the same variable or variables. So examples of this will be terms like 3xy and 7xy or -4b and 15b. On top of this I have to add that each of these variables that correspond to another have to have the same powers or the same exponents. So, if we have the term 3x^2 and the term 6x, and we try to add those together, we cannot combine them. These are not like terms, even though they have x's in them, this is 3x^2 and this is just 6x to the first power. They don't have the same power, so we can't squish them down into 1 term. Another example of this would be something like 11ab^3 + 12a^2b3. Even if the b^3 factors have the same power, the a here only has a power of 1 and the a here has the power of 2. We cannot add these two things together because one of the variables involved does not have the same power in both terms. So, we cannot squish them down into one term.
## Practice
Now that we've talked explicitly about what it means to combine like terms, or combine terms that have the same variables with the same powers in the them, I'd like you to try an example of how to do this. Please simplify this expression, Start by figuring out which terms in this expression are like terms, and then figure out how to combine them. Good luck.
## Practice
Just like we did in the example, we're going to start by rearranging the order of the terms in this expression, so the terms with the same variable are next to one another. Great, now, we have 7x-10x+5y+3y. The next step is to add together the coefficients of the like terms. Great, so now we have -3x, since 7-10 is negative three and the variable there was x, plus make this a little bit prettier, since we have a negative sign at the front, we could because of the commutative property, rearrange the order of the terms one more time. So, I personally prefer to write it this way, 8y-3x. So this is our new version of the expression on the left. It's almost hard to tell from looking at these two expressions that they're actually equal to each other, but that just shows you how powerful combining like terms is. We end up with an expression that's much nicer to look at and much easier to use.
## More Practice
Now this time we have an expression thats a bit more complicated than the past few that weve seen. However, if we keep in mind our rules that we know for combining like terms, that we can only combine terms that have the same variables with the same powers, then this actually shouldnt be that much harder than the other ones that we've done. Just give it a try, write the simplest version of this expression that you can in this box over here.
## More Practice
The first thing we need to do in order to start simplifying this expression is to identify which terms are like terms. -5x^2 is the only term in this expression that has an x^2 in it so it is not like terms with anything else here. However, we have seem related to the x^2 term but remember, the power of the term matters. Both of these terms have x^1, remember, there are little invisible ones right when you just have a variable on its own. x is just equal to x^1. Anyway, these 2 terms are like terms, so I'm going to start to rewrite this expression with the like terms next to one another. Remember that the sign of the term, it belongs to the term itself, and moves along with it when we rearrange the order. Then, the 2 terms that we haven't written are 14 and -3. These are just numbers, so they're definitely like terms, and we'll keep them next to one another. Now, that we've identified which terms are like terms, it's time to combining those like terms. So, -5x^2 stays by itself, since we can't combine it with anything else. For the x^1 terms, we end up with a new coefficient of 6-1 or 5, so plus 5 times the variable, which is x. And then, all we have left to deal with are other numbers. 14-3 is 11 so we add 11 to the end. Once you've written down our final expression, we can check and make sure that none of the terms in it are like terms with one another. That is, we only have one term of each type in the final expression. This is an 2 term, this is an x^1 term, and this is a constant term. So, there's nothing more that we can combine. That means that we've reached the final stage of our simplification. Awesome.
## Simplifying Four Terms
By now you've had a lot of practice with simplifying expressions. So here's a sort of challenge problem for you. Please try to simplify x^2 + 3xy - 7yx - y^2. As always, type your answer into the box right here. Now this is definitely more difficult, or at least a little bit trickier than what I've asked you to do before, but just give it a try.
## Simplifying Four Terms
So, like we've done a couple of times before, let's start off by going through the terms one by one to see if any of them are like terms. x^2 right here is the only term with an x^2 in it, and -y2 right here is also the only term with a y^2 in it. However, we have these two middle terms that each have an x^1 and a y^1 in them. So, are they like terms? Well, according to our rules up here, they do have the same variables. And those two variables, x and y, have the same power. The x here is x^1, as is the x here. And the y here is y^1, as is the y here. So, presumably they are like terms. What we need to do is use the communicative property of multiplication that we talked about a long time ago to make these look the same. We know from the communicative property of multiplication that xy, or just xy, is equal to yx, or just yx. So, I'm going to rewrite this term right here, 7yx, as 7xy instead. It's amazing how switching around the orders of factors within terms can change the way an entire expression looks. Now, our job is pretty stand. The terms that we're not combining, I'm just going to write as they are, so x^2 is the same. And then, I'm going to combine these two terms in the middle. So remember, we add their coefficients. 3+-7 or 3-7 which is -4 times the variables x and y, -y^2, which doesn't change.
## Grants Equation
By this point, you've had a bunch of practice with combining like terms. So, let's go back to that last problem we were doing with Grant, and this is glasses, wipers, and nozzles. Here's the equation we had A, the total amount of money he's going to earn from his friends buying his products is equal to 36w+51w+22n+50n. Last time you saw this, we didn't know how to combine like terms, but now you do. So in this box I would like you to take the most simplified version of this entire equation that you can come up with. Remember, I am looking for the whole equation not just this expression. You need to include the a equals in the equation down here.
## Grants Equation
So, since we know we're trying to write an equation and not just an expression, I'm going to start off by writing a = in our box down here, since I know that the left side of the equation is not going to change at all. Then I can start to combine my like terms. Conveniently our terms with w are already written next to each other and are terms with n. It was so nice that we did that for ourselves earlier. This is pretty straightforward then. Since these are like terms, I can just add their coefficients. 36 + 51 = 87 and I multiply that by the variable w, 22 + 50 = 72 and that gets multiplied by the variable as well. Awesome, we're one step closer to helping Grant figure out how much money he's going to have after these first 2 batches of friends pay him.
## Put It Together
We've simplified terms by combining factors within them and we've combined like terms. So, let's try to do both of those things at the same time. Here, we have a very long expression, That took a really long time to write and a really long time to say, so it would be awesome if we could simplify this. That is what I would like you to try to do. Now if this looks daunting, no big deal. Just give it a try. You have absolutely nothing to lose. Writing your work on paper first will definitely help you. Also, remember to try to simplify within each term first, and then, once you've done that, to identify what the like terms are in this expression, then you can work on combining them together. Good luck.
## Put it Together
The first thing that I am going to do, in trying to simplify this expression, is to look at each of the terms and figure out if I can squish it down at all. So first we have 15x^2. There's nothing that I can do to make that more simple on its own, so I'm just going to rewrite it. Then, 3x^7, same thing, then I come to. -7x2x. Now there are definitely some factors here that I can, can combine. If I rearrange the order of these things I can put -7 and the end, -72 is -14. So I have a coefficient of -14. And then we have xx. We know that xx is just X^2. So I can write that as well. Moving on, we have -42x. We can, again,combine the two factors. So you have -8x, -54, 54 is 20, so we have -20+x3. We can just rearrange the order of those two, and then we have 3x, which is just terms, in and of itself, is as simplified as it can get. The next step is to figure out which terms are like terms. I'm also going to already start writing like terms next to each other in a modified version of the equation. We have 2x^2 terms, only just need to combine the terms that I know are like terms. Remember that we add the coefficients of like terms together, and then multiply by the variable. 15-14 is 1. So we have 1x^2, or just x^2, 3x^7 is on its own. It's not combined with anything else, -8+3 is -5, times the variable x, and then we have our constant term. So this right here is our final answer. Our long, not very pretty expression has been squished down to be something much more manageable.
## Polynomials
In the next few minutes, I'm going to throw a couple more vocabulary words into our mix. First, I want to talk about a special kind of expression, in fact, the kind that we've seen most up to this time. These are polynomials, a polynomial is an expression made up of constants, variables or both that are combined using division, subtraction, or multiplication. So this basically means that we have one 1 or more terms like we've talked about before added together. The variables and I suppose the constants as well in a polynomial, also have to have non-negative integer exponents. So as an example of a polynomial, we might have something like So some polynomials that we see will have more than one variable in them, like these two right here. But often times we'll also see polynomials that have just 1 variable involved, or maybe even none. So an example of that might be something like But again, any combination of constants and variables, using these operators, and only these kind of exponents makes a polynomial.
## Not Polynomials
So now that we've talked about what polynomials are, and seen a few examples of them, which of these expressions are not polynomials? Notice I want you to check the ones that are not polynomials, not the ones that are polynomials. Remember the three requirements that an expression must fit in order to count as a polynomial. I have listed them right here in case you need to check. And if you have trouble with this just go back and watch the last video to refresh yourself on what apolynomial is. Goodluck.
## Not Polynomials
Three of these are not polynomials, but the rest of them are. We learned that a polynomial is an expression that only uses addition, subtraction, and multiplication to combine constants variables. But this first trace right here has a big division sign in it, dividing one expression by another expression. Now if we had either the numerator or the denominator of this fraction on its own, then both of them would be polynomials. But because they're divided, this is not a polynomial, so we'll check that one off. We'll talk more about expressions that look like this later on the course. One of our other important rules is that a polynomial must have exponents in it that are only non negative integers. Right here we have x1/2 and 1/2 may be positive, but it's not an integer, so that means that this is not a polynomial. We can think about that rule again when we look at this answer choice right here, -6x^5+x^-3-11x+9. All of these terms in here are fine for being part of polynomials, except for this one x^-3, because -3 is a negative integer exponent, not a non-negative integer exponent. So that means this expression is not a polynomial. It may seem a little bit funny that 6 counts as a polynomial. We don't often talk about numbers or variables on their own as polynomials, but they technically do qualify since they do fit our definition. We said that polynomials could have just variables, just constants, or both. So 6 and all other constant terms are technically polynomials. We're going to talk about polynomials throughout the entire rest of the course, so it's great to get a handle on how to find them.
## Identifying Degree
We just said that the degree of return in a polynomial is the sum of all the exponents of all the variables in that term, so the degree is a number. Now knowing that, I would like you to write in each of these boxes, what the degree of the term next to them is. So just fill in the proper number in each of these blanks.
## Identifying Degree
Our first term right here only has one variable in it, x, and the power that x is taken to is four so that means the degree of this term is four. This is a fourth-degree term. Now this next one is a little bit tricky. 100 is just a constant term. It doesn't have any variable factors in it, or in other words, it has 0 variable factors. So, this means that its degree is 0. This is true of any constant term. If we had the number, say, 78 here instead or -432 or 19.3, any constant term no matter what it's value is has degree 0. So, that means that 1/2 over here, which is also a constant term, has a degree of that if we desperately wanted to have a variable in a constant term, but we didn't want to change the value of the term, what power would that variable need to be taken to? So, let's say, we have 1/2 here and we want an x in that term. In order to keep this term equal to 1/2, we need to have x be to the 0 power since anything, any variable, or any constant, to the 0 power equals 1. That means that we would actually have, 1/2 times 1, which is just equal to 1/2. But even if we choose to write the term in this way with the variable involved, the power of that variable is 0. This is still a zero-degree term. For this next term, y, we need to remember that any variable that doesn't have an exponent written explicitly, actually has an invisible one as its power. So, this term has a degree of 1. It's a first-degree term. And lastly, we have x^2, y^2, z^3. So, the degree of this term is just going to be 2+2+3, which is equal to 7.
## Degree
Now that you know what a polynomial is, we're going to talk briefly about a word that we can use to characterize a give term in a polynomial. The degree of a term. Now the degree of a term is equal to the sum of all the exponents of all the variables that are in that term. So if we have a term like -4x^3 then the degree of this term is 3. Since we have an exponent of 3 for the only variable that's in the term x. Another way we can say this is that, this is a third degree term. Now, if, in contrast, we have a term like 6y^7 z^4,, the degree is 11. Or, we could also say, this is an eleventh degree term. Now the degree is 11 here, because, for our first variable we see, we have a power of power of 4. y and z are the only two variables in this expression, so the degree is equal to the sum of their powers. 7 + 4 = 11.
## Polynomial Degree
Just as we can talk about the degree of a term, we can also talk about the degree of an entire polynomial. The degree of a polynomial is just equal to the highest degree of any of its terms. So to figure out the degree of a polynomial we first need to figure out the degree of each of its terms just like we did in the last quiz. If we look back at one of the polynomials we used earlier. -12x^7+3x^2+64x, we can see that this is a by first calculating the degree of each term, so this one is a seventh degree term. This is a second degree term, and this is a first degree term, because of the invisible 1 next to this x that stands on its own. The highest number out of 7, 2 and 1 is 7, so this is a 7th degree polynomial.
## Polynomial Degree ID
Considering this definition of the degree of a polynomial that we just discussed. What is the degree of each of these polynomials down here? Please fill in your answer in the box to the right of each expression
## Polynomial Degree ID
Let's go through these one by one. So first x^3+6y^2. We want to start by finding the degree of each term. So the degree of this first one is 3 and the second term is 2, since we have exponents of 3 and 2 respectively. 3 is greater than 2 so this is a third degree polynomial. Next 7-3x+8x^3y, we have degrees of 0, 1 and 4. Since we have numbers. So this polynomial is of degree last two polynomials as well. One interesting thing to note is that the degree of a polynomial is usually information that comes from just one term in the expression. The term with the highest degree. But in some cases, like in this last example, you might have more than one term that's of the same degree. So for example here we have x^2 which is a second degree term and z^2 which is also a second degree term. Having two terms of this same degree Doesn't change what the highest degree we see here is. We just happen to see that highest degree twice. We still follow the typical rule and say that this is a polynomial of degree two.
## Standard Form
So far when we've seen polynomials, the terms haven't written in any particular order. Remember, we learned before about the commutative property of addition. Changing the order that you add terms together in has no affect on the value of the expression, a+b is just equal to b+a. So any set of terms that you have added together can be written together in any order. And we'll still be mathematically correct regardless of which of those orders you choose to use. However, there is a convention that people use in algebra to help them figure out what order to write the terms of the polynomial in. It's pretty simple. The tendency is to write terms from highest degree to lowest degree. So, for example, if we have this polynomial y+6xy-y^3, we can first figure out the degree of each term and then rearrange these terms so that the degree with the highest degree comes first, and then the rest of the terms continue in descending order of degree. A polynomial written in this way is said to be written in standard form. So again, writing a polynomial in standard form doesn't make it any more mathematically correct than writing the terms in any other order. But mathematicians usually find the standard form a bit more, visually appealing, and it also can help us understand the polynomial as a whole a bit more quickly than we could if we wrote the terms in a different order. Since in standard form, the term with the highest degree comes first, we only need to look at that first term to figure out what the degree of the entire polynomial is. So that's why standard form is particularly convenient.
## Rewriting
Please write these two polynomials in the standard form. If you need to peek, the definition of standard form is right here on the top right-hand corner, but try to do it without looking up here.
## Rewriting
Let's start by finding the degree of each term in either polynomial. I'll go ahead and do that right now. Once we figure out the degree of each term in either expression, we rearrange those terms that the term at the highest degree comes first, and then the rest of the terms go in order of decreasing degree. So for this top polynomial, we'll need the terms to go in order of degree from 3 to 2 to 1 to 0. So that's going to give us We can do the same thing for the second polynomial. Written in standard form, this polynomial is -12x^7+3x^2+64x. Now that we have them written in this way, we can see right off the bat that this top polynomial is a third degree polynomial and this bottom one is a seventh degree one. So standard form definitely makes our job easier. Under that standard form is something that applies to all polynomials not just ones with single variables or ones with just x's. You'll get more practice with other polynomials in standard form later.
## Exponent Notation
So basically exponents give us a convenient notation for showing repeated multiplication of a given number or variable or a combination of numbers and variables. So knowing that, how would you write 7777 using exponent notation? So I know that you can evaluate this expression to equal just a number without any exponent, but for right now I want you to make sure that you use exponent notation for this question.
## Exponent Notation
So, since seven is the number that we're multiplying by itself over and over again, it is the base number. And it goes here as the big number that we write first. Now we have four of these sevens multiplied together so the exponent that we want is four. So that means that 77 77=7^4. Now there are several different ways of saying this answer out loud. You can say seven to the fourth power Seven to the four, seven to the power of four, or just seven to the fourth. Certain other exponents have special names that we use, but they're pretty self-explanatory. For example, 77=7^2, but instead of saying that, we might also say seven squared right here. In the same way, if we have three sevens multiplied together, 777 we get 7^3. But sometimes we say seven cubed instead.
## xxxx
This time, we have xxxxxx. That's a lot of x's to write down. So, what's a different way that you could rewrite this term using exponent notation? Please just use one number or variable in the base, and one number or variable in the exponent. Remember that on a computer, you need to write the base number and then a caret sign and then the exponent number.
## xxxx
X is the thing that we're multiplying by itself, so it is the base. And then, there are six of them multiplied together, so that is the exponent number. Again, the way that you needed to write this on the computer was x^6. This shows that 6 is being shifted up into the exponent slot.
## Exponent Practice
So now I'm going to give you a break and let you actually write just a number as an answer to a quiz. What number, not written in exponent notation or anything, is -3, that quantity to the 4th power equal to?
## Exponent Practice
Since we have parentheses around the negative three here, and the exponent, the four is written outside of those parentheses, that means that the exponent applies to the entire quantity that's inside the parentheses. So, the number that counts as the base number is negative three. Negative three is the thing that we want to multiply by itself four times. So that means we can rewrite this as -3-3-3-3. Now we can just evaluate that numerically. -3-3 is just positive nine, so we get positive nine multiplied by itself, which is just equal to 81. So our final answer is 81.
## No Parentheses
Now if instead I have -3^4, what number does that equal? Is this any different from the quiz before this one?
## Order of Operations Practice
To make sure that you're super solid on order of operations and evaluating expressions using exponents. He'res a kind of fun quiz for you. Please decide whether each of these expressions, is equal to 8, -8, or something else, neither of those 2. Pick the circle, and the proper column for each row.
## Order of Operations Practice
So again, in order to figure out how to evaluate each of these expressions, we need to use our order of operations knowledge. We need to remember our PEMDAS. For this first problem, -2^3, we don't have any parenthess, so that means we need to take the exponent into account before the negative sign. So, we have -12^3, which is the same as -18, so we get negative eight. The next problem has some parentheses in it, so we need to deal with what's inside of those first, and inside, we have -2^2. Just like in this first problem, we need to do the exponent before the negative sign. So, what's inside the parentheses here is negative four since we have -2^2, which is negative four. So this equals For the third problem, we have an exponent outside of something that's inside parentheses. So we know the negative sign is going to be part of the number that is taken to the exponent. So the entire quantity, negative two is squared. So this is equal to 2-2-2, which is the same as have a negative sign inside the parentheses, so its part of this number that's taken to the third power. So -2-2-2 is negative eight. Here, the negative sign comes outside the parentheses, so we have -12^3, to the third is eight and -18 is negative eight. Our last two problems both fall into the neither category, 2+2^2 is just equal to either eight or negative eight. And here, we have -2^2+2^2. Since there is not a parentheses around this negative two we know that we need to square two before multiplying it by negative one. So this is actually equal to -4+4 and that's equal to zero. Great job. I know this is a lot to do in one quiz, but I think that having to think through all of these different options that are sort of similar to each other can be a really good way to make sure you have your order of operations cemented. And if you don't, not a big deal at all. Remember, just go back and practice a little bit more.
## Find the Exponent
Just to change things up a little bit, what if we have 3^2 times 3^4? That's going to equal three to some power, but what is the exponent that should go here?
## Find the Exponent
Let's start by expanding out each of the things that we have with an exponent. So, we know that 3^2 is just equal to 2 threes multiplied together, so 3 times 3. And we know that these two things are also multiplied together, so we need a multiplication sign between these two threes and these four threes. So, again, we just have a bunch of threes multiplied together and, as we know, exponents are just a tool for writing repeated multiplication of the same number in a shorthand way. So our base is going to be three since three is being multiplied over and over again, and we have six of them multiplied together if you count them out. So the exponent is six. Remember, typed in, you need to type 3^6.
## Multiplying Exponents
So, what we saw in this last quiz was really interesting. Remember that we started out with 3^2 times 3^4, and we ended up with 3^6 power. What we need to notice here is how the exponents are related to each other. 2+4, our two original exponents, is equal to 6, the final exponent. So, this actually shows us a general rule for multiplying factors that have exponents. If the two numbers are multiplying together have the same base, then their exponents just add to one another, and the base stays the same. So, let's write that in a more general way. If we have some number, or variable a, and it's taken to the power of b, and that's multiplied by another number a that's taken to the power c. Then together, that multiplication can be written as a^b+c. So, like we saw in the last quiz, in the end. Since exponents indicate repeated multiplication, since each of these factors right here is just the number or variable a being multiplied by itself over and over again some number of times. When they are multiplied together, it's just even more a's multiplied together, or some different number of a's multiplied together. This is just a convenient way for us to not have to write out all of the numbers like we did when we were doing this last quiz.
## Sum of Exponents
Remember that x^2 is just x x or two xs multiplied together. X^4 to the fourth is just 4 xs multiplied together. And we're also multiplying all of that, by another 3 xs that are multiplied together. So here we have a big string of Xs all multiplied together, just like we would expect considering how many exponents we see here, but the same base over and over again. So, in total here, we have 9 ex's multiplied all together.And we know that this just equals x^9. However, we can use our rule to do this in a much shorter and easier way. We can get the same answer by just adding these three exponents together. We know that our base is still x, but our power is just 2 + 4 + answer.
## Different Bases
So what if we have the term x^53^2y^3x^8? How would you simplify that? Please write your answer in a simplified form as you can.
## Different Bases
Let's first rewrite the factors within this term so that the factors with the same bases are next to each other, and I'm also going to put the constant factor first. So I'm going to start with 3^2, then we have two factors that have a base of x. So I'll put those next to each other and the last thing we have is the y cubed. Well we know that 3 ^2 is just 3 3 and 3 3 is just 9. We also know that we have x ^5 x ^8 That's the same as x ^5 + 8 power. And, nothing is being involved with the y cubed so it's just going to stay the same. You'll notice I got rid of those multiplication signs between the different factors in the term since they're implied if we just don't write them. Now the only thing you need to simplify here is add together the two numbers in the exponent of the x. So we get a final answer of 9 x^13 y^3 I think that you are going to find all this practice of manipulating exponents really useful as we keep simplifying expressions
## More Exponent Practice
How would you handle this term y^4 x^2 y^-2? Remember, all these are multiplied together. Please write the most simplified version of this term that you can right here.
## More Exponent Practice
To solve this problem, we can, once again, use this trick that we learned earlier. We have two factors inside this term that have the same base. So, we have y^4 and y^-2. So, I'm going to start by writing those next to each other. And now, we know that y^4 times y^-2, is just going to be equal to y^4+-2. So, I rewrite the x^2 factor and we have y^4+-2, which is the same as 4- 2power. y^2.
## Negative Exponents
So remember at the, in the last quiz, we simplified h^4 x^2 y^-2 to equal x^2 y^2. But in doing this, we actually dealt with something we haven't talked about explicitly before. This negative exponent right here. My question for you now is basically, what do negative exponents mean? So, which of these five answers down here is an equivalent expression to what we started out with, y^4x^2y^-2. Remember, whatever you pick down here also needs to give us the final answer of x^2 y^2 in the end. So, think about what intermediate step you need between here and here and which one of these answer choices fits that. This is definitely a little bit tricky so good luck.
## Negative Exponents
As we saw in the quiz before this one, when we multiplied y^4 times y^-2, we used our short cut to say that this is just equal to, of course, leaving the x^2 there, y^4-2 power. The role that this -2 exponent here plays then, is that it makes it so that, in the final answer, which we know is x^2y^2, we have two fewer y's multiplied together than we did in at least this first part, the y^4 factor of the original expression. But how do you write y^-2 in terms of multiplying some number of y's together. Well if we know that y^4xy^-2=y^2. And also, we remember that y^4 is four ys multiplied together. And similarly, y^2 is two ys multiplied together. This y^ -2 needs to cancel out two of these other four ys that are multiplied together, to give us our final answer. Now, we know that the way that we undo multiplication is division. y^4 needs to be divided by y^2, to equal y squared, we can write this out like this. We have four y's multiplied together, divided by 2 y's multiplied together, and each of these y's in the denominator cancels out one of the y's in the numerator, since everything here is just multiplied together. This is how we end up with just two y's multiplied together. Together, since we can see that we only have y times y left on the left side. If we just look at this way of writing our expression though, we can write both the numerator and the denominator in terms of exponents. So, on the top, we still have y^4 and the bottom of our fraction we have y times y, which is just y^2. So, if we move this way where an expression appear to be end up with y^4 times y^-2=y^4/y^2. We see this factor may be not we so need to multiply this pair x ^ 2 to get a final answer. In this answer choice right here, y^4x^2/y^2.
## Up or Down
So, what we learned from the last quiz is that, when you have a negative exponent, you can rewrite whatever term you're dealing with, so that we're instead, dividing by that factor inside the term. So, negative exponents are actually veiled ways of writing division into our term. The way we know what we're dividing by, is to find the factor with a negative exponent, which is just y^-2, in this case. And we move it underneath the factors of the positive exponents to make it the denominator of the term. So, on the right side of the equation where we've moved it, it's now in the denominator. And we've also changed the power of the base to be positive instead of negative. So, we flip the sign of an exponent from negative to positive or from positive to negative. We need to move the factor or the base number that the exponent is applied to, to the opposite side of the fraction. If it's in the top, it needs to move to the bottom and if it's in the bottom, it needs to move to the top, and we also flip the sign of the exponent. So here, we change from negative to positive. So basically, if we have some number, let's call it x and it's taken to a negative power, let's say, that's -a, where a could be any number, or really any expression. Then, this is equal to 1/x^a. So again, we multiply the exponent of a number by -1. We need to switch which part of the fraction the factor it belongs to is part of. I know that what's on the left side here doesn't look like a fraction, but this is actually secretly x^-a/1. So, anything that doesn't look like it's part of a fraction is actually in the numerator of your fraction, where the denominator is 1.
## No Negative Exponents
Using what you just learned about signs of exponents and how that relates to the side of the fraction they're on, how could you rewrite 3y-1 x3 in fraction notation? So, just fill in what you think belongs in the numerator here and what belong in the denominator here. There are a bunch of different mathematically equivalent ways of doing this, but I want you to do it in a way so that you have something that's equal to this expression but so that there are no negative exponents in either the numerator or the denominator over here.
## No Negative Exponents
We know that this exponent of -1, attached to the base of y here, means that we can rewrite this factor, y^-1 as 1 / y^1. And we know that y^1 is just y. So y^-1 = of y^-1 in this term. So now, we have All of these factors are just multiplied together, so we can write our fraction right away. In the numerator, we have 3 and x^3. And, the only thing written in the denominator is the y. So, our final answer is 3x^3 / y.
## No Negative Exponents 2
So here's a quiz that looks pretty similar to the last one we did. How can you rewrite 3m ^ 2 / n ^ -4 so that it contains no negative exponents?
## No Negative Exponents 2
What I'm going to do first to deal with this negative exponent factor is separate it out from the rest of the factors. So I'm just going to multiply a little bit more explicitly. So you have 3m^21/n^-4. However, we know that when we have a negative exponent, n^4 in our case, these factors actually equal to 1/n^4. So I need to replace just the denominator of this fraction right here with this number. So that's going to give us This is really not looking very pretty. However, we know how to handle this. Dividing by a fraction is the same as multiplying by its reciprocal. So, for example, we have 1/a/b. That's just equal to 1b/a. So we can continue modifying this expression using that trick. This is going to equal, keeping the 3m^2, we keep the numerator here, and we multiply by the reciprocal of the denominator. So the reciprocal of 1/n^4 is just n^4/1. Well now this is easy. You know that anything times 1 is just itself. And we know anything divided by 1 is just itself. So this leaves us with 3m^2n^4. So again, we see that switching the sign of an exponent, so switching from negative the n base. Just requires a flipping of the exponent sign and a flipping of the side of the equation that factors on. We switch from having n^-4 in the denominator to having n^4 in the numerator. If you found working with fractions like this a little bit difficult, not a big deal at all. Just take some time to review manipulation of fractions with the materials that we've directed you to. | 15,784 | 66,271 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2017-17 | latest | en | 0.984916 |
https://dev.balancer.fi/resources/pool-math/weighted-math | 1,670,360,672,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00049.warc.gz | 240,964,010 | 78,378 | Developers
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⌃K
# Weighted Math
## Overview
Weighted Math is designed to allow for swaps between any assets whether or not they have any price correlation. Prices are determined by the pool balances, pool weights, and amounts of the tokens that are being swapped.
Balancer's Weighted Math equation is a generalization of the
$x*y=k$
constant product formula, accounting for cases with
$n \geq2$
tokens as well as weightings that are not an even 50/50 split.
For more formulas and derivations of the below formulas, please refer to the Balancer Whitepaper.
## Implementations
### TypeScript
Developers can use the TypeScript math implementations used by the Smart Order router
### Python
There are also Python implementations in progress
## Invariant
The value function
$V$
is defined as:
$V= \prod_t B_t^{W_t}$
Where
• $t$
ranges over the tokens in the pool
• $B_t$
is the balance of the token in the pool
• $W_t$
is the normalized weight of the tokens, such that the sum of all normalized weights is 1.
## Spot Price
Each pair of tokens in a pool has a spot price defined entirely by the weights and balances of just that pair of tokens. The spot price between any two tokens,
$SpotPrice^o_i$
, or in short
$SP^o_i$
, is the the ratio of the token balances normalized by their weights:
$SP^o_i = \frac{\frac{B_i}{W_i}}{\frac{B_o}{W_o}}$
• $B_i$
is the balance of token
$i$
, the token being sold by the trader which is going into the pool
• $B_o$
is the balance of token
$o$
, the token being bought by the trader which is going out of the pool
• $W_i$
is the weight of token
$i$
• $W_o$
is the weight of token
$o$
### Spot Price with Swap Fees
When we consider swap fees, we do exactly the same calculations as without fees, but using
$A_i \cdot (1-swapFee)$
$A_i$
since fees are taken out of the input amount. The equation then becomes:
$SP^o_i = \frac{\frac{B_i}{W_i}}{\frac{B_o}{W_o}} \cdot \frac{1}{1-swapFee}$
### outGivenIn
When a user sends tokens
$i$
to get tokens
$o$
, all other token balances remain the same. Therefore, if we define
$A_i$
and
$A_o$
as the amount of tokens
$i$
and
$o$
exchanged, and since the value function
$V$
must be constant before and after the trade, we can calculate the amount
$A_o$
a users gets when sending
$A_i$
.
$A_o = B_o \cdot \left(1-\left(\frac{B_i}{B_i + A_i}\right)^{\frac{W_i}{W_o}}\right)$
If you're computing this value yourself, remember that the pool collects swap fees as a percentage of the input token. In the equation above,
$A_i$
is the amount that the pool actually swaps into the output token, not the amount sent by a trader,
$A_{sent}$
. To calculate through, we must compute:
$A_i = A_{sent} * (1-swapFee)$
### inGivenOut
It is also very useful for traders to know how much they need to send of the input token
$A_i$
to get a desired amount of output token
$A_o$
:
$A_i = B_i \cdot \left(\left(\frac{B_o}{B_o - A_o}\right)^{\frac{W_o}{W_i}}-1\right)$ | 827 | 2,940 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 37, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2022-49 | latest | en | 0.885278 |
https://www.proprofs.com/discuss/q/470659/scenario-2the-production-function-earthquake-detectors-follo | 1,586,384,446,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371824409.86/warc/CC-MAIN-20200408202012-20200408232512-00325.warc.gz | 1,114,644,840 | 66,245 | Scenario 2:The production function for earthquake detectors (Q) is - ProProfs Discuss
# Scenario 2: The production function for earthquake detectors (Q) is given as follows:Q = 4K1/2L1/2 , where K is the amount of capital employed and L is the amount of labor employed. The price of capital, PK, is \$18 and the price of labor, PL, is \$2. Refer to Scenario 2. Suppose that you receive an order for 80 earthquake detectors. How much capital will you use to minimize the cost of 80 earthquake detectors?
A. A. 20/3
B. B. 5
C. C. 2/3
D. D. 80/18
E. E. none of the above
This question is part of Chapter 7: Microeconomics
Asked by Twright, Last updated: Apr 05, 2020
John Smith | 199 | 678 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2020-16 | latest | en | 0.920651 |
http://www.pokeronlineguru.com/resources/casino/games/others/red-dog/ | 1,542,317,099,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039742937.37/warc/CC-MAIN-20181115203132-20181115225132-00164.warc.gz | 495,853,822 | 4,412 | Poker Games All about Poker Types of Poker Games Poker Basics The Mathematics of Poker Poker Strategies Poker Game Cases Poker Volcablury Video Poker Online Poker
Red Dog
The player's objective in this games is to guess if the value of a randomly selected card will fall between the values of two previously exposed cards. The games is played in the following manner:
The player places a bet on the layout (see illustration at the end of this website).
The dealer places two "community" cards (used by all players) in the center of the layout. If the cards are paired, a third card is automatically dealt. If this card matches the pair, the player wins and is paid eleven to one on the initial bet. If it doesn't match the pair, the hand is a push.
If the first two cards are consecutive in value (6, 7 or J, Q, etc.) the hand is a push.
If the cards are nonconsecutive (e.g. 3, 8 or 2, K) the player may make an additional bet, up to the amount of the original bet, in hopes of winning a payoff ranging from even money to five to one if the third card dealt falls between the values of the initial two cards.
If the third card falls outside the range of the first two cards, or ties the value of either card, the original bet and the additional bet are lost.
The only strategy recommended for this games is to not make the additional bet-the raise bet-unless the range between the values of the first two cards is seven or more. Even following this strategy, the casino still maintains an edge of 3.5 percent, which makes it a bad games for the knowledgeable player.
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https://www.bartleby.com/questions-and-answers/638-north-manufacturing-has-a-demand-for-1000-pumps-each-year.-chapter-6-inventory-con-230-a-manufac/b9105701-5983-4665-ad4a-b97e70f66fb0 | 1,576,026,715,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540529516.84/warc/CC-MAIN-20191210233444-20191211021444-00456.warc.gz | 626,145,147 | 24,165 | # :6-38 North Manufacturing has a demand for 1,000 pumpseach year.CHAPTER 6 INVENTORY CON230aManufacturing \$40 to place an order, and the carry-ing cost is 25% of the unit cost. If pumps are orderedin quantities of 200, North Manufacturing can get a3% discount on the cost of the pumps. Should NorthManufacturing order 200 pumps at a time and takethe 3% discount?The cost of a pump is \$50. It costs North6-39 Linda Lechner is in charge of maintaining hospitalsupplies at General Hospital. During the past year,the mean lead time demand for bandage BX-5 was60. Furthermore, the standard deviation for BX-5was 7. Linda would like to maintain a 90% servicelevel. What safety stock level do you recommend forВХ-5?brtQUA31-199X200:6-40 Linda Lechner has just been severely chastised forher inventory policy. (See Problem 6-39.) Sue Sur-rowski, her boss, believes that the service levelshould be either 95% or 98%. Compute the safetystock levels for a 95% and a 98% service level.5006-43Linda knows that the carrying cost of BX-5 is 50cents per unit per year. Compute the carrying costthat is associated with a 90%, a 95%, and a 98% ser-vice level.6-41 Ralph Janaro simply does not have time to ana-lyze all of the items in his company's inventory. Asa young manager, he has more important things todo. The following is a table of six items in inventoryalong with the unit cost and the demand in units.(a) Find the total amount spent on each item duringthe year. What is the total investment for all of3dthese?(b) Find the percentage of the total investment in in-ventory that is spent on each item.93
Question
15 views
6-39
check_circle
Step 1
To determine question no. 6-39, where we need to find out safety stock level for BX-5.
Step 2
At first it is important to know the meaning of safety stock level. There can be situations where stock would be required for emergency purpose, so that it saves us from running out of the product. For example, in case of breakdown of machinery, any natural disaster which could affect the product flows from supplier, etc.
Step 3
Data available for calculation:
St...
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Tagged in | 596 | 2,390 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-51 | latest | en | 0.921907 |
https://www.student-portal.net/codehs-5-9-7-fraction-math-solution.edu | 1,714,018,486,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712297284704.94/warc/CC-MAIN-20240425032156-20240425062156-00143.warc.gz | 909,484,948 | 20,853 | # CodeHS 5.9.7 Fraction Math Solution
Posted on
For anyone who needs help with the CodeHs 5.9.7 Fraction Math (Java), you might want to check out a thread on the popular forum called Reddit made by u/xxdani0336xx two years ago. Keep reading the post until the end if you are interested.
As stated on the post, the user has no idea what he is doing wrong. He thinks he is using the ”this” keyword incorrectly, but he is not sure. Below is what he has so far:
//Calculate by using the FractionMath class, then update
//the numerator and denominator from the returned Fraction
{
}
/**
* Updates this fraction by multiplying another fraction
* @param other Fraction to multiply to existing fraction
*/
//Calculate by using the FractionMath class, then update
//the numerator and denominator from the returned Fraction
public void multiplyFraction(Fraction other)
{
FractionMath.multiply(this, other);
}
There are a total of four responses under the thread. Here is the detail of each response:
• The first one is from _andy_andy_andy_. This user asks if this code giving errors. Aside from that, he also adds that the OP will need to modify the numerator and denominator of this Fraction instance.
• The second one is from bic204. This user says that technically, the OP is using the FractionMath.add() and FractionMath.multiply() correctly, using the correct arguments. The thing that the OP is forgetting to do is to set the numerator and denominator.
• The third one is from MeganStormblessed. This user suggests the OP to add this.numerator = numerator; this.denominator = denominator;. By following the step, there will be no error created. However, it still does not work as intended.
• The last one is from PlatoAssortedCheeses. This user writes public void addFraction(Fraction other) { numerator = FractionMath.add(this,other).getNumerator(); denominator = FractionMath.add(this,other).getDenominator();.
For more information about the topic, it is better for you to go to Reddit. If you have something to ask, you are suggested to log in to your Reddit account and join the discussion. If you do not have a Reddit account, you can create one first. There are two methods to choose from to make one.
The first method to make a Reddit account is by using a browser. Here is every step to follow if you want to do it on a browser:
1. First of all, you should open the official website of Reddit at https://www.reddit.com in your internet browser.
2. When you are there, click the SIGN UP button. If you do not know where it is located, it is on the top right corner of the page.
5. The next thing that you have to do is to enter a username for your new Reddit account.
6. Aside from the username, you will also have to enter an account password in the PASSWORD field.
7. Do not forget to click and check I’m not a robot box to verify that you are a real human and not a malicious computer bot or connection.
8. The eighth step is to click the SIGN UP button located in the lower right corner of the pop up window to make your new account.
9. Afterward, click a category on the left menu. Actually, it is not a must, meaning it is optional.
10. When everything is done, you can just click the FINISH button. If you have no idea where to find this button, it is in the lower right corner. By clicking the button, the registration pop up will be closed and you will sign in to Reddit.
1. The first thing that you have to do is to open the app called Reddit on your phone. If it is not easy to find one as there are a lot of apps installed on your phone, you can just look for an icon that looks like a white alien face in an orange circle. This one is able to be found on your home screen, in a folder, or on the Apps tray.
2. Once you manage to find one, tap the figurehead icon on the top left. By doing so, a new panel will be opened on the left hand side.
4. The second thing that you have to tap is the blue SIGN UP option in order to open the sign up form on a new page. If you are on an iPhone and iPad, it is a blue button found at the bottom of the page. As for those who are on Android, this button is located under the Password field on the login form.
5. In the next step, enter an email address, username, and password that you want to use. When it’s complete, there will be a green checkmark next to each text box. Feel free to tap the eye icon next to the Password field if you want to see what you type. Talking about the password, it should be noted that it is a must for it to be a minimum 6 characters long. | 1,041 | 4,549 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2024-18 | latest | en | 0.89522 |
https://www.teachoo.com/13942/644/Ex-13.2--11-iii/category/Ex-13.2-Term-2/ | 1,726,704,111,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651944.55/warc/CC-MAIN-20240918233405-20240919023405-00676.warc.gz | 916,836,468 | 21,567 | Ex 12.2
Chapter 12 Class 11 Limits and Derivatives
Serial order wise
### Transcript
Ex 12.2, 11 Find the derivative of the following functions: (iii) 5 sec x + 4 cos x Let f (x) = 5 sec x + 4 cos x. Now, f’ (x) = ( 5 sec x + 4 cos x)’ = (5 sec x)’ + (4 cos x)’ = 5 (sec x . tan x) + 4 ( – sin x) = 5 sec x . tan x – 4 sin x Derivative of sec x = sec x tan x (calculated in Ex 12.2.11 (ii)) & Derivative of cos x = – sin x | 169 | 424 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2024-38 | latest | en | 0.751244 |
https://www.physicsforums.com/threads/tangential-and-centripetal-acceleration-problem.351011/ | 1,531,837,484,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589726.60/warc/CC-MAIN-20180717125344-20180717145344-00344.warc.gz | 921,770,852 | 13,677 | # Homework Help: Tangential and centripetal acceleration problem
1. Nov 1, 2009
### r_swayze
A windmill starts from rest and rotates with a constant angular acceleration of 0.25 rad/s2. How many seconds after starting will the magnitude of the tangential acceleration of the tip of a blade equal the magnitude of the centripetal acceleration at the same point?
I dont exactly know where to start with this problem. Wouldnt I need the radius to solve for the tangential acceleration as well as the centripetal acceleration?
2. Nov 1, 2009
### Delphi51
It might work out without r. Give it a try! I suggest you begin with putting that condition into symbols:
tangential acceleration = centripetal acceleration
rα = v²/r (pardon the poor alpha character after the first r)
Fill in the details and see if the r's cancel out!
3. Nov 1, 2009
### Andrew Mason
No. You have to work it out to see why.
What is the tangential acceleration (convert angular acceleration to tangential acceleration - use r for the radius).
Now, write out the expression for centripetal acceleration of a mass located at the tip in terms of angular speed.
At what speed does the centripetal acceleration equal the tangential acceleration?
AM
4. Nov 2, 2009
### r_swayze
I dont see how the r's can cancel out with ra = v^2/r
And how can I covert angular acceleration to tangential acceleration?
5. Nov 2, 2009
### Delphi51
It was rα = v²/r where the 2nd character is an alpha, angular acceleration.
No r's cancel at this point, but you are given that α = .25 and of course v = rω.
Since it is constant angular acceleration, you can also get a value for ω as a function of time . . . just keep working on that equation with these details and see what happens. | 429 | 1,748 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2018-30 | latest | en | 0.910837 |
https://www.qimacros.com/free-excel-tips/spc-case-study-screws/ | 1,575,655,496,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540490743.16/warc/CC-MAIN-20191206173152-20191206201152-00556.warc.gz | 853,070,291 | 13,021 | # Analyzing Different Machines
## SPC Case Study - Machine Screws
On the governments statistic website, I found a case study about analyzing machines for replacement. The machines produce screws.
The essence of the case study is that:
• A machine shop has three automatic screw machines that produce various parts.
• The shop has enough capital to replace one of the machines.
• The quality control department has been asked to conduct a study and make a recommendation as to which machine should be replaced.
• The production specifications for the machines are 0.125+/-0.003 (LSL=0.122, USL=0.128)
The first task is to get the data off the webpage and into Excel.
### Converting HTML Data into an Excel Workbook
Using your mouse, all you have to do is select the data in the webpage:
Then use EDIT-COPY to copy it to a Windows clipboard. Next, open Excel and try pasting it into a worksheet. If the data is in an html table, Excel will paste it easily. In this case, however, the data isn't. It's just numbers with spaces between them. So what do you do?
I opened up WordPad (or you could use Word) and pasted the data into a blank page. Then I saved it as a text file (filename.txt):
Excel can take this format and figure out how to import the columns. So I started Excel and opened the text file which starts the text import wizard which will figure out where each column of data belongs:
When finished, Excel gave me the following:
As you can see, there are 10 samples, but they're in a column. To get them into a format that will be usable for graphing with QI Macros, I need to get the data oriented into groups of 10. To do this, I selected the diameter data and used CTRL-SHIFT-G to start the gen table macro which prompts me for the sample size. It will convert any size array to a different sized array based on sample size:
The result is 10 columns of samples by machine/day/time:
Next, I want labels for each of these rows that correspond to the machine/day/time. So I can use a formula to combine columns A&B&C (D is the sample number):
Then I can use QI Macros data transformation tools (or gen table macro in older versions) to sort these and give me a set of headings which I can insert in front of the data:
### Using the Box and Whisker Chart To Analyze The Data
Just select all of the data (A1:K19) and select Box and Whisker from the QI Macros menu:
We could also use the data transformation tools (or gen table macro) to combine all of the data into three machines and draw a box and whisker of that data:
Just by looking at these charts we can see that:
1. Machine 1's output fits squarely between our upper and lower specification limits (LSL=0.122, USL=0.128).
2. Machine 2's output has some below the LSL (0.122). The variation is small, so maybe all we need to do is adjust the machine to move the results up to the target of 0.125.
3. Machine 3 has much more variation and output below the LSL.
Based on just this analysis, I'd recommend replacing machine number 3.
### Using Stair Step Control Charts To Analyze The Data
Another way to approach this would be to use the XbarR chart. If we insert blank rows between the three machines, we can analyze the data using stair step limits:
Again You can see from both the average (X) and the range charts that the variation for machine # 3 is much wider. Again, I'd recommend replacing machine #3.
### Using Histograms To Analyze The Data
Another way to do this is to select the data for each machine, run a histogram for each machine, then compare:
Machine 1 has a Cp of .8879 and a Cpk of .8793 (1.0 is considered to be capable). These capability measures tell us that machine 1 has enough variation from part to part that it could produce non-conforming parts.
Machine 2 has a Cp of 1.126 (capable) and a Cpk of 0.36 (off center). Based on these measures, Machine 2 has the least variation; it just needs to be adjusted to center the output on the target (0.125).
Machine 3 has a Cp of .5919 (not capable) and a Cpk of .3989 (not centered). Again, based on Cp and Cpk, I'd recommend replacing machine number 3.
### Recommendations
It's so easy to draw charts with QI Macros that it makes sense to use several different approaches and see what they tell you. In this case, we used the box and whisker, the XbarR using the stair step capabilities of the macro and three histograms to verify and validate our decision. I don't know about you, but I find that managers often challenge one graph, but when you give them three ways to see the same thing, they're often convinced. | 1,085 | 4,580 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2019-51 | longest | en | 0.922406 |
https://socratic.org/questions/a-wall-in-marcus-s-bedroom-is-8-2-5-feet-high-and-18-1-3-feet-long-if-he-paints- | 1,529,955,584,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267868876.81/warc/CC-MAIN-20180625185510-20180625205510-00454.warc.gz | 726,334,792 | 84,812 | # A wall in Marcus's bedroom is 8 2/5 feet high and 18 1/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
2
Mark D. Share
May 22, 2018
$77 f e e {t}^{2}$
#### Explanation:
Area of the wall is $8 \frac{2}{5} \times 18 \frac{1}{3}$
$\frac{42}{5} \times \frac{55}{3}$
$\frac{14}{5} \times \frac{55}{1}$
$\frac{14}{1} \times \frac{11}{1} = 154 f e e {t}^{2}$
The area we want is half of this $77 f e e {t}^{2}$
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http://www.velocityreviews.com/forums/t340052-display-function-code-body.html | 1,398,037,664,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00431-ip-10-147-4-33.ec2.internal.warc.gz | 749,281,048 | 9,523 | Velocity Reviews > Display Function Code Body?
# Display Function Code Body?
Haibao Tang
Guest
Posts: n/a
01-07-2005
Hail Python pals! I played with the R (http://r-project.cran.org) last
night to do some statistics and it has an interactive session too, and
I found a feature that is quite useful.
I found by actually typing a function name, the R gives you a code body
output.
> f1 = function(x){x*x}
> f1
function(x){x*x}
# more examples (you can try some)
> sd
function (x, na.rm = FALSE)
{
if (is.matrix(x))
apply(x, 2, sd, na.rm = na.rm)
else if (is.vector(x))
sqrt(var(x, na.rm = na.rm))
else if (is.data.frame(x))
sapply(x, sd, na.rm = na.rm)
else sqrt(var(as.vector(x), na.rm = na.rm))
}
<environment: namespace:stats>
# ------------------------------------------------
While our python gives an output which is more pro but less
informational.
>>> def f1(x):return x*x
>>> f1
<function f1 at 0x00F522B0>
What I would like to do is to write a function like disp(), when typed,
it can give you the code infomation.
>>> disp(f1)
<function f1 at 0x00F522B0>
def f1(x):
return x*x
<environment: interactive>
# or any shallow function code from a file
>>> import calendar; disp(calendar.isleap)
<function isleap at 0x00F795B0>
def isleap(year):
"""Return 1 for leap years, 0 for non-leap years."""
return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)
<environment: C:\Python23\Lib\calendar.py>
# surely the compiled function code cannot be displayed
>>> disp(blabla)
<function isleap at 0x00F79B30>
: internal/compiled function
<environment: C:\Python23\DLLs\_blabla.pyd>
Can someone please point out how this can be achieved nicely. I've
tried some text searching approach, too dirty I must say.
Oh! Thank you ...
Haibao Tang
Steven Bethard
Guest
Posts: n/a
01-07-2005
Haibao Tang wrote:
> What I would like to do is to write a function like disp(), when typed,
> it can give you the code infomation.
Check the docs entitled "Retrieving source code":
http://docs.python.org/lib/inspect-source.html
Depending on what you want, you may be able to use inspect.getsource:
py> import inspect
py> import string
py> print inspect.getsource(string.split)
def split(s, sep=None, maxsplit=-1):
"""split(s [,sep [,maxsplit]]) -> list of strings
Return a list of the words in the string s, using sep as the
delimiter string. If maxsplit is given, splits at no more than
maxsplit places (resulting in at most maxsplit+1 words). If sep
is not specified or is None, any whitespace string is a separator.
(split and splitfields are synonymous)
"""
return s.split(sep, maxsplit)
However, this won't work for functions you've defined interactively I
don't think. On the other hand, if you defined them interactively, you
can just scroll up.
Steve
Fernando Perez
Guest
Posts: n/a
01-09-2005
Haibao Tang wrote:
>
> Hail Python pals! I played with the R (http://r-project.cran.org) last
> night to do some statistics and it has an interactive session too, and
> I found a feature that is quite useful.
[...]
> # or any shallow function code from a file
>>>> import calendar; disp(calendar.isleap)
> <function isleap at 0x00F795B0>
> def isleap(year):
> """Return 1 for leap years, 0 for non-leap years."""
> return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)
> <environment: C:\Python23\Lib\calendar.py>
>
> # surely the compiled function code cannot be displayed
>>>> disp(blabla)
> <function isleap at 0x00F79B30>
> : internal/compiled function
> <environment: C:\Python23\DLLs\_blabla.pyd>
>
> Can someone please point out how this can be achieved nicely. I've
> tried some text searching approach, too dirty I must say.
> Oh! Thank you ...
[~/tmp]> ipython
Python 2.3.4 (#1, Oct 26 2004, 16:42:40)
IPython 0.6.7_rc1 -- An enhanced Interactive Python.
? -> Introduction to IPython's features.
%magic -> Information about IPython's 'magic' % functions.
help -> Python's own help system.
object? -> Details about 'object'. ?object also works, ?? prints more.
In [1]: import calendar
In [2]: calendar.isleap??
Type: function
Base Class: <type 'function'>
String Form: <function isleap at 0x403bb6bc>
Namespace: Interactive
File: /usr/src/build/475206-i386/install/usr/lib/python2.3/calendar.py
Definition: calendar.isleap(year)
Source:
def isleap(year):
"""Return 1 for leap years, 0 for non-leap years."""
return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)
Note that the source display won't work for interactively defined functions,
because their source is thrown away by the bytecode compiler. There are
discussions of a PEP for adding a __source__ attribute to functions which would
solve this limitation, but that is still in the future.
Cheers,
f | 1,327 | 4,717 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2014-15 | latest | en | 0.686412 |
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# ICSE Class 10 Mathematics Previous Year Question Paper 2012
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Question 1
If (x + 2) is a factor of the polynomial x3 - kx2 - 5x + 6 then the value of k is: [1]
1. 1
2. 2
3. -2
Question 2
The solution set of the inequation x - 3 ≥ - 5, x ∊ R is: [1]
1. {x : x > - 2, x ∊ R}
2. {x : x ≤ -2, x ∊ R}
3. {x : x ≥ -2, x ∊ R}
4. {-2, -1, 0, 1, 2}
Question 3
The product AB of two matrices A and B is possible if: [1]
1. A and B have the same number of rows.
2. The number of columns of A is equal to the number of rows of B.
3. The number of rows of A is equal to the number of columns of B.
4. A and B have the same number of columns.
Question 4
If 70, 75, 80, 85 are the first four terms of an Arithmetic Progression. Then the 10th term is: [1]
1. 35
2. 25
3. 115
4. 105
Question 5
The selling price of a shirt excluding GST is Rs. 800. If the rate of GST is 12% then the total price of the shirt is: [1]
1. Rs. 704
2. Rs. 96
3. Rs. 896
4. Rs. 848
Question 6
Which of the following quadratic equations has 2 end 3 as its roots? [1]
1. x2 - 5x + 6 = 0
2. x2 + 5x + 6 = 0
3. x2 - 5x - 6 = 0
4. x2 + 5x -6 = 0
Question 7
If x, 5.4, 5, 9 are in proportion then x is: [1]
1. 9.72
2. 25
3. 25/3
Question 8
Mohit opened a Recurring deposit account in a bank for 2 years. He deposits Rs. 1000 every month and receives Rs. 25500 on maturity. The interest he earned in 2 years is: [1]
1. Rs. 13500
2. Rs. 3000
3. Rs. 24000
4. Rs. 1500
Question 9
In the given figure AB = 24 cm, AC = 18 cm, DE = 12cm, DF = 9 cm and ∠BAC = ∠EDF. Then ΔABC ~ ΔDEF by the condition: [1]
1. AAA
2. SAS
3. SSS
4. AAS
Question 10
[1]
Question 11
The polynomial x3 - 2x2 + ax + 12 when divided by (x + 1) leaves a remainder 20, then 'a' is equal to:[1]
1. - 31
2. 11
3. - 11
Question 12
In an Arithmetic Progression (A.P.) if, first term is 5, common difference is - 3 and then nth term is - 7, then n is equal to:[1]
1. 17
2. - 13
3. 7
Question 13
In the given figure PQ is parallel to TR, then by using condition of similarity: [1]
1.
Question 14
If a, b, c, and d are proportional then is equal to: [1]
1.
2.
3.
Question 15
The first four terms of an Arithmetic Progression (A. P.), whose first term is 4 and common difference is -6, are: [1]
1. 4, -10, -16, -22
2. 4, 10, 16, 22
3. 4, -2, -8, -14
4. 4, 2, 8, 14
Question 16
One of the roots of the quadratic equation x2 – 8x + 5 = 0 is 7.3166. The root of the equation correct to 4 significant figures is: [1]
1. 7.3166
2. 7.317
3. 7.316
4. 7.32
Question 17
(x + 2) and (x + 3) are two factors of the polynomial x3 + 6x2 + 11x + 6. If this polynomial is completely factorised the result is: [2]
1. (x – 2)(x + 3)(x + 1)
2. (x + 2)(x – 3)(x – 1)
3. (x + 2)(x + 3)(x – 1)
4. (x + 2)(x + 3)(x + 1)
Question 18
The sum of the first 20 terms of the Arithmetic Progression 2, 4, 6, 8,....is : [2]
1. 400
2. 840
3. 420
4. 800
Question 19
The solution set on the number line of the linear inequation: [2]
2y – 6 < y + 2 ≤ 2y, y ∈ N is
1.
Question 20
If x, y, z are in continued proportion then (y2 + z2): (x2 + y2) is equal to: [2]
1. z : x
2. x : z
3. zx
4. (y + z) : (x + y)
Question 21
The marked price of an article is Rs. 5,000. The shopkeeper gives a discount of 10%. If the rate of GST is 12%, then the amount paid by the customer including GST is: [2]
1. Rs. 5040
2. Rs. 6100
3. Rs. 6272
4. Rs. 6160
Question 22
If A = then 5A – BC is equal to: [2]
Question 23
In the given figure ABCD is a trapezium in which DC is parallel to AB.
AB = 16 cm and DC = 8 cm. OD = 5 cm, OB = (y + 3) cm, OA = 11 cm and OC = (x – 1) cm.
Using the given information answer the following questions.
i. From the given figure name the pair of similar triangles: [1]
1. ∆OAB, ∆OBC
2. ∆COD, ∆AOB
4. ∆COD, ∆COB
ii. The corresponding proportional sides with respect to the pair of similar triangles obtained in (i): [1]
iii. The ratio of the sides of the pair of similar triangles is: [1]
1. 1 : 3
2. 1 : 2
3. 2 : 3
4. 3 : 1
iv. Using the ratio of sides of the pair of similar triangles the values of x and y are respectively: [1]
1. x = 4.6, y = 7
2. x = 7, y = 7
3. x = 6.5, y = 7
4. x = 6.5, y = 2
Question 24
Two cars X and Y use 1 litre of diesel to travel x km and (x + 3) km respectively. If both the cars covered a distance of 72 km, then:
i. The number of litres of diesel used by car X is : [1]
ii. The number of litres of diesel used by car Y is: [1]
iii. If car X used 4 litres of diesel more than car Y in the journey, then: [1]
iv. The amount of diesel used by the car X is: [1]
1. 6 litres
2. 12 litres
3. 18 litres
4. 24 litres
Question 25
Joseph has a recurring deposit account in a bank for two years at the rate of 8% per annum simple interest
i. If at the time of maturity Joseph receives Rs. 2000 as interest then the mostly instalment is: [1]
1. Rs. 1200
2. Rs. 600
3. Rs. 1000
4. Rs. 1600
ii. The total amount deposited in the bank: [1]
1. Rs. 25000
2. Rs. 24000
3. Rs. 26000
4. Rs. 23000
iii. The amount Joseph receives on maturity is: [1]
1. Rs. 27000
2. Rs. 25000
3. Rs. 26000
4. Rs. 28000
iv. If the monthly instalment is Rs. 100 and the rate of interest is 8%, in how many months Joseph will receive Rs. 52 as interest? [1]
1. 18
2. 30
3. 12
4. 6
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• Useful for doing quick revision | 2,608 | 8,036 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-23 | longest | en | 0.943068 |
https://community.tableau.com/thread/197949 | 1,553,343,698,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202804.80/warc/CC-MAIN-20190323121241-20190323143241-00101.warc.gz | 459,989,143 | 28,084 | 5 Replies Latest reply on Jan 25, 2016 9:50 AM by Eric Decker
# Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
Calling all Tableau Experts!
I have 10 months of data, January thru October. I’m trying to write a table calculation that sets a new goal for First Pass Yield that’s 50% higher than the previous high First Pass Yield monthly aggregate. That’s a bit of a mouthful, so here’s an example to better illustrate what I’m looking for (Reference the below table for the values I’m talking about):
First, obviously, January has no previous lookup value to measure against so I’m setting that Goal value to just be .5 (just so there are no Null values in the table calc).
For February’s goal, the calculation should be January’s FPY actual plus 50%, which in this case would be 77.27%.
Goal % Calc = ((1-((Lookup(Previous High Value)))*.5)+(Lookup([Previous High Value)))
Now, because February’s FPY was lower than the first month, the goal would still be set at 77.27%. This trend continues until we get to June where we see our first FPY value that surpasses our first FPY max. Therefore, the goal for July should be 50% higher than the newest FPY high of 72.97%, giving us a new goal of 86.49%. Lastly we see yet one more increase to the monthly FPY in August, which bumps up the new goal to 87.06%.
Now, it would be pretty simple to just find the window_max of FPY, add 50% and make that goal for all months, but I want to maintain the integrity of the goal values for the time frames they were applicable. (This way I can keep and track the history of our goal progressions)
Does anyone have any suggestions how to write a table calc (or multiple table calcs) to accomplish this task? I’ve been trying to use Lookups, Window_Maxs, etc. in multilple calculations but I’m just not able to get all the way there.
Attached is a Packaged workbook using the above table to show what the desired results for the goal bars *should* be.
• ###### 1. Re: Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
You lost me at 54.55% + 50% = 77.27% (for Feb) and 72.97% + 50% = 86.49% (for July)
Maybe I'm looking at it wrong, can you send the data in Excel (assuming you have the calculation working there)
• ###### 2. Re: Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
Chris,
Thanks for the reply and willingness to look into this. I probably didn't articulate the 50% portion of the calculation very well the first time. Because First Pass Yield has a maximum percentage of 100, the 50% improvement calculation is (((1-([Previous FPY])) *.5) + [Previous FPY] ), this way we'll always get the improvement relative to the previous period and still under the 100% mark. Obviously, the higher the Previous FPY % is, the less room for improvement you can have in the next month's goal.
I've added an additional column in my spreadsheet to help show the difference between the hard calculation for the 50% improvement as well as the overriding calculation to show what the goal should be showing in Tableau based on maintaining the integrity of the new FPY goals at the time they are applicable. I've also added a comments column that depicts how/why this logic should be working for each month to help illustrate my desired results.
Thanks again Chris!
-Eric
• ###### 3. Re: Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
Hello,
This looks similar to what you want, but I am not sure this is how you want it to be done. I just used your calculation to get the 'Table Calc' percentage for each month and then did a running max table calculation based off the 'Table Calc' percentage.
1 of 1 people found this helpful
• ###### 4. Re: Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
Brent,
I believe this is indeed the answer! Obviously the spreadsheet example was simplified just to get some data out there, whereas my SQL connection to data has other calculations involved. But the important thing was just getting the right type of table calc, and I believe Running_Max will do the trick! Once I (hopefully) verify this to be true, I'll be sure to mark this as the correct answer
Thanks for your help on this, sir. It's much appreciated!
-Eric
• ###### 5. Re: Creating a table calculation that sets goals to be 50% higher than the previous high value in data set
Brent,
Sure enough, this worked as it's setup in my workbook! You have no idea the background table calc coding that was going on to the level of assigning numeric values for each month based on it's relative performance from the month before and then doing several lookups to pull the previous month's goal forward. All I needed was one simple Running_Max calc
As usual, there's a simple solution using a calculation already there, thank you for showing me the light! | 1,172 | 5,025 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2019-13 | latest | en | 0.92387 |
https://www.airmilescalculator.com/distance/ngo-to-oka/ | 1,686,347,057,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224656833.99/warc/CC-MAIN-20230609201549-20230609231549-00170.warc.gz | 720,560,191 | 50,385 | # How far is Naha from Tokoname?
The distance between Tokoname (Chubu Centrair International Airport) and Naha (Naha Airport) is 808 miles / 1301 kilometers / 702 nautical miles.
The driving distance from Tokoname (NGO) to Naha (OKA) is 1140 miles / 1834 kilometers, and travel time by car is about 146 hours 50 minutes.
808
Miles
1301
Kilometers
702
Nautical miles
2 h 1 min
136 kg
## Distance from Tokoname to Naha
There are several ways to calculate the distance from Tokoname to Naha. Here are two standard methods:
Vincenty's formula (applied above)
• 808.142 miles
• 1300.579 kilometers
• 702.256 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 808.739 miles
• 1301.539 kilometers
• 702.775 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Tokoname to Naha?
The estimated flight time from Chubu Centrair International Airport to Naha Airport is 2 hours and 1 minutes.
## What is the time difference between Tokoname and Naha?
There is no time difference between Tokoname and Naha.
## Flight carbon footprint between Chubu Centrair International Airport (NGO) and Naha Airport (OKA)
On average, flying from Tokoname to Naha generates about 136 kg of CO2 per passenger, and 136 kilograms equals 299 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Tokoname to Naha
See the map of the shortest flight path between Chubu Centrair International Airport (NGO) and Naha Airport (OKA).
## Airport information
Origin Chubu Centrair International Airport
City: Tokoname
Country: Japan
IATA Code: NGO
ICAO Code: RJGG
Coordinates: 34°51′30″N, 136°48′17″E
Destination Naha Airport
City: Naha
Country: Japan
IATA Code: OKA
ICAO Code: ROAH
Coordinates: 26°11′44″N, 127°38′45″E | 557 | 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} | 2.890625 | 3 | CC-MAIN-2023-23 | latest | en | 0.830652 |
https://www.coursehero.com/file/6518884/Lecture21-Tridiagona-LUdecomposition/ | 1,518,918,061,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891811243.29/warc/CC-MAIN-20180218003946-20180218023946-00652.warc.gz | 835,131,210 | 26,427 | {[ promptMessage ]}
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Lecture+21--Tridiagona.+_+LU+decomposition
# Lecture+21--Tridiagona.+_+LU+decomposition - Hand...
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Unformatted text preview: Hand Calculations: Tridiagonal Matrix (a) Forward elimination 1-2-3 1-1-1 1-0.5 1 1 4 - = ------ 5 3 2 5 3 x x x x 25 1 5 5 2 1 1 5 2 2 1 4 3 2 1 . . . . 2 2 2 1 1 2 2 2 1 1 2 5 ( 2) 1 1 2 5 ( 3) 1 1 e f f g f e r r r f- =- =-- = - =- =-- = - 3 3 3 2 2 2 3 2 1 1 1 2 ( 1) 1 1 1 2 ( 1) 1 1 e f f g f e r r r f- =- =-- = - =- =-- = 4 4 4 3 3 4 4 4 3 3 0.5 1.25 ( 0.5) 1 1 0.5 3.5 (1) 4 1 e f f g f e r r r f- =- =-- = - =- =- = Hand Calculations: Tridiagonal Matrix (b) Back substitution 1 2 3 4 1 2 3 1 1 1 1 0.5 1 1 4 x x x x-- -- = - 4 4 4 4 4 1 r x f = = = 1 1 2 1 1 3 ( 2)(2) 1 1 r g x x f-- - - = = = 3 3 4 3 3 1 ( 0.5)(4) 3 1 r g x x f-- - = = = 2 2 3 2 2 1 ( 1)(3) 2 1 r g x x f-- - - = = = MATLAB M-file: Tridiag function x = Tridiag(e,f,g,r) % Tridiag: Tridiagonal equation solver banded system % x = Tridiag(e,f,g,r): Tridiagonal system solver. % input: % e = subdiagonal vector % f = diagonal vector % g = superdiagonal vector % r = right hand side vector % output: % x = solution vector n=length(f); % forward elimination for k = 2:n factor = e(k)/f(k-1); f(k) = f(k) - factor*g(k-1); r(k) = r(k) - factor*r(k-1); end % back substitution x(n) = r(n)/f(n); for k = n-1:-1:1 x(k) = (r(k)-g(k)*x(k+1))/f(k); end One loop; Operation count: ~8n NOT 2 n3/3 No modification on g » [e,f,g,r] = example...
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Lecture+21--Tridiagona.+_+LU+decomposition - Hand...
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Ask a homework question - tutors are online | 875 | 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} | 3.375 | 3 | CC-MAIN-2018-09 | latest | en | 0.591939 |
http://www.nag.com/numeric/fl/nagdoc_fl24/examples/source/g13cefe.f90 | 1,438,521,905,000,000,000 | text/plain | crawl-data/CC-MAIN-2015-32/segments/1438042989043.35/warc/CC-MAIN-20150728002309-00018-ip-10-236-191-2.ec2.internal.warc.gz | 605,015,946 | 1,331 | Program g13cefe ! G13CEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: g13cef, nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: t Integer :: i, ifail, j, ng ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: ca(:), calw(:), caup(:), sc(:), & sclw(:), scup(:), xg(:), xyig(:), & xyrg(:), yg(:) Real (Kind=nag_wp) :: stats(4) ! .. Executable Statements .. Write (nout,*) 'G13CEF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) ! Read in the problem size Read (nin,*) ng ! Read in statistics Read (nin,*) stats(1:4) Allocate (xg(ng),yg(ng),xyrg(ng),xyig(ng),ca(ng),calw(ng),caup(ng), & sc(ng),sclw(ng),scup(ng)) ! Read in data Read (nin,*)(xg(i),yg(i),xyrg(i),xyig(i),i=1,ng) ! Calculate cross-amplitude spectrum ifail = -1 Call g13cef(xg,yg,xyrg,xyig,ng,stats,ca,calw,caup,t,sc,sclw,scup,ifail) If (ifail/=0) Then If (ifail<2) Then Go To 100 End If End If ! Display results Write (nout,*) ' Cross amplitude spectrum' Write (nout,*) Write (nout,*) ' Lower Upper' Write (nout,*) ' Value bound bound' Write (nout,99999)(j-1,ca(j),calw(j),caup(j),j=1,ng) Write (nout,*) Write (nout,99998) 'Squared coherency test statistic =', t Write (nout,*) Write (nout,*) ' Squared coherency' Write (nout,*) Write (nout,*) ' Lower Upper' Write (nout,*) ' Value bound bound' Write (nout,99999)(j-1,sc(j),sclw(j),scup(j),j=1,ng) 100 Continue 99999 Format (1X,I5,3F10.4) 99998 Format (1X,A,F12.4) End Program g13cefe | 571 | 1,599 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-32 | latest | en | 0.551948 |
http://nrich.maths.org/public/leg.php?code=12&cl=3&cldcmpid=6251 | 1,432,343,570,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207926964.7/warc/CC-MAIN-20150521113206-00153-ip-10-180-206-219.ec2.internal.warc.gz | 182,697,424 | 10,123 | # Search by Topic
#### Resources tagged with Factors and multiples similar to Weekly Problem 22 - 2009:
Filter by: Content type:
Stage:
Challenge level:
### There are 92 results
Broad Topics > Numbers and the Number System > Factors and multiples
### Power Crazy
##### Stage: 3 Challenge Level:
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
### Diggits
##### Stage: 3 Challenge Level:
Can you find what the last two digits of the number $4^{1999}$ are?
### Three Times Seven
##### Stage: 3 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
### Gaxinta
##### Stage: 3 Challenge Level:
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
### Ewa's Eggs
##### Stage: 3 Challenge Level:
I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?
### Number Rules - OK
##### Stage: 4 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### How Old Are the Children?
##### Stage: 3 Challenge Level:
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
### AB Search
##### Stage: 3 Challenge Level:
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
### Really Mr. Bond
##### Stage: 4 Challenge Level:
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
### Divisively So
##### Stage: 3 Challenge Level:
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
### Sieve of Eratosthenes
##### Stage: 3 Challenge Level:
Follow this recipe for sieving numbers and see what interesting patterns emerge.
### Remainders
##### Stage: 3 Challenge Level:
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
### Even So
##### Stage: 3 Challenge Level:
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
### Digat
##### Stage: 3 Challenge Level:
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
### Oh! Hidden Inside?
##### Stage: 3 Challenge Level:
Find the number which has 8 divisors, such that the product of the divisors is 331776.
### Thirty Six Exactly
##### Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
### Repeaters
##### Stage: 3 Challenge Level:
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
### Eminit
##### Stage: 3 Challenge Level:
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
### Exploring Simple Mappings
##### Stage: 3 Challenge Level:
Explore the relationship between simple linear functions and their graphs.
### Napier's Location Arithmetic
##### Stage: 4 Challenge Level:
Have you seen this way of doing multiplication ?
### Factors and Multiple Challenges
##### Stage: 3 Challenge Level:
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
### Remainder
##### Stage: 3 Challenge Level:
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
### 14 Divisors
##### Stage: 3 Challenge Level:
What is the smallest number with exactly 14 divisors?
### Mathematical Swimmer
##### Stage: 3 Challenge Level:
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
### Counting Cogs
##### Stage: 2 and 3 Challenge Level:
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
### Times Right
##### Stage: 3 and 4 Challenge Level:
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
### Factor Track
##### Stage: 2 and 3 Challenge Level:
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
### Hot Pursuit
##### Stage: 3 Challenge Level:
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
### Inclusion Exclusion
##### Stage: 3 Challenge Level:
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
### Big Powers
##### Stage: 3 and 4 Challenge Level:
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
### Factoring Factorials
##### Stage: 3 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
### Factorial
##### Stage: 4 Challenge Level:
How many zeros are there at the end of the number which is the product of first hundred positive integers?
### Multiplication Magic
##### Stage: 4 Challenge Level:
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
##### Stage: 3 Challenge Level:
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
### Special Sums and Products
##### Stage: 3 Challenge Level:
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
### One to Eight
##### Stage: 3 Challenge Level:
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
### X Marks the Spot
##### Stage: 3 Challenge Level:
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
### A Biggy
##### Stage: 4 Challenge Level:
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
### Powerful Factorial
##### Stage: 3 Challenge Level:
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
### Expenses
##### Stage: 4 Challenge Level:
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
### Dozens
##### Stage: 3 Challenge Level:
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
### Helen's Conjecture
##### Stage: 3 Challenge Level:
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
### Sixational
##### Stage: 4 and 5 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
### Reverse to Order
##### Stage: 3 Challenge Level:
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
### For What?
##### Stage: 4 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
### Squaresearch
##### Stage: 4 Challenge Level:
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
### LCM Sudoku II
##### Stage: 3, 4 and 5 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
### Data Chunks
##### Stage: 4 Challenge Level:
Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .
### The Remainders Game
##### Stage: 2 and 3 Challenge Level:
A game that tests your understanding of remainders. | 2,425 | 9,379 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2015-22 | longest | en | 0.921532 |
http://en.m.wikibooks.org/wiki/Algorithm_Implementation/Sorting/Radix_sort | 1,432,982,389,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207930995.36/warc/CC-MAIN-20150521113210-00215-ip-10-180-206-219.ec2.internal.warc.gz | 77,338,998 | 8,056 | Last modified on 3 April 2012, at 10:06
# Algorithm Implementation/Sorting/Radix sort
## Radix SortEdit
Radix Sort is a sorting algorithm designed to work on items where the key of each item is an ordered set of integers in the range 0 to (N-1) inclusive both ends, or can be transformed into such an ordered set.
### C# least significant digit (LSD) radix sort implementationEdit
Here we sort an integer array that's passed to the RadixSort method (Note: all arrays in C#/.NET are reference types, and therefore a is a reference to an array).
Source: article on www.osix.net (here)
```public void RadixSort(int[] a)
{
// our helper array
int[] t=new int[a.Length];
// number of bits our group will be long
int r=4; // try to set this also to 2, 8 or 16 to see if it is quicker or not
// number of bits of a C# int
int b=32;
// counting and prefix arrays
// (note dimensions 2^r which is the number of all possible values of a r-bit number)
int[] count=new int[1<<r];
int[] pref=new int[1<<r];
// number of groups
int groups=(int)Math.Ceiling((double)b/(double)r);
// the mask to identify groups
int mask = (1<<r)-1;
// the algorithm:
for (int c=0, shift=0; c<groups; c++, shift+=r)
{
// reset count array
for (int j=0; j<count.Length; j++)
count[j]=0;
// counting elements of the c-th group
for (int i=0; i<a.Length; i++)
count[(a[i]>>shift)&mask]++;
// calculating prefixes
pref[0]=0;
for (int i=1; i<count.Length; i++)
pref[i]=pref[i-1]+count[i-1];
// from a[] to t[] elements ordered by c-th group
for (int i=0; i<a.Length; i++)
t[pref[(a[i]>>shift)&mask]++]=a[i];
// a[]=t[] and start again until the last group
t.CopyTo(a,0);
}
// a is sorted
}
```
### C++ LSD radix sort example of non-recursive implementationEdit
```// C++ LSD Radix Sort example, queue implementation
#include <iostream.h>
#include <cstdlib.h>
#include <ctime.h>
using std::cout; // Remove this line for older C++ compilers
typedef struct slist_ {
int val;
struct slist_ *next;
} slist;
slist *radixsort(slist *L, int t)
{
int i, j, d, m=1;
slist *temp, *head[10], *tail[10];
// Process t digits
for (j=1; j<=t; j++)
{
// Initialize the queues, 0 to 9
for (i=0; i<=9; i++)
{
head[i] = NULL;
tail[i] = NULL;
}
// Process the list L
while ( L != NULL )
{
// Get the decimal digit with place value m
d = static_cast<int>(L->val/m)%10;
// Make temp point to the current list item
temp = L;
// Make L point to the next list item
L = L->next;
// Disconnect the current list item, making it self-contained
temp->next = NULL;
if (head[d]!= NULL)
{ // The queue for digit d is not empty
// Add the list item to the end of the queue for digit d
tail[d]->next = temp;
// Make tail[d] point to the new tail item of queue d
tail[d] = temp;
}
else
{ // The queue for digit d is empty
head[d] = temp; // Point to the new head
tail[d] = temp; // Point to the new tail
}
} // while
// Find the index, d, of the first non-empty queue
d=0;
while (head[d]==NULL)
d++;
// Point to the first item of the first non-empty queue
L = head[d];
// Point to the last item of the first non-empty queue
temp = tail[d];
// Append the items of the remaining non-empty queues
// to the tail of list L.
d++;
while (d<10)
{
if (head[d]!=NULL)
{
// Append the items of non-empty queue d to list L
temp->next = head[d];
// Point to the new tail of list L
temp = tail[d];
}
d++;
} // while
// Prepare to process the next more significant digit
m = m*10;
} // for
return L;
}
int main()
{
// Initialize the random number seed with the time
srand( static_cast<unsigned int>(time(NULL)) );
const int size = 20;
int n[size];
int i, max=-1, t=0;
// Generate some random numbers
slist *start=NULL,*end=NULL,*temp;
for (i=0; i<size; i++)
{
n[i] = rand();
}
// Find the largest value and create a linked list of the random values
for (i=0; i<size; i++)
{
// Find the largest value
if (n[i] > max)
max = n[i];
// Create a new node
temp = new slist;
// Fill the node with a random value
temp->val = n[i];
// Seal the node
temp->next = NULL;
if (start != NULL)
{ // Append the new node to the linked list
end->next = temp;
end = temp;
}
else
{ // Add the first node to the linked list
start = temp;
end = temp;
}
}
// Find the number of decimal digits in the largest random value
while (max>0)
{
t=t+1;
max=max/10;
}
// Perform the radix sort
start = radixsort(start, t);
// Display the results
cout << "after radix sort.\n";
temp = start;
for (i=0; i<size; i++)
{
cout << temp->val << "\n";
temp = temp->next;
}
// Return a zero to the calling script, batch file, or command shell
// to indicate successful completion.
return 0;
} // main
```
### Python LSD radix sortEdit
```def radixSort(a,n,maxLen):
for x in range(maxLen):
bins = [[] for i in range(n)]
for y in a:
bins[(y/10**x)%n].append(y)
a=[]
for section in bins:
a.extend(section)
return a
if __name__ == "__main__":
import random
import timeit
a = [random.randint(0,10000) for i in xrange(1000000)]
t = timeit.Timer('radixSort(a, 10, 5)', 'from __main__ import radixSort, a')
print t.timeit(number=1)
```
It took on my Mac 2.3601 seconds to sort 1,000,000 items.
// Asghar Khan MCS from QAU | 1,542 | 5,144 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2015-22 | latest | en | 0.547217 |
gpalle.blogspot.com | 1,531,820,230,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589634.23/warc/CC-MAIN-20180717090227-20180717110227-00606.warc.gz | 143,056,185 | 24,479 | ## Friday, August 19, 2011
### Trying to explain Shutter Speed!
Now that we’ve understood aperture and what it controls, its time to understand the second aspect of the photographic triangle. Its known as “Shutter Speed”. Its defined as the duration for which the camera’s shutter stays open.
Along with the aperture, the shutter speed determines how much light reaches the image sensor. The longer the shutter stays open, the more light can get inside the camera to make the exposure.
Shutter speed being a measure of time, its values are expressed in seconds…or, most cases in microseconds. For example, values like 1/1000, 1/500, 1/250, 1/125, 1/60, 1/30, 1/15 and such. These values shows the fraction of a second that the shutter stays open. The bigger the denominator the faster is the shutter speed. And, if you notice, with every change of the shutter speed, the light entering the camera is either doubled or halved
(It’s the same in case of the aperture too! That with every stop down of the aperture, the area of the hole that opens, halves. Its just not as obvious as the shutter speed and beyond the scope of this blog to explain the math behind that!)
Since, the amount of light that one would need to make a perfect exposure is fixed, it means…any changes in aperture will have to be compensated with a corresponding change to the shutter speed (considering we are not changing the ISO value!) , for the same exposure.
Say, you are able to get a perfect exposure at
aperture = f/5.6
shutter speed = 1/125
ISO = 400
Now lets decrease the depth of field in the picture, say, we want to drop down the f-number..to, f/2.8.
That would mean, moving the f-number by 4 stops…
f/5.6, f/4.8, f/4, f/3.3, f/2.8
To not change the exposure, we would have to make a corresponding change to the shutter speed by raising the shutter speed by 4 stops. That would be
1/125, 1/250, 1/500, 1/1000, 1/2000
So, to get the same exposure with a shallow depth of field, The values will now have to be
aperture = f/2.8
shutter speed = 1/2000
ISO = 400
Keeping this in mind, you wonder, if the exposure needs to be the same…why would one want to change shutter speed?! Lots of reasons..
You can use low shutter speed to show the effect of moving objects in your pictures.. You can use high shutter speed to freeze an action. For example..in the picture below..when P was jumping on her trampoline..a shutter speed of 1/500 sufficed at f/2.8, ISO 200 to catch her in action.
You would slow down the shutter speed if you want to show some motion blur in your picture. Blur is not always bad… Sometimes, it can be used creatively, to show motion in your picture. Almost like a still video, as paradoxical as that sounds..For example…in the picture below, you can see that Hubby dear was trying to throw the rope up somewhere!! You can almost see the rope flying up. Isn’t it?
Or in here, that K was trying to lift a box of cheerios! The exposure values for this was f/2.8, shutter speed of 1/6 sec and ISO of 200.
When a slower shutter speed is selected, a longer time passes from the moment the shutter opens till the moment it closes. More time is available for movement in the subject to be recorded by the camera.
Now that we know, slow shutter speeds cause blurs, what is the minimum shutter speed that one could use to have a picture taken so, there’s no blur?
If you are hand holding your camera, ( and considering you have a static subject! ) most photographic pros consider having a minimum of 1/60 shutter speed. (That should roughly be about the focal length of a 50mm lens, for a full frame sensor.)
Some cameras give you the ability for very slow shutter speeds also. For example, 1”, 10”, 30”…measured in seconds. Why would you needs such shutter speeds? Suppose you want to take a shot of a night scenario. This calls for very long shutter speeds, measured in seconds..For eg.
This image was exposed , for 30 seconds at f/16 and ISO of 200. (You can see..there’s still, a slight blur in this image..caused by the action of clicking the pic itself…To get tack sharp images..as the pros call them..they suggest using remote release cables or wireless shutter release or just plain self timer to release the shutter ).
To click such images, you would first fix your camera, to a TRIPOD, then, set your shutter speed to a value that gives you the best shot and click, considering that you have moved your mode dial on the camera to Shutter prority mode, or, the “S” mode!
You can use low shutter speeds to picture night skies, where you want to show how the stars move over a period of time. You can use it to show light painting, by making patterns with sparklers as you hold them. You can use it to picture streets at nights.
The picture below shows a light trail of a vehicle that was passing by my tent at a camp ground. You could use such shots to creatively picture city streets..at night. The light trails left by passing vehicles leave beautiful patterns.
There is another use of slow shutter speeds. Do you remember seeing posters of water falls were the water fall looks so silky smooth. This is achieved by using low shutter speeds too. One would need to use special filters to achieve these effects like neutral density filters. They cut the amount of light reaching the camera..allowing the photographer to use a very low shutter speed even during the day!…Here’s my experiment, I did at my kitchen sink!!! Which obviously shows..that I wasn’t thinking much in terms of being creative !
See, how the flow of water is softer in the second pic. Its because I had used a neutral density filter (0.6) on the lens..which required a longer exposure compared to the exposure of the first pic, thereby making the flow of water look softer.
Now that you know some things you could do by controlling shutter speed. Don’t forget to turn the mode dial on your camera to “S” and try out some shots that you had just been wondering how to!
You know, after writing all this…I come across this clip from Calvin and Hobbes and I thought it was worth mentioning for all that effort
Calvin: As far as I'm concerned, if something is so complicated that you can't explain it in 10 seconds, then it's probably not worth knowing anyway.
## Sunday, August 7, 2011
### The ABC’s of Photography!
Introduction or whatever!!
Recently, back in India, as I clicked the pictures of my family, I spoke to them of the camera settings and other fundas while clicking…My brother had remarked
“Why don’t you write a blog that explains the basic concepts in photography that one would need to know to click a decent pic…..in layman terms?!”
That had gotten me thinking of what one would need to know. What was the information I would have wished I had known when I first got a hand on a camera.
It had gotten me thinking of how cameras had become cheaper and owing a DSLR is no more a dream for a non professional. In spite of owning one, how I had found most people, using them as point and shoots (Me included, for so many years!!!).
Surely, we’ve come a long way from the “film roll” times where, every click took away the option of another click. Every click meant more money, even to view it (Thank you LCD!!!!)
(Recently, the kids and me were going through the index prints of numerous rolls that I had clicked of their infanthood and before that…of Hubby’s and Mine, of Hobbes. Some roles had good pictures while most of them were either blurry, overexposed, or just wasted clicks that today, I wouldn’t have bothered to get them in print. But, how do you know until you see the picture!!!)
And every click meant that there was no room for experimentation, the shot had to be good, creative, and there was no scope for mistakes. Photography was a field that was left only for the fiercely passionate kind of people with an extra buck to spare.
Today, not only can one own a decently priced DSLR, one can shoot a couple of hundred times in a span of a few minutes, just to get that good shot to share with friends or (annoy them!!!)…, or, display them on your digital frames, leaving more room on your table for other stuff , like “Ganesha” art ..
So, I thought I would share, in these series of blogs, the basics that I have learnt. I myself am no far from a beginner, when it comes to understanding my camera, and its myriad options.
I wish I had known some of these facts, I now know, years ago when I had wasted so many rolls and used my D40 as a point and shoot and wondered why the bokeh’s I sometimes see were not consistent. I had wondered if I could even control that!
Even today, when I pick up my camera, I’m learning something new and I feel that I haven’t progressed at all! And the worst is when you actually know what to do..but, don’t remember to do so, and find your pictures not coming the way you’d think they should, only to realize later…your ISO setting or the white balance settings had not been reset from the last time you changed them.
As the word photography, Photo+Graphy means…writing with light without which there wouldn’t be any thing to write. Right?! As basic as this sounds…it does get intimidating and challenging to get this light in the right amount.
How can one get a perfect exposure? How we can get the correct amount of light to light up the sensor, to create this wonderful picture you have in mind?! (The sensor in your digital camera is the light sensitive computer chip, the equivalent of a film roll.) It all revolves around 3 settings on your camera called…
1. Aperture or f-stop
2. Shutter Speed
3. ISO (remember those film roles with ISO #s of 100, 200, 400, 800..)
They are also known as the Photographic triangle that when set right, will get you the most wonderful picture with everything appearing the way it should, the way you had envisioned it in your mind.
Lets first understand what an Aperture means.
Aperture or f-stop:
This refers to how wide the hole in the lens opens, when you take a picture. This determines how much light passes on to the sensor. It can also be expressed in terms of f-stops or f-numbers. The lower this F number, the wider the opening is and more light that reaches the sensor.
Do you remember coming across this information on pictures… f/2, f/2.8, f/3.3, f/4, f/5.6, f/8, f/11, f/16, f/22 . At f/2 , the lens is supposed to be wide open, which means a lot of light can enter through the lens, which means that, its not possible for the camera to see the whole image clearly.
What?!!
Just like you remember, when the ophthalmologist had put those drops in your eyes to dilate it. Do you remember, trying to open your eyes when your eyes are fully dilated? Its difficult to see things clearly because of that blast of light entering your eyes. It’s the same in case of the camera. The picture gets a bit blurry, while the subject you want to focus on, stays clear!
Aperture and Bokeh:
Bokeh is a word that comes from Japanese meaning ‘Blur’. By lowering the Aperture, i.e., when the f-number is the smallest enough, one can get dreamy portraits of your subject with blurred out surroundings, with bubbles of light in the background. It gives a lot of situations to get creative with your pictures.
For eg
As we start to raise the f-number, the lens opening gets smaller and the blurs start to disappear. The picture starts to get clear. At f/8 or f/11, most of the surroundings of the subject becomes clear. This is called the sweet spot for most lens. Watch the difference in the pictures below…The only thing I varied below is the F-stop. Can you guess which one is the picture with a lower F-stop?!
At higher f-stops, everything in the picture is crisp and clear. This way, one can use the Aperture mode to be creative, using wide open apertures for creating pictures with beautiful bokehs, to make the pictures softer, to create portraits and smaller apertures to picture landscapes.
Opening the camera wide (lowering the f-stop or f-number) in low light conditions, is another way to use ambient light/surrounding light, to lighten up your photograph. It gives the scope for one to get creative with light, rather than make your picture feel like a snap shot.
Aperture and Depth of Field:
Changing the Aperture also gives a 3-dimensional feel to your pictures which can be expressed in terms of DoF, Depth-of-Field. The wider the aperture, the shallow the DoF which explains the blurred surroundings even better. So you see, Aperture controls the Depth of Field.
For landscape pictures, where you want the whole composition to be clear, raising the f-number, or Aperture value will help you achieve that.
For group photos where people are standing at various distances…f values of f/11 or higher are used.
Aperture Mode:
Now that you know the pluses of controlling the Aperture on your camera, why don’t you move that dial from “P” mode or program mode, which in other words means, automatic mode of your camera (On a Nikon) to the “A” or “Av” mode on your DSLR camera.
In this mode, while you set the Aperture value, the camera decides the Shutter speed, for you, when you click a picture.
( You must wonder that there is another mode that is called “Automatic mode” in your camera. On a Nikon, it has a flash symbol on it, or a green box. This mode forces the flash to fire if the light is not enough while the P mode lets you decide when the flash is to be fired.)
Now that you’ve moved the mode dial to the “A” or “Av” mode on your camera, you’re in Aperture mode. Its so much easier to deal with one aspect at a time, rather than you have to deal with setting everything on the camera, like you would do in the “M” mode, or the Manual.
Why would I want to get to this mode. Exactly for the same reason that I explained earlier. If I’m taking portrait shot and I want that 3 – dimensional, softer feel to the pic, I want the subject to stand out against its surrounding, when I feel I could use the boken effects in the blur to enhance the picture, when I don’t want to emphasis the surroundings of the suject, instead use the colors in the surrounding to make the picture bright..I would use this mode. In fact, most times this is the default mode that I am in.
In my next blog…lets see how shutter speed effects a picture or, when would one find it necessary to be in “S” mode. | 3,385 | 14,379 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2018-30 | latest | en | 0.921929 |
https://forum.solar-electric.com/discussion/353713/i-thought-i-understood-the-math-behind-sizing-a-charge-controller-but-now-im-not-sure | 1,723,032,589,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640694449.36/warc/CC-MAIN-20240807111957-20240807141957-00856.warc.gz | 207,312,799 | 81,444 | # I thought I understood the math behind sizing a charge controller, but now I'm not sure
Registered Users Posts: 11✭✭
Had a professional installer come out and help me setup a system. 9 panels, 250 watts, VMP 30.1V, IMP: 8.30A, VOC 37.2V, ISC 8.87A. I don't have immediate access to check how he wired them, but I can't even figure out how any combination would not over drive the charge controller.
The panels come into a combiner box, three breakers (each 15 amp, 150v) and then it combines into a single breaker 80 amp 150v. That makes me thing they did 3 panels in a series and then paralleled the 3 series via the combiner box. Does that seem about right?
That goes to a Schneider MPPT 60 amp 150 volt charge controller. That's connected to a a 740 ah battery bank that's 24 Volt. Goes to a Schneider SW 4024 Off Grid Inverter. Distance from panels to all the equipment is 30 feet. Pretty sure it's all PV wire from panels to Charge controller, 10 awg (don't quote me on that).
Questions:
• Does that seem right, how is it not over driving charge controller?
• What is the correct formula to crunch the numbers for sizing a charge controller?
• Does the combiner box impact things? Is it like running them in parallel?
• Solar Expert Posts: 6,006✭✭✭✭✭
I'd say at first glance it might be a bit over paneled for a 60 amp MPPT charge controller. Lets' look at the numbers.
The 3 in series and 3 breakers looks right, Don't need that high a amp breaker once combined. but perhaps room for expansion. You'll have less than 30 amps coming in... It is also under sized for 10 gauge wire. perhaps he had 4 gauge between the combiner and the breaker?
You have 9 panels at 250 watts or 2250 watts of array, at 24 volts you have the potential at charging voltage of 2250 watts ÷ 29 volts (charging voltage for 24 volt bank) 77.6 amps. and a realistic expectation of about 75% of that on normal days or 58.2 amps. So it's a little under what I would like to see, but within the 'cost effective' range.
I would call a foul on a maximum of 60 amps coming into a 740 amp hour battery bank. That is less than 10% this would be okay if it's a stand by/weekend use type situation. It's also okay if you are in a particularly sunny area, like the desert southwest. But undersized in general for daily cycling. Are you sure that's the '20 hour rate' for the batteries?
If you are in the desert southwest, it would make more sense. The voltage drop would be even greater in the heat there making the 60 amp charge controller make more sense. and the long sunny days would give you the extra time to charge making up for the lower than normal charge rate.
Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites, Midnite E-panel, Magnum MS4024, Prosine 1800(now backup) and Exeltech 1100(former backup...lol), 660 ah 24v Forklift battery(now 10 years old). Off grid for 20 years (if I include 8 months on a bicycle).
- Assorted other systems, pieces and to many panels in the closet to not do more projects.
• Solar Expert Posts: 6,006✭✭✭✭✭
The charge controller can be infinitely 'over paneled' In general it's cost effective to over panel up to 20%.
With an MPPT controller the formula is roughly total wattage of the array ÷ the charging voltage (some use system voltage 29 vs 24 volts in this case) x .75 (this is a correction factor for the solar panels name plate vs what they will normally produce, most 100 watt panels will produce about 75 watts under Normal Operating Cell Temperature(NOCT).
The combiner box allows each panel or string of panels to have protection from being over powered in case of a short, from the other panels. It is also handy to combine the panels so a single pair of wires can make the run to the charge controller. Yes, it's running 3 strings in parallel.
Home system 4000 watt (Evergreen) array standing, with 2 Midnite Classic Lites, Midnite E-panel, Magnum MS4024, Prosine 1800(now backup) and Exeltech 1100(former backup...lol), 660 ah 24v Forklift battery(now 10 years old). Off grid for 20 years (if I include 8 months on a bicycle).
- Assorted other systems, pieces and to many panels in the closet to not do more projects.
• Solar Expert Posts: 891✭✭✭✭
Had a professional installer come out and help me setup a system. 9 panels, 250 watts, VMP 30.1V, IMP: 8.30A, VOC 37.2V, ISC 8.87A. I don't have immediate access to check how he wired them, but I can't even figure out how any combination would not over drive the charge controller.
The panels come into a combiner box, three breakers (each 15 amp, 150v) and then it combines into a single breaker 80 amp 150v. That makes me thing they did 3 panels in a series and then paralleled the 3 series via the combiner box. Does that seem about right?
That goes to a Schneider MPPT 60 amp 150 volt charge controller. That's connected to a a 740 ah battery bank that's 24 Volt. Goes to a Schneider SW 4024 Off Grid Inverter. Distance from panels to all the equipment is 30 feet. Pretty sure it's all PV wire from panels to Charge controller, 10 awg (don't quote me on that).
Questions:
• Does that seem right, how is it not over driving charge controller?
• What is the correct formula to crunch the numbers for sizing a charge controller?
• Does the combiner box impact things? Is it like running them in parallel?
That's about right. At a charge voltage of 30 volts that's 75 amps. Using the normal 80% of STC number that's 60 amps, so that's OK.
To calculate:
Take total wattage, divide by output voltage. That's max amps at STC. Now multiply by .8 or so to account for normal performance, and multiply by the efficiency of the MPPT controller. That gives you max amps.
Combiner box just combines the leads. You could do the same thing electrically by plugging the panels directly via 2 to 1 MC adapters; the combiner just gives you a place for fuses/breakers and makes wiring easier/safer/legal.
BTW for 740 amp hours you want at LEAST 60 amps charge current, so you are close to the minimum for that bank.
• Solar Expert Posts: 9,583✭✭✭✭✭
MPPT controllers are easy Watts in = watts out (minus a % for losses)
5kw in = 4.99kw out . Then you just figure the voltage your batteries charge at, and you have your amps.
Powerfab top of pole PV mount | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
|| Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
|| VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A
solar: http://tinyurl.com/LMR-Solar
gen: http://tinyurl.com/LMR-Lister ,
• Solar Expert Posts: 3,854✭✭✭✭✭✭
The system was well calculated, the added PV will be useful during non peak periods, the 10% charging versus battery capacity, really depends on overnight loads, assuming off grid, if dipping into capacity is low, then a few days of reduced output can be made up during the next few days of normal output, if all else fails a generator is a helpful addition. This has been my case, there have been more overcast days in the last 3 weeks than the last 3 years combined , climate change perhaps ? Getting to know the system will take some time, a year minimum, but nature has its ways of throwing curve balls, every once in a while, if there is no generator I would highly suggest getting one to allow the CSW 4024 to charge, should the need present itself. The 740Ah battery I'm assuming, again, is lead acid in which case the depth of discharge should be kept to 50% maximum as a general rule, the deeper the discharge the harder the recovery.
1500W, 6× Schutten 250W Poly panels , Schneider MPPT 60 150 CC, Schneider SW 2524 inverter, 400Ah LFP 24V nominal battery with Battery Bodyguard BMS
Second system 1890W 3 × 300W No name brand poly, 3×330 Sunsolar Poly panels, Morningstar TS 60 PWM controller, no name 2000W inverter 400Ah LFP 24V nominal battery with Daly BMS, used for water pumping and day time air conditioning.
5Kw Yanmar clone single cylinder air cooled diesel generator for rare emergency charging and welding. | 2,181 | 8,269 | {"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} | 2.6875 | 3 | CC-MAIN-2024-33 | latest | en | 0.949755 |
http://freqnbytes.com/confidence-interval/computing-confidence-interval-standard-error.php | 1,524,798,422,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125948950.83/warc/CC-MAIN-20180427021556-20180427041556-00349.warc.gz | 121,522,808 | 6,012 | Home > Confidence Interval > Computing Confidence Interval Standard Error
Computing Confidence Interval Standard Error
Contents
Another way of looking at this is to see that if you chose one child at random out of the 140, the chance that the child's urinary lead concentration will exceed See unbiased estimation of standard deviation for further discussion. Figure 2. 95% of the area is between -1.96 and 1.96. Note: the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations: the standard error of the mean is a biased estimator http://freqnbytes.com/confidence-interval/computing-confidence-intervals-standard-error.php
The confidence interval is then computed just as it is when σM. As an example of the use of the relative standard error, consider two surveys of household income that both result in a sample mean of $50,000. Home | Blog | Calculators | Products | Services | Contact(303) 578-2801 © 2016 Measuring Usability LLC All Rights Reserved. When you need to be sure you've computed an accurate interval then use the online calculators (which we use). Discover More Calculate Confidence Interval From Standard Error In R This is the 99.73% confidence interval, and the chance of this interval excluding the population mean is 1 in 370. Therefore the confidence interval is computed as follows: Lower limit = 16.362 - (2.013)(1.090) = 14.17 Upper limit = 16.362 + (2.013)(1.090) = 18.56 Therefore, the interference effect (difference) for the SMD, risk difference, rate difference), then the standard error can be calculated as SE = (upper limit – lower limit) / 3.92. The next graph shows the sampling distribution of the mean (the distribution of the 20,000 sample means) superimposed on the distribution of ages for the 9,732 women. However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and v t e Statistics Outline Index Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Moments Confidence Interval Margin Of Error With small samples, this asymmetry is quite noticeable. In general, you compute the 95% confidence interval for the mean with the following formula: Lower limit = M - Z.95σM Upper limit = M + Z.95σM where Z.95 is the Confidence Interval Standard Error Of The Mean Example 1 A general practitioner has been investigating whether the diastolic blood pressure of men aged 20-44 differs between printers and farm workers. As the level of confidence decreases, the size of the corresponding interval will decrease. http://onlinestatbook.com/2/estimation/mean.html They report that, in a sample of 400 patients, the new drug lowers cholesterol by an average of 20 units (mg/dL). For example, if p = 0.025, the value z* such that P(Z > z*) = 0.025, or P(Z < z*) = 0.975, is equal to 1.96. Confidence Interval Sampling Error In our sample of 72 printers, the standard error of the mean was 0.53 mmHg. Confidence interval for a proportion In a survey of 120 people operated on for appendicitis 37 were men. It's not done often, but it is certainly possible to compute a CI for a SD. Confidence Interval Standard Error Of The Mean Bence (1995) Analysis of short time series: Correcting for autocorrelation. This can be proven mathematically and is known as the "Central Limit Theorem". Calculate Confidence Interval From Standard Error In R We will finish with an analysis of the Stroop Data. Confidence Interval Standard Error Of Measurement Therefore we can be fairly confident that the brand favorability toward LinkedIN is at least above the average threshold of 4 because the lower end of the confidence interval exceeds 4. The standard error of a proportion and the standard error of the mean describe the possible variability of the estimated value based on the sample around the true proportion or true navigate to this website If you want more a more precise confidence interval, use the online calculator and feel free to read the mathematical foundation for this interval in Chapter 3 of our book, Quantifying The only differences are that sM and t rather than σM and Z are used. The first step is to obtain the Z value corresponding to the reported P value from a table of the standard normal distribution. Confidence Interval Standard Error Or Standard Deviation This can be obtained from a table of the standard normal distribution or a computer (for example, by entering =abs(normsinv(0.008/2) into any cell in a Microsoft Excel spreadsheet). Figure 2. 95% of the area is between -1.96 and 1.96. The sampling distribution of the mean for N=9. http://freqnbytes.com/confidence-interval/confidence-interval-standard-deviation-or-standard-error.php Most people are surprised that small samples define the SD so poorly. A t table shows the critical value of t for 47 - 1 = 46 degrees of freedom is 2.013 (for a 95% confidence interval). Convert Confidence Interval Standard Deviation If we knew the population variance, we could use the following formula: Instead we compute an estimate of the standard error (sM): = 1.225 The next step is to find the For a population with unknown mean and unknown standard deviation, a confidence interval for the population mean, based on a simple random sample (SRS) of size n, is + t*, where Learn MoreYou Might Also Be Interested In: 10 Things to know about Confidence Intervals Restoring Confidence in Usability Results 8 Core Concepts for Quantifying the User Experience Related Topics Confidence Intervals For example, the U.S. This 2 as a multiplier works for 95% confidence levels for most sample sizes. Correction for correlation in the sample Expected error in the mean of A for a sample of n data points with sample bias coefficient ρ. Calculate Confidence Interval Variance For each sample, the mean age of the 16 runners in the sample can be calculated. But the true standard deviation of the population from which the values were sampled might be quite different. The series of means, like the series of observations in each sample, has a standard deviation. McColl's Statistics Glossary v1.1) The common notation for the parameter in question is . click site The graph shows the ages for the 16 runners in the sample, plotted on the distribution of ages for all 9,732 runners. Figure 1 shows that 95% of the means are no more than 23.52 units (1.96 standard deviations) from the mean of 90. If one survey has a standard error of$10,000 and the other has a standard error of \$5,000, then the relative standard errors are 20% and 10% respectively. Where exact P values are quoted alongside estimates of intervention effect, it is possible to estimate standard errors. Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma }
From the n=5 row of the table, the 95% confidence interval extends from 0.60 times the SD to 2.87 times the SD. Specifically, we will compute a confidence interval on the mean difference score. That means we're pretty sure that at least 13% of customers have security as a major reason why they don't pay their credit card bills using mobile apps (also a true To compute a 95% confidence interval, you need three pieces of data:The mean (for continuous data) or proportion (for binary data)The standard deviation, which describes how dispersed the data is around
The standard error of the mean is 1.090. He is the author of over 20 journal articles and 5 books on statistics and the user-experience. However, to explain how confidence intervals are constructed, we are going to work backwards and begin by assuming characteristics of the population. Dataset available through the JSE Dataset Archive.
I know it is usually pretty close to 2, but shouldn't it be the table value (in this case a T-distribution value because we have an unknown population mean and variance). Using a dummy variable you can code yes = 1 and no = 0. Since 95% of the distribution is within 23.52 of 90, the probability that the mean from any given sample will be within 23.52 of 90 is 0.95. The standard error of the mean is 1.090.
Related This entry was posted in Part A, Statistical Methods (1b). Given a sample of disease free subjects, an alternative method of defining a normal range would be simply to define points that exclude 2.5% of subjects at the top end and | 1,916 | 8,661 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2018-17 | latest | en | 0.876371 |
https://whatasker.com/newtons-third-law/ | 1,719,129,081,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862464.38/warc/CC-MAIN-20240623064523-20240623094523-00494.warc.gz | 534,139,355 | 43,388 | # Newton’s third law
Galileo , through his speeches and mathematical demonstrations, had managed to explain the movement that was involved in the fall of the bodies and the trajectory of the projectiles. Putting aside Aristotle’s speculations on motion, he founded kinematics on scientific and experimental bases , that is, the part of mechanics that describes the motion of bodies regardless of the forces that produce it. From these studies, Newton managed to develop dynamics , a science that studied the relationships that occurred between theforces and the movements that they originate. In the second section of the Mathematical Principles of Natural Philosophy, Newton established the three “axioms or laws of motion .
## What is Newton’s third law?
The Newton ‘s third law tells us that the interactions that occur between two bodies are always equal but will be directed in direction opposite to the first body that for every action there is a reaction .
• What is Newton’s third law?
• Who proposed it
• History
• Statement
• Characteristics of Newton’s third law
• Formula
• Target
• Explanation
• Applications of Newton’s third law
• Experiment
• Examples
• Conclution
## What is Newton’s third law?
The law is that when an object displays a force on another object , the second object exerts a force of equal magnitude and direction opposite the first. When any type of interaction occurs, there is also a pair of action and reaction forces , whose magnitude is equal and the directions are opposite. These forces occur in pairs, so the pair of action and reaction forces form an interaction between two objects.
Newton’s third law is also known as the action and reaction principle .
## Who proposed it
Newton’s third law is completely unique to Isaac Newton . Let us remember that the other two laws already had an elaborate scientific basis for Galileo, Hooke and Huygens.
## History
The Third Law as its name implies was created by Isaac Newton , when he began to wonder why objects were moving . The story of the third law is based on an apple, and how the scientist inspired his knowledge from the fall of an apple from a tree.
## Statement
The original statement of the law says the following:
“Action is always opposed an equal reaction: or the mutual actions of two bodies are always equal, and directed opposing parties.”
In Spanish, this statement says the following: with every action an equal and opposite reaction always occurs : it means that the mutual actions of two bodies are always equal and directed in the opposite direction.
## Characteristics of Newton’s third law
The main characteristics of Newton’s third law are as follows:
• It is an original law formulated by Isaac Newton .
• One object exerts a force on a second object
• Forces never occur individually , but rather in equal and opposite pairs.
• It is only possible to work in a vector way, since like any vector it has magnitude , direction and meaning .
• The action and reaction force act at the same time with the same magnitude and direction but in the opposite direction.
• The direction is given by the angle of inclination of both forces.
## Formula
Mathematically, the third law of motion of Newton can be expressed by the following formula: F1 = F2 ‘Where F1 is the force that acts on the body 1 and F2′ force reactive acting on the body 2.
## Target
The main objective of Newton’s third law is to identify the types of forces involved in the motion of objects. He also made great contributions to classical mechanics as it is a system that explains how force is related to the movement of bodies.
## Explanation
This law explains the forces of action and reaction, which are forces that can be exerted by all bodies that come into contact with another. These forces are equal but at the same time they are opposite in the aspect of the direction . Every time one body exerts force on another, the latter also exerts force on the first object.
In Newton’s third law, what we know as the action force intervenes and this force is the one that is exerted by the first body that makes force on the other, and the reaction force also intervenes , which is the one possessed by the body that receives and reacts .
## Applications of Newton’s third law
Some of the applications in which we can observe the third law are the following:
• Row in boats.
• Takeoffs rockets .
• A being in position of standing on the ground.
• In gun shots .
• It is also used in structures and buildings .
• Satellite repair .
## Experiment
#### The Reactive Balloon
• Materials: a balloon , string , tape , and an L-shaped straw .
• Procedure: first we must inflate the balloon, then we put the folded straw in the mouth of the balloon and it is fixed with adhesive tape. On the line of the largest diameter of the balloon, we glue the end of the thread and hold the other end of the thread at a certain height . Hold the balloon and you will see the balloon spin as it deflates.
## Examples
Some examples of Newton’s third law are:
• When we swim in a pool because when we look for the wall and push ourselves to get momentum we can detect an action and a reaction .
• When a nail is hammered into a surface, the hammer makes a backward motion, which is identified as the reaction to its own blow .
• When a person pushes another with a similar body . In this case, the person will not only go back but also the one who pushed him.
• When you are rowing a boat because while move the water to back with the paddle, it reacts pushing the boat in its opposite direction .
## Conclution
Newton’s third law explains the forces of action and reaction and teaches us that they are forces that we can find in all bodies when they are in contact with each other, that they are equal but at the same time are opposite ; they have the same module and sense , but in direction they are opposite . By this we mean that one body exerts a force on another but that this other also exerts a force on it.
We know by the name of action force the force that is exerted by the first body and therefore, we call the reaction force that which is originated by the body that receives and reacts to the force. | 1,564 | 6,210 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2024-26 | latest | en | 0.776728 |
https://simplywall.st/stocks/no/insurance/ob-gjf/gjensidige-forsikring-shares/news/is-gjensidige-forsikring-asas-obgjf-stocks-recent-performanc | 1,653,297,406,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662556725.76/warc/CC-MAIN-20220523071517-20220523101517-00112.warc.gz | 575,103,700 | 26,063 | # Is Gjensidige Forsikring ASA's (OB:GJF) Stock's Recent Performance A Reflection Of Its Financial Health?
By
Simply Wall St
Published
April 12, 2022
Most readers would already know that Gjensidige Forsikring's (OB:GJF) stock increased by 2.2% over the past month. Given its impressive performance, we decided to study the company's key financial indicators as a company's long-term fundamentals usually dictate market outcomes. Specifically, we decided to study Gjensidige Forsikring's ROE in this article.
Return on equity or ROE is a key measure used to assess how efficiently a company's management is utilizing the company's capital. In other words, it is a profitability ratio which measures the rate of return on the capital provided by the company's shareholders.
Check out our latest analysis for Gjensidige Forsikring
### How To Calculate Return On Equity?
ROE can be calculated by using the formula:
Return on Equity = Net Profit (from continuing operations) ÷ Shareholders' Equity
So, based on the above formula, the ROE for Gjensidige Forsikring is:
28% = kr7.1b ÷ kr25b (Based on the trailing twelve months to December 2021).
The 'return' refers to a company's earnings over the last year. Another way to think of that is that for every NOK1 worth of equity, the company was able to earn NOK0.28 in profit.
### Why Is ROE Important For Earnings Growth?
Thus far, we have learned that ROE measures how efficiently a company is generating its profits. Based on how much of its profits the company chooses to reinvest or "retain", we are then able to evaluate a company's future ability to generate profits. Assuming all else is equal, companies that have both a higher return on equity and higher profit retention are usually the ones that have a higher growth rate when compared to companies that don't have the same features.
### Gjensidige Forsikring's Earnings Growth And 28% ROE
First thing first, we like that Gjensidige Forsikring has an impressive ROE. Secondly, even when compared to the industry average of 10% the company's ROE is quite impressive. This probably laid the groundwork for Gjensidige Forsikring's moderate 10% net income growth seen over the past five years.
Next, on comparing with the industry net income growth, we found that Gjensidige Forsikring's growth is quite high when compared to the industry average growth of 7.5% in the same period, which is great to see.
Earnings growth is a huge factor in stock valuation. It’s important for an investor to know whether the market has priced in the company's expected earnings growth (or decline). This then helps them determine if the stock is placed for a bright or bleak future. What is GJF worth today? The intrinsic value infographic in our free research report helps visualize whether GJF is currently mispriced by the market.
### Is Gjensidige Forsikring Using Its Retained Earnings Effectively?
The high three-year median payout ratio of 57% (or a retention ratio of 43%) for Gjensidige Forsikring suggests that the company's growth wasn't really hampered despite it returning most of its income to its shareholders.
Besides, Gjensidige Forsikring has been paying dividends for at least ten years or more. This shows that the company is committed to sharing profits with its shareholders. Upon studying the latest analysts' consensus data, we found that the company's future payout ratio is expected to rise to 83% over the next three years. Accordingly, the expected increase in the payout ratio explains the expected decline in the company's ROE to 22%, over the same period.
### Conclusion
Overall, we are quite pleased with Gjensidige Forsikring's performance. In particular, its high ROE is quite noteworthy and also the probable explanation behind its considerable earnings growth. Yet, the company is retaining a small portion of its profits. Which means that the company has been able to grow its earnings in spite of it, so that's not too bad. Having said that, on studying current analyst estimates, we were concerned to see that while the company has grown its earnings in the past, analysts expect its earnings to shrink in the future. Are these analysts expectations based on the broad expectations for the industry, or on the company's fundamentals? Click here to be taken to our analyst's forecasts page for the company.
### Discounted cash flow calculation for every stock
Simply Wall St does a detailed discounted cash flow calculation every 6 hours for every stock on the market, so if you want to find the intrinsic value of any company just search here. It’s FREE.
### Make Confident Investment Decisions
Simply Wall St's Editorial Team provides unbiased, factual reporting on global stocks using in-depth fundamental analysis.
Find out more about our editorial guidelines and team. | 1,062 | 4,822 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2022-21 | latest | en | 0.938132 |
https://www.cfd-online.com/Forums/openfoam-pre-processing/121982-computing-courant-number-print.html | 1,519,578,666,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816841.86/warc/CC-MAIN-20180225170106-20180225190106-00105.warc.gz | 826,033,104 | 3,304 | CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
- OpenFOAM Pre-Processing (https://www.cfd-online.com/Forums/openfoam-pre-processing/)
- - Computing Courant number (https://www.cfd-online.com/Forums/openfoam-pre-processing/121982-computing-courant-number.html)
Many August 9, 2013 09:50
Computing Courant number
Hi everyone,
I have one question related to Courant number. I am trying to simulate a flow in a complex channel with icoFoam, and Courant number is giving me some problems.
I have info about pressure on both inlet and outlet, but no velocity values are given. Also I have made a tetrahedral mesh and on another stage a hybrid mesh (tetra+prism). In order to satisfy stability criterion based on Courant<1, I am not sure about:
1. Which is delta_x? The maximum edge lenght of tetrahedrons?Minimum? This is an unstructured mesh so delta_x is not fixed!
2. How can I stablish a characteristic velocity magnitude for the formula if I donīt have any info about velocity values? (pressure driven flow)
3. IS there any way of fixing the maximum Courant number (less than 0.75 for example) in all mesh and let OpenFOAM work with time step?
Sorry for that stupids questions, but the beginnings are always hard...:eek:
Thank you so much in advance!
Benedikt September 12, 2013 06:18
First about the mesh: I'm not sure, but I reckon in general a hexaedral mesh should work better than a tetrahedral mesh.
The courant number will be calculated for each cell.
I would suggest to just run the solver and have a look at the logfile afterwards. There you can see the mean Courant number and the max Courant number. If it is too high, decrease deltaT or change the mesh. It is also possible to have a look in paraview in which cell the Courant number is too high. See http://www.cfd-online.com/Forums/ope...nt-number.html
Regarding question 3. Have a look at the systemDic.
There is an entry called "adjustTimeStep".
GerhardHolzinger September 12, 2013 06:48
Quote:
Originally Posted by Many (Post 444734) Hi everyone, I have one question related to Courant number. I am trying to simulate a flow in a complex channel with icoFoam, and Courant number is giving me some problems. I have info about pressure on both inlet and outlet, but no velocity values are given. Also I have made a tetrahedral mesh and on another stage a hybrid mesh (tetra+prism). In order to satisfy stability criterion based on Courant<1, I am not sure about: 1. Which is delta_x? The maximum edge lenght of tetrahedrons?Minimum? This is an unstructured mesh so delta_x is not fixed! 2. How can I stablish a characteristic velocity magnitude for the formula if I donīt have any info about velocity values? (pressure driven flow) 3. IS there any way of fixing the maximum Courant number (less than 0.75 for example) in all mesh and let OpenFOAM work with time step? Sorry for that stupids questions, but the beginnings are always hard...:eek: Thank you so much in advance!
icoFoam is a transient solver that used fixed time steps. You need to use e.g. simpleFoam for transient simulations with variable time steps. Then you can specify a maximum Courant number and OF will compute the appropriate time step size.
According to my studies of the sources, the Courant number is computed by OF using the flux, the cell volume instead of velocity and discretization length.
The above equation is strictly true only for homogeneous uniform hex-grids. However, it demonstrates how you can calculate a Courant number from fluxes and cells volumes.
So your first question is handled by OF. It computes the Courant number of all cells and then looks for the maximum value. delta_x is not used in the equations.
Is your second question related to estimating the allowed time step size prior to the simulation? With variable time step size solvers, the initial time step size is not that important. If it is too big, you will see it in the solver output, when the solver drastically reduces time step size to match the maxCo criterion.
All times are GMT -4. The time now is 13:11. | 974 | 4,086 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-09 | latest | en | 0.897221 |
https://github.com/htm-community/htm.core/wiki/Sparse-Distributed-Representations | 1,563,943,426,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195530385.82/warc/CC-MAIN-20190724041048-20190724063048-00262.warc.gz | 401,639,265 | 17,290 | # Sparse Distributed Representations
A sparse distributed representation (SDR) is a set of boolean values which represent the state of a group of neurons or their associated processes. There is a new class to represent an SDR. The SDR class has methods to hold, measure, and manipulate them. Many of the algorithms pass and return SDRs. For complete documentation see `help(nupic.bindings.sdr.SDR)`. Here is a shortened except from the documentation:
SDR's have three commonly used data formats which are:
• dense A numpy array of boolean values, representing all of the bits in the SDR. This format allows random-access queries of the SDRs values.
• sparse A numpy array containing the indices of only the true values in the SDR. These are indices into the flattened SDR. This format allows for quickly accessing all of the true bits in the SDR.
• coordinates List of numpy arrays, containing the indices of only the true values in the SDR. This is a list of lists: the outer list contains an entry for each dimension in the SDR. The inner lists contain the coordinates of each true bit. The inner lists run in parallel. This format is useful because it contains the location of each true bit inside of the SDR's dimensional space.
The SDR class has three magic properties, one for each of these data formats. These properties are the primary way of accessing the SDR's data. When these properties are read from, the data is automatically converted to the requested format and is cached so getting a value in one format many times incurs no extra performance cost. Assigning to the SDR via any one of these properties clears the cached values and causes them to be recomputed as needed.
### Example usage:
```from nupic.bindings.sdr import SDR
import numpy # SDR uses all numpy arrays, but will accept lists instead.
# Make an SDR with 9 values, arranged in a (3 x 3) grid.
X = SDR(dimensions = (3, 3))
# These three statements are equivalent.
X.dense = [[0, 1, 0],
[0, 1, 0],
[0, 0, 1]]
X.sparse = [ 1, 4, 8 ]
X.coordinates = [[0, 1, 2], [1, 1, 2]]
# Access data in any format, SDR will automatically convert data formats,
# even if it was not the format used by the most recent assignment to the
# SDR.
X.dense == [[ 0, 1, 0 ],
[ 0, 1, 0 ],
[ 0, 0, 1 ]]
X.sparse == [ 1, 4, 8 ]
X.coordinates == [[ 0, 1, 2 ], [1, 1, 2 ]]
# Data format conversions are cached, and when an SDR value changes the
# cache is cleared.
X.sparse = [1, 2, 3] # Assign new data to the SDR, clearing the cache.
X.dense # This line will convert formats
X.dense # This line will resuse the result of the previous line```
Here are some other interesting SDR methods:
```sdr.getSparsity()
sdr.getOverlap( sdr ) # Returns number of bits which overlap
sdr.randomize( sparsity )
sdr.addNoise( percentNoise ) # Moves a fraction of the active bits to new locations.
sdr.concatenate( sdr_A, sdr_B )
sdr.intersection( sdr_A, sdr_B )
sdr.reshape( new_dimensions )
sdr.flatten()```
## Measurement Tools
The SDR has tools to measure it. The class `sdr.Metrics` combines all of these measurement tools into one convenient class. It can be setup to automatically track an SDR via callbacks.
These tools use exponential moving averages to incorporate data. These exponents are controlled by a parameter `period` which is related to the time-scale of the data, how fast it moves. While there are fewer data points than the period, a regular average is used instead of an exponential moving average.
### Example Usage of `sdr.Metrics`.
```from nupic.bindings.sdr import SDR, Metrics
A = SDR( 2000 )
M = Metrics( A, period = 1000 ) # This will automatically track SDR A.
for i in range( 345 ):
A.randomize( sparsity = .10 )
print( M )
"""
SDR( 2000 )
Sparsity Min/Mean/Std/Max 0.1 / 0.0999997 / 1.33063e-06 / 0.1
Activation Frequency Min/Mean/Std/Max 0.0492753 / 0.1 / 0.0163682 / 0.156522
Entropy 0.995378
Overlap Min/Mean/Std/Max 0.05 / 0.0986482 / 0.0210721 / 0.165
"""```
``````help( nupic.bindings.sdr.Sparsity ) | 1,091 | 4,011 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2019-30 | latest | en | 0.836008 |
https://math.stackexchange.com/questions/592896/calculating-sum-of-a-series?noredirect=1 | 1,581,922,745,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875141749.3/warc/CC-MAIN-20200217055517-20200217085517-00034.warc.gz | 482,166,814 | 28,198 | # Calculating sum of a series [duplicate]
$\sum_{n=1}^{\infty} nx^n$ for $x \neq 1$
It is quite obvious that for $q>1$ the sum will be $\infty$, but how to calculate it for $q<1$?
Also, here is a solution with a derivative, but I want to find one without the use of derivative.
$\sum_{n=1}^{\infty} nx^n = x+2x^2+3x^3+ \ldots=x(1+2x+3x^2+\ldots)=x(x'+(x^2)'+(x^3)'+\ldots)= x(x+x^2+x^3+\ldots)'=x \cdot \frac{1}{{(x-1)}^2}$
But as I said, I would like to find a solution without derivative.
$S = x + 2x^2 + 3x^3 + ...$
$xS = x^2 + 2x^3 + ...$
Subtracting
$S(1-x) = x + x^2 + x^3 + ...$
Using sum of infinite GP
$S(1-x) = \frac{x}{1-x}$
$S = \frac{x}{(1-x)^2}$
hint: Consruct the sequence of partial sums and try to work out a closed formula then take the limit as $n \to \infty$. See the proof of the geometric series.
Now that you have the answer, you can expand it in a Taylor series and see that it is right
• I don't want to use Taylor series, derivatives etc. The solution should be as basic as possible. – Josh Dec 4 '13 at 19:23 | 386 | 1,050 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2020-10 | latest | en | 0.884439 |
http://www.cactus2000.de/uk/unit/massfl2.shtml | 1,369,017,628,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368698207393/warc/CC-MAIN-20130516095647-00063-ip-10-60-113-184.ec2.internal.warc.gz | 362,816,941 | 9,276 | # Area 2
SI (metric): km2 ha a m2 cm2
Imperial, U.S. customary: mi2 a. yd2 ft2 in2
U.S. survey: township mi2 a. rood square chain square perch yd2 ft2 in2
The results have been rounded to significant digits.
This is a converter for units of area. Non-decimal units are partitioned into the correspondig subunits.
The values of the Imperial system in the United Kingdom and in the U.S. customary system are the same (e.g. international inch). In the U.S.A. the U.S. survey-system is still in use for land survey. These areas are a little larger.
Usage: Type the known values into the fields in front of the corresponding units. After a mouseclick on any free space of the window or on the "calculate" button the calculation is performed. Read the result.
In the non-metric unit systems you may choose the units for display by a click on the corresponding checkbox. Units not chosen have a darker background. The calculated area is the sum of all displayed values in a system. The smallest unit in each system is displayed with decimal partitioning, if needed. The values in the SI-units (km2, ha, a, m2, cm2) each correspond to the total calculated area.
Move the mouse over a unit to read its full name. For another calculation just change the input values or you may click the "reset" button, eventually. A previous choice of units is not reset by this.
Example: You want to convert 3 hectare into acre and square yard in the U.S. survey system. In the area for the U.S. survey units choose a. and yd2 to be displayed. Type "3" into the field in front of "ha". After a mouseclick on any free space of the window or on the "calculate" button you can read the result. 3 ha corresponds to 7 acre and 1999.6 yd2. In U. S. customary units this would be 7 acre and 1999.7 yd2.
Remarks:
- Large and small numbers are written exponentially. As example 2.3e5 = 2.3⋅105 = 230000 or 4.5e-5 = 4.5⋅10-5 = 0.000045.
- There is no warranty for the conversion. Cactus2000 is not responsible for damage of any kind caused by wrong results.
- Please send an email if you have suggestions or if you would like to see more conversions to be included. | 552 | 2,140 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-20 | longest | en | 0.859007 |
https://courses.p2pu.org/sv/groups/ed218-developing-mathematics-the-early-years/content/week-6-scratch-the-missing-manual-february-20-26/ | 1,444,134,552,000,000,000 | text/html | crawl-data/CC-MAIN-2015-40/segments/1443736678654.30/warc/CC-MAIN-20151001215758-00180-ip-10-137-6-227.ec2.internal.warc.gz | 415,057,134 | 19,307 | This course will become read-only in the near future. Tell us at community.p2pu.org if that is a problem.
# Week 6 Scratch: The missing manual ( February 20-26)
In the task about mathematics and Scratch, open exploration worked, but everybody would appreciate examples, explanations and materials for starting. I think it would be hugely useful to many people! I am likely to lead this course again in the near future. You may want to lead a similar task for teacher and parent workshops, or for students. Educators from all over the world in the ScratchEd community may want it.
1. Ask three particular questions you had when you were starting Scratch. For example, SandraG said she needed to know about show/hide. If you found good materials to help with the questions eventually, link them.
2. Pose a little Scratch task for a newbie who wants to do something about mathematics on Scratch. For example, one of the first tasks MIT people suggest for Scratch Day events is to make the sprite walk around a perfect square.
3. Make a brief (2-3 minutes) screencast explaining your way of doing it. Here is an example of a screencast explaining how to make a sprite follow your mouse: http://www.screenr.com/HWL There are several good free screencast programs out there - my favorite is Jing and Screenr is good too.
Screencasting is a popular way for educators to communicate with one another and students, and an excellent learning task for kids. It makes a lot of difference for learning communities. It's at the top of my list of useful, simple teacher tools.
• Part One:
What is a Sprite? Can I add more than one?
How do I extend the "forever" control?
What is a costume?
How do you remove a control once its been placed?
Part Two: moving sprite in a straight line and turning him 180 degrees
1. Select sprite or use the cat alread on the white screen.
2. Under "motion" (purple) select "move 10 steps" and change 10 to 150
3. Select "control" (yellow) and select "wait 1 sec" and place it under "move 150 steps"
4. Select "turn 15 degrees" from the motion tab and change 15 to 180. Place it under "wait one sec"
5. Go back to the motion tab and select "move 10 steps" again and change 10 to 100 and place it under "turn 180 degrees"
6. Under "control" select "wait 1 second" again and place it under "move 100 steps"
7. Under the control tap select the "forever" control and place it around all 5 steps
8. The select the "when (flag) clicked" and place it on top of the "forever control"
9. Click the green flag in the upper right hand corner. Done!
• “Math games make learning Math fun. When we're having fun, we're more open to learning. When we're having fun, we want to keep doing whatever we're doing” (Everybody loves games…especially kids, 2012). I found this quote on a math game website, and it states quite simply why programs like Scratch work in education.
According to one article, “Current research suggests Net Gen students are more likely to engage in online games than to interact with other students or the instructor when in face-to-face learning environments” (Annetta, Murray, Laird, Bohr, & Park, 2006). Though I had not yet heard of today’s children referred to as the N generation, it certainly makes sense. The study by Annetta et al. (2006) notes, “studies have suggested students as young as second grade opted to play a geography video game rather than go to the park”. Clearly the case can be made that today’s students can and do learn through the use of games or other visual technology such as Scratch.
With your questions, I noticed two of them dealt with number concepts; that is, adding one more (“Can I add more than one?”) and infinity (“How do I extend the "forever" control?”). It is easy to see how a program such as Scratch can help explore these concepts in a visually stimulating learning environment.
By asking students to add or delete Sprites, math is happening without explicitly stating the problem. Allowing the student to manipulate the sprites appeals to different learning styles. The kinesthetic movement of the hand in creating the Sprites can really bring a concept alive, and a discussion about “forever” movement vs. a finite number of steps can take the concept of infinity from abstract to observable.
Applications such as Scratch that are free for educators are a great tool to differentiate instruction. The fact that what the student produces will be as simple or as complicated as their skills allow, really makes for an experience that tailors itself to each student’s needs. Therefore, each student will learn but at a level that suits them. Because a lesson using Scrtach can be done individually, as a team, or as a class, it really would be effective.
Everybody loves games…especially kids. (2012). Retrieved March 2012, from Learn with Math Games: http://www.learn-with-math-games.com/
Annetta, L. A., Murray, M. R., Laird, S. G., Bohr, S. C., & Park, J. C. (2006). Serious games: Incorporating video games in the classroom. Educause Quarterly, 9(3), 1-6.
• To answer your 3rd question, "What is a costume?" here is a link that I found that explains exactly what it is. I actually just discovered this myself. It is a wikipage just for scratch and is very helpful for any questions. http://wiki.scratch.mit.edu/wiki/Costume
Basiclly a sprite doesn't have a visual appearance without a costume. It acts sort of like an avatar to represent the sprite visually in the program. Here are some example costumes: http://scratch.mit.edu/projects/balgangsak/203385
• Kommentaren togs bort.
• To answer your first question "How do you change the size of a sprite?" I found a website to explain it. http://wiki.scratch.mit.edu/wiki/Change_Size_by_()_(block)
Here is explains that you can go to the "Look" block and click the "change size by ()" block and change the size by a number. The default is 100.
As for making your sprite move, there are various ways to do this. Under the "moton" block you can have the sprite move to different coordinates. This website also shows you how to move the sprite to follow the mouse. http://wiki.scratch.mit.edu/wiki/Making_a_Sprite_Follow_the_Mouse
• Part 1:
1) How do you get your sprite to move?
2) What do some of the puzzle pieces mean?
3) What's the correct way to use the puzzle pieces?
Part 2:
How to move your Sprite in a triangle.
1) To begin moving your Sprite in a triangle the first step is to go to the control tab and click on the first puzzle piece that says "When 'green flag' clicked" and drag it to center.
2) Second step is to drag the puzzle piece that says " repeat" underneath the first puzzle piece you moved in step one.
3) Next you will go to the "Motion" tab and grag the 8th puzzle piece that says "Glide 1 secs to x: __ y:__" and drag it inside the "repeat" puzzle piece. Drag 3 of them into the "repeat" puzzle piece.
4) Then you will move your mouse inside the white space where your Sprite is and put your mouse near the corner. You're going to record the x andy axis that is in the right hand corner into the first blue puzzle piece. Do this one more time and then go to the center/top to make that triangle shape and record that x and y axis.
5) Finally all you need to do is click the green flag in the upper right corner and your Sprite should be moving in a triangle.
• Hey Keisha! Here's what I know in terms of Scratch.
To answer your first question, you first click on the sprite you want to move, so that the script is open. Then you go to the top left and click on motion, and drag the first "puzzle piece" that says "move 10 steps" into the script section. If you click on that blue puzzle piece now, the sprite will move.
Overall, the puzzle pieces are just the building blocks of Scratch. Connecting them together puts in a combination of moves for the sprite. Personally, my main way of finding out what each of the pieces meant was to try it out and find out. A lot of it was trial and error until I got it right! This page is pretty helpful in figuring out some of the basic moves and commands:
http://llk.media.mit.edu/projects/scratch/help/
I don't think there's one "right" way to use the puzzle pieces, it's all about figuring out whatever you want to do! Just have fun with it!
•
How do you clear a script?
Can you make the sprites interact with each other?
Can you upload a sprite template or image to the database?
Make the sprite walk back and forth across the grid
1. Select desired sprite and double click so the “Script” tab is open in the middle box
2. Drag sprite to either side of the grid
3. Go to “Control” in the top box, and drag “When [flag] clicked” into the box in the middle
4. Go to “Motion” in the top box and drag over “Move 10 steps”
5. Go to “Control” and drag “Repeat 10,” placing it over “Move 10 steps”
6. Change “Repeat 10” to “Repeat 36”
7. In the top of the middle box, click the small, middle box with an arrow lying horizontally, so that the sprite will only face left-right
8. Go to “Motion” and drag “Turn 15 degrees”
9. Change “15 degrees” to “180 degrees”
10. Go to “Control” and drag “Wait 1 sec”
11. Go to “Control” and drag “Forever,” placing it over everything except “When [flag] clicked”
12. Click on [flag] to see the sprite move!
•
Part One:
How do I make a new script?
How do I make a sprite make sound like a drum beat at the same time the sprite is doing an action?
How do I make the hide/show work for one sprite correspond with other sprites?
Part two:
Walking in a square
1. Delete Cat
2. Pick a new sprite
3. Shrink sprite and move to corner
4. Choose the move 10 steps button and type in 250 steps
5. Choose the turn right 15 degrees button and type in 90 degrees
6. Go to the control tab and click on the wait one second and type in 2 seconds
7. Click on the forever button and wrap it around the rest of the tabs
8. Click on the When green flag clicked button
9. Click on green flag and watch sprite walk in a square
Part 3:
• Part I-
1) How do you add different backgrounds to make it look like different scenes?
2) How do you hide/show different Sprites on those different backgrounds?
3) How do you a start a new script?
Part II-
1) Delete Scratch the cat
2) Change the backgound to yellow
3) Create 5 new sprites: 1) red circle 2) purple oval 3) green square 4) pink rectangle 5) blue triangle
From this basic assignment, I could move on to asking the students to move the shapes around and placing them at specific points on the background using the X and Y grid background.
Part III:
<iframe src="http://www.screenr.com/embed/SAIs" width="650" height="396" frameborder="0"></iframe>
OR
• 1. How can I delete an unwanted sprite? I can do this by right clicking on the sprite icon at the bottom right of the screen, and clickin "delete."
2. How can I change a sprite while to show change or motion? By using "costumes" and making a copy of the sprite, editing the appearance, then using the "looks" option and selecting "Switch costume"
3. How can I control the placement of sound effects throughout the animation? By selecting another green start flag and adding the new sound
• I'm in a little panic now as this seems like a huge task. If we didn't find any good tutorials or sources, am I correct to assume we simply don't attach anything?
• This is correct. You simply write questions - whether you know answers to them or not! If you have happened to find a good answer ALREADY (as you searched last week), please share, if not, just write the question.
The screencast part, again, should be about something quick and simple; maybe "make your sprite walk backwards" or "draw a shape."
Does it make sense, Sandy?
• It does. Drawing shapes is exactly what I had in mind to do! | 2,843 | 11,887 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2015-40 | longest | en | 0.94516 |
https://math.stackexchange.com/questions/2600213/resolvent-estimate-self-adjoint-operator | 1,566,063,324,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313436.2/warc/CC-MAIN-20190817164742-20190817190742-00473.warc.gz | 534,945,799 | 31,983 | Let $A:D(A)\longrightarrow H$ be an unbounded self-adjoint (or normal) operator on a Hilbert space $H$. Then we know that $\sigma(A) \neq \emptyset$ and $$\|(\lambda-A)^{-1}\|=\frac{1}{d(\lambda,\sigma(A))}, \quad \forall \lambda \in \rho(A),$$ where $d(\lambda,\sigma(A))=\min_{\mu \in \sigma(A)} |\lambda-\mu|>0$. Do we have a similar formula for $$\|A(\lambda-A)^{-1}\|= ?$$ I point out that $A(\lambda-A)^{-1}$ is a bounded operator since $A(\lambda-A)^{-1}x=-x+\lambda(\lambda-A)^{-1}x$ for any $x \in H$. I have the basic estimate $$\|A(\lambda-A)^{-1}\| \leq 1+\frac{|\lambda|}{d(\lambda,\sigma(A))}.$$ Is it sharp ?
The following is exact: $$\|A(\lambda I-A)^{-1}\|=\sup_{\mu\in\sigma(A)}\left|\frac{\mu}{\lambda-\mu}\right| % \\ = \sup_{\mu\in\sigma(A)}\left|-1+\frac{\lambda}{\lambda-\mu}\right|.$$ If $\sigma(A)=\mathbb{R}$ and $\lambda=i$, then the above gives $$\|A(\lambda I-A)^{-1}\| = \sup_{\mu\in\mathbb{R}}\frac{|\mu|}{\sqrt{\mu^2+1}} =1.$$ while your expression gives $$1+\frac{1}{1}=2.$$
• Thanks for you answer. Do you use the spectral theorem for self-adjoint operators to prove it ? If so, do you have a more elementary proof (similar to the one to establish the expression for $\|(\lambda-A)^{-1}\|$) ? – perturbation Jan 10 '18 at 22:20
Recall that $A(\lambda-A)^{-1}=-Id+\lambda(\lambda-A)^{-1}$. Since $A$ is normal, the bounded operator $B=-Id+\lambda(\lambda-A)^{-1}$ is normal. Therefore, we have the know fact that $$\|B\|=\sup_{\eta \in \sigma(B)} |\eta|.$$ Since $\sigma(B)=\sigma(-Id+\lambda(\lambda-A)^{-1})=f(\sigma(A))$ with $f(\mu)=-1+\frac{\lambda}{\lambda-\mu}$, we have $$\begin{array}{rl} \|A(\lambda-A)^{-1}\| &=\sup_{\eta \in \sigma(A(\lambda-A)^{-1})} |\eta| \\ &=\sup_{\eta \in f(\sigma(A))} |\eta| \\ &=\sup_{\mu \in \sigma(A)} |f(\mu)| \\ &=\sup_{\mu \in \sigma(A)} |-1+\frac{\lambda}{\lambda-\mu}| \\ &=\sup_{\mu \in \sigma(A)} |\frac{\mu}{\lambda-\mu}| \end{array}.$$ | 704 | 1,918 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2019-35 | latest | en | 0.571212 |
http://electronics-electrical-engineering.blogspot.com/2008/09/simple-ac-circuit-calculations-basic-ac.html | 1,508,699,346,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825436.78/warc/CC-MAIN-20171022184824-20171022204824-00529.warc.gz | 99,912,987 | 17,176 | ## Subscribe
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## Monday, September 1, 2008
### Simple AC circuit calculations BASIC AC THEORY
Over the course of the next few chapters, you will learn that AC circuit measurements and calculations can get very complicated due to the complex nature of alternating current in circuits with inductance and capacitance. However, with simple circuits (figure below) involving nothing more than an AC power source and resistance, the same laws and rules of DC apply simply and directly.
AC circuit calculations for resistive circuits are the same as for DC.
Series resistances still add, parallel resistances still diminish, and the Laws of Kirchhoff and Ohm still hold true. Actually, as we will discover later on, these rules and laws always hold true, it's just that we have to express the quantities of voltage, current, and opposition to current in more advanced mathematical forms. With purely resistive circuits, however, these complexities of AC are of no practical consequence, and so we can treat the numbers as though we were dealing with simple DC quantities.
Because all these mathematical relationships still hold true, we can make use of our familiar “table” method of organizing circuit values just as with DC:
One major caveat needs to be given here: all measurements of AC voltage and current must be expressed in the same terms (peak, peak-to-peak, average, or RMS). If the source voltage is given in peak AC volts, then all currents and voltages subsequently calculated are cast in terms of peak units. If the source voltage is given in AC RMS volts, then all calculated currents and voltages are cast in AC RMS units as well. This holds true for any calculation based on Ohm's Laws, Kirchhoff's Laws, etc. Unless otherwise stated, all values of voltage and current in AC circuits are generally assumed to be RMS rather than peak, average, or peak-to-peak. In some areas of electronics, peak measurements are assumed, but in most applications (especially industrial electronics) the assumption is RMS.
• REVIEW:
• All the old rules and laws of DC (Kirchhoff's Voltage and Current Laws, Ohm's Law) still hold true for AC. However, with more complex circuits, we may need to represent the AC quantities in more complex form. More on this later, I promise!
• The “table” method of organizing circuit values is still a valid analysis tool for AC circuits.
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[Page 226 ( continued )]
Because a transportation problem is formulated as a linear programming model, it can be solved with Excel and using the linear programming module of QM for Windows that we introduced in previous chapters. However, management science packages such as QM for Windows also have transportation modules that enable problems to be input in a special transportation tableau format. We will first demonstrate solution of the wheat shipping problem solved earlier in this chapter, this time by using Excel spreadsheets.
Computer Solution with Excel
We will first demonstrate how to solve a transportation problem by using Excel. A transportation problem must be solved in Excel as a linear programming model, using Solver, as demonstrated in Chapters 3 and 4. Exhibit 6.1 shows a spreadsheet setup to solve our wheat-shipping example. Notice that the objective function formula for total cost is contained in cell C10 and is shown on the formula bar at the top of the spreadsheet. It is constructed as a SUMPRODUCT of the decision variables in cells C5:E7 and a cost array in cells K5:M7 . Cells G5:G7 in column G and cells C9:E9 in row 9, labeled "Grain Shipped," contain the constraint formulas for supply and demand, respectively. For example, the constraint formula in cell G7 for the grain shipped from Des Moines to the three mills is =C7+D7+E7 , and the right-hand-side quantity value of 275 available tons is in cell F7.
[Page 227]
Exhibit 6.1.
Exhibit 6.2 shows the Solver Parameters screen for our example. Cell C10, containing the objective function formula, is minimized. The constraint formula C9:E9=C8:E8 includes all three demand constraints, and the constraint formula G5:G7=F5:F7 includes all three supply constraints. Before solving this problem, remember to click on "Options" and then, on the resulting screen, click on "Assume Linear Model" to invoke the linear programming solution approach and click on "Assume Non-negative."
Exhibit 6.2.
Exhibit 6.3 shows the optimal solution, with the amounts shipped from sources to destinations and the total cost. Figure 6.2 shows a network diagram of the optimal shipments.
[Page 228]
Computer Solution with Excel QM
Excel QM, which we introduced in Chapter 1, includes a spreadsheet macro for transportation problems. Recall from Chapter 1 that when Excel QM is activated, "QM" is shown on the menu bar at the top of the spreadsheet. Clicking on "QM" and then selecting "Transportation" will result in the Spreadsheet Initialization window appearing, as shown in Exhibit 6.4. In this window we set the number of sources (i.e., origins) and destinations to 3, select "Minimize" as the objective, and type in the title for our example. To exit this window, we click on "OK," and the spreadsheet shown in Exhibit 6.5 is displayed. The transportation problem is completely set up as shown, with all the necessary formulas already in the cells. However, initially the data values in cells B10:E13 are empty; the spreadsheet in Exhibit 6.5 includes the values that we have typed in.
[Page 229]
Exhibit 6.5.
To solve the problem, we follow the instructions in the box superimposed on the spreadsheet in Exhibit 6.5click on "Tools" at the top of the spreadsheet, then click on "Solver," and when Solver appears, click on "Solve." We have not shown the Solver window here; however, it is very similar to the one shown in Exhibit 6.2. It already includes all the decision variables and constraints required to solve the problem; thus, all that is needed is to click on "Solve." The spreadsheet with the solution is shown in Exhibit 6.6. You will notice that although the total cost is the same as in the solution we obtained with Excel in Exhibit 6.3, the decision variable values in cells B17:D19 are different. This is because this problem has multiple optimal solutions, and this is an alternate solution to the one we got previously.
QM for Windows Solution
To access the transportation module for QM for Windows, click on "Module" at the top of the screen and then click on "Transportation." Once you are in the transportation module, click on "File" and then "New" to input the problem data. QM for Windows allows for any of three initial solution methodsnorthwest corner, minimum cell cost, or VAMto be selected. These are the three starting solution procedures used in the mathematical procedure for solving transportation problems. Because these techniques are not included in the text (but are included on the accompanying CD), it makes no difference which starting procedure we use. Exhibit 6.7 shows the input data for our wheat shipping example.
[Page 230]
Exhibit 6.7.
Once the data are input, clicking on "Solve" at the top of the screen will generate the solution, as shown in Exhibits 6.8 and 6.9. QM for Windows will indicate if multiple optimal solutions exist, but it will not identify alternate solutions. This is the same optimal solution that we achieved earlier in our Excel QM solution. Exhibits 6.8 and 6.9 show the solution results in two different tables, or formats. Exhibit 6.8 shows the shipments in each cell (or decision variable) plus total cost, while Exhibit 6.9 lists the individual shipments from each source to destination and their costs.
Exhibit 6.9.
Introduction to Management Science (10th Edition)
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# The abstract paintings made by first year students in the
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01 Oct 2011, 11:37
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The abstract paintings made by first year students in the Juliet academy reveal more about their artistic growth than do the realist sketches required during their third year.
A) their artistic growth that do
B) how they grow artistically than
C) growing artistically than
D) how one grows artistically than
E) how the students grow artistically than do
Attachment:
11.JPG [ 26.58 KiB | Viewed 3996 times ]
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01 Oct 2011, 11:48
their, they are all ambiguous as the antecedent can be the paintings or the students. A and B are out.
E is the only other relevant choice.
Crick
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Updated on: 04 Oct 2011, 07:10
crick20002002 wrote:
their, they are all ambiguous as the antecedent can be the paintings or the students. A and B are out.
E is the only other relevant choice.
Crick
Hi Crick,
I thought that followings were not parallel:
1. How the students grow artistically
2. Realist sketches required during their third year
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Originally posted by akbism on 02 Oct 2011, 02:13.
Last edited by akbism on 04 Oct 2011, 07:10, edited 1 time in total.
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02 Oct 2011, 22:27
1
A,B,C,D - none of them clearly states whose growth is being talked about : the paintings or the students ? I did not check whether these choices contain any other errors.
E - Clearly connects 'the growth' to 'the students'. With no other errors in it, E is undoubtedly the best choice.
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Re: The abstract paintings made by first year students in the [#permalink]
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18 Oct 2011, 09:25
Yes. It has to be accepted that E is the only sustainable choice in terms of grammar. However, whether it is logically so, one cannot say, because the comparison is between the growth of students and the growth of sketches. How logical is it to compare students’ growth with sketches’ growth? Do sketches ever grow?
One can reconcile to the fact that students grow artistically (improve on their art skills) but cannot digest sketches growing (no one knows, whether growing physically or abstractly in quality)
However, E’s grammar is impeccable and E is the best of the lot.
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Re: The abstract paintings made by first year students in the [#permalink]
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01 Nov 2011, 22:23
akbism wrote:
The abstract paintings made by first year students in the Juliet academy reveal more about their artistic growth than do the realist sketches required during their third year.
A) their artistic growth that do
B) how they grow artistically than
C) growing artistically than
D) how one grows artistically than
E) how the students grow artistically than do
Attachment:
11.JPG
E wins.
"Do"is required at the end of the sentence to complete the comparison.
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Re: The abstract paintings made by first year students in the [#permalink]
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03 Nov 2011, 13:01
I chose B, Can anyone point out why B is not correct ? E looks good as well.
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Re: The abstract paintings made by first year students in the [#permalink]
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03 Nov 2011, 13:27
E modifies the meaning. Than do.. doesn't seem right. I thought D is close but D is also ambigous like A, B , C.
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Re: The abstract paintings made by first year students in the [#permalink]
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03 Nov 2011, 13:34
Than do .. does not seem right to me as well.
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Re: The abstract paintings made by first year students in the [#permalink]
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03 Nov 2011, 18:24
1
E. Do is required... to compare the the actions.. paintings reveal more than the sketches do (reveal).
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Re: The abstract paintings made by first year students in the [#permalink]
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22 Nov 2011, 17:55
+1 E
I'm not sure that "do" is necessary. I think that can be omitted. What do you think?
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24 Jun 2014, 10:29
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I think A is also correct, we have another their in non underline portion thus we should assume that first occurrence of their is also referring to the same group. Further paintings can not grow artistically or we can not say sketches required during paintings third year. Both ways such substitution sounds nonsensical.
X reveal more about Y than do (reveal) Z ed-mod-required during their third year.
Does above mentioned understanding makes sense ?
I think this question poorly rendered from following question, in which pronoun ambiguity clearly exist.
The mistakes children make in learning to speak tell linguists more about how they learn language than the correct forms they use.
(A) how they learn language than
(B) how one learns language than
(C) how children learn language than do
(D) learning language than
(E) their language learning than do
ThANKS
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Re: The abstract paintings made by first year students in the [#permalink]
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09 Dec 2015, 05:34
PiyushK wrote:
I think A is also correct, we have another their in non underline portion thus we should assume that first occurrence of their is also referring to the same group. Further paintings can not grow artistically or we can not say sketches required during paintings third year. Both ways such substitution sounds nonsensical.
X reveal more about Y than do (reveal) Z ed-mod-required during their third year.
Does above mentioned understanding makes sense ?
I think this question poorly rendered from following question, in which pronoun ambiguity clearly exist.
The mistakes children make in learning to speak tell linguists more about how they learn language than the correct forms they use.
(A) how they learn language than
(B) how one learns language than
(C) how children learn language than do
(D) learning language than
(E) their language learning than do
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Totally agreed. I answered A right away, realizing that other choices are simply wordy. Pronoun ambiguity is the last issue to be looked upon on GMAT and I am sure in this sentence there is no ambiguity in the first place.
At best, this is a bad copy of the official Q PiyushK has provided. Kudos!!
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Re: The abstract paintings made by first year students in the [#permalink]
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29 Aug 2016, 17:06
To me both A and E are correct. I picked A as E is wordy.
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Re: The abstract paintings made by first year students in the [#permalink]
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29 Aug 2016, 17:24
PiyushK wrote:
I think A is also correct, we have another their in non underline portion thus we should assume that first occurrence of their is also referring to the same group. Further paintings can not grow artistically or we can not say sketches required during paintings third year. Both ways such substitution sounds nonsensical.
X reveal more about Y than do (reveal) Z ed-mod-required during their third year.
Does above mentioned understanding makes sense ?
I think this question poorly rendered from following question, in which pronoun ambiguity clearly exist.
The mistakes children make in learning to speak tell linguists more about how they learn language than the correct forms they use.
(A) how they learn language than
(B) how one learns language than
(C) how children learn language than do
(D) learning language than
(E) their language learning than do
ThANKS
I did similar POE. Any other ways to rule to out A, if it is not the correct option?
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Re: The abstract paintings made by first year students in the [#permalink]
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21 Feb 2019, 02:35
D and C are both wrong. They change the meaning of the sentence. They both change it to mean ‘growing artistically’, in general.
In A, ‘their’ incorrectly refers to the paintings.
Same problem in B, with the pronoun ‘they’.
E is the clear right answer.
Re: The abstract paintings made by first year students in the [#permalink] 21 Feb 2019, 02:35
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# How to Incorporate Present and Future Values
Do you accept jobs that take several years to complete? If so, it’s important to consider the time value of money. The idea is that money isn’t worth as much in the future as it is right now. Though the face value of the money doesn’t change, its purchasing power fluctuates as years go by. In some cases, money becomes less valuable because of inflation. In rare cases, though, money could increase in value due to deflation. To take advantage of the time value of money, it’s helpful to understand present value and future value and how to calculate these essential amounts.
## Calculating Present Value of Money
Suppose your business has a job from a new customer that requires a time frame of three years to complete. In contract negotiations, you both settled on a price of \$100,000, and now you’re bouncing around different possibilities for payment terms. Your company prefers to receive payment up front, but the client wants to pay after your company completes the work.
The client is so adamant about paying when you finish the job that he threatens to walk if you don’t agree to his terms. Your company agrees, but points out that, due to inflation, \$100,000 received in three years isn’t really \$100,000. The client doesn’t understand, so you show him the present value calculation to explain.
To determine what money today could be worth in three years, you have to subtract the inflation accumulated during that time. The equation goes like this: PV = FV (1+i)^-n, where PV equals present value, FV equals future value, i equals annual inflation, and n equals number of years.
Assuming an inflation rate of 3% (or 0.03), the equation looks like this: PV = \$100,000 * 1.03^-3. The present value of \$100,000 in three years is \$91,514. If the customer waits to pay you the agreed-upon \$100,000, he essentially shorts your company \$8,486.
## Calculating Future Value of Money
Continuing with this example, you show the customer why \$100,000 in three years isn’t the same as \$100,000 today. The customer still wants to pay after you complete the project, but the customer is willing to renegotiate a higher payment amount that represents what \$100,000 today is worth in three years.
The future value formula exists to find this value, and the calculation looks a lot like the formula for present value: FV = PV (1+i)^n. Since you already know that the present value is \$100,000, the annual inflation rate is 0.03, and the number of years is three, you can plug in the numbers and calculate the future value: FV = \$100,000 * 1.03^3. The client should pay your company \$109,272 in three years to offer the equivalent of paying \$100,000 today.
## Why Calculate Present and Future Value
When making long-term business decisions, calculating present and future values gives you a better picture of your future cash flow and accounts for inflation and opportunity costs. In the above example, not accounting for the time value of money could cost your business nearly \$10,000 by incorrectly assuming that \$100,000 is \$100,000, whether you receive it today or in three years. The time value of money also helps you match expected future revenues to expenses and get a more accurate picture of expected cash flows.
## Present Value Calculation Tables
You can also calculate the present value of an annuity, which is a series of equal payments over a period of time. For example, if the client mentioned above agreed to divide \$100,000 into 36 equal payments and pay monthly for three years, you can use the present value calculation to determine how much the sum of these payments is worth today.
You can make this calculation with present value tables without having to memorize formulas or plug in numbers. Instead, you simply locate the number of periods, find the interest or inflation rate per period on the table, find the cell where they intersect, and multiply that number by the annuity amount. The only drawback to using present value tables is a lack of precision.
As inflation or interest rates usually round off to whole numbers on tables, accurately calculating present or future value when the value is a decimal requires using a formula. The value of money changes over time. Accounting for these changes is vital for making good long-term business decisions. Understanding the time value of money lets you plan for the future with confidence.
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http://primes.utm.edu/curios/page.php?short=30 | 1,387,658,674,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1387345776444/warc/CC-MAIN-20131218054936-00060-ip-10-33-133-15.ec2.internal.warc.gz | 154,044,439 | 3,040 | 30 (another Prime Pages' Curiosity)
Curios: Curios Search: Participate: The largest integer n with the property that every smaller integer relatively prime to n is itself a prime. 3030 + 1 - 30 + 1 is prime. [Luhn] n is a Giuga number if p divides (n/p-1) for every prime divisor p of n. 30 is the smallest such number. 30*2^30-1 is a Woodall prime. [Dobb] 30 is the largest two-digit number such that 30^30+30-1 is prime. [Opao] The product of first five nonzero Fibonacci numbers. Note that 30 + 1 and 30 - 1 are twin primes. [Gupta] Zhi-Wei SUN conjectured in May 2008 that exactly 30 odd integers > 1, all multiples of 3, cannot be written in the form p + n(n+1), where p is a prime congruent to 1 (mod 4) and n a natural number. It is twice more than when p is congruent to 3 (mod 4). [Capelle] Least integer the sum of whose distinct semiprime factors is prime. Semiprimes (6, 10, 15) divide 30, and 6 + 10 + 15 = 31. [Post] (There is one curio for this number that has not yet been approved by an editor.) Prime Curios! © 1999-2013 (all rights reserved) | 332 | 1,063 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-48 | latest | en | 0.891848 |
http://www.cfd-online.com/Forums/main/6938-pressure-boundary-condition-wall.html | 1,436,222,896,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375098849.37/warc/CC-MAIN-20150627031818-00039-ip-10-179-60-89.ec2.internal.warc.gz | 402,075,627 | 18,246 | # pressure boundary condition on the wall
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December 19, 2003, 01:28 pressure boundary condition on the wall #1 fluideniro Guest Posts: n/a I have a problem unsolved till now. I study the flow around a square cylinder by using SIMPLER method. I had to deal with the pressure boundary condition on the wall of the square cylinder because I define the grid node on the wall. As you know, the four corners of the cylinder are special nodes in this problem. Does anybody know how to give the pressure condition on the wall especially on the corners? please give me your advice! Thank you for any help you can give me!
December 19, 2003, 04:55 Re: pressure boundary condition on the wall #2 Praveen Guest Posts: n/a You can use normal momentum equation dp/dn = ρ n.u.∇u where n is unit normal vector. But at a corner there is no unique normal. Mathematically pde does not make sense at such corners. The correct equations to use would be integral equations which are statements of conservation but have to be applied to a control volume. In your case you will have to use some tricks which cannot be fully justified in terms of the governing equations. The simplest option is to just interpolate the pressure from the surrounding nodes. Or you could apply the normal momentum equation using an average normal taken from the two sides of the corner. Generally such tricks work.
December 19, 2003, 06:08 Re: pressure boundary condition on the wall #3 Tom Guest Posts: n/a If I remember correctly the pressure in the corner is singular and so your finite difference approximation will be badly in error here - I think it was D.W. Moore did some work on this. What he did was subtract the singularity off and then solve for the smooth bit. (It's the singularity which creates the Moffat eddies near the corner). Tom.
December 20, 2003, 07:55 Re: pressure boundary condition on the wall #4 kenn Guest Posts: n/a if you use MAC staggered grid, how can you get a velocity nodes at corners? and how can you get a pressure nodes on wall boundaries? the correct boundary conditions for pressure poisson equation is not the one believed by many, which is derived from normal component of momentum equation. it is simply "partial p partial n = 0" essnetially, application of momentum equation on wall boundaries is an illegal but sometimes helpful operation.
December 22, 2003, 09:30 Re: pressure boundary condition on the wall #5 Praveen Guest Posts: n/a I have to make some corrections to my previous post. There should be a negative sign on the right hand side. The equation I wrote is for inviscid flows. For viscous flows, we have dp/dn = n.∇.τ where τ is the shear stress tensor. For some references see Roger Peyret, Handbook of Computational Fluid Mechanics, Academic Press. Check chapter 3. In boundary layer theory we study that at high Reynolds numbers, when boundary layers are thin, the pressure gradient normal to the wall is zero. Obviously, this is not true in general.
December 22, 2003, 18:53 Re: pressure boundary condition on the wall #6 grad Guest Posts: n/a One may wish to look at applied mechanics reviews aug 2003 :"On boundary conditions for incompressible Navier-stokes equation" by Dietmer Rempfer in this regard...this paper tells the truth that the bc to pressure poisson equation cannot be specified with local relationships at the boundary... a guy with time energy money and proper training can implement Kleiser and Schumann's influence matrix method (proceedings of GAMM conference 1980) in a preprocessing step for BC... in my opinion : "partial p partial n = 0" is fair (if we trust the schemes we are using).... "That derived from from normal component of momentum equation" leads to 'ill-posed differential equation problem'
December 22, 2003, 18:56 Re: pressure boundary condition on the wall #7 grad Guest Posts: n/a thanks...the idea about normals clarified a problem with boundary condition to electric field on the corners of a liquid-solid interface...
December 23, 2003, 01:28 BC for PPE is resolved. #8 kenn Guest Posts: n/a boundary conditions for pressre poisson equations have been resolved. I would like to look at the paper on applied mechanics review, but just keep track of Journal of Computational Physics from 2005 papers. basically, if you need boundary conditions for pressure poisson, then I always can find an alternative but similar method which does not need any numerical BC at all. tentatively, I name these methods as: exact factorization, approximate factorization, and variable splitting for indefinite system. I am submitting the paper on ef, and will submit the af next month, and then variable splitting two months later; all to JCP.
December 23, 2003, 01:29 Re: pressure boundary condition on the wall #9 Praveen Guest Posts: n/a I was unable to locate applied mechanics reviews aug 2003 :"On boundary conditions for incompressible Navier-stokes equation" by Dietmer Rempfer There is no issue in Aug 2003.
December 23, 2003, 23:38 Re: pressure boundary condition on the wall #10 fluideniro Guest Posts: n/a In my case, the primitive variable method (SIMPLER scheme)and the stagged grid is used. The main nodes are set to the wall of the square cylinder. So on the wall, there are only pressure nodes. In my opinion, the boundary conditions for pressure on the wall,which is derived from normal component of momentum equation, may not be "partial p partial n = 0" .Because another item of the equation--the second normal derivative of velocity is not equal to zero. by the way, can you tell me how can I DOWNLOAD the paper you've said about the BC for PPE? Thank you very much and Merry Christmas!
December 24, 2003, 00:55 Re: pressure boundary condition on the wall #11 grad Guest Posts: n/a sorry...I have the manuscript of the paper the author submitted..... I can mail you the same(1103k)...
December 24, 2003, 00:58 Re: pressure boundary condition on the wall #12 Praveen Guest Posts: n/a If you can mail it to me then that would be great. My id is praveen[at]aero.iisc.ernet.in
December 24, 2003, 02:10 Re: pressure boundary condition on the wall #13 Apurva Shukla Guest Posts: n/a can you mail the manuscript at : apurvas@aero.iitb.ac.in Thanks Apurva
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All times are GMT -4. The time now is 18:48. | 1,666 | 6,976 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-27 | longest | en | 0.939914 |
https://illustratedfirstworldwar.com/books/by-meredith-d-gall-educational-research-an-introduction-7-th-edition | 1,638,659,948,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00305.warc.gz | 389,491,594 | 11,313 | # Educational Research: An Introduction (7th Edition) by Meredith D. Gall, Walter R. Borg, Joyce P. Gall
By Meredith D. Gall, Walter R. Borg, Joyce P. Gall
Academic study: An advent, 7th variation, is the main complete and commonly revered examine textual content for the training of graduate-level scholars and students who may have to provide a dissertation or thesis. A finished advent to the key examine equipment and kinds of information research used this present day, this article offers in-depth insurance of all aspects of analysis, from the epistemology of clinical inquiry to investigate layout, information assortment, research, and reporting of the finished examine.
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Extra resources for Educational Research: An Introduction (7th Edition)
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4), provided that the product m ˙ · Af · χ is known. This is seldom the case for fires burning in enclosures, but the rate may be estimated if the rate of air inflow (m ˙ air ) is known. 2). The only situation where it is reasonable to ignore heat loss (at least to a first approximation) is in premixed burning, when the fuel and air are intimately mixed and the reaction rates are high, independent of diffusive or mixing processes. This is the ‘adiabatic’ model, in which it is assumed that none of the heat generated within the system is lost to the environment, thus producing the maximum theoretical rise in temperature.
27 g of air for stoichiometric burning to CO2 and water. 11). More generally, we can write: 1 kg fuel + r kg air → (1 + r) kg products where r is the stoichiometric air requirement for the fuel in question. 2. The stoichiometric air requirement can be used to estimate the heat of combustion of any fuel, if this is not known. 13. R7) define the stoichiometry of the complete reaction but hide the complexity of the overall process. 16 Mechanism of the gas-phase oxidation of methane (after Bowman, 1975) H• H• H• + + + CH4 CH4 CH4 CH4 O2 • CH3 CH2 O CH2 O CH2 O H2 H2 • CHO • CHO • CHO CO • OH H• O2 + + + + + + + + + + + + + + + + + + M OH H• • • O H• O2 • • O • OH H• • • O • OH • • O • OH H• • OH M M M • = = = = = = = = = = = = = = = = = = • CH3 CH3 • CH3 • CH3 • • O CH2 O • CHO • CHO • CHO H• H• CO CO CO CO2 H2 O H2 HO•2 • + + + + + + + + + + + + + + + + + + H• H2 O H2 • OH • OH • OH • OH H2 O H2 • OH H2 O • OH H2 O H2 H• M M M + M a b c d e f g h i j k l m n o p q r This reaction scheme is by no means complete.
Assuming that there is no heat loss (the system is adiabatic), the quantity of heat released is calculated from the temperature rise of the calorimeter and its contents, whose thermal capacities are accurately known. R4). The difference between the enthalpy change ( H ) and the internal energy change ( U ) exists because at constant pressure some of the chemical energy is effectively lost as work done (P V ) in the expansion process. e. 18) U are negative. 5) where n is the number of moles of gas involved. | 965 | 3,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2021-49 | latest | en | 0.885032 |
http://library.kiwix.org/ell.stackexchange.com_en_all_2020-11/A/question/10785.html | 1,618,243,860,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038067870.12/warc/CC-MAIN-20210412144351-20210412174351-00588.warc.gz | 52,839,721 | 5,654 | ## Preterite perfects with a doubly remote intrepretation
4
2
If they had gone tomorrow they would have met her son.
I’d rather you had gone tomorrow.
-- The Cambridge Grammar of the English Language
I have familiarity with temporal anteriority of perfect tense, but not with the perfect above. The book says they are doubly remote with future time. It seems like it says the preterite expresses modal remoteness and the perfect makes further remoteness, and so they call it doubly remote construction. It amazes me that perfect tense makes time distance not backward but forward for making psychological remoteness.
Do you really make psychological distance by using preterite prefect with future time, or is it just an imaginary possibility?
2Doubly remote is misleading. Ordinary tense-expressions are remote in a single dimension, along a Newtonian timeline extending indefinitely to the past and future from the deictic moment (ST). Conditionals and modals introduce a second dimension: if marks a point where a timeline forks, with one branch leading to a 'future' (or, with perfects, a past) where the condition is true and the other toward a future where it is false. (Your expression "imaginary possibility" is apt: think of imaginary numbers, which cannot be graphed on a real-number axis but require expansion to a plane.) – StoneyB on hiatus – 2013-09-27T14:34:53.307
1I suppose CGEL is "scraping the bottom of the barrel" in order to illustrate the potential usage, but it just comes across as clunky to me. More naturally, *If they went tomorrow they would meet her son.* In general, I wouldn't advise learners to use would have [past participle] when referring to a hypothetical *future* possibility. – FumbleFingers Reinstate Monica – 2013-09-27T16:28:27.107
2@FumbleFingers But that doesn't express the same thing. This is expressing (as Listenever says) "I'd rather you had gone tomorrow." As in: "I wish they hadn't gone yesterday. If they had gone tomorrow they would have met her son." – snailplane – 2013-09-27T17:09:58.593
2@snailboat Exactly. Tomorrow modifies the lexical verb gone, not the perfect construction, which identifies the point at which the hypothetical forks the timeline. ... The great joy of playing here is that NNSes constantly call my attention to figures like this which I've never noticed but which demonstrate the marvellous ingenuity of the language in coping with situations it wasn't designed for. – StoneyB on hiatus – 2013-09-27T22:22:12.633
@StoneyB: As you say, English tenses aren't designed for this particular kind of "unreal future". I can't see that snailboat's specific temporal interpretation is any more strongly implied than, say, "I wish they hadn't gone tomorrow. If they had gone next week they would have met her son." There's a law of diminishing returns when you attempt to put an unambiguous interpretation on this kind of "mend and make do" use of the tense/mood forms we have available. – FumbleFingers Reinstate Monica – 2013-09-27T22:44:29.553
@FumbleFingers Mmm... There's got to be some sort of anteriority for a speaker to select a perfect. I can't imagine anyone coming up with a perfect if the fork was still in the future, as in your example. They'd say "I wish they wouldn't go tomorrow. If they went next week they would meet her son." – StoneyB on hiatus – 2013-09-28T12:01:46.427
@StoneyB: I think it depends how you choose to interpret the context. To my mind, "I wish they hadn't gone tomorrow" means *"I wish they hadn't decided [in the past] that they would go tomorrow [in the future]"*. I'd still prefer "I wish they weren't going tomorrow", but they both have the same "fixed future" implication to me. – FumbleFingers Reinstate Monica – 2013-09-28T19:19:27.293
@FumbleFingers I had a bet with myself that you would come up with that, and I won! Of course you're right; but what that marks is I think your unusual linguistic competence. – StoneyB on hiatus – 2013-09-28T19:22:13.707
@StoneyB: haha nice of you to say so! Mind you, I'd certainly go for *"I wish you wouldn't go tomorrow"* if I was still hoping the person I was speaking to might change their mind. I'd tend to reserve the "past tense" versions for contexts where I acknowledged that the current situation wasn't going to change (i.e. - I'd just be moaning about what was presumably someone's prior decision, rather than seriously trying to get them to change their plans). – FumbleFingers Reinstate Monica – 2013-09-28T19:32:58.217
4
You seem to be misreading slightly.
It seems like it says the preterite expresses modal remoteness and the perfect makes further remoteness, and so they call it doubly remote construction.
Yes. In both of your examples, CGEL makes the point that the doubly remote construction is necessarily counterfactual ("If they had gone tomorrow" necessarily means "they're not going tomorrow", perhaps because they already went yesterday, and "I'd rather you had gone tomorrow" necessarily means "you're not going tomorrow"); whereas with the preterite alone, as in "If they went tomorrow" and "I'd rather you went tomorrow", they wouldn't necessarily be counterfactual. (However, CGEL also gives some present-time examples where the doubly remote construction is not necessarily counterfactual.)
It amazes me that perfect tense makes time distance not backward but forward for making psychological remoteness.
No. The remoteness here is not the remoteness of future time; after all, CGEL says this construction can occur "with present and future time" (emphasis mine), and explains in a footnote that "The double remote construction is not available for past time because the perfect construction is not recursive"; that is, the reason you can use the doubly remote construction with present and future time, but not with past time, is that with past time the perfect is already being used to express anteriority, so it can't be re-used to express remoteness (since *"if they had had gone yesterday" is ungrammatical).
-3
"If they had gone tomorrow they would have met her son" does not make sense. You could say "If they had gone yesterday they would have met her son", or if you really mean tomorrow you could say "If they go tomorrow they will meet her son."
Similarly "I’d rather you had gone tomorrow" is not correct. Either "I’d rather you had gone yesterday" or "I’d rather you go tomorrow" is ok.
3Sure it does. "I wish they hadn't gone yesterday. If they had gone tomorrow they would have met her son." It's the proper way to say what it's trying to say. – snailplane – 2013-09-27T17:08:42.307
Yikes - fair enough! Yes, you could say that, though I might argue with the use of "would have met her son", which implies something definite (would have) about something indefinite (the future.) I'd prefer "could have" - but this is a slightly separate issue. I stand corrected. – Phil – 2013-09-27T17:23:39.277
Ah, please don't be discouraged! I didn't mean to prod you hard enough to cause a "Yikes"! ;-) If you'd like to contribute to ELL in the future, I'm sure it would be more than welcome. – snailplane – 2013-10-02T08:28:45.967 | 1,722 | 7,147 | {"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} | 2.671875 | 3 | CC-MAIN-2021-17 | latest | en | 0.953102 |
http://mail.ivoa.net/pipermail/dm/2005-February/003177.html | 1,725,788,535,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650976.41/warc/CC-MAIN-20240908083737-20240908113737-00773.warc.gz | 20,536,324 | 2,526 | # SED Data Model: Questions and Comments
Ed Shaya edward.j.shaya.1 at gsfc.nasa.gov
Fri Feb 18 12:43:38 PST 2005
```David Berry wrote:
>AST can determine and evaluate mappings between any two equivalent
>units strings based on FITS-WCS paper I, with a range of tolerated
>variations (cm2->cm^2, micron->um, etc). This includes the log, ln, and
>exp functions which FITS-WCS paper I specified. But I cannot currently
>see how to do a dimensional analysis of say "log(Jy)/sr". Anyone got any
>ideas?
>
>
I don't think you should try to handle log(Jy)/sr. Nor should you
handle [Jy + 7]/sr. These both break the rules of a physical formula.
During scientific manipulations you should only take log, exponents,
or trigonometric functions of unitless variables. If you have exp(kt),
k needs to have dimension 1/T. One sees the seriousness of taking
the logarithm of a unit when you look at the expansion:
ln(x) = (x-1)/x + 1/2[(x-1)/x]^2 + 1/3[(x-1)/x]^3 ...
There is just no defineable resulting dimension to this.
Now, log(Jy)/sr is particularly insidious, because you can not recover
back to Jy/sr unless you know what number of sr was used to derive this
value. If you took 10 Jy, and take the log(Jy)=1 and divided by 1 sr,
then to undo you just exponentiate. But you took 15 Jy and tak
log(Jy)=1.17, and divide by 1.5 sr you get 0.784. So log(15Jy)/1.5 sr
is not the same as log(10Jy)/1sr. So what does it mean physically, nothing.
So, you ask, what about the thousands of tables and plots with
log(whatever) in them? It is fine for display or as a compact form to
store or show anything after you take its log. But, if you are going to
do any further processing of it, you need to undo it (exponentiate).
Think about FITS integer format, it takes the values and adds a constant
and then multiplies by a constant. You can't do dimensional analysis
with these numbers because, what are the units of (Jy + 7)?
Bottom line, <units name="Jy/sr" factor="1e7"
storageAlgorighm="log(\$v)+17">
I hope that helps,
Ed
``` | 599 | 2,039 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2024-38 | latest | en | 0.920566 |
https://www.numbersaplenty.com/16080683441 | 1,670,404,283,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00527.warc.gz | 949,336,656 | 3,309 | Cookie Consent by FreePrivacyPolicy.com
Search a number
16080683441 is a prime number
BaseRepresentation
bin11101111100111101…
…11100000110110001
31112111200122100200012
432332132330012301
5230413123332231
611215400504305
71106331361004
oct167636740661
945450570605
1016080683441
116902143529
12314947b095
1316936c5704
14ac797553b
15641b31e2b
hex3be7bc1b1
16080683441 has 2 divisors, whose sum is σ = 16080683442. Its totient is φ = 16080683440.
The previous prime is 16080683417. The next prime is 16080683461. The reversal of 16080683441 is 14438608061.
It is a strong prime.
It can be written as a sum of positive squares in only one way, i.e., 15124080400 + 956603041 = 122980^2 + 30929^2 .
It is an emirp because it is prime and its reverse (14438608061) is a distict prime.
It is a cyclic number.
It is not a de Polignac number, because 16080683441 - 222 = 16076489137 is a prime.
It is a Sophie Germain prime.
It is a Curzon number.
It is not a weakly prime, because it can be changed into another prime (16080683461) by changing a digit.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 8040341720 + 8040341721.
It is an arithmetic number, because the mean of its divisors is an integer number (8040341721).
Almost surely, 216080683441 is an apocalyptic number.
It is an amenable number.
16080683441 is a deficient number, since it is larger than the sum of its proper divisors (1).
16080683441 is an equidigital number, since it uses as much as digits as its factorization.
16080683441 is an odious number, because the sum of its binary digits is odd.
The product of its (nonzero) digits is 110592, while the sum is 41.
The spelling of 16080683441 in words is "sixteen billion, eighty million, six hundred eighty-three thousand, four hundred forty-one". | 546 | 1,821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2022-49 | latest | en | 0.860677 |
https://www.lessonplanet.com/teachers/percent-of-a-number-homework-195 | 1,526,854,238,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863689.50/warc/CC-MAIN-20180520205455-20180520225455-00435.warc.gz | 783,672,532 | 20,724 | # Percent of a Number - Homework 19.5
Fifth and sixth graders review two steps to find percents of a number. They solve the first nine problems by writing the percent as a ratio. Everyone solves the second set by writing the percent as a decimal and use any method for the last four problems. Pupils finish one word problem to percents.
Concepts
Resource Details | 82 | 365 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-22 | latest | en | 0.947344 |
https://www.drillingformulas.com/basic-of-drillpipe-tensile-capacity-and-its-calculation/ | 1,708,555,550,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473558.16/warc/CC-MAIN-20240221202132-20240221232132-00733.warc.gz | 765,621,253 | 25,975 | Basic of Drillpipe Tensile Capacity and Its Calculation
This article demonstrates basic knowledge understanding of tensile capacity of the drill pipe and some calculation. First of all we need to know basic of material strength and for our case is strength of metal.
There are few simple terminologies which we would like to explain.
Stress (σ)
Stress (σ) equals to force divided by cross sectional area of the material (F/A). For our case, we will discuss about only stress in tensile because the drill pipe is almost always designed to work in a tensile condition.
Stress (σ) = F/A
Figure 1 – Stress (σ) = F/A
Strain (ε)
Strain (ε) is a change of material per an original length. From the definition, it equals to ∆L/L (see Figure 2).
Strain (ε) = ∆L/L
Figure 2 – Strain Relationship
Young’s Modulus (Modulus of Elasticity)
Young’s modulus (the tensile modulus or elastic modulus) is a ratio of stress and strain along the axis and we can write into the following equation.
Young’s modulus = Stress (σ) ÷ Strain (ε) = (F x L) ÷ (∆L x A)
Where;
F is pulling force.
L is an original length of pipe.
∆L is an amount by which the length of the pipe changes.
A is a cross sectional area of object.
The Young’s Modulus of material represents the factor of proportional in Hook’s Law therefore it will valid under the elastic zone. There are several units for Young’s Modulus as N/m2 (Newton), Maga Pascal (N/mm2) and Pound per Square Inch (psi).
Stress-Strain Curve
A stress-strain curve is a graph derived from Stress (σ) versus Strain (ε) for a sample of a material. The nature of the curve varies from material to material. The following curve shows a behavior of metal.
Figure 3 – Stress-Strain Curve
Yield Point or Yield strength, is defined as the stress at which a material begins to plastically deform. Before the yield point the material will deform elastically and it will return to its original shape when the stress is released. If the tension applied is over the yield point, the deformation will be permanent and non-reversible.
Ultimate strength is the maximum stress applied before the material is completely parted.
Young’s Modulus (modulus of elasticity) is the slope of the Stress-Strain curve within the elastic limit (see Figure 4). It means that once tensile is less than Yield Point, the Young’s Modulus is valid for the calculation.
Young’s Modulus of steel is 30 x 106 psi.
Figure 4– Young’s Modulus in The Elastic Zone
In drilling operation, we must operate within Yield point because the metal will become the original shape. For example, if you get stuck, the maximum tension applied to free the stuck drillstring must be always under yield point with a designed safety factor for the operation.
API RP7G classifies a grade of drill pipe body according to yield strength and tensile requirement (see Table 1 and Table 2). Four grades of drill pipe are “E”, “X”, “G” and “S”.
Table 1 – API Drill Pipe Grade US customary unit (Ref: API Specification 5DP Specification for Drill Pipe EFFECTIVE DATE: AUGUST 1, 2010 Page 87))
Table 2 – API Drill Pipe Grade SI unit (Ref: API Specification 5DP Specification for Drill Pipe EFFECTIVE DATE: AUGUST 1, 2010 Page 55)
Drillpipe Tensile Capacity
Tensile capacity of drill pipe is maximum tension applied before the elastic limit is reached and the formula is below;
Tensile Capacity = Cross Sectional Area x Yield Strength
In this article, we refer to US customary unit therefore the units for calculations are as follows;
Tensile Capacity is in lb.
Cross Sectional Area is in square inch.
Yield Strength is in psi.
Example
API 5”, S-135, NC50, Class New (100% Wall Thickness)
OD = 5 inch
Nominal ID = 4.276 inch
Minimum yield strength = 135,000 psi
What is the tensile capacity of this new pipe (100% wall thickness)?
Figure 5 – Diagram of new pipe (100% wall thickness)
Wall thickness = (5-4.276) ÷2 = 0.362 inch
Figure 6 – Wall Thickness of New Pipe
Cross Sectional Area of New Pipe = π x (OD2 – ID2) ÷ 4 = π x (5.02 – 4.2762) ÷ 4
Cross Sectional Area of New Pipe = 5.275 square inch
Tensile Capacity = Cross Sectional Area x Yield Strength
Tensile Capacity = 5.275 x 135,000 = 712,070 lb.
What is the tensile capacity of the premium class (80% wall thickness)?
Premium class is defined as the minimum of wall thickness is 80% of new pipe. We will discuss a little more about class of pipe later.
Wall thickness of new pipe = 0.362 inch
Wall thickness of premium class pipe = 0.8 x 0.362 = 0.290 inch therefore the OD is 4.856”.
Figure 7 – Wall Thickness of Premium Class Pipe
Cross Sectional Area of New Pipe = π x (OD2 – ID2) ÷ 4 = π x (4.8562 – 4.2762) ÷ 4
Cross Sectional Area of New Pipe = 4.154 square inch
Tensile Capacity = Cross Sectional Area x Yield Strength
Tensile Capacity = 4.154 x 135,000 = 560,764 lb.
As you see from the calculation, premium class drill pipe has approximately 79% of tensile of new pipe. This figure is very important for engineering design and drilling operation. For instant, if you get stuck with the premium class pipe, you must apply tension less than the tensile capacity of 560 Klb in order to ensure that you will not deform or damage your drillstring.
Please always remember that in our drilling operation, we must operate the drillstring within the tensile limit.
Reference – Applied Drilling Engineering Book
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15 Responses to Basic of Drillpipe Tensile Capacity and Its Calculation
sir,
i commend you on your effort to make drilling easy. please i want to read more or if there is text book for maintenance on drilling rigs and equipment
2. JAIRO C. MOLERO says:
I need to known How I calculeted for one Drill Pipe Type Class 2….Thank
Sir,
Those you send different information regarding using of drilling is very very important for the TOOL PUSHER , RIG MANAGER & RIG LIAISON MAN persons,
Thank you & Keep it up
Rig Manager KSA
4. Alvis says:
Referring to table 1, what is the min and max yield strength and min tensile strength?
Why is there a min and max for yield strength? It’s just a point in the graph.
Is min tensile strength ultimate strength?
• Alvis,
There is a min and max for yield strength because the manufactures need to make the pipe within the specific window in order to meet the API requirement.
Regards,
Shyne.
5. reza says:
Dear
Thanks.
Could you please explain the difference between “min. Yield strength, max. Yield strength and min. Tensile strength” with example?
Best Regards,
• Min Yield strength = The stress level above which a material begins undergoing to plastic deformation.
Min Tensile strength = the minimum stress at which a material breaks.
• Hussain says:
Isn’t that just the definition of Yield point ? If material begins undergoing to plastic deformation after exceeding Min Yield strength then how is there a maximum Yield Strength ? For example, DP grade E has min YS 75k psi and max YS105k psi. if it deforms plastically after exceeding 75k psi. what is max YS ?
I would appreciate an answer, because im confused.
Thank you so much for all the valuable info.
6. reza says:
Dear Mr. Shyne
Again me!!!.
As you know the min. yield strength for all drill pipes are 120 psi. Therefore, to calculate the tensile capacity for drill pipes with min. YS more than 120 psi, for example grade S135, we should use the 120psi or not?
Regards,
• All standard tool joint is 120 psi but the tensile strength to meet pipe tensile strength by increase cross-sectional area. You can see that tool joint will have various size of OD and ID even though they are all 120 psi strength.
Strength = Force x Cross Sectional Area.
7. Haytham Elkamash says:
This is very useful information.
Keep up with this useful data.
Thanks.
8. omar hassan says:
thank u very much
9. Ahmed says:
thank you man
god save u for ever to us
• mohamed jamal says:
god save you guys
10. mohamed jamal says:
thanks very much
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https://www.goconqr.com/flashcard/488038/equations-in-p4 | 1,618,719,384,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038464146.56/warc/CC-MAIN-20210418013444-20210418043444-00367.warc.gz | 883,886,365 | 8,852 | # Equations in P4
Flashcards by caitlinjardine, updated more than 1 year ago
Created by caitlinjardine over 7 years ago
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### Description
GCSE Additional Science (Physics 4) Flashcards on Equations in P4, created by caitlinjardine on 01/16/2014.
## Resource summary
Question Answer Momentum= Mass X Velocity Acceleration= Change in velocity/ Time taken Work done= Force (N) X Distance moved in direction by force Change in momentum= Resultant force X Time for which the forces act Distance= Speed X Time Kinetic Energy= 1/2 X Mass (kg) X Velocity ([m/s])2 Change in Gravitational Potential Energy= Weight X Vertical Height Difference
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# Retrieving triangles from a vertex buffer. Help needed.
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3 replies to this topic
### #1Boulougou Members - Reputation: 190
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Posted 11 October 2005 - 11:07 PM
I'm using the index buffer to get the vertices of the triangles from the vertex buffer. Then with the vertices, I create the triangles. The triangles are stored as a D3DTRIANGLE_LIST in the buffers. I suspect that there is something wrong with the way that I retrieving the vertices from the vertex buffer. Is there any other way to retrieve the position of the vertices from a vertex buffer?
// Get the vertex declaration of the mesh.
D3DVERTEXELEMENT9 vertexDeclaration[MAX_FVF_DECL_SIZE];
pMesh->GetDeclaration( vertexDeclaration );
// Find the offset of the declaration.
DWORD offset = 0;
// Scan the vertex declaration array.
int i = 0;
while( vertexDeclaration[i].Type != D3DDECLTYPE_UNUSED )
{
if( vertexDeclaration[i].Usage == D3DDECLUSAGE_POSITION )
{
offset = vertexDeclaration[i].Offset;
break;
}
i++;
}
// Lock the vertex and index buffer of the mesh.
void* pData = 0;
WORD* pIndexData = 0;
// Scan the triangles.
D3DXVECTOR3 vertexPosition[3];
Triangle3 tri;
for( DWORD i = 0, iTriangle = 0; iTriangle < pMeshContainer->MeshData.pMesh->GetNumFaces(); i+=3, iTriangle++ )
{
// Get the position.
memcpy( &vertexPosition[0], &((D3DVERTEXELEMENT9*)pData)[pIndexData[i]] + offset, sizeof(D3DXVECTOR3) );
memcpy( &vertexPosition[1], &((D3DVERTEXELEMENT9*)pData)[pIndexData[i+1]] + offset, sizeof(D3DXVECTOR3) );
memcpy( &vertexPosition[2], &((D3DVERTEXELEMENT9*)pData)[pIndexData[i+2]] + offset, sizeof(D3DXVECTOR3) );
// Build the triangle.
tri.origin() = vertexPosition[0];
tri.edge0() = vertexPosition[1] - vertexPosition[0];
tri.edge1() = vertexPosition[2] - vertexPosition[0];
// Store it in the triangle list.
memcpy( pTriangleList[iTriangle].triangle, &tri, sizeof(Triangle3) );
}
pMesh->UnlockVertexBuffer();
pMesh->UnlockIndexBuffer();
### #2matches81 Members - Reputation: 474
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Posted 12 October 2005 - 03:02 AM
What is the error/problem you get? Perhaps if you give a problem, you might get a helpful answer?
### #3neneboricua19 Members - Reputation: 634
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Posted 12 October 2005 - 05:12 AM
Scanning through your code, I think that the part where you retreive the actual positions might be a bit off.
Try changing
void* pData = 0;
to this
char* pData = 0; // mainly cuz char is an 8-bit pointer.
Your loop should look like this:
for( DWORD dwFace; dwFace < pMeshContainer->MeshData.pMesh->GetNumFaces(); dwFace++ ){ // Get the position memcpy( &vertexPosition[0], reinterpret_cast<D3DXVECTOR3*>( pData + (pIndexData[dwFace*3 + 0]*m_pMeshContainer-MeshData.pMesh->GetNumBytesPerVertex()) ), sizeof(D3DXVECTOR3) ); memcpy( &vertexPosition[1], reinterpret_cast<D3DXVECTOR3*>( pData + (pIndexData[dwFace*3 + 1]*m_pMeshContainer-MeshData.pMesh->GetNumBytesPerVertex()) ), sizeof(D3DXVECTOR3) ); memcpy( &vertexPosition[2], reinterpret_cast<D3DXVECTOR3*>( pData + (pIndexData[dwFace*3 + 2]*m_pMeshContainer-MeshData.pMesh->GetNumBytesPerVertex()) ), sizeof(D3DXVECTOR3) ); // Build the triangle. tri.origin() = vertexPosition[0]; tri.edge0() = vertexPosition[1] - vertexPosition[0]; tri.edge1() = vertexPosition[2] - vertexPosition[0]; // Store it in the triangle list. memcpy( pTriangleList[iTriangle].triangle, &tri, sizeof(Triangle3) ); }
Notice that since you don't know the exact vertex format, the indexing into the vertex buffer data is more complicated.
The "pIndexData[dwFace*3 + #]" indicates the vertices of a particular triangle. "dwFace" is which triangle in the mesh we're dealing with. You need to multiply by 3 because the index buffer stores the 3 indices of each face consecutively. The "+ #" indicates which vertex of the triangle you refer to.
This value must then be multiplied by the number of bytes per vertex because we don't know what other data each vertex has. It could have a normal vector, texture coordinates, etc... So even though the index buffer tells us logically where in the vertex buffer the actual vertices are, since our vertex buffer pointer isn't of the correct type, we cannot just add this to the vertex buffer pointer. This is why I changed the type of "pData" to char; it lets offset by bytes into the vertex buffer memory.
Once we have the number of bytes into the vertex buffer that the data is located at, we can then copy this data. Notice that I didn't use your "offset" variable. The reason is because I'm assuming that the position of the vertex is always at the start of the vertex; i.e., offset 0. To be technically correct, you should add "offset" to "pData".
Hope this helps,
neneboricua
[Edited by - Coder on October 13, 2005 9:12:28 AM]
### #4Boulougou Members - Reputation: 190
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Posted 12 October 2005 - 10:51 PM
That seems to work neneboricua. Thanks for replies!
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https://mathematica.stackexchange.com/questions/135376/how-to-rotate-the-curve-but-not-the-axes | 1,653,565,909,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00033.warc.gz | 443,432,313 | 69,510 | How to rotate the curve but not the axes?
I have a such graphic:
data = {{0, 5}, {1.9, 7.5}, {0, 12}, {-5, 15.5}, {-1.2, 33.4}};
p=Plot[Interpolation[Reverse /@ data, x, InterpolationOrder -> 2], {x,
0, 55}, Epilog -> {Red, PointSize[.01], Point[Reverse /@ data]}]
But acutually this picture is expected(except that ticks label rotated)
Note the interpolation method should be used,but not the fit method here.How to get such graphic?
Update:
I get a lot solution in following answers.But I realize if I have a option Filling -> Axis in my p.All solution cannot work anymore.
• Closely related: (18655), (104727) Jan 14, 2017 at 23:09
p = Plot[Interpolation[Reverse /@ data, x, InterpolationOrder -> 2], {x, 0, 55},
Epilog -> {Red, PointSize[.01], Point[Reverse /@ data]}, Filling -> Axis]
You can post-process p to rotate the graphics primitives:
Show[Normal[p] /. prim : _Line | _Point | _Polygon :>
GeometricTransformation[prim, RotationTransform[Pi/2]],
PlotRange -> All, AspectRatio -> GoldenRatio]
• Congratulation for 100K. :) And I realize if we have a option Filling -> Axis in p.The rotate graphic cannot include anymore?
– yode
Jan 14, 2017 at 23:35
• Thank you @yode. Please the new version to deal with Filling.
– kglr
Jan 15, 2017 at 1:52
This is pretty neat:
data = {{0, 5}, {1.9, 7.5}, {0, 12}, {-5, 15.5}, {-1.2, 33.4}};
iFun = Interpolation[Reverse[data, 2], InterpolationOrder -> 2];
ParametricPlot[Cross[{x, iFun[x]}], {x, 0, 55}, AspectRatio -> GoldenRatio,
Epilog -> {Directive[Red, PointSize[.01]],
Point[Cross /@ Reverse[data, 2]]}]
I'll leave fiddling with the ticks up to you.
data = {{0, 5}, {1.9, 7.5}, {0, 12}, {-5, 15.5}, {-1.2, 33.4}};
plot = Plot[
Interpolation[Reverse /@ data, x, InterpolationOrder -> 2], {x, 0,
55}, Epilog -> {Red, PointSize[.01], Point[Reverse /@ data]}];
Graphics[
Rotate[{#, Epilog /. {##2}}, Pi/2, {0, 0}],
AspectRatio -> GoldenRatio, Axes -> True
] & @@ plot
data = {{0, 5}, {1.9, 7.5}, {0, 12}, {-5, 15.5}, {-1.2, 33.4}};
p = Plot[Interpolation[Reverse /@ data, x, InterpolationOrder -> 2], {x, 0, 55},
Epilog -> {Red, PointSize[.01], Point[Reverse /@ data]}, Filling -> Axis]
A variation of axisFlip from How can I transpose x and y axis on a Plot? and Plot time along the y-axis?
axisRotate = # /. {x_Point | x_Line | x_GraphicsComplex :>
MapAt[(#.{{0, 1}, {-1, 0}}) &, x, 1]} &;
Show[axisRotate@p, AspectRatio -> GoldenRatio/1, PlotRange -> All]
Tick labels still show negative values however. If we are going to fiddle with tick labels another approach opens up: just counter-rotate the labels:
rR = {#, Rotate[#, -90 °]} &;
Show[p, Ticks -> {rR /@ Range[10, 50, 10], rR /@ Range[20, 60, 20]}] //
Rotate[#, 90 °] &
This is not as nice for further processing and use so I favor the first method.
• An alternative is to use GeometricTransformation, as in: p /. Graphics[g_, r___] :> Graphics[GeometricTransformation[g, RotationTransform[Pi/2]], PlotRange -> All, AspectRatio -> GoldenRatio, r] Jan 15, 2017 at 0:38
• @CarlWoll That certainly could be useful for more complicated transformations, but is there any advantage in this case over Dot? Jan 15, 2017 at 0:39
• It is useful because you don't have to have consider every possible Graphics primitive, e.g., Arrow, Polygon, etc. The OP example only has Point and Line, so using explicit rules for these objects works just as well. Jan 15, 2017 at 0:53
• @CarlWoll I overlooked that part of your code entirely. Thanks! Jan 15, 2017 at 0:55
• @CarlWoll Your method misses the Epilog graphics which is undesirable for the example at hand. What solution do you propose for that? One could target Epilog expressly but I wonder if there is a more general way in the spirit of that replacement rule. Jan 15, 2017 at 16:00 | 1,200 | 3,764 | {"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} | 3.140625 | 3 | CC-MAIN-2022-21 | longest | en | 0.693228 |
http://www.extremeoptimization.com/QuickStart/VisualBasic/StructuredLinearEquations.aspx | 1,653,425,270,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662577259.70/warc/CC-MAIN-20220524203438-20220524233438-00231.warc.gz | 80,262,893 | 7,342 | Data Analysis Mathematics Linear Algebra Statistics
New Version 8.1!
Supports .NET 6.0. Try it for free with our fully functional 60-day trial version.
QuickStart Samples
# Structured Linear Equations QuickStart Sample (Visual Basic)
Illustrates how to solve systems of simultaneous linear equations that have special structure in Visual Basic.
```Option Infer On
' The structured matrix classes reside in the
' Extreme.Mathematics.LinearAlgebra namespace.
Imports Extreme.Mathematics
Imports Extreme.Mathematics.LinearAlgebra
Namespace Extreme.Numerics.QuickStart.VB
' Illustrates solving symmetrical and triangular systems
' of simultaneous linear equations using classes
' in the Extreme.Mathematics.LinearAlgebra namespace of the Extreme
' Optimization Numerical Libraries for .NET.
Module StructuredLinearEquations
Sub Main()
' simultaneous linear equations, see the
' LinearEquations QuickStart Sample.
'
' The methods and classes available for solving
' structured systems of equations are similar
' to those for general equations.
'
' Triangular systems and matrices
'
Console.WriteLine("Triangular matrices:")
' For the basics of working with triangular
' matrices, see the TriangularMatrices QuickStart
' Sample.
'
' that elements are stored in column-major order
' by default.
Dim t = Matrix.CreateUpperTriangular(
4, 4, New Double() _
{1, 0, 0, 0,
1, 2, 0, 0,
1, 4, 1, 0,
1, 3, 1, 2}, MatrixElementOrder.ColumnMajor)
Dim b1 = Vector.Create(New Double() {1, 3, 6, 3})
Dim b2 = Matrix.Create(4, 2, New Double() _
{1, 3, 6, 3, _
2, 3, 5, 8}, MatrixElementOrder.ColumnMajor)
Console.WriteLine("t = {0:F4}", t)
'
' The Solve method
'
' The following solves m x = b1. The second
' parameter specifies whether to overwrite the
' right-hand side with the result.
Dim x1 = t.Solve(b1, False)
Console.WriteLine("x1 = {0:F4}", x1)
' If the overwrite parameter is omitted, the
' right-hand-side is overwritten with the solution:
t.Solve(b1)
Console.WriteLine("b1 = {0:F4}", b1)
' You can solve for multiple right hand side
' vectors by passing them in a DenseMatrix:
Dim x2 = t.Solve(b2, False)
Console.WriteLine("x2 = {0:F4}", x2)
'
' Related Methods
'
' You can verify whether a matrix is singular
' using the IsSingular method:
Console.WriteLine("IsSingular(t) = {0:F4}", _
t.IsSingular())
' The inverse matrix is returned by the GetInverse
' method:
Console.WriteLine("GetInverse(t) = {0:F4}", t.GetInverse())
' The determinant is also available:
Console.WriteLine("Det(t) = {0:F4}", t.GetDeterminant())
' The condition number is an estimate for the
' loss of precision in solving the equations
Console.WriteLine("Cond(t) = {0:F4}", t.EstimateConditionNumber())
Console.WriteLine()
'
' Symmetric systems and matrices
'
Console.WriteLine("Symmetric matrices:")
' For the basics of working with symmetric
' matrices, see the SymmetricMatrices QuickStart
' Sample.
'
' that elements are stored in column-major order
' by default.
Dim s = Matrix.CreateSymmetric(4, New Double() _
{1, 0, 0, 0,
1, 2, 0, 0,
1, 1, 2, 0,
1, 0, 1, 4}, MatrixTriangle.Upper, MatrixElementOrder.ColumnMajor)
b1 = Vector.Create(New Double() {1, 3, 6, 3})
Console.WriteLine("s = {0:F4}", s)
'
' The Solve method
'
' The following solves m x = b1. The second
' parameter specifies whether to overwrite the
' right-hand side with the result.
x1 = s.Solve(b1, False)
Console.WriteLine("x1 = {0:F4}", x1)
' If the overwrite parameter is omitted, the
' right-hand-side is overwritten with the solution:
s.Solve(b1)
Console.WriteLine("b1 = {0:F4}", b1)
' You can solve for multiple right hand side
' vectors by passing them in a DenseMatrix:
x2 = s.Solve(b2, False)
Console.WriteLine("x2 = {0:F4}", x2)
'
' Related Methods
'
' You can verify whether a matrix is singular
' using the IsSingular method:
Console.WriteLine("IsSingular(s) = {0}", _
s.IsSingular())
' The inverse matrix is returned by the GetInverse
' method:
Console.WriteLine("GetInverse(s) = {0:F4}", s.GetInverse())
' The determinant is also available:
Console.WriteLine("Det(s) = {0:F4}", s.GetDeterminant())
' The condition number is an estimate for the
' loss of precision in solving the equations
Console.WriteLine("Cond(s) = {0:F4}", s.EstimateConditionNumber())
Console.WriteLine()
'
' The CholeskyDecomposition class
'
' If the symmetric matrix is positive definite,
' you can use the CholeskyDecomposition class
' to optimize performance if multiple operations
' need to be performed. This class does the
' bulk of the calculations only once. This
' decomposes the matrix into G x transpose(G)
' where G is a lower triangular matrix.
'
' If the matrix is indefinite, you need to use
' the LUDecomposition class instead. See the
' LinearEquations QuickStart Sample for details.
Console.WriteLine("Using Cholesky Decomposition:")
' The constructor takes an optional second argument
' indicating whether to overwrite the original
' matrix with its decomposition:
Dim cf = s.GetCholeskyDecomposition(False)
' The Factorize method performs the actual
' factorization. It is called automatically
' if needed.
cf.Decompose()
' All methods mentioned earlier are still available:
x2 = cf.Solve(b2, False)
Console.WriteLine("x2 = {0:F4}", x2)
Console.WriteLine("IsSingular(m) = {0}", _
cf.IsSingular())
Console.WriteLine("Inverse(m) = {0:F4}", cf.GetInverse())
Console.WriteLine("Det(m) = {0:F4}", cf.GetDeterminant())
Console.WriteLine("Cond(m) = {0:F4}", cf.EstimateConditionNumber())
' triangular matrix, G, of the composition.
Console.WriteLine(" G = {0:F4}", cf.LowerTriangularFactor)
' Note that if the matrix is indefinite,
' the factorization will fail and throw a
' MatrixNotPositiveDefiniteException.
s(0, 0) = -99
cf = s.GetCholeskyDecomposition()
Try
cf.Decompose()
Catch e As MatrixNotPositiveDefiniteException
Console.WriteLine(e.Message)
End Try
' It is better to use the TryDecompose method,
' which returns true if the decomposition succeeded:
If cf.TryDecompose() Then
Console.WriteLine("The decomposition succeeded!")
Else
Console.WriteLine("The decomposition failed!")
End If
Console.Write("Press Enter key to exit...") | 1,598 | 6,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-21 | latest | en | 0.601004 |
http://www.math.toronto.edu/preparing-for-calculus/7_geometry/we_6_parabolas.html | 1,513,449,622,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948588420.68/warc/CC-MAIN-20171216181940-20171216203940-00785.warc.gz | 406,318,056 | 2,300 | # Geometry of the Plane
## Parabolas
The formula for a parabola with vertex $(h,k)$ is $$y-k = a(x-h)^2.$$
### Example.
Find the equation of a parabola that passes through the points $(0,3)$, $(1,6)$, and $(3,6)$.
We plug in these values in the formula as the $x$ and $y$ values: \begin{align} 3-k & = a(0-h)^2 \\ 6-k & = a(1-h)^2 \\ 6-k & = a(3-h)^2 \end{align} We now solve this (nonlinear) system of 3 equations to 3 unknowns.
Setting the two last equations equal to each other: $$(1-h)^2 = (3-h)^2,$$ so $1-h = \pm(3-h)$, which implies that $h=2$. (Details) So $$1-h = \pm (3-h)$$ which implies that either $$1-h = 3-h \; , \quad \text{thus } \; 1=3$$ (which is FALSE), or $$1-h = -(3-h) \; , \quad \text{so } \; h=2.$$ We deduce that $h=2$.
Let us rewrite all 3 equations: \begin{align} 3-k & = 4a \\ 6-k & = a \\ 6-k & = a \end{align} Since the last 2 equations are equal, we can disregard one of them.
From the first two equations, we solve for $k$: \begin{align} k & = 3-4a \\ k & = 6-a \end{align} so $3-4a=6-a$, which implies that $a=-1$, thus $k=6-a = 7$.
The equation of the parabola that passes through these 3 points is: $$y-7=-(x-2)^2.$$ It has vertex at $(2,7)$ and is turned downwards ($a<0$). | 451 | 1,217 | {"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": 3, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2017-51 | latest | en | 0.832329 |
http://stackoverflow.com/questions/7759701/how-to-compute-the-sum-of-unpaired-numbers-up-to-n | 1,411,021,663,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1410657125654.84/warc/CC-MAIN-20140914011205-00229-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | 268,579,256 | 16,929 | # How to compute the sum of unpaired numbers up to N?
I have some code on prolog, but this code does not work.
``````sum(N,_):-N<0,fail.
sum(N,S):-N=0,S=0,!.
sum(N,S):-N1=N-1,sum(N1,S1),S=S1+N.
?-sum(4,X),write(X).
``````
Correct recursive function on PHP
``````function sum(\$n)
{
if(\$n < 0) return;
if(\$n%2 == 0) return sum(\$n-1);
else return (\$n+sum(\$n-2));
}
``````
I need to convert this function to prolog.
For example, sum(N, Result).
?- sum(6,Result),write(Result).
expected 9
-
I write recursive function in procedural language. How to convert in prolog? – BILL Oct 13 '11 at 21:41
function sum(\$n){ if(\$n < 0) return; if(\$n%2 == 0) return sum(\$n-1); else return (\$n+sum(\$n-2)); } – BILL Oct 13 '11 at 21:50
I think php returns 0 if N < 1. So you cannot just fail – Joe Lehmann Oct 14 '11 at 4:15
Here a rather direct translation of the PHP code, that incidentally highlights the (IMO) weaker point of Prolog code when applied to numerical problems: the need to explicitly represent expressions intermediate results. Conventionally, we use the last argument to represent the 'return value'.
``````sum(N, S) :-
( N < 0
-> S = 0
; ( Q is N mod 2,
Q == 0
-> M is N - 1,
sum(M, S)
; M is N - 2,
sum(M, T),
S is N + T
)
).
``````
Test:
``````?- sum(6,X).
X = 9.
``````
-
You might try something like this...
``````sum(N,X) :-
sum(N,0,X)
.
sum( 0 , X , X ).
sum( N , T , X ) :-
N > 0 ,
T1 is T+N ,
N1 is N-1 ,
sum( N1 , T1 , X )
.
sum( N , T , X ) :-
N < 0 ,
T1 is T+N ,
N1 is N+1 ,
sum( N1 , T1 , X )
.
``````
All you want to do is sum the odd numbers between 0 and N inclusive? I think this should do the trick:
``````sum(0,0).
sum(N,X) :-
N > 0 ,
( N mod 2 is 0 , N1 is N-1 ; N1 is N ) ,
sum(N1,0,X)
.
sum(N,X,X) :- N < 0 .
sum(N,T,X) :-
N1 is N - 2
T1 is T+N ,
sum(N1,T1,X)
.
``````
-
wrong result. Please see my recursive function. – BILL Oct 13 '11 at 21:52
How about you write a readable problem statement in English, with sample inputs and their expected output? – Nicholas Carey Oct 13 '11 at 22:41
This one works
``````sum(0,0).
sum(-1,0).
sum(N,R) :- N > 0, 0 is N mod 2,!, N1 is N - 1, sum(N1,R).
sum(N,R) :- N > 0, N2 is N - 2, sum(N2,R1), R is N + R1.
``````
However I would write it this way:
``````sum(N,R) :- sum(N,0,R).
sum(0,A,A) :- !.
sum(N,A,R) :- N1 is N-1, (1 is N mod 2 -> A1 is A + N; A1 = A), sum(N1,A1,R).
``````
It is equivalent to something like:
``````int a = 0;
for(int i=N;i>0;i--) { if (i % 2==1) a += i; }
``````
- | 940 | 2,502 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2014-41 | latest | en | 0.808046 |
http://msdn.microsoft.com/en-us/library/office/aa164573(v=office.10).aspx | 1,410,927,760,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1410657120974.20/warc/CC-MAIN-20140914011200-00020-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | 185,998,240 | 8,705 | The topic you requested is included in another documentation set. For convenience, it's displayed below. Choose Switch to see the topic in its original location.
# The Floating-Point Data Types
This content is no longer actively maintained. It is provided as is, for anyone who may still be using these technologies, with no warranties or claims of accuracy with regard to the most recent product version or service release.
Microsoft® Visual Basic® for Applications (VBA) provides two floating-point data types, Single and Double. The Single data type requires 4 bytes of memory and can store negative values between -3.402823 x 1038 and -1.401298 x 10-45 and positive values between 1.401298 x 10-45 and 3.402823 x 1038. The Double data type requires 8 bytes of memory and can store negative values between -1.79769313486232 x 10308 and -4.94065645841247 x 10-324 and positive values between 4.94065645841247 x 10-324 and 1.79769313486232 x 10308.
The Single and Double data types are very precise — that is, they make it possible for you to specify extremely small or large numbers. However, these data types are not very accurate because they use floating-point mathematics. Floating-point mathematics has an inherent limitation in that it uses binary digits to represent decimals. Not all the numbers within the range available to the Single or Double data type can be represented exactly in binary form, so they are rounded. Also, some numbers cannot be represented exactly with any finite number of digits — pi, for example, or the decimal resulting from 1/3.
Because of these limitations to floating-point mathematics, you might encounter rounding errors when you perform operations on floating-point numbers. Compared to the size of the value you are working with, the rounding error will be very small. If you do not require absolute accuracy and can afford relatively small rounding errors, the floating-point data types are ideal for representing very small or very large values. On the other hand, if your values must be accurate — for example, if you are working with money values — you should consider one of the scaled integer data types. | 464 | 2,159 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2014-41 | latest | en | 0.89618 |
http://blog.etestseries.in/canopy-growth-blpoxjy/numpy-array-operations-e850ef | 1,642,903,898,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303956.14/warc/CC-MAIN-20220123015212-20220123045212-00573.warc.gz | 7,048,469 | 31,852 | # numpy array operations
NumPy - Advanced Indexing. We will do all of them one by one. numpy documentation: Matrix operations on arrays of vectors. Slicing in python means taking elements from one given index to another given index. The homogeneity helps to perform smoother mathematical operations. For elements with absolute values larger than … Conditional operations on numpy arrays. For advanced use: master the indexing with arrays of integers, as well as NumPy arrays can execute vectorized operations, processing a complete array, in contrast to Python lists, where you usually have to loop through the list and execute the operation on each element. Below are few examples, import numpy as np arr = np. code. 2. If we don't pass start its considered 0. However, operations on arrays of non-similar shapes is still possible in NumPy, because of the broadcasting capability. random walker after t left or right jumps? Know more NumPy functions to handle various array Basic Operations in NumPy. simulate many “walkers” to find this law, and we are going to do so Let us consider a simple 1D random walk process: at each time step a The key to making it fast is to use vectorized operations, generally implemented through NumPy's universal functions (ufuncs). close, link This returns an array for a given interval between your start and end values. Mathematical operations can be completed using NumPy arrays. with more dimensions than input data. That’s because NumPy implicitly uses broadcasting, meaning it internally converts our scalar values to arrays. 2. We can initialize NumPy arrays from nested Python lists and access it elements. Linear algebra with NumPy arrays (numpy.linalg) Linear algebra is fundamental in the field of data science. prod (a[, axis, dtype, out, keepdims]): Return the product of array elements over a given axis. While NumPy provides the computational foundation for these operations, you will likely want to use pandas as your basis for most kinds of data analysis (especially for structured or tabular data) as it provides a rich, high-level interface making most common data tasks very concise and simple. Ask Question Asked 3 years, 10 months ago. Text on GitHub with a CC-BY-NC-ND license >>> import numpy as np #load the Library NumPy array is a powerful N-dimensional array object which is in the form of rows and columns. On the other hand, np.mgrid directly This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook.The ebook and printed book are available for purchase at Packt Publishing. In case of +=, -=, *= operators, the exsisting array is modified. NumPy - Array Creation Routines. This is one of the primary advantages of NumPy, and makes it quite easy to do computations. Numpy provides a powerful mechanism, called Broadcasting, which allows to perform arithmetic operations on arrays of different shapes. generate link and share the link here. NumPy’s N-dimenisonal array structure offers fantastic tools to numerical computing with Python. This example shows how to add, subtract, and multiply values on 1D, 2D, and multi-dimensional array. Return a new array of given shape and type, without initializing entries. However, various operations are performed over vectors. For those who are unaware of what numpy arrays are, let’s begin with its definition. In order to perform these NumPy operations, the next question which will come in your mind is: Linear algebra operations: scipy.linalg. a = np. Amarillo, Santa Fe, Albuquerque, Flagstaff and Los Angeles. (array.max(), array.mean()). Python Numpy allows you to perform arithmetic operations on an array using Arithmetic Operators. Array From Numerical Ranges. The NumPy library is a popular Python library used for scientific computing applications, and is an acronym for \"Numerical Python\". Vectors are created using the import array class. NumPy is one of most fundamental Python packages for doing any scientific computing in Python. NumPy Arithmetic Operations. If the dimensions of two arrays are dissimilar, element-to-element operations are not possible. NumPy - Broadcasting. Viewed 19k times 9. Created using, array([ 0. , 0.84147098, 0.90929743, 0.14112001, -0.7568025 ]), array([ -inf, 0. , 0.69314718, 1.09861229, 1.38629436]), array([ 1. , 2.71828183, 7.3890561 , 20.08553692, 54.59815003]), operands could not be broadcast together with shapes (4) (2), [, ], Text(...'$\\sqrt{\\langle (\\delta x)^2 \\rangle}$'), # we assign an array of dimension 0 to an array of dimension 1. array([[ 0, 198, 303, 736, 871, 1175, 1475, 1544, 1913, 2448]. Similar to array with array operations, a NumPy array can be operated with any scalar numbers. In this tutorial, we will see how to perform basic arithmetic operations, apply trigonometric and logarithmic functions on the array elements of a NumPy array. asarray_chkfinite (a[, dtype, order]) Convert the input to an array, checking for NaNs or Infs. Scalar Addition. with masks. NumPy - Iterating … If you would like to know the different techniques to create an array, refer to my previous guide: … Strengthen your foundations with the Python Programming Foundation Course and learn the basics. Slicing arrays. That means NumPy array can be any dimension. Route 66: Chicago, Springfield, Saint-Louis, Tulsa, Oklahoma City, ]. Till now, you have seen some basics numpy array operations. Python NumPy Array: Numpy array is a powerful N-dimensional array object which is in the form of rows and columns. The NumPy module provides a ndarray object using which we can use to perform operations on an array of any dimension. We use +=, -=, *= operators, to manipulate the existing array. NumPy is a Python Library/ module which is used for scientific calculations in Python programming.In this tutorial, you will learn how to perform many operations on NumPy arrays such as adding, removing, sorting, and manipulating elements in many ways. NumPy arrays facilitate advanced mathematical and other types of operations on large numbers of data. want to) benefit from broadcasting: Broadcasting: discussion of broadcasting in Return an array laid out in Fortran order in memory. Remark : the numpy.ogrid() function allows to directly create vectors x You can use np.may_share_memory() to check if two arrays share the same memory block. We can also define the step, like this: [start:end:step]. This can be achieved by using the sum () or mean () NumPy function and specifying the “ axis ” on which to perform the operation. In numpy array, you can perform various operations like – finding dimension of an array, finding byte size of each element in array, finding the data type of elements and many more. Please use ide.geeksforgeeks.org, NumPy makes it simple to perform mathematical operations on arrays. The 2-D array in NumPy is called as Matrix. The function numpy.remainder() also produces the same result. Matrix Operations: Creation of Matrix. NumPy - Arithmetic Operations. the origin of points on a 5x5 grid, we can do. The ndarray stands for N-dimensional array where N is any number. A boolean array is a numpy array with boolean (True/False) values. In this post, I will show how t o fast compute local histograms using NumPy array operations. In that sense, it’s very similar to MATLAB. You will be required to import NumPy as ‘np’ and late… 1. ndim – It returns the dimensions of the array. … well as to do some more exercices. The remainder of this chapter is not necessary to follow the rest of [3. , 3.16227766, 3.60555128, 4.24264069, 5. reshape (np. Adjust the shape of the array using reshape or flatten it While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book. The first argument is the start value of your array, the second is the end value (where it stops creating values), and the third one is the interval. not guaranteed to be compiled using efficient routines, and thus we Operations on single array: We can use overloaded arithmetic operators to do element-wise operation on array to create a new array. Get to know them well! This means that we have a smaller array and a larger array, and we transform or apply the smaller array multiple times to perform some operation on the larger array. Thus the original array is not copied in memory. In principle, this could be changed without too much work. But, in real-world applications, you will rarely come across arrays that have the same shape. Plethora of built-in arithmetic functions are provided in NumPy. Changing number of dimensions ¶. There are several ways to create a NumPy array. Python NumPy Array: Numpy array is a powerful N-dimensional array object which is in the form of rows and columns. Assignment 2 - Numpy Array Operations. or copy. Python NumPy Operations Tutorial – Minimum, Maximum And Sum Array with Scalar operations. [1. , 1.41421356, 2.23606798, 3.16227766, 4.12310563]. Let’s construct an array of distances (in miles) between cities of Basic operations ¶. [ 736, 538, 433, 0, 135, 439, 739, 808, 1177, 1712]. 16. Example: numpy_array_from_list + 10. NumPy is, just like SciPy, Scikit-Learn, Pandas, etc. In order to perform these NumPy operations, the next question which will come in your mind is: Changing kind of array ¶. flipud (m) Flip array in the up/down direction. NumPy Basic Array Operations There is a vast range of built-in operations that we can perform on these arrays. To give one a brief intro, NumPy is a very powerful library that can be used to perform all kinds of operations, from finding the mean of an array to fast Fourier transform and signal analysis. Know the shape of the array with array.shape, then use slicing Worked Example: diffusion using a random walk algorithm. By using our site, you np.ones generates a matrix full of 1s. This means that we have a smaller array and a larger array, and we transform or apply the smaller array multiple times to perform some operation on the larger array. This guide will provide you with a set of tools that you can use to manipulate the arrays. brightness_4 [ 303, 105, 0, 433, 568, 872, 1172, 1241, 1610, 2145]. Assignment 2 - Numpy Array Operations. recommend the use of scipy.linalg, as detailed in section Obtain a subset of the elements of an array and/or modify their values In my previous post, I talk about Reduction Operations in Numpy Arrays. Assignment 2 - Numpy Array Operations. No need to retain everything, but The transpose returns a view of the original array: The sub-module numpy.linalg implements basic linear algebra, such as It is the library for logical computing, which contains a powerful n-dimensional array object, gives tools to integrate C, C++ and so on. Typically, such operations are executed more efficiently and with less code than is possible using Python’s built-in sequences. Nevertheless, It’s also possible to do operations on arrays of different sizes if NumPy can transform these arrays so that they all have Python Vector operations using NumPy library: Single dimensional arrays are created in python by importing an array module. provides matrices full of indices for cases where we can’t (or don’t We are going to This function returns the reciprocal of argument, element-wise. … and many more (best to learn as you go). For elements with absolute values larger than 1, the result is always 0 and for integer 0, overflow warning is issued. NumPy: creating and manipulating numerical data, Try simple arithmetic elementwise operations: add even elements Such array can be obtained by applying a logical operator to another numpy array: import numpy as np a = np. The following line of code is used to create the Matrix. Det. ndarray.reshape may return a view (cf help(np.reshape))), We can initialize NumPy arrays from nested Python lists and access it elements. ma.indices (dimensions[, dtype]) Return an array representing the indices of a grid. We are interested in finding the typical distance from the origin of a [1475, 1277, 1172, 739, 604, 300, 0, 69, 438, 973]. For example, we may need to sum values or calculate a mean for a matrix of data by row or by column. : Broadcasting seems a bit magical, but it is actually quite natural to have the reflex to search in the documentation (online docs, Arithmetic operations may also be executed on arrays of different shapes by means of Numpy broadcasting. You can also create a numpy array from a Tuple. Active 7 months ago. Creating arrays. We can perform arithmetic operations on the array to do an element-wise operation to create a new array. time in the other: We randomly choose all the steps 1 or -1 of the walk: We build the walks by summing steps along the time: We get the mean in the axis of the stories: We find a well-known result in physics: the RMS distance grows as the NumPy provides familiar mathematical functions such as sin, cos, and exp. The syntax is the array name followed by the operation (+.-,*,/) followed by the operand. learn the ecosystem, you can directly skip to the next chapter: The array Method Within NumPy, these functions operate elementwise on an array, producing an array as output. [ 198, 0, 105, 538, 673, 977, 1277, 1346, 1715, 2250]. NumPy is founded around its multidimensional array object, numpy.ndarray. A Numpy array on a structural level is made up of a combination of: The Data pointer indicates the memory address of the first byte in the array. We can create a NumPy ndarray object by using the array () function. … NumPy - Indexing & Slicing. array([[0. , 1. , 2. , 3. , 4. This section motivates the need for NumPy's ufuncs, which can be used to make repeated calculations on array elements much more efficient. reshape (a, newshape [, order]) Gives a new shape to an array without changing its data. Array manipulation routines ¶. In this section, we will discuss a few of them. A slicing operation creates a view on the original array, which is just a way of accessing array data. This can be accomplished by simply performing an operation on the array, which will then be applied to each element. Visually, we can represent a simple NumPy array sort of like this: Let’s break this down. ma.ediff1d (arr[, to_end, to_begin]) Compute the differences between consecutive elements of an array. with odd elements, Time them against their pure python counterparts using. Getting started with Python for science, 1.4. NumPy Array Operations By Row and Column We often need to perform operations on NumPy arrays by column or by row. broadcasting. Below are few examples, import numpy as np arr = np. If the arrays have different shapes, then the element-by-element operation is not possible. numpy.dot can be used to multiply a list of vectors by a matrix but the orientation of the vectors must be vertical so that a list of eight two component vectors appears like two eight components vectors: Create Sets in NumPy We can use NumPy's unique () method to find unique elements from any array. This section will present several examples of using NumPy array manipulation to access data and subarrays, and to split, reshape, and join the arrays. A NumPy array is a collection of elements that have the same data type. NumPy utilizes an optimized C API to make the array operations particularly quick. By storing the data in this way NumPy can handle arithmetic and mathematical operations at high speed. 1.4.1.6. It is likewise helpful in linear based math, arbitrary number capacity and so on. The smaller array is broadcast to the size of the larger array … Mathematical Operations on an Array. Benefit of NumPy arrays over Python arrays, Python | Numpy numpy.ndarray.__truediv__(), Python | Numpy numpy.ndarray.__floordiv__(), Python | Numpy numpy.ndarray.__invert__(), Python | Numpy numpy.ndarray.__divmod__(), Python | Numpy numpy.ndarray.__rshift__(), Python | Numpy numpy.ndarray.__lshift__(), Data Structures and Algorithms – Self Paced Course, Ad-Free Experience – GeeksforGeeks Premium, We use cookies to ensure you have the best browsing experience on our website. Assignment 2 - Numpy Array Operations. Aside from the methods that we’ve seen above, there are a few more functions for generating NumPy arrays. arange (0, 11) print (arr) print (arr ** 2) print (arr + 1) print (arr -2) print (arr * 100) print (arr / 100) Output Use the resize function, 1. Matplotlib: plotting. This assignment is part of the course "Data Analysis with Python: Zero to Pandas".The objective of this assignment is to develop a solid understanding of Numpy array operations. copyto (dst, src [, casting, where]) Copies values from one array to another, broadcasting as necessary. If we don't pass end its considered length of array in that dimension © Copyright 2012,2013,2015,2016,2017,2018,2019,2020. use it when we want to solve a problem whose output data is an array Similar to array with array operations, a NumPy array can be operated with any scalar numbers. A lot of grid-based or network-based problems can also use A Numpy array on a structural level is made up of a combination of: edit Example. This article is supposed to serve a similar purpose for NumPy. Experience. In Python, Lists are more popular which can replace the working of an Array or even multiple Arrays, as Python does not have built-in support for Arrays. A set in mathematics is a collection of unique elements. This function returns the remainder of division of the corresponding elements in the input array. We can initialize NumPy arrays from nested Python lists and access it elements. Arrays in NumPy are synonymous with lists in Python with a homogenous nature. We can initialize NumPy arrays from nested Python lists and access it elements. array ([1, 2, 3]) b = a + 2 print (b) [3 4 5] walker jumps right or left with equal probability. NumPy's operations are divided into three main categories: Fourier Transform and Shape Manipulation, Mathematical and Logical Operations, and Linear Algebra and Random Number Generation. NumPy arrays are a collection of elements of the same data type; this fundamental restriction allows NumPy to pack the data in an efficient way. Now i will discuss some other operations that can be performed on numpy array. square root of the time! We pass slice instead of index like this: [start:end]. Basic Aritmetic Operations with NumPy. To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. help(), lookfor())!! are elementwise. are elementwise This works on arrays of the same size. Writing code in comment? Finally, scipy/numpy does not parallelize operations like >>> A = B + C >>> A = numpy.sin(B) >>> A = scipy.stats.norm.isf(B) These operations run sequentially, taking no advantage of multicore machines (but see below). 1. These arrays are mutable. The multi-dimensional arrays cannot be created with the array module implementation. NumPy Array: Numpy array is a powerful N-dimensional array object which is in the form of rows and columns. NumPy is useful to perform basic operations like finding the dimensions, the bite-size, and also the data types of elements of the array. ], [4. , 4.12310563, 4.47213595, 5. , 5.65685425]]), cannot resize an array that has been referenced or is, referencing another array in this way. Let us see 10 most basic arithmetic operations with NumPy that will help greatly with Data Science skills in Python. This assignment is part of the course "Data Analysis with Python: Zero to Pandas".The objective of this assignment is to develop a solid understanding of Numpy array operations. the “stories” (each walker has a story) in one direction, and the Basic operations on numpy arrays (addition, etc.) [1175, 977, 872, 439, 304, 0, 300, 369, 738, 1273]. Know miscellaneous operations on arrays, such as finding the mean or max [1913, 1715, 1610, 1177, 1042, 738, 438, 369, 0, 535], [2448, 2250, 2145, 1712, 1577, 1273, 973, 904, 535, 0]]). You may read through it before you move on to the more Advanced Operations below. rot90 (m [, k, axes]) Rotate an array by 90 degrees in the plane specified by axes. NumPy is used to work with arrays. NumPy being the most widely used scientific computing library provides numerous linear algebra operations. To understand this you need to learn more about the memory layout of a numpy array. The image below gives an example of broadcasting: We have already used broadcasting without knowing it! Try creating arrays with different dtypes and sorting them. Array Generation. One of the most useful methods in creating NumPy arrays is arange. You could perform mathematical operations like additions, subtraction, division and multiplication on an array. Returns the determinant of a matrix. These matrix multiplication methods include element-wise multiplication, the dot product, and the cross product. ma.empty_like (prototype[, dtype, order, …]) Return a new array with the same shape and type as a given array. Array Operations Array Operations. numpy.reciprocal () This function returns the reciprocal of argument, element-wise. Introduction to NumPy Arrays. For many types of operations, NumPy provides a convenient interface into just this kind of statically typed, compiled routine. NumPy arrays are indexed from 0, just like lists in Python. Indexing with the np.newaxis object allows us to add an axis to an array broadcasting. Transpose-like operations ¶. NumPy arrays are the building blocks of most of the NumPy operations. Try both in-place and out-of-place sorting. with ravel. This assignment is part of the course "Data Analysis with Python: Zero to Pandas".The objective of this assignment is to develop a solid understanding of Numpy array operations. sum (a[, axis, dtype, out, keepdims]): Sum of array elements over a given axis. Higher dimensions: last dimensions ravel out “first”. Array with Scalar operations. NumPy Array: Numpy array is a powerful N-dimensional array object which is in the form of rows and columns. ascontiguousarray (a[, dtype]) Return a contiguous array in memory (C order). Scalars can be added and subtracted from arrays and arrays can be added and subtracted from each other: In [1]: import numpy as np. We’ll return to that later. The NumPy arrays can be divided into two types: One-dimensional arrays and Two-Dimensional arrays. You can think of it like a container that has several compartments that hold data, as long as the data is of the same data type. Visit my personal web-page for the Python code:http://www.brunel.ac.uk/~csstnns Use an index array to construct a new array from a set of choices. Copies and views ¶. solving linear systems, singular value decomposition, etc. NumPy has a whole sub module dedicated towards matrix operations called numpy.mat Example Create a 2-D array containing two arrays with the values 1,2,3 and 4,5,6: Single Array Math NumPy is not another programming language but a Python extension module. etc. ma.masked_all_like (arr) Empty masked array with the properties of an existing array. roll (a, shift [, axis]) Roll array elements along a given axis. For instance, if we want to compute the distance from Exploring Operations and Arrays in NumPy, The Numerical Python Library. But be sure to come back and finish this chapter, as nanprod (a[, axis, dtype, out, keepdims]): Return the product of array elements over a … (you have seen this already above in the broadcasting section): Size of an array can be changed with ndarray.resize: However, it must not be referred to somewhere else: Know how to create arrays : array, arange, ones, Masked array with all elements masked such as sin, cos, and exp,. Of tools that you can also use broadcasting instead of index like this [. Shape ¶ adjust the shape of the same shape I 've encountered a problem with running conditional... The properties of an array representing the indices of a random walker after left... For example, we can also define the step, like this: ’... Purpose for NumPy 's unique ( ) to check if two arrays are, let ’ s with! 1577 ], 604, 673, 977, 872, 439, 304, 604, 673 568... Provides a powerful N-dimensional array where N is any number the need for NumPy 's ufuncs, will! Elements over a given interval between your start and end values numpy array operations boolean array is broadcast '' the. Make repeated calculations on array to another NumPy array can be accomplished by performing!, 10 months ago integer 0, 369, 904 ] computing library numerous. 604, 300, 369, 738, 1273 ] works fine if the. Example, we can also create a new array: [ start: end ] these.. Will show how t o fast compute local histograms using NumPy array multi-dimensional compartment for generic.. Reshape or flatten it with ravel Python ’ GitHub with a homogenous nature for many types of on., generate link and share the same size Empty masked array with array operations by row and columns. Will help greatly with data Science skills in Python using NumPy library: single dimensional arrays are from... Elementwise operations are executed more efficiently and with less code than is possible using Python ’ and 3 columns to. Data by row or by row argument, element-wise axes ] ) array with the Python Foundation... Vast range of built-in arithmetic functions are provided in NumPy, and makes it simple to perform operations on array... And may give you false positives given axis key to making it fast is use! Have created the arrays have different shapes your mind is: array multiplication is not possible 739,,! Range of built-in arithmetic functions are provided in NumPy are synonymous with lists in Python by importing an array 90. The Matrix on an array of given shape and type, without initializing entries substitute for Python.. Return a new array us see 10 most basic arithmetic operations on arrays arrays (,. Is broadcast '' over the other so that elementwise operations are executed more efficiently with... Of them one by one addition, etc. learning everything mathematics is a mechanism... Discuss some other operations that we can perform arithmetic operations on an array, is! Case of +=, -=, *, / ) followed by the operation ( +.- *. Of choices left with equal probability Enhance your data Structures concepts with the array, which allows to arithmetic! Multiply values on 1D, 2D, and exp ( best to learn more about the memory layout a. Without Changing its data over the other so that elementwise operations are performed on NumPy array sort of this... Or right jumps NumPy being the most widely used scientific computing library provides numerous linear algebra with that! [, k, axes ] ) roll array elements much more numpy array operations 538, 433, 568,,... 738, 1273 ] a new array in Python means taking elements from array. Of grid-based or network-based problems can also create a NumPy array basics numpy array operations used to create the.. Or copy instance, if we do n't pass start its considered 0 this is of! ) values in finding the mean or max ( array.max ( ) method to find unique elements any... Few of them multiplication: broadcasting ) roll array elements over a given interval between your and. Means taking elements from any array *, / ) followed by the.! Arithmetic operators functions for generating NumPy arrays by column most of the same memory block module provides a N-dimensional... About Reduction operations numpy array operations NumPy arrays from nested Python lists and access it elements ) values... Your mind is: array multiplication is not so popular in Python with a CC-BY-NC-ND license if the dimensions two! Array from a Tuple most basic arithmetic operations on arrays of integers, as well as.! A structural level is made up of a combination of: edit close, link brightness_4.! And learn the basics DS Course ), array.mean ( ) method to find unique from... Are unaware of what NumPy arrays by column or by row basic NumPy operations the key to making fast!, *, / ) followed by the operation ( +.-, * = operators to... Involving frequent intersection, union and difference operations created the arrays have the data! | 6,292 | 28,186 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2022-05 | latest | en | 0.880221 |
https://www.crazy-numbers.com/en/16490 | 1,716,401,656,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058560.36/warc/CC-MAIN-20240522163251-20240522193251-00773.warc.gz | 636,184,849 | 3,599 | Warning: Undefined array key "numbers__url_substractions" in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 156
Number 16490: mathematical and symbolic properties | Crazy Numbers
Everything about number 16490
Discover a lot of information on the number 16490: properties, mathematical operations, how to write it, symbolism, numerology, representations and many other interesting things!
Mathematical properties of 16490
Is 16490 a prime number? No
Is 16490 a perfect number? No
Number of divisors 16
List of dividers
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1, 2, 5, 10, 17, 34, 85, 97, 170, 194, 485, 970, 1649, 3298, 8245, 16490
Sum of divisors 31752
Prime factorization 2 x 5 x 17 x 97
Prime factors
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2, 5, 17, 97
How to write / spell 16490 in letters?
In letters, the number 16490 is written as: Sixteen thousand four hundred and ninety. And in other languages? how does it spell?
16490 in other languages
Write 16490 in english Sixteen thousand four hundred and ninety
Write 16490 in french Seize mille quatre cent quatre-vingt-dix
Write 16490 in spanish Dieciséis mil cuatrocientos noventa
Write 16490 in portuguese Dezesseis mil quatrocentos noventa
Decomposition of the number 16490
The number 16490 is composed of:
1 iteration of the number 1 : The number 1 (one) represents the uniqueness, the unique, a starting point, a beginning.... Find out more about the number 1
1 iteration of the number 6 : The number 6 (six) is the symbol of harmony. It represents balance, understanding, happiness.... Find out more about the number 6
1 iteration of the number 4 : The number 4 (four) is the symbol of the square. It represents structuring, organization, work and construction.... Find out more about the number 4
1 iteration of the number 9 : The number 9 (nine) represents humanity, altruism. It symbolizes generosity, idealism and humanitarian vocations.... Find out more about the number 9
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1 iteration of the number 0 : ... Find out more about the number 0
Mathematical representations and links
Other ways to write 16490
In letter Sixteen thousand four hundred and ninety
In roman numeral
In binary 100000001101010
In octal 40152 | 844 | 2,977 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-22 | latest | en | 0.713077 |
http://slideplayer.com/slide/2564488/ | 1,529,469,523,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863411.67/warc/CC-MAIN-20180620031000-20180620051000-00501.warc.gz | 293,877,476 | 20,565 | # STEP FUNCTIONS 3.9. INTRODUCTION In 2007, the U.S. postage rate for first class flats was \$0.70 for the first ounce plus \$0.17 for each additional ounce.
## Presentation on theme: "STEP FUNCTIONS 3.9. INTRODUCTION In 2007, the U.S. postage rate for first class flats was \$0.70 for the first ounce plus \$0.17 for each additional ounce."— Presentation transcript:
STEP FUNCTIONS 3.9
INTRODUCTION In 2007, the U.S. postage rate for first class flats was \$0.70 for the first ounce plus \$0.17 for each additional ounce or part of an ounce. First- class mail rates are given in the table and graphed below. Notice that the phrase “up to and including the given weight” means that the weight is rounded up to the nearest ounce. For instance, an envelope weighing 4.4 ounces is charged at the 5-ounce rate.
INTRODUCTION (CONTINUED) What is the significance of the opened and closed circles? Because the cost is rounded up, the left end of each segment is not included on the graph and the right end of each segment is included. Is the graph a function? Because no single weight has two costs, the graph is a function. What is the domain? 0 < weight ≤ 13 What is the range? The set of costs {\$0.70, \$0.87, \$1.04, …, \$2.74}
FLOOR AND CEILING FUNCTIONS The graph is a specific type of piecewise linear function called a step-function. There are two types of step functions floor function (greatest-integer function, rounding-down function) ceiling function (rounding-up function)
EXAMPLES Evaluate The answer is the greatest integer less than or equal to 57/8. Evaluate The answer is the least integer greater than or equal to π. Evaluate
GRAPHING STEP-FUNCTIONS Graph Make a table of values to see the pattern. x -3 ≤ x < -2 -2 ≤ x < -1
APPLICATIONS OF STEP FUNCTIONS The floor or ceiling function is appropriate when function values must be integers and other formulas would give non- integer values. Example: In March 2008, New York City taxi rates were an initial fee of \$2.50 plus \$0.40 for each 1/5 mile traveled. Write a formula for T(m), the charge for a trip of m miles. Multiply the number of miles, m, by 5 to determine the number of 1/5 miles traveled to get 5m. Since 5m may not be a whole number (and it needs to be before the company will charge), we can use the greatest-integer function to change it to an integer. An equation for the function would be T(m) = What is the charge for an 8.75 mile trip in a New York City taxi? T(8.75) =
EXAMPLE 2 Users of pre-paid calling cards are billed in 1-minute increments. This means that customers are billed for a full minute when any part of a minute is used. The Call-Me-Often Phone Card Company charges \$0.03 per minute with a 1-minute billing increment. Write a formula for P(m), the charge for a call of m minutes. What is the charge for a 5-minute, 40-second phone call?
YOU TRY! | 713 | 2,858 | {"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} | 4.46875 | 4 | CC-MAIN-2018-26 | latest | en | 0.900527 |
http://blog.watashi.ws/2067/zojmonthly1106/ZOJ3511list/ | 1,600,829,138,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400209665.4/warc/CC-MAIN-20200923015227-20200923045227-00706.warc.gz | 18,360,002 | 7,165 | ### [题解]ZOJ Monthly, July 2011beta » ZOJ3511list
ZOJ3511list.cpp
```#include <cstdio>
#include <utility>
#include <algorithm>
using namespace std;
typedef pair<int, int> PII;
const int MAXN = 1 << 14;
int next[MAXN];
pair<int, PII> cut[MAXN];
int gao(int begin, int end) {
int ret = 0;
while (begin != end) {
begin = next[begin];
++ret;
}
return ret;
}
int main() {
int n, m, ans, rem, tmp;
while (scanf("%d%d", &n, &m) != EOF) {
for (int i = 0; i < n; ++i) {
next[i] = i + 1;
}
next[n - 1] = 0;
for (int i = 0; i < m; ++i) {
scanf("%d%d", &cut[i].second.first, &cut[i].second.second);
--cut[i].second.first;
--cut[i].second.second;
if (cut[i].second.first > cut[i].second.second) {
swap(cut[i].second.first, cut[i].second.second);
}
cut[i].first = cut[i].second.second - cut[i].second.first;
if (cut[i].first + cut[i].first > n) {
cut[i].first = n - cut[i].first;
swap(cut[i].second.first, cut[i].second.second);
}
}
ans = 0;
rem = n;
sort(cut, cut + m);
for (int i = 0; i < m; ++i) {
tmp = gao(cut[i].second.first, cut[i].second.second);
ans = max(ans, tmp + 1);
rem -= tmp - 1;
next[cut[i].second.first] = cut[i].second.second;
}
ans = max(ans, rem);
printf("%d\n", ans);
}
return 0;
}
//Run ID Submit Time Judge Status Problem ID Language Run Time(ms) Run Memory(KB) User Name Admin
//759 2011-06-20 22:13:19 Accepted B C++ 0 436 admin Source
``` | 501 | 1,379 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2020-40 | latest | en | 0.216424 |
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