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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
http://openwetware.org/index.php?title=Matthew_E._Jurek_Week_9&diff=prev&oldid=688378 | 1,454,769,841,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701146550.16/warc/CC-MAIN-20160205193906-00134-ip-10-236-182-209.ec2.internal.warc.gz | 169,577,844 | 5,702 | # Matthew E. Jurek Week 9
(Difference between revisions)
Revision as of 21:10, 2 April 2013 (view source) (→Sanity Check: added ".")← Previous diff Revision as of 21:12, 2 April 2013 (view source) (→Sanity Check)Next diff → Line 30: Line 30: ##t90= 0 ##t90= 0 ##t120= 0 ##t120= 0 - #For the timepoint that had the greatest number of genes significantly changed at p < 0.05, answer the following: + #For the timepoint that had the greatest number of genes significantly changed at p < 0.05, answer the following: Following the correction, there were no p values <.05. Thus, the following are calculations for each time point. - Following the correction, there were no p values <.05. Thus, the following are calculations for each time point. + Keeping the "Pval" filter at p < 0.05, filter the "AvgLogFC" column to show all genes with an average log fold change greater than zero. How many meet these two criteria? Keeping the "Pval" filter at p < 0.05, filter the "AvgLogFC" column to show all genes with an average log fold change greater than zero. How many meet these two criteria? ##t15= 203 ##t15= 203
## Sanity Check
1. How many genes have p value < 0.05?
1. t15= 385
2. t30= 544
3. t60= 434
4. t90= 231
5. t120= 190
2. What about p < 0.01?
1. t15= 81
2. t30= 108
3. t60= 87
4. t90= 28
5. t120= 34
3. What about p < 0.001?
1. t15= 8
2. t30= 10
3. t60= 6
4. t90= 5
5. t120= 4
4. What about p < 0.0001?
1. t15= 0
2. t30= 1
3. t60= 1
4. t90= 1
5. t120= 0
5. Perform this correction and determine whether and how many of the genes are still significantly changed at p < 0.05 after the Bonferroni correction.
1. t15= 0
2. t30= 0
3. t60= 0
4. t90= 0
5. t120= 0
6. For the timepoint that had the greatest number of genes significantly changed at p < 0.05, answer the following: Following the correction, there were no p values <.05. Thus, the following are calculations for each time point.
Keeping the "Pval" filter at p < 0.05, filter the "AvgLogFC" column to show all genes with an average log fold change greater than zero. How many meet these two criteria?
1. t15= 203
2. t30= 332
3. t60= 168
4. t90= 118
5. t120= 104
1. Keeping the "Pval" filter at p < 0.05, filter the "AvgLogFC" column to show all genes with an average log fold change less than zero. How many meet these two criteria?
1. t15= 182
2. t30= 212
3. t60= 266
4. t90= 86
5. t120= 86
2. Keeping the "Pval" filter at p < 0.05, How many have an average log fold change of > 0.25 and p < 0.05?
1. t15= 0
2. t30= 0
3. t60= 0
4. t90= 0
5. t120= 0
3. How many have an average log fold change of < -0.25 and p < 0.05? (These are more realistic values for the fold change cut-offs because it represents about a 20% fold change which is about the level of detection of this technology.)
1. t15= 150
2. t30= 198
3. t60= 247
4. t90= 63
5. t120= 74 | 994 | 2,811 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2016-07 | longest | en | 0.918006 |
https://discuss.leetcode.com/topic/94442/java-5-lines-o-1-space-solution | 1,513,164,496,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948522999.27/warc/CC-MAIN-20171213104259-20171213124259-00650.warc.gz | 552,766,680 | 11,495 | # [Java] 5 lines O(1) space solution
• Details can be found from wiki:
https://en.wikipedia.org/wiki/Derangement#Counting_derangements
`````` private static final int M = 1000000007;
public int findDerangement(int n) {
long ans = 1;
for (int i = 1; i <= n; i++)
ans = (i * ans % M + (i % 2 == 0 ? 1 : -1)) % M;
return (int) ans;
}
``````
• Thanks for provide wiki link
• Very cool simplification of the formula on wikipedia. I tried playing around, and I see the similarities to a normal factorial, but don't know how to prove it. Would you be able to share the proof for why your formula works? Thanks!
• @baselRus Denote `E_n = D_n - n D_{n-1}`.
From the formula `D_n = (n-1)(D_{n-1} + D_{n-2})`, we have:
`E_n = -D_{n-1} + (n-1) (D_{n-2}) = -E_{n-1}`.
Together with `E_0 = -1`, this shows `E_n = (-1)^n` as desired.
• @awice Very cool, thanks!
Just to write the result explicitly:
We rewrite first line of @awice's proof, to get `D_n = n D_{n-1} - E_n`.
Combine with last line of @awice's proof, we get `D_n = n D_{n-1} - (-1)^n`, which is the formula used in @MichaelPhelps' function.
• Here is my DP solution:
For `ith` element, we have switch it with one of the previous numbers `1,2,...,i-1`, and for each picked number j, for the positions left except the one take by `i`, j can take anyone of them. So there are `dp[i - 2]` permutation if `j` can take the original position of `i`, and `dp[i - 1]` permutations if `j` can not take the original position of `i`.
``````public int findDerangement(int n) {
if(n <= 1) return 0;
long[] dp = new long[n + 1];
long mod = 1000000007;
dp[2] = 1;
for(int i = 3; i < dp.length; i++){
dp[i] = (long)(i - 1) * (dp[i - 1] + dp[i - 2]) % mod;
}
return (int)dp[dp.length - 1];
}
``````
• I also came up with a similar solution in C++. I have written my solution along with a verbose thought process to hopefully help other folks better understand this formula: https://discuss.leetcode.com/topic/102738/very-easy-to-understand-c-with-explanation
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 670 | 2,101 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-51 | latest | en | 0.798791 |
https://www.mscroggs.co.uk/puzzles/LI | 1,606,467,568,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00716.warc.gz | 770,536,670 | 7,180 | mscroggs.co.uk
mscroggs.co.uk
subscribe
# Sunday Afternoon Maths LI
Posted on 2016-04-03
## Doubling cribbage
Brendan and Adam are playing high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
Adam wins the first game then loses the second game. They then notice that they each have £180. How much did each player start with?
## Two semicircles
The diagram shows two semicircles.
$$CD$$ is a chord of the larger circle and is parallel to $$AB$$. The length of $$CD$$ is 8m. What is the area of the shaded region (in terms of $$\pi$$)?
## What is the sum?
What is $$\displaystyle\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}$$?
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about prime numbers, or a random puzzle.
## Archive
Show me a random puzzle
▼ show ▼ | 282 | 970 | {"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} | 3.28125 | 3 | CC-MAIN-2020-50 | latest | en | 0.902664 |
https://byjus.com/question-answer/a-village-has-10-players-a-team-of-6-players-is-to-be-formed-5/ | 1,642,798,957,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00289.warc.gz | 216,606,426 | 23,189 | Question
# A village has $$10$$ players. A team of $$6$$ players is to be formed. $$5$$ members are chosen first out of these $$10$$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is
A
1260
B
210
C
(10C6)5!
D
10C56
Solution
## The correct option is A $$1260$$A village has $$10$$ players.Now a team of $$6$$ players is to be formed.Thus $$1^{st}$$ we select the $$5$$ players from total $$10$$ players in $${ _{ }^{ 10 }{ C } }_{ 5 }$$ ways and $$6^{th}$$ person will select from the remaining $$5$$ players in $$5$$ ways.Total number of ways $$={ _{ }^{ 10 }{ C } }_{ 5 }\times 5=1260$$Mathematics
Suggest Corrections
Â
0
Similar questions
View More
People also searched for
View More | 227 | 755 | {"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} | 3.546875 | 4 | CC-MAIN-2022-05 | latest | en | 0.937124 |
https://www.expertsmind.com/library/way-out-of-a-traffic-violation-for-running-a-red-light-5542896.aspx | 1,726,627,849,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.68/warc/CC-MAIN-20240918000844-20240918030844-00215.warc.gz | 710,347,097 | 12,983 | Way out of a traffic violation for running a red light
Assignment Help Physics
Reference no: EM13542896
An astronaut tries to talk his way out of a traffic violation for running a red light (? = 670 nm) by telling the judge that the light appeared green (? = 540 nm) to him as he passed by in his expensive sports car. If this is true, how fast was the astronaut going? Will this excuse get him out of trouble?
Questions Cloud
Values of the current and voltage under operating conditions : A common flashlight bulb is rated at 0.30 A and 2.9 V (the values of the current and voltage under operating conditions). If the resistance of the bulb filament at room temperature (20°C) is 1.7 , what is the temperature of the filament when the bulb.. What is the magnitude of the electric field between them : Two parallel planes have surface charge densities +5.0 nC/m2 and -3.0 nC/m2. What is the magnitude of the electric field between them Trie in java to implement simplified search engine : Write small program to use trie in Java to implement simplified search engine for one page of a small website. Use all the word in the page of the site as index terms. How to calculate the heat released per gram of b2h6 : Use standard heat of formation data to calculate the heat released per gram of B2H6 when burned with O2(g) to afford boric acid (H2BO3 (s)). Way out of a traffic violation for running a red light : An astronaut tries to talk his way out of a traffic violation for running a red light (? = 670 nm) by telling the judge that the light appeared green (? = 540 nm) to him as he passed by in his expensive sports car. If this is true, how fast was the a.. What is the external force encountered by this object : An object of mass 5kg has an initial velocity of 10m/s, if this object has moved a distance of 40m and maintains a final velocity of 20m/s. What is the external force encountered by this object Explain silicone has a face centered cubic crystal structure : silicone has a face centered cubic crystal structure with unit cell length of 5.43 angstroms and four atoms per unit cell. A) how many silicon atoms are there in 1 cm3 of material Create three best practices for creating ppt : Create three best practices for creating a PowerPoint presentation. Depict a molecular orbital diagram for c2 : Draw a molecular orbital diagram for C2 and use it to predict the bond order and magnetic properties for this gas phase diatomic allotrope of carbon.
Write a Review
Find the magnitude of the resulting magnetic field
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
Find the equivalent resistance
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
What is the electric field at the location
Question: Field and force with three charges? What is the electric field at the location of Q1, due to Q 2 ?
What is the maximum displacement of the bridge deck
What is the maximum displacement of the bridge deck?
What is the magnitude of the current in the wire
What is the magnitude of the current in the wire as a function of time?
Blackbody
Questions on blackbody, Infra-Red Detectors & Optic Lens and Digital Image.
Gravity conveyor
Illustrate the cause of the components accelerating from rest down the conveyor.
Calculate the dc voltage
Calculate the dc voltage applied to the circuit.
Quadrupole moments in the shell model
Quadrupole moments in the shell model
Determine the tension in each string
Determine the tension in each string
Introductory mechanics: dynamics
Calculate the smallest coefficient of static friction necessary for mass A to remain stationary.
Evaluate maximum altitude
Evaluate maximum altitude? | 855 | 3,939 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-38 | latest | en | 0.949448 |
https://synth-diy.org/pipermail/synth-diy/2020-December/125242.html | 1,722,792,816,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640408316.13/warc/CC-MAIN-20240804164455-20240804194455-00154.warc.gz | 434,371,628 | 3,186 | # [sdiy] CV input op-amp circuit
David G Dixon dixon at mail.ubc.ca
Sat Dec 5 00:23:50 CET 2020
```Just to clarify, my design did not require an inverting opamp. The operation was all done in a single opamp. I just showed two opamps in the picture because one was processing -5V and other +7V, to show that the proper voltages were obtained.
_____
From: Ian Fritz [mailto:ijfritz at comcast.net]
Sent: Friday, December 04, 2020 1:26 PM
To: David G Dixon
Cc: synth-diy at synth-diy.org
Subject: Re: [sdiy] CV input op-amp circuit
[CAUTION: Non-UBC Email]
IMO, everyone should at some point go through the derivation of the equations for the generalized opamp summer. This often makes it easy to avoid using unneeded inverting stages. One thing to watch, though, is that the resulting equations assume zero impedance voltage sources for inputs. Usually you have to take source impedances into account.
Ian
On Dec 4, 2020, at 12:03 PM, David G Dixon <dixon at mail.ubc.ca> wrote:
Hello Christian,
It seems to me that your circuit will invert the CV, which is not what you want.
Here's how I would do it: First, I calculated that the range of -5V to +7V is 12V, and the range of 0 to 3V is 3V, so you need a gain of 25%. This alone would change the range to -1.25V to +1.75V. Hence, this needs to be shifted by +1.25V. So, you need a circuit that will apply a gain of 25% and a shift of +1.25V. I am going to assume that you have a -5V reference source available (or an inverted +5V reference). So, the -5V reference requires a gain of -25%. So, what circuit will apply a (non-inverting) gain of 25% to one input, and an (inverting) gain of -25% to another input? This one, with 5% resistors:
<CVShifter.png>
Or, a slightly more accurate version with 1% resistors:
<poop.png>
The CV comes into the + input through a 4:1 voltage divider which applies a gain of 20%. However, the 1:4 ratio of feedback to inverting input resistors applies a gain of 125% to the non-inverting input, and (125%)(20%) = 25%.
The -5V reference comes into the - input through feedback/input resistor ratio of 1:4, which applies an inverting gain of -25% to that voltage, creating a level shift of +1.25V.
The convenient aspect of this is that both pairs of resistors have a 4:1 ratio. The closest 5% standard values are 33k and 8.2k. The closest 1% values are 102k and 25.5k.
Cheers,
Doc Sketchy
_____
From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of Christian Maniewski via Synth-diy
Sent: Friday, December 04, 2020 5:31 AM
To: synth-diy at synth-diy.org
Subject: [sdiy] CV input op-amp circuit
Hi all!
I’m trying to come up with an op-amp design for a CV input. I want to transform a signal ranging from -5V to +7V to a more MCU digestable 0-3.3V. I came up with the circuit you’ll find attached.
I have seen other approaches, where an offset reference is injected in the feedback loop, while the positive op-amp input is grounded. Are there any disadvantages to my approach or is it also valid?
Thank you so much!
I’ve been following this email list for some time now. This is my first question and first email entirely. Please bear with me.
Chris
_______________________________________________
Synth-diy mailing list
Synth-diy at synth-diy.org
http://synth-diy.org/mailman/listinfo/synth-diy
Selling or trading? Use marketplace at synth-diy.org
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20201204/99d7a0cb/attachment.htm>
``` | 1,012 | 3,560 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-33 | latest | en | 0.923499 |
https://words-wiki.com/axis-of-a-curve-definition-meaning/ | 1,726,254,120,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651535.66/warc/CC-MAIN-20240913165920-20240913195920-00468.warc.gz | 576,958,020 | 11,087 | # Axis of a curve – Definition & Meaning
The axis of a curve is a fundamental concept in mathematics and science that is used to describe the central line or point of symmetry of a curve. The axis of a curve plays a crucial role in the study of functions, geometry, and physics, and is an essential tool for understanding and analyzing a variety of phenomena.
## Definitions
The axis of a curve is defined as the line or point that divides the curve into two symmetrical halves. It is the line or point around which the curve is symmetric, and any point on the curve that is equidistant from the axis is said to be symmetric to its counterpart on the other side of the axis.
## Origin
The concept of the axis of a curve can be traced back to the ancient Greeks, who were the first to study geometry and the properties of curves. The word “axis” comes from the Greek word “axios,” which means “worthy” or “having value.” The Greeks used the concept of the axis to describe the central line of symmetry of various geometric shapes, including circles and ellipses.
## Meaning in different dictionaries
The axis of a curve is defined in various dictionaries as the line or point that divides a curve into two symmetrical halves. It is described as the central line or point of symmetry of a curve and is used in mathematics, physics, and engineering to analyze and understand various phenomena.
## Associations
The axis of a curve is associated with various mathematical and scientific concepts, including functions, geometry, and physics. It is used to describe the central line or point of symmetry of a curve, and is an essential tool for understanding and analyzing a variety of phenomena, including the behavior of waves, the shape of objects, and the properties of functions.
## Synonyms
Synonyms for the axis of a curve include the central line, the line of symmetry, the point of symmetry, and the axis of symmetry.
## Antonyms
Antonyms for the axis of a curve include asymmetry, irregularity, and lack of symmetry.
## The same root words
The root word for axis is “axis,” which means “a central line around which a body rotates.” The word “curve” comes from the Latin word “curvus,” which means “bent” or “curved.”
## Example Sentences
1. The axis of the parabola is the vertical line that passes through its vertex.
2. The axis of symmetry of a circle is the line that passes through its center.
3. The axis of the sine wave is the horizontal line that passes through its peak and trough.
4. The axis of a hyperbola is the line that passes through its two foci.
5. The axis of a cylinder is the line that passes through its center and is perpendicular to its base. | 573 | 2,687 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-38 | latest | en | 0.950815 |
https://openwetware.org/wiki/?title=User:Timothee_Flutre/Notebook/Postdoc/2011/06/28&diff=prev&oldid=618356 | 1,511,357,185,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806586.6/warc/CC-MAIN-20171122122605-20171122142605-00519.warc.gz | 672,137,864 | 11,313 | # Difference between revisions of "User:Timothee Flutre/Notebook/Postdoc/2011/06/28"
Project name <html><img src="/images/9/94/Report.png" border="0" /></html> Main project page
Next entry<html><img src="/images/5/5c/Resultset_next.png" border="0" /></html>
## Linear regression by ordinary least squares
• Data: let's assume that we obtained data from $\displaystyle N$ individuals. We note $\displaystyle y_1,\ldots,y_N$ the (quantitative) phenotypes (eg. expression level at a given gene), and $\displaystyle g_1,\ldots,g_N$ the genotypes at a given SNP. We want to assess their linear relationship.
• Model: to start with, we use a simple linear regression (univariate phenotype, single predictor).
$\displaystyle \forall n \in {1,\ldots,N}, \; y_n = \mu + \beta g_n + \epsilon_n \text{ with } \epsilon_n \sim N(0,\sigma^2)$
In matrix notation:
$\displaystyle y = X \theta + \epsilon$ with $\displaystyle \epsilon \sim N_N(0,\sigma^2 I_N)$ and $\displaystyle \theta^T = (\mu, \beta)$
• Use only summary statistics: most importantly, we want the following estimates: $\displaystyle \hat{\beta}$ , $\displaystyle se(\hat{\beta})$ (its standard error) and $\displaystyle \hat{\sigma}$ . In the case where we don't have access to the original data (eg. because genotypes are confidential) but only to some summary statistics (see below), it is still possible to calculate the estimates.
Here is the ordinary-least-square (OLS) estimator of $\displaystyle \theta$ :
$\displaystyle \hat{\theta} = (X^T X)^{-1} X^T Y$
$\displaystyle \begin{bmatrix} \hat{\mu} \\ \hat{\beta} \end{bmatrix} = \left( \begin{bmatrix} 1 & \ldots & 1 \\ g_1 & \ldots & g_N \end{bmatrix} \begin{bmatrix} 1 & g_1 \\ \vdots & \vdots \\ 1 & g_N \end{bmatrix} \right)^{-1} \begin{bmatrix} 1 & \ldots & 1 \\ g_1 & \ldots & g_N \end{bmatrix} \begin{bmatrix} y_1 \\ \vdots \\ y_N \end{bmatrix}$
$\displaystyle \begin{bmatrix} \hat{\mu} \\ \hat{\beta} \end{bmatrix} = \begin{bmatrix} N & \sum_n g_n \\ \sum_n g_n & \sum_n g_n^2 \end{bmatrix}^{-1} \begin{bmatrix} \sum_n y_n \\ \sum_n g_n y_n \end{bmatrix}$
$\displaystyle \begin{bmatrix} \hat{\mu} \\ \hat{\beta} \end{bmatrix} = \frac{1}{N \sum_n g_n^2 - (\sum_n g_n)^2} \begin{bmatrix} \sum_n g_n^2 & - \sum_n g_n \\ - \sum_n g_n & N \end{bmatrix} \begin{bmatrix} \sum_n y_n \\ \sum_n g_n y_n \end{bmatrix}$
$\displaystyle \begin{bmatrix} \hat{\mu} \\ \hat{\beta} \end{bmatrix} = \frac{1}{N \sum_n g_n^2 - (\sum_n g_n)^2} \begin{bmatrix} \sum_n g_n^2 \sum_n y_n - \sum_n g_n \sum_n g_n y_n \\ - \sum_n g_n \sum_n y_n + N \sum_n g_n y_n \end{bmatrix}$
Let's now define 4 summary statistics, very easy to compute:
$\displaystyle \bar{y} = \frac{1}{N} \sum_{n=1}^N y_n$
$\displaystyle \bar{g} = \frac{1}{N} \sum_{n=1}^N g_n$
$\displaystyle g^T g = \sum_{n=1}^N g_n^2$
$\displaystyle g^T y = \sum_{n=1}^N g_n y_n$
This allows to obtain the estimate of the effect size only by having the summary statistics available:
$\displaystyle \hat{\beta} = \frac{g^T y - N \bar{g} \bar{y}}{g^T g - N \bar{g}^2}$
The same works for the estimate of the standard deviation of the errors:
$\displaystyle \hat{\sigma}^2 = \frac{1}{N-r}(y - X\hat{\theta})^T(y - X\hat{\theta})$
We can also benefit from this for the standard error of the parameters:
$\displaystyle V(\hat{\theta}) = \hat{\sigma}^2 (X^T X)^{-1}$
$\displaystyle V(\hat{\theta}) = \hat{\sigma}^2 \frac{1}{N g^T g - N^2 \bar{g}^2} \begin{bmatrix} g^Tg & -N\bar{g} \\ -N\bar{g} & N \end{bmatrix}$
$\displaystyle V(\hat{\beta}) = \frac{\hat{\sigma}^2}{g^Tg - N\bar{g}^2}$
• Simulation with a given PVE: when testing an inference model, the first step is usually to simulate data. However, how do we choose the parameters? In our case, the model is $\displaystyle y = \mu + \beta g + \epsilon$ ). Therefore, the variance of $\displaystyle y$ can be decomposed like this:
$\displaystyle V(y) = V(\mu + \beta g + \epsilon) = V(\mu) + V(\beta g) + V(\epsilon) = \beta^2 V(g) + \sigma^2$
The most intuitive way to simulate data is therefore to fix the proportion of variance in $\displaystyle y$ explained by the genotype, for instance $\displaystyle PVE=60%$ , as well as the standard deviation of the errors, typically $\displaystyle \sigma=1$ . From this, we can calculate the corresponding effect size $\displaystyle \beta$ of the genotype:
$\displaystyle PVE = \frac{V(\beta g)}{V(y)}$
Therefore: $\displaystyle \beta = \pm \sigma \sqrt{\frac{PVE}{(1 - PVE) * V(g)}}$
Note that $\displaystyle g$ is the random variable corresponding to the genotype encoded in allele dose, such that it is equal to 0, 1 or 2 copies of the minor allele. For our simulation, we will fix the minor allele frequency $\displaystyle f$ (eg. $\displaystyle f=0.3$ ) and we will assume Hardy-Weinberg equilibrium. Then $\displaystyle g$ is distributed according to a binomial distribution with 2 trials for which the probability of success is $\displaystyle f$ . As a consequence, its variance is $\displaystyle V(g)=2f(1-f)$ .
Here is some R code implementing all this:
set.seed(1859)
N <- 100 # sample size
mu <- 4
pve <- 0.6
sigma <- 1
maf <- 0.3
beta <- sigma * sqrt(pve / ((1 - pve) * 2 * maf * (1 - maf))) # 1.88
g <- sample(x=0:2, size=N, replace=TRUE, prob=c(maf^2, 2*maf*(1-maf), (1-maf)^2))
y <- mu + beta * g + rnorm(n=N, mean=0, sd=sigma)
ols <- lm(y ~ g)
summary(ols) # muhat=3.5, betahat=2.1, R2=0.64
sqrt(mean(ols$residuals^2)) # sigmahat = 0.98 plot(x=0, type="n", xlim=range(g), ylim=range(y), xlab="genotypes", ylab="phenotypes", main="Simple linear regression") for(i in unique(g)) points(x=jitter(g[g == i]), y=y[g == i], col=i+1, pch=19) abline(a=coefficients(ols)[1], b=coefficients(ols)[2]) • Several predictors: let's now imagine that we also know the gender of the N sampled individuals. We hence want to account for that in our estimate of the genotypic effect. In matrix notation, we still have the same model Y = XB + E with Y an Nx1 vector, X an Nx3 matrix with 1's in the first column, the genotypes in the second and the genders in the third, B a 3x1 vector and E an Nx1 vector following a multivariate Normal distribution centered on 0 and with covariance matrix $\displaystyle \sigma^2 I_N$ . As above, we want $\displaystyle \hat{B}$ , $\displaystyle \hat{\sigma}$ and $\displaystyle V(\hat{B})$ . To efficiently get them, we start with the singular value decomposition of X: $\displaystyle X = U D V^T$ This allows us to get the Moore-Penrose pseudoinverse matrix of X: $\displaystyle X^+ = (X^TX)^{-1}X^T$ $\displaystyle X^+ = V D^{-1} U^T$ From this, we get the OLS estimate of the effect sizes: $\displaystyle \hat{B} = X^+ Y$ Then it's straightforward to get the residuals: $\displaystyle \hat{E} = Y - X \hat{B}$ With them we can calculate the estimate of the error variance: $\displaystyle \hat{\sigma} = \sqrt{\frac{1}{N-3} \hat{E}^T \hat{E}}$ And finally the standard errors of the estimates of the effect sizes: $\displaystyle V(\hat{B}) = \hat{\sigma}^2 V D^{-2} V^T$ We can check this with some R code: ## simulate the data set.seed(1859) N <- 100 mu <- 5 Xg <- sample(x=0:2, size=N, replace=TRUE, prob=c(0.5, 0.3, 0.2)) # genotypes beta.g <- 0.5 Xc <- sample(x=0:1, size=N, replace=TRUE, prob=c(0.7, 0.3)) # gender beta.c <- 0.3 pve <- 0.8 betas.gc.bar <- mean(beta.g * Xg + beta.c * Xc) # 0.405 sigma <- sqrt((1/N) * sum((beta.g * Xg + beta.c * Xc - betas.gc.bar)^2) * (1-pve) / pve) # 0.2 y <- mu + beta.g * Xg + beta.c * Xc + rnorm(n=N, mean=0, sd=sigma) ## perform the OLS analysis with the SVD of X X <- cbind(rep(1,N), Xg, Xc) Xp <- svd(x=X) B.hat <- Xp$v %*% diag(1/Xp$d) %*% t(Xp$u) %*% y
E.hat <- y - X %*% B.hat
sigma.hat <- as.numeric(sqrt((1/(N-3)) * t(E.hat) %*% E.hat)) # 0.211
var.theta.hat <- sigma.hat^2 * Xp$v %*% diag((1/Xp$d)^2) %*% t(Xp\$v)
sqrt(diag(var.theta.hat)) # 0.0304 0.0290 0.0463
## check all this
ols <- lm(y ~ Xg + Xc)
summary(ols) # muhat=4.99+-0.03, beta.g.hat=0.52+--.-29, beta.c.hat=0.24+-0.046, R2=0.789
Such an analysis can also be done easily in a custom C/C++ program thanks to the GSL (here). | 2,771 | 8,051 | {"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": 51} | 4 | 4 | CC-MAIN-2017-47 | latest | en | 0.558573 |
https://chat.stackexchange.com/transcript/71?m=65840481 | 1,726,345,335,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651580.74/warc/CC-MAIN-20240914193334-20240914223334-00531.warc.gz | 142,069,725 | 8,603 | 10:27 AM
Guys, in an exercise, how do you understand if there is inertia?
10:38 AM
Does it happen in our universe
If so, yes, there is inertia
10:52 AM
@Relativisticcucumber grrrr
@ClaudioMenchinelli +1 for my UG and it was all the profs except one :,(
ok i see in the chat history i have asked this 2x but i am still quite confused on the role of schurs lemma. i have revisted rep theory in qm and an more familiar with the spin case. i thought it was to label the spin irreps but now im questioning that since it seems this is done purely by experiments.
isnt the second point just true for anything that commutes w the ham? what does this have to do w rep theory at all?
11:16 AM
@Relativisticcucumber he is just stating that it is a consequence of the observation in the paragraph above the statemet
@Relativisticcucumber it is true that if $[A, H] = 0$, then (actually an iff) $A$ and $H$ are simultaneously diagonalizable and so share eigenstates. Which means that an $A,H$ eigenstate $\lvert a, E \rangle$ indeed will not change its energy upon an action such as $e^{-i\theta A } \lvert a, E \rangle$
i want to give up on schurs lemma but in every "physics and rep theory" resource it seems to be plopped in and left
and never revisited XD but i feel bad to just leave w o it
@SillyGoose yeah thats why iw as thinking
Hi guys, can anyone tell me if my approach for this exercise is correct?
A small sphere of mass m = 100g is attached to an ideal spring with elastic constant k = 19.6 N/m, rest length L = 40 cm, massless, whose second end is fixed at point A, as shown in the figure. The system is placed on a rough horizontal plane (dynamic friction coefficient μ= 0.5). If the spring is extended by a distance ∆l_0 = 20cm and the ball is then allowed to move under the action of the spring, the minimum distance from A reached by the ball in its motion is determined.
I would do it like this:
$E_p = \frac{1}{2}k\Delta l_0^2$
$F_f = \mu \cdot m \cdot g$
$W_f = F_f \cdot d$
$E_p = W_f$
$d_A= d + \Delta l_0$
@SillyGoose also note that the energy eigenstate need not be simultaneously of both A and H for this to hold. take $He^{-iAa}|E\rangle=e^{-iAa}H|E\rangle=E e^{-iAa}|E\rangle$
i suppose that is true, but i believe that it is always true that if $[A, H] = 0$, then any eigenstate of $H$ will also be an eigenstate of $A$
@SillyGoose no. e.g. degeneracy
assuming no degeneracy, that is correct
11:29 AM
I see
I think the statemetn I am lookign for is just that $[X, Y] = 0 \iff$ $X$ and $Y$ are simultaneously diagonalizable $\iff$ share a common eigenbasis
yeah. that is correct
which is consistent with not every eigenbasis for each operator being shared
also, how can i understand the difference between isomorphic and bijective for representations ?
specifically, i think there is a bijection between the projective reps of $SO(3)$ and reps of $SU(2)$, but are these necessarily isomorphic?
11:47 AM
Bijection just maps points uniquely, it doesn't have to imply that the group structure is preserved
There's a bijection between any Lie groups that isn't zero dimensional, since they all have the cardinality of the continuum
12:02 PM
bargmann's theorem (applied here) states that projective representations of $SO(3)$ "lift" to representations of $SU(2)$ where "lift" seems to mean the following. let $\rho : SO(3) \to GL(V)$. the lift of $\rho$ is a $\tilde{\rho}: SU(2) \to GL(V)$ such that $\pi \circ \tilde{\rho} = \rho$ where $\pi: SU(2) \to SO(3)$ is the projection
"Among these, the most universal and fundamental one is Ptolemy's law stating that the space of our world has three dimensions."
Who the hell calls it Ptolemy's law
this book states and proves bargmann's theorem it seems: link.springer.com/chapter/10.1007/978-3-540-70690-8_5
Oh god apparently there is a super obscure book of Ptolemy on the topics of dimensions
Peri diastaseos
12:19 PM
@SillyGoose oh no
i dont think i want to welcome that into my life
hm it seems like bargmann's theorem does not establish a bijection between the two sets of representations.
@SillyGoose damn it
is it: Let $G$ be a connected, simply-connected Lie group with trivial 2nd Lie algebra cohomology class. Then, for every projective representation $\rho: G \to GL(P(V))$, we can lift it to a representation of the universal cover of $G$, $\tilde{G}$, $\tilde{\rho}: \tilde{G} \to GL(V)$ such that $\pi \circ \tilde{\rho} = \rho$.
In particular, there may exist representations of the universal cover that are not in unique correspondence with representations of the original group.
So is the real correspondence is between projective representations $\rho$ and projected representations of the universal cover $\pi \circ \tilde{\rho}$ where $\pi: \tilde{G} \to G$ is the projection?
i mean certainly the above is a bijection, but i am wondering if bargmann's theorem makes the stronger claim that there is a bijection between representations of the universal cover and projective representations of the group
12:45 PM
> The gifted Ptolemy in his book On Dimension showed that there are not more than three dimensions;
Pretty short statement
Alas the book itself is lost
Alas, indeed.
2 hours later…
2:53 PM
@SillyGoose Bargmann's theorem is the statement that for $G$ simply-connected and $H^2(\mathfrak{g},R) = 0$, all projective representations of $G$ lift to unitary representations of $G$. So from "projective representations of group" = "projective representations of universal cover" and Bargmann's theorem you get "projective representations of group" = "unitary representations of universal cover". What exactly are you asking?
h o n k ~
7 hours later…
10:12 PM
Regarding fock states. Is there an intuitive explanation as to why a fock state doesn't have a definite phase? Can this be shown/derived mathematically? | 1,567 | 5,797 | {"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} | 3.0625 | 3 | CC-MAIN-2024-38 | latest | en | 0.935423 |
http://sand.thewaygookeffect.com/standard-measurement-conversion-worksheets/ | 1,600,792,047,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400206329.28/warc/CC-MAIN-20200922161302-20200922191302-00068.warc.gz | 110,673,101 | 18,290 | # Standard Measurement Conversion Worksheets
## Measurement Worksheets K5 Learning
Measurement Worksheets Beginning With Size Comparisons E G Longer Vs Shorter And Measuring In Non Standard Units The Pencil Is 3 Erasers Long And Progressing To Measuring Length Weight Capacity And Temperature In Customary And Metric Units Conversion Of Measurement Units Both Within And Between The Different Measurement Systems Are Also Included Free Math Worksheets From K5 Learning No Login Required
### Metric Unit Conversion Worksheets
Trigger Some Interesting Practice Along The Way With This Huge Compilation Of Metric Unit Conversion Worksheets Comprising A Conversion Factors Cheat Sheet And Exercises To Convert Metric Units Of Length Mass Or Weight And Capacity The Resources Here Cater To The Learning Requirements Of Grade 3 Grade 4 Grade 5 And Grade 6 Our Free Sample Worksheets Are Sure To Leave Kids Yearning For
#### Standard Measurement Conversions Worksheets Kiddy Math
Standard Measurement Conversions Standard Measurement Conversions Displaying Top 8 Worksheets Found For This Concept Some Of The Worksheets For This Concept Are Measurement And Conversion Table Customary System Converting Units Of Measure Math Measurement Word Problems No Problem Lesson 11 Measurement And Units Of Measure Maths Work Third Term Measurement Grade 3 Measurement Work
##### Measurement Worksheets Free Math Worksheets
Welcome To The Measurement Worksheets Page At Math Drills Where You Can Measure Up Measure Down Or Measure All Around This Page Includes Measurement Worksheets For Length Area Angles Volume Capacity Mass Time And Temperature In Metric U S And Imperial Units Measurement Concepts And Skills Give Students The Ability To Perform Tasks Related To Everyday Life
###### U S Customary Unit Conversion Worksheets
Converting Teaspoons Tablespoons And Fluid Ounces Finds Immense Application In Our Kitchens Remember The Formula 1 Tbsp 3 Tsp And 1 Fl Oz 6 Tsps For A Hassle Free Ride Through These Worksheets 18 Worksheets Converting Cups Pints Quarts And Gallons
Customary Measuring Units Worksheets Homeschool Math
Measurement Units Worksheets Generator Use The Generator To Make Customized Worksheets For Conversions Between Measuring Units You Can Choose To Include Inches Feet Yards Miles Ounces Cups Pints Quarts Gallons Ounces Pounds Millimeters Centimeters Meters Kilometers Grams Kilograms Liters And Milliliters You Can Also Make Worksheets For The Metric System Units With The Prefixes Milli Centi Deci Deka Hecto And Kilo
Conversion Worksheets Questions And Revision Mme
Conversions Worksheets Questions And Revision Level 4 5 In This Topic Revise Worksheets Exam Questions Learning Resources Previous Topic Next Topic Conversions A Unit Is A Standard Measurement Of A Particular Quantity For Example Metres And Kilometres Are Both Units For Measuring Distance And Seconds Minutes And Hours Are All Units For Measuring Time You Will Need To Be
Standard Measurement Conversion Lesson Plans Worksheets
Find Standard Measurement Conversion Lesson Plans And Teaching Resources Quickly Find That Inspire Student Learning In This Units Of Measure Conversion Worksheet Students Use Their Problem Solving Skills To Convert The 9 Metric Measurements Listed To The Assigned Metric Units Get Free Access See Review 1 In 1 Collection Engageny Getting The Job Done Speed Work And Measurement
Free Printable Worksheets For Measuring Units Metric
Make Worksheets For Conversion Of Various Measuring Units Both Customary And Metric Units With The Generator Below You Can Choose To Include Inches Feet Yards Miles Ounces Cups Pints Quarts Gallons Ounces Pounds Millimeters Centimeters Meters Kilometers Grams Kilograms Liters And Milliliters
Grade 3 Measurement Worksheets Free Printable K5
Worksheets Math Grade 3 Measurement Grade 3 Measurement Worksheets Our Grade 3 Measurement Worksheets Are Designed To Help Students Understand Measurements Of Length Weight Capacity And Temperaturenversion Between Customary And Metric Units Is Also Reviewed
Standard Measurement Conversion Worksheets. The worksheet is an assortment of 4 intriguing pursuits that will enhance your kid's knowledge and abilities. The worksheets are offered in developmentally appropriate versions for kids of different ages. Adding and subtracting integers worksheets in many ranges including a number of choices for parentheses use.
You can begin with the uppercase cursives and after that move forward with the lowercase cursives. Handwriting for kids will also be rather simple to develop in such a fashion. If you're an adult and wish to increase your handwriting, it can be accomplished. As a result, in the event that you really wish to enhance handwriting of your kid, hurry to explore the advantages of an intelligent learning tool now!
Consider how you wish to compose your private faith statement. Sometimes letters have to be adjusted to fit in a particular space. When a letter does not have any verticals like a capital A or V, the very first diagonal stroke is regarded as the stem. The connected and slanted letters will be quite simple to form once the many shapes re learnt well. Even something as easy as guessing the beginning letter of long words can assist your child improve his phonics abilities. Standard Measurement Conversion Worksheets.
There isn't anything like a superb story, and nothing like being the person who started a renowned urban legend. Deciding upon the ideal approach route Cursive writing is basically joined-up handwriting. Practice reading by yourself as often as possible.
Research urban legends to obtain a concept of what's out there prior to making a new one. You are still not sure the radicals have the proper idea. Naturally, you won't use the majority of your ideas. If you've got an idea for a tool please inform us. That means you can begin right where you are no matter how little you might feel you've got to give. You are also quite suspicious of any revolutionary shift. In earlier times you've stated that the move of independence may be too early.
Each lesson in handwriting should start on a fresh new page, so the little one becomes enough room to practice. Every handwriting lesson should begin with the alphabets. Handwriting learning is just one of the most important learning needs of a kid. Learning how to read isn't just challenging, but fun too.
The use of grids The use of grids is vital in earning your child learn to Improve handwriting. Also, bear in mind that maybe your very first try at brainstorming may not bring anything relevant, but don't stop trying. Once you are able to work, you might be surprised how much you get done. Take into consideration how you feel about yourself. Getting able to modify the tracking helps fit more letters in a little space or spread out letters if they're too tight. Perhaps you must enlist the aid of another man to encourage or help you keep focused.
Standard Measurement Conversion Worksheets. Try to remember, you always have to care for your child with amazing care, compassion and affection to be able to help him learn. You may also ask your kid's teacher for extra worksheets. Your son or daughter is not going to just learn a different sort of font but in addition learn how to write elegantly because cursive writing is quite beautiful to check out. As a result, if a kid is already suffering from ADHD his handwriting will definitely be affected. Accordingly, to be able to accomplish this, if children are taught to form different shapes in a suitable fashion, it is going to enable them to compose the letters in a really smooth and easy method. Although it can be cute every time a youngster says he runned on the playground, students want to understand how to use past tense so as to speak and write correctly. Let say, you would like to boost your son's or daughter's handwriting, it is but obvious that you want to give your son or daughter plenty of practice, as they say, practice makes perfect.
Without phonics skills, it's almost impossible, especially for kids, to learn how to read new words. Techniques to Handle Attention Issues It is extremely essential that should you discover your kid is inattentive to his learning especially when it has to do with reading and writing issues you must begin working on various ways and to improve it. Use a student's name in every sentence so there's a single sentence for each kid. Because he or she learns at his own rate, there is some variability in the age when a child is ready to learn to read. Teaching your kid to form the alphabets is quite a complicated practice. | 1,657 | 8,645 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2020-40 | latest | en | 0.555272 |
https://www.freedomplaybypost.com/topic/12565-tech-compliance-ooc/ | 1,653,802,482,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663039492.94/warc/CC-MAIN-20220529041832-20220529071832-00611.warc.gz | 881,271,417 | 24,704 | # ooc Tech Compliance (OOC)
## Recommended Posts
It may be a little like trying to herd cats but let's try and give a little structure here, let me know who's sitting where so we can have a rough seating plan.
Heroditus had joined Octo-Ben, Leroy, and Benny, but it looks like Benny left and joined Ashley & Judy?
Ashley and Judy are together and will try and get Mia and Nick to sit with them - they do not want to sit with Claude or Octo-Ben.
Leroy'swith Benicio.
Claudes' willing to work with anybody, but it looks Mia, Micah, and Nick in the group at the moment.
Extra Effort to stunt an extra AP off Sun Dragon's Array:
Create Object 1(5ft blocks 'programmable matter', Extras: Duration 2(Permanent); Feats: Precise)[5PP]
Edited by Ari
Learned that was not how the power worked.
Nick returning to the group of Mia, Micah, and Claude was the original plan. As noted though, herding cats.
Don't leave Judy, she likes Nick!
1 hour ago, Ari said:
Extra Effort to stunt an extra AP off Sun Dragon's Array:
Create Object 1(1ft blocks 'programmable matter', Feats: Precise; Drawbacks: Progression 2(size))[1PP]
Create Object starts at [power rank] 5 ft. cubes, and Progression increases the size of the cube (10 ft., then 25, then 50, etc.). So that build would let him create one 25-ft. cube!
My B there. Need to get the Permanent Duration on there as well, but how would you diminish the size except by making a Drawback of the size Progression?
FYI Shofet, I think right now we've got Mia, Claude, and Micah at one table, and then Judy, Ashley, and (temporarily) Nick at a different table, possibly with 1-2 more.
Meanwhile, I think Leroy, Heroditus, Benny, and OctoDude are at a third table, with the latter showing us his general awesomeness form the ceiling?
• 2 weeks later...
What would be a good way to roll for properly changing the programmable matter? Idea is he's trying to make a food replicator that spits out controlled amounts of ideal versions of the materials making up the sandwich.
Just an Intelligence or Wisdom check?
Edited by Ari
Let's do Intelligence. DC10 + rank, so DC11. 11. So that's good.
Benny is sort of hovering around the Smiths.
Quote
Extra Effort to stunt an extra AP off Sun Dragon's Array:
Create Object 1(5ft blocks 'programmable matter', Extras: Duration 2(Permanent); Feats: Precise)[5PP]
Create Object is Sustained duration by default, so making it Permanent is a +0 change (+1 to go up to Continuous, -1 to add the Permanent flaw).
The Toughness and lifting Strength of the object are also limited by the power rank, so anything made with Rank 1 Create Object is going to be pretty flimsy.
Since you have 22PP to work with, here's how I'd do it:
Create Object 10 (Extras: Affects Others, Duration [Continuous]; Flaws: Action [Full], Permanent, Range [Touch]; Feats: Extended Reach [10ft], Innate, Precise, Subtle) [14PP]
That opens up our options to stuff that's potentially as strong as steel and/or strong enough to hold a fighter jet or an 18-wheeler without collapsing.
Affects Others lets him touch someone and give them the power, which is basically what he did by handing a cube to OctoBen.
Permanent (and Continuous) Created Objects don't go away when you swap to a different AP.
Innate means they won't vanish if someone counters/Nullifies your Create Object effect after the fact.
Subtle means that whatever objects they become seem "real"/"normal", not like some weird version of themselves.
Ahhhh, that does make more sense. Thanks Grumble!
• 3 weeks later...
Trying to give other folks a chance to react to Leroy's casual attempt to create a mini-black-hole before Micah speaks up again. In the meantime, who would be able to pick up the following, and in what way would it manifest for them? This is pure fluff.
1.) Trace amounts of ozone in the air/an increase in trace amounts of ozone in the air.
2.) Ionization in the air upticking a small amount. No one's hair is standing on end (yet) but if you have a sense that could pick this up it's there.
3.) Extremely weak x-ray production (lightning actually produces x-rays!).
4.) Visual acuity strong enough to notice lightning bolts a third as wide as a human hair and a quarter as long sparking up along Micah, spread out at a density of 1-2 every few square inches of his body.
Octoman's got great eyesight and superhuman smell/taste, so definitely the first one and maybe the second.
Definitely three and probably two for Vox. He'd hear the x-rays for sure, and the uptick would register similarly.
• 2 weeks later...
@Tiffany Korta Checking in because it's been 9 IC posts (including one GM post) since OctoBen basically flipped the "ON" switch. Does anything come of his attempt to turn the cube of programmable matter into the seat of an artificial intelligence? Does he need to make any rolls?
Sorry about that, will get the baby AI to life soon. In the mean time if you want to post assume the machine is still compiling for a bit.
## Create an account
Register a new account | 1,242 | 5,041 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2022-21 | longest | en | 0.925756 |
https://davidlowryduda.com/response-to-bnelo12s-question-on-reddit/?replytocom=8640 | 1,632,204,141,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057158.19/warc/CC-MAIN-20210921041059-20210921071059-00364.warc.gz | 263,208,376 | 16,102 | # Response to bnelo12’s question on Reddit (or the Internet storm on $1 + 2 + \ldots = -1/12$)
bnelo12 writes (slightly paraphrased)
Can you explain exactly how ${1 + 2 + 3 + 4 + \ldots = – \frac{1}{12}}$ in the context of the Riemann ${\zeta}$ function?
We are going to approach this problem through a related problem that is easier to understand at first. Many are familiar with summing geometric series
$\displaystyle g(r) = 1 + r + r^2 + r^3 + \ldots = \frac{1}{1-r},$
which makes sense as long as ${|r| < 1}$. But if you’re not, let’s see how we do that. Let ${S(n)}$ denote the sum of the terms up to ${r^n}$, so that
$\displaystyle S(n) = 1 + r + r^2 + \ldots + r^n.$
Then for a finite ${n}$, ${S(n)}$ makes complete sense. It’s just a sum of a few numbers. What if we multiply ${S(n)}$ by ${r}$? Then we get
$\displaystyle rS(n) = r + r^2 + \ldots + r^n + r^{n+1}.$
Notice how similar this is to ${S(n)}$. It’s very similar, but missing the first term and containing an extra last term. If we subtract them, we get
$\displaystyle S(n) – rS(n) = 1 – r^{n+1},$
which is a very simple expression. But we can factor out the ${S(n)}$ on the left and solve for it. In total, we get
$\displaystyle S(n) = \frac{1 – r^{n+1}}{1 – r}. \ \ \ \ \ (1)$
This works for any natural number ${n}$. What if we let ${n}$ get arbitrarily large? Then if ${|r|<1}$, then ${|r|^{n+1} \rightarrow 0}$, and so we get that the sum of the geometric series is
$\displaystyle g(r) = 1 + r + r^2 + r^3 + \ldots = \frac{1}{1-r}.$
But this looks like it makes sense for almost any ${r}$, in that we can plug in any value for ${r}$ that we want on the right and get a number, unless ${r = 1}$. In this sense, we might say that ${\frac{1}{1-r}}$ extends the geometric series ${g(r)}$, in that whenever ${|r|<1}$, the geometric series ${g(r)}$ agrees with this function. But this function makes sense in a larger domain then ${g(r)}$.
People find it convenient to abuse notation slightly and call the new function ${\frac{1}{1-r} = g(r)}$, (i.e. use the same notation for the extension) because any time you might want to plug in ${r}$ when ${|r|<1}$, you still get the same value. But really, it’s not true that ${\frac{1}{1-r} = g(r)}$, since the domain on the left is bigger than the domain on the right. This can be confusing. It’s things like this that cause people to say that
$\displaystyle 1 + 2 + 4 + 8 + 16 + \ldots = \frac{1}{1-2} = -1,$
simply because ${g(2) = -1}$. This is conflating two different ideas together. What this means is that the function that extends the geometric series takes the value ${-1}$ when ${r = 2}$. But this has nothing to do with actually summing up the ${2}$ powers at all.
So it is with the ${\zeta}$ function. Even though the ${\zeta}$ function only makes sense at first when ${\text{Re}(s) > 1}$, people have extended it for almost all ${s}$ in the complex plane. It just so happens that the great functional equation for the Riemann ${\zeta}$ function that relates the right and left half planes (across the line ${\text{Re}(s) = \frac{1}{2}}$) is
$\displaystyle \pi^{\frac{-s}{2}}\Gamma\left( \frac{s}{2} \right) \zeta(s) = \pi^{\frac{s-1}{2}}\Gamma\left( \frac{1-s}{2} \right) \zeta(1-s), \ \ \ \ \ (2)$
where ${\Gamma}$ is the gamma function, a sort of generalization of the factorial function. If we solve for ${\zeta(1-s)}$, then we get
$\displaystyle \zeta(1-s) = \frac{\pi^{\frac{-s}{2}}\Gamma\left( \frac{s}{2} \right) \zeta(s)}{\pi^{\frac{s-1}{2}}\Gamma\left( \frac{1-s}{2} \right)}.$
If we stick in ${s = 2}$, we get
$\displaystyle \zeta(-1) = \frac{\pi^{-1}\Gamma(1) \zeta(2)}{\pi^{\frac{-1}{2}}\Gamma\left( \frac{-1}{2} \right)}.$
We happen to know that ${\zeta(2) = \frac{\pi^2}{6}}$ (this is called Basel’s problem) and that ${\Gamma(\frac{1}{2}) = \sqrt \pi}$. We also happen to know that in general, ${\Gamma(t+1) = t\Gamma(t)}$ (it is partially in this sense that the ${\Gamma}$ function generalizes the factorial function), so that ${\Gamma(\frac{1}{2}) = \frac{-1}{2} \Gamma(\frac{-1}{2})}$, or rather that ${\Gamma(\frac{-1}{2}) = -2 \sqrt \pi.}$ Finally, ${\Gamma(1) = 1}$ (on integers, it agrees with the one-lower factorial).
Putting these together, we get that
$\displaystyle \zeta(-1) = \frac{\pi^2/6}{-2\pi^2} = \frac{-1}{12},$
which is what we wanted to show. ${\diamondsuit}$
The information I quoted about the Gamma function and the zeta function’s functional equation can be found on Wikipedia or any introductory book on analytic number theory. Evaluating ${\zeta(2)}$ is a classic problem that has been in many ways, but is most often taught in a first course on complex analysis or as a clever iterated integral problem (you can prove it with Fubini’s theorem). Evaluating ${\Gamma(\frac{1}{2})}$ is rarely done and is sort of a trick, usually done with Fourier analysis.
As usual, I have also created a paper version. You can find that here.
This entry was posted in Expository, Math.NT, Mathematics and tagged , , , , . Bookmark the permalink.
### 4 Responses to Response to bnelo12’s question on Reddit (or the Internet storm on $1 + 2 + \ldots = -1/12$)
1. Cal Harding says:
Great article! I think you may have a typo, though. The line after you mention the Basel problem, it should be gamma(1/2) = (-1/2) gamma(-1/2), as t in this case is minus half, not a half. Unless I am mistaken, of course.
Again, great job!
• David Lowry-Duda says:
Oh, you’re right! I make this mistake all the time. Thank you for the correction, and I’ve updated the article.
2. Quilan Hanniffy says:
3. David Lowry-Duda says:
I should have guessed that a post derived from reddit would garner the most spam. | 1,776 | 5,678 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2021-39 | longest | en | 0.867945 |
https://queslers.com/implement-queue-using-stacks-leetcode-solution-queslers/ | 1,702,324,539,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679516047.98/warc/CC-MAIN-20231211174901-20231211204901-00456.warc.gz | 546,428,918 | 23,578 | 304 North Cardinal St.
Dorchester Center, MA 02124
# Implement Queue using Stacks LeetCode Solution – Queslers
## Problem – Implement Queue using Stacks
Implement a first in first out (FIFO) queue using only two stacks. The implemented queue should support all the functions of a normal queue (`push``peek``pop`, and `empty`).
Implement the `MyQueue` class:
• `void push(int x)` Pushes element x to the back of the queue.
• `int pop()` Removes the element from the front of the queue and returns it.
• `int peek()` Returns the element at the front of the queue.
• `boolean empty()` Returns `true` if the queue is empty, `false` otherwise.
Notes:
• You must use only standard operations of a stack, which means only `push to top``peek/pop from top``size`, and `is empty` operations are valid.
• Depending on your language, the stack may not be supported natively. You may simulate a stack using a list or deque (double-ended queue) as long as you use only a stack’s standard operations.
Example 1:
``````Input
["MyQueue", "push", "push", "peek", "pop", "empty"]
[[], [1], [2], [], [], []]
Output
[null, null, null, 1, 1, false]
Explanation
MyQueue myQueue = new MyQueue();
myQueue.push(1); // queue is: [1]
myQueue.push(2); // queue is: [1, 2] (leftmost is front of the queue)
myQueue.peek(); // return 1
myQueue.pop(); // return 1, queue is [2]
myQueue.empty(); // return false``````
Constraints:
• `1 <= x <= 9`
• At most `100` calls will be made to `push``pop``peek`, and `empty`.
• All the calls to `pop` and `peek` are valid.
Follow-up: Can you implement the queue such that each operation is amortized`O(1)` time complexity? In other words, performing `n` operations will take overall `O(n)` time even if one of those operations may take longer.
### Implement Queue using Stacks LeetCode Solution in Java
``````class MyQueue {
Stack<Integer> input = new Stack();
Stack<Integer> output = new Stack();
public void push(int x) {
input.push(x);
}
public void pop() {
peek();
output.pop();
}
public int peek() {
if (output.empty())
while (!input.empty())
output.push(input.pop());
return output.peek();
}
public boolean empty() {
return input.empty() && output.empty();
}
}
``````
### Implement Queue using Stacks LeetCode Solution in C++
``````class Queue {
stack<int> input, output;
public:
void push(int x) {
input.push(x);
}
void pop(void) {
peek();
output.pop();
}
int peek(void) {
if (output.empty())
while (input.size())
output.push(input.top()), input.pop();
return output.top();
}
bool empty(void) {
return input.empty() && output.empty();
}
};
``````
### Implement Queue using Stacks LeetCode Solution in Python
``````class Queue(object):
def __init__(self):
"""
"""
self.inStack, self.outStack = [], []
def push(self, x):
"""
:type x: int
:rtype: nothing
"""
self.inStack.append(x)
def pop(self):
"""
:rtype: nothing
"""
self.move()
self.outStack.pop()
def peek(self):
"""
:rtype: int
"""
self.move()
return self.outStack[-1]
def empty(self):
"""
:rtype: bool
"""
return (not self.inStack) and (not self.outStack)
def move(self):
"""
:rtype nothing
"""
if not self.outStack:
while self.inStack:
self.outStack.append(self.inStack.pop())
``````
##### Implement Queue using Stacks LeetCode Solution Review:
In our experience, we suggest you solve this Implement Queue using Stacks LeetCode Solution and gain some new skills from Professionals completely free and we assure you will be worth it.
If you are stuck anywhere between any coding problem, just visit Queslers to get the Implement Queue using Stacks LeetCode Solution
Find on LeetCode
##### Conclusion:
I hope this Implement Queue using Stacks LeetCode Solution would be useful for you to learn something new from this problem. If it helped you then don’t forget to bookmark our site for more Coding Solutions.
This Problem is intended for audiences of all experiences who are interested in learning about Data Science in a business context; there are no prerequisites.
Keep Learning!
More Coding Solutions >>
LeetCode Solutions
Hacker Rank Solutions
CodeChef Solutions | 1,033 | 4,080 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2023-50 | latest | en | 0.616783 |
https://relativeathleticscores.com/2020/01/31/jason-strowbridge-ras/ | 1,590,536,238,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347391923.3/warc/CC-MAIN-20200526222359-20200527012359-00343.warc.gz | 522,861,176 | 36,827 | # Jason Strowbridge RAS
ESPN High School Recruiting
Jason Strowbridge was drafted by Dolphins with pick 154 in round 5 in the 2020 NFL Draft out of North Carolina.
He recorded a Relative Athletic Score of 9.47, out of a possible 10.0. RAS is a composite metric on a 0 to 10 scale based on the average of all of the percentile for each of the metrics the player completed either at the Combine or pro day.
He had a recorded height of 6042 that season, recorded as XYYZ where X is feet, YY is inches, and Z is eighths of an inch. That correlates to 6 feet, 4 and 2/8 of an inch or 76.25 inches, or 193.675 centimeters. This correlates to a 8.58 score out of 10.0.
He recorded a weight of 275 in pounds, which is approximately 125 kilograms. This correlates to a 1.0 score out of 10.0.
Based on his weight, he has a projected 40 yard dash time of 4.96. This is calculated by taking 0.00554 multiplied by his weight and then adding 3.433.
At the Combine, he recorded a 40 yard dash of 4.89 seconds. This was a difference of -0.07 seconds from his projected time. This forty time correlates to a 9.46 score out of 10.0.
Using Bill Barnwell’s calculation, this Combine 40 time gave him a Speed Score of 96.19.
The time traveled between the 20 and 40 yard lines is known as the Flying Twenty. As the distance is also known, we can calculate the player’s speed over that distance. The time he traveled the last twenty yards at the Combine was 2.03 seconds. Over 20 yards, we can calculate his speed in yards per second to 9.85. Taking into account the distance in feet (60 feet), we can calculate his speed in feet per second to 29.56. Breaking it down further, we can calculate his speed in inches per second to 354.68. Knowing the feet per second of 29.56, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 20.2 in the last 20 yards of his run.
At the Combine, he recorded a 20 yard split of 2.86 seconds. This correlates to a 8.8 score out of 10.0.
We can calculate the speed traveled over the second ten yards of the 40 yard dash easily, as the distance and time are both known. The time he traveled the second ten yards at the Combine was 1.14 seconds. Over 10 yards, we can calculate his speed in yards per second to 8.77. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 26.32. Breaking it down further, we can calculate his speed in inches per second to 315.79. Knowing the feet per second of 26.32, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 17.9 in the second ten yards of his run.
At the Combine, he recorded a 10 yard split of 1.72 seconds. This correlates to a 8.53 score out of 10.0.
The time he traveled the first ten yards at the Combine was 1.72 seconds. Over 10 yards, we can calculate his speed in yards per second to 6.0. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 17.0. Breaking it down further, we can calculate his speed in inches per second to 209.0. Knowing the feet per second of 17.0, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 11.6 in the first ten yards of his run.
At the Combine, he recorded a bench press of 26 repetitions of 225 pounds. This correlates to a 6.23 score out of 10.0.
At the Combine, he recorded a vertical jump of 31.0 inches. This correlates to a 8.09 score out of 10.0.
At the Combine, he recorded a broad jump of 905, which is recorded as FII or FFII . where F is feet and I is inches. This correlates to a 9.24 score out of 10.0.
At the Combine, he recorded a 5-10-5 or 20 yard short shuttle of 4.37 seconds. This correlates to a 9.54 score out of 10.0.
At the Combine, he recorded a 3 cone L drill of 7.45 seconds. This correlates to a 8.41 score out of 10.0.
This player did not record any measurements at their pro day that we were able to find. If they recorded Combine measurements, they stood on them. | 1,089 | 4,095 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-24 | latest | en | 0.976783 |
https://www.dsprelated.com/showthread/comp.dsp/65805-1.php | 1,713,463,793,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817222.1/warc/CC-MAIN-20240418160034-20240418190034-00624.warc.gz | 676,866,732 | 14,639 | Sensor fusion with Kalman filtering with different sensor sample rates?
Started by October 13, 2006
Could you explain how to combine two different measurements with two
different sample rates to make an estimate with a Kalman filter?
Lets say I have want to estimate a position and I have an eccelerometer and
something else that measures position (a radar or something). The position
(radar) measurement has a rate of 1 measurement per second and the
eccelerometer has 1000 measurements per second.
Must the 1 Hz be up sampled to 1000 Hz before the measurements are used by
the Kalman filter to estimate position? Or how does it work?
Sven wrote:
> Could you explain how to combine two different measurements with two > different sample rates to make an estimate with a Kalman filter? > > > > Lets say I have want to estimate a position and I have an eccelerometer and > something else that measures position (a radar or something). The position > (radar) measurement has a rate of 1 measurement per second and the > eccelerometer has 1000 measurements per second. > > > > Must the 1 Hz be up sampled to 1000 Hz before the measurements are used by > the Kalman filter to estimate position?
No
> Or how does it work?
Oh my. You'd have to dig a bit into Kalman filter theory, but I think you could make this work quite well. The basic idea of Kalman filtering is that you take an input, and at each time step you update your best estimate of the state vector of your system, x, and you update the covariance matrix of x, which expresses how good a measurement of x you have. The way that you derive the Kalman filtering equations is to say "Given the known covariance of the estimate that I have, the estimate, and a noisy measurement of the process, what is my new estimate, and my new covariance?" So you just do that -- but you recognize that you have one set of equations that only takes accelerometer input (no gyro?) that you implement 999 times, and another one that uses the accelerometer input and your position measurement that you implement once. I'm currently expanding my knowledge of Kalman filtering by reading "Optimal State Estimation" by Dan Simon, Wiley 2006. If you're up to understanding Kalman filtering at all it should be just the book for you. You _will_ have to extend it's results somewhat, but I think it'll be straightforward. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html | 589 | 2,613 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-18 | latest | en | 0.934486 |
https://www.physicsforums.com/threads/definition-of-discrete-subgroup-quick-q.900857/ | 1,726,553,064,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651739.72/warc/CC-MAIN-20240917040428-20240917070428-00071.warc.gz | 879,989,101 | 22,141 | # Definition of discrete Subgroup quick q
• I
• binbagsss
In summary, the statement is saying that the subset is discrete if there is an open set that contains only that one element.
binbagsss
Hello,
Just a really quick question on definition of discrete subgroup.
This is for an elliptic functions course, I have not done any courses on topology nor is it needed, and most of the stuff I can see online refer to topology alot, so I thought I'd ask here.
I need it in the complex plane
I have : A subset ##S## of a topological space is called discrete if for any ##s \in S## there is an open set ##U## s.t
## U \cap S = \{s\} ##
So can someone clarfiy this, in really simple terms please, I'm not too familiar with such notation ...
Is ##s## a single element?
So it is saying that the intersection of ##U## and ##S## is the set of elements ##{s}##, or just the element ##s##, I'm unsure what the curled brackets {} denote.
Many thanks
binbagsss said:
Hello,
Just a really quick question on definition of discrete subgroup.
This is for an elliptic functions course, I have not done any courses on topology nor is it needed, and most of the stuff I can see online refer to topology alot, so I thought I'd ask here.
I need it in the complex plane
I have : A subset ##S## of a topological space is called discrete if for any ##s \in S## there is an open set ##U## s.t
## U \cap S = \{s\} ##
So can someone clarfiy this, in really simple terms please, I'm not too familiar with such notation ...
Is ##s## a single element?
So it is saying that the intersection of ##U## and ##S## is the set of elements ##{s}##, or just the element ##s##, I'm unsure what the curled brackets {} denote.
Many thanks
The curly brackets enclose the elements of a set, in this case the set ##U \cap S##. The element ##s## is a single element (but you should be able to select it to be any element in ##S##). The statement just says that the subset is discrete if there for every ##s## in ##S## exists an open set in the topological space such that ##s## is the only element in ##S## that belongs to it.
binbagsss said:
Hello,
Just a really quick question on definition of discrete subgroup.
This is for an elliptic functions course, I have not done any courses on topology nor is it needed, and most of the stuff I can see online refer to topology alot, so I thought I'd ask here.
I need it in the complex plane
I have : A subset ##S## of a topological space is called discrete if for any ##s \in S## there is an open set ##U## s.t
## U \cap S = \{s\} ##
So can someone clarfiy this, in really simple terms please, I'm not too familiar with such notation ...
Is ##s## a single element?
So it is saying that the intersection of ##U## and ##S## is the set of elements ##{s}##, or just the element ##s##, I'm unsure what the curled brackets {} denote.
Many thanks
The brackets denote a set. ##U## and ##S## are sets, so is ##U \cap S##. In case ##S## is discrete, ##U_s \cap S = \{s\}## the set which contains exactly one element ##s##. I wrote ##U=U_s## because different ##s## result in different open neighborhoods ##U_s##.
An example for a discrete set in the complex plane is ##S=\mathbb{Z} +i\mathbb{Z}##, the knots of a lattice. Around a knot ##s##, there is a neighborhood ##U_s## without any other points of ##S##.
To emphasize the importance of how "open set" restricts the choice of ##U##, consider the vertical line ##x = 1## in the xy-plane. The set ## S## of points on that line is not discrete. Let ##U## be the set of points on the perimeter of the unit circle. Then ## U \cap S = {(1,0)} ##, which is a single point. However, the set of points on the perimeter of the unit circle is not an open set. A crude intuitive notion of an open set in the xy plane is that it is "the insides" of one or more closed geometric figures , but not including their perimeters. For example, the set of points within the unit circle is an open set. The set of points within the unit circle plus some points on the perimeter of that circle is not an open set.
With that intuition of an open set, you can appreciate the intuitive idea that if an open set "hits" the line S then it must hit it at more than one point. For example, for any ##\epsilon > 0## the interior of any circle with center ##(0,0)## and radius ## r > 1 + \epsilon## contains more than one point of the line ## S: \{(x,y): x = 1\} ##.
If we now let ##S## be the discrete set of points ##\{(1,0) ,(1,1),(1,2)\}## then for each point in ##S## we can find some circle whose interior contains only that point. (Of course, we are free to pick circles with centers different that (0,0).)
Just to say that all of this depends on the topology imposed on the original set. A topological space is not only a set, it also contains a definition of what is considered to be an open set. What Stephen just said is true for the usual topology on ##\mathbb R^n##. However, there are other choices, such as the discrete topology where any subset of the full set is an open set. In the discrete topology, any subset of the topological space would therefore be a discrete subset.
Stephen Tashi said:
Let ##U## be the set of points on the perimeter of the unit circle. Then ## U \cap S = {(1,0)} ##, which is a single point. However, the set of points on the perimeter of the unit circle is not an open set.
Okay thanks, to just to confirm my understanding, if I have understood correctly, for every point on a circle, ##s## due to it's curvature you can find a set ##U## such tthat ## U \cap S = {s} ##, but this doesn't 'count' as it's curvature also means that no other points are contained within ##U## ?
binbagsss said:
but this doesn't 'count' as it's curvature also means that no other points are contained within U ?
No, it does not work because ##U## is not an open set. The point was that for any point on the line, you cannot find an open set that contains that point but does not contain any other points on the line.
binbagsss said:
Okay thanks, to just to confirm my understanding, if I have understood correctly, for every point on a circle, ##s## due to it's curvature you can find a set ##U## such tthat ## U \cap S = {s} ##, but this doesn't 'count' as it's curvature also means that no other points are contained within ##U## ?
It doesn't have anything to do with curvature. It is just an example which happens to be curved. For any point you can always find a set ##U## such that ##U \cap S = \{s\}##. Only take ##U=\{s\}##. This doesn't mean anything.
First of all, ##U## has to be open.
This rules out my example, except in the case of a discrete topology (see post #5).
Next, the point ##s## has to be alone, i.e. no other point of ##S## lies in ##U##. It is nothing said about the points in ##U## other than ##s## is one of them. Sometimes it's the only one as in the discrete topology, and sometimes it's an entire inner area of a circle as with the metric induced topology of the Euclidean plane.
The shape of ##U## isn't important either.
It's only that open circles (as in post #4) often form a basis of the topology (as in the usual topology of ##\mathbb{R}^n##, see explanation in post #4 and #5). I gave you an example of a discrete set ##S## in the complex plane or if you like ##\mathbb{R}^2## where you can think about differently shaped ##U## (see post #3).
fresh_42 said:
It doesn't have anything to do with curvature. It is just an example which happens to be curved. For any point you can always find a set ##U## such that ##U \cap S = \{s\}##. Only take ##U=\{s\}##.
So the example of the perimenter did not count because it was taking ##U=\{s\}## only?
binbagsss said:
So the example of the perimenter did not count because it was taking ##U=\{s\}## only?
I assume we are talking about the following situation:
The topological space is the Euclidean real plane and the set ##S_1## is the perimeter of a circle and ##s## a point of ##S_1##.
Now every open set ##U## that contains ##s## has automatically another point ##s' \in S_1## in it. No matter how you shape ##U## you cannot manage to have only one perimeter point in it. The only way out would be ##U=\{s\}##, but this is not an open set in the given topology.
If we are talking about the line ##S_2=\{(x,y)\in \mathbb{R^2}\,\vert \,x=1\}## as our set, then the situation is completely the same:
Now every open set ##U## that contains ##s## has automatically another point ##s' \in S_2## in it. No matter how you shape ##U## you cannot manage to have only one line point in it. The only way out would be ##U=\{s\}##, but this is not an open set in the given topology.
This shows that neither ##S_1## nor ##S_2## are discrete (in the topology induced by the metric). Especially curvature doesn't play a role!
An example for a discrete set would be ##S_3 = \{(x,y)\in \mathbb{R^2}\,\vert \, x,y \in \mathbb{Z}\}##, the knots of the integer lattice. Here we can define for each point ##s = (x_s,y_s) \in S_3 ## a open neighborhood, i.e. open set ## U_s = \{(x,y) \in \mathbb{R^2} \,\vert \, (x-x_s)^2-(y-y_s)^2<1 \} ##, which is the inner of a unit circle with radius ##1## and center ##(x_s,y_s)##, that does not contain any other point ##s'=(x_0,y_0)## with integer coordinates, i.e. points of ##S_3##. Thus ##U_s \cap S_3 = \{s\}## for any ##s\in S_3## and ##S_3## is discrete.
The fact that I have chosen the inner area of circles for ##U_s## is obviously only, because it is convenient: to define and to prove. You may decrease the radius, or shape it differently. There are plenty of possibilities to define an open set ##U_s## which doesn't contain more than a single point ##s \in S_3## for the lattice gives us enough space to do so. All knots of the lattice are kind of alone, i.e. discrete.
binbagsss said:
Okay thanks, to just to confirm my understanding, if I have understood correctly, for every point on a circle, ##s## due to it's curvature you can find a set ##U## such tthat ## U \cap S = {s} ##, but this doesn't 'count' as it's curvature also means that no other points are contained within ##U## ?
If you are using "curvature" to mean "perimeter" then yes. But what happens in not due to the fact that the perimeter of a circle has a curved shape. For example, if we let ##U## be the triangle with vertices (0,-1),(0,1),(1,0) then the perimeter of ##U## intersects the line ##x = 1## in a single point. But you can't find a triangle whose interior (sans the perimeter) intersects the line in a single point.
## What is a discrete subgroup?
A discrete subgroup is a subgroup of a mathematical group that is made up of a finite number of elements or has a finite index. This means that the elements of the subgroup are distinct and do not overlap with each other.
## What is the difference between a discrete subgroup and a continuous subgroup?
The main difference between a discrete subgroup and a continuous subgroup is in the number of elements they contain. A discrete subgroup has a finite number of elements or a finite index, while a continuous subgroup has an infinite number of elements.
## What is the significance of discrete subgroups in mathematics?
Discrete subgroups are significant in many areas of mathematics, including group theory, number theory, and geometry. They are used to study the structure and properties of mathematical objects, and have applications in fields such as cryptography, coding theory, and physics.
## How are discrete subgroups related to lattices?
A lattice is a set of points in space that are arranged in a regular pattern. Discrete subgroups can be used to generate lattices, where the elements of the subgroup act as the basis vectors for the lattice. In this way, discrete subgroups play a crucial role in the study of crystal structures and other geometric structures.
## What are some examples of discrete subgroups?
Some examples of discrete subgroups include the integers under addition, the rational numbers under multiplication, and the rotational symmetries of a regular polygon. Other examples can be found in the study of Lie groups, which are continuous groups that can have both discrete and continuous subgroups.
Replies
11
Views
2K
Replies
16
Views
6K
Replies
1
Views
1K
Replies
5
Views
2K
Replies
1
Views
1K
Replies
5
Views
860
Replies
19
Views
2K
Replies
15
Views
2K
Replies
4
Views
952
Replies
1
Views
880 | 3,215 | 12,354 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2024-38 | latest | en | 0.91451 |
http://mathhelpforum.com/differential-equations/91047-differiential-equation-mixing-problem.html | 1,481,216,861,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541864.24/warc/CC-MAIN-20161202170901-00196-ip-10-31-129-80.ec2.internal.warc.gz | 174,912,101 | 10,838 | 1. Differiential Equation, Mixing problem
A 50 litre tank is initially filled with 10 litres pf brine solution containing 20 kg of salt. Starting from time t=0, distilled water is poured into the tank at a constant rate of 4 litres per minute. At the same time, the mixture leaves the tank at a constant rate of k^(1/2) litre per minute, where k^(1/2) >0. The time taken for overflow to occur is 20 minutes.
(a) Let Q be the amount of salt in the tank at time t minutes. Show that the rate of change of Q is given by:
dQ/dt= (-Qk^(1/2))/(10+(4-k^(1/2))t)
* k^(1/2) means square root of k,
Hence, express Q in term of t,
(b) Show that k = 4, and calculate the amount of salt in the tank at the instant outflow occurs.
(c) Sketch the graph of Q against t for 0 < t < 20
2. a.)
$\frac{dQ}{dt} = C(t) \times (- \sqrt{k})$
where $C(t)$ is the concentration of salt in the water at time $t$. Hence this states that the rate of salt loss is the concentration at time $t$ multiplied by the rate of loss of salty water volume. Now the concentration is simply the amount of salt $Q$ at time $t$ divided by the total volume of water in the tank at time $t$ so:
$
C(t) = \frac{Q}{V(t)} = \frac{Q}{10 +(4-\sqrt{k}) t}$
hence
$\frac{dQ}{dt} = -\frac{Q \sqrt{k}}{10 +(4-\sqrt{k}) t}$ .
b.)
Here you know the time taken for overflow is 20 minutes and you know the tank has total volume 50 litres so use the relationship for the volume that:
$V(t) = 10 +(4-\sqrt{k}) t$
put $V = 50$ and $t = 20$ and then solve for $k$.
Then substituting back into your original differential equation you should find
$\frac{dQ}{dt} = -\frac{Q}{5 + t}$
so
$\int_{Q_0}^{Q_f} \frac{1}{Q} \, \mathrm{d}Q = - \int_{0}^{20} \frac{1}{5+t} \, \mathrm{d}t$
where $Q_0$ is the initial amount of salt (20 kg) and $Q_f$ is the amount of salt when overflow occurs.
I think you can take it from there, right?
3. See attachment | 595 | 1,901 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2016-50 | longest | en | 0.877618 |
https://moneyfyi.wordpress.com/2013/11/24/5428/ | 1,642,993,388,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304471.99/warc/CC-MAIN-20220124023407-20220124053407-00600.warc.gz | 427,863,759 | 22,393 | Outcomes Rely On Circumstances
Some time ago I wrote about statistical tricks that can influence your thinking. In my vehicle’s owner manual I found one that I had mentioned earlier. Three out of four accidents occur within 25 miles of home. The idea in the manual being that you should use your seat-belts for short journeys.
Is this persuasive or even useful information? Given that seat-belt use is a habit, every time is best. Even backing out of the garage, then getting out to close the door, which used to fascinate my wife. Do not try to pick and choose. Seat-belts matter whenever you are in a crash. The airbags are relying on their working, for example. An airbag that hits you when you are not restrained by a seat-belt can be dangerous.
Back to the point. Should you be surprised that 3 out 4 accidents happen within 25 miles of home? Similarly should you be surprised that a majority of home accidents happen in the kitchen? Or, that if you are bitten by a dog, the most probable offender is a Labrador Retriever? Or if you are analyzing expense accounts, 30% of the amounts claimed should begin with the digit “1”?
For the first three above, this distribution occurs because most of the miles driven are within 25 miles of home, most of the time is spent in the kitchen, (could be an implement and distraction component) and the most common dog by far is the Labrador Retriever. When analyzing expectation, it is always smart to assume that the most common things will influence occurrences most often.
For example, I doubt my car is 25 miles from home more than five times a month, but it moves at least three times a day. In my case, the expectation of an accident within 25 miles of home is more like 95%. (the first 25 miles of a longer trip are still within 25 miles of home and so are the last 25 miles of that trip.)
The fourth condition, 30% of the expense reports begin with the digit 1 is less obvious. It is known as Benford’s Law. There is an excellent discussion at Wikipedia. Suffice it to say that all accountants distrust expense reports or invoices that begin with a number bigger than 3. According to Benford’s Law, 60% start with 1, 2 or 3. Most accountants are suspicious of expense reports ending in 4 zeroes. Your expectation of an unchallenged expense report that claims \$900.00 is approximately the same as the probability of Richard Nixon being elected president in 2016.
We find statistics everywhere. It pays to have a little insight before trusting them. Here is my favourite example of how statistically accurate information is misleading.
The probability of someone being struck by lightening on a golf course is about one in six million. If you know and believe that fact, the odds of being struck by lightening can become about one in ten. The difference here is that the one in six million assumes that the one strike is unexpected. If you play during a storm, the circumstances are much different and therefore so are the probabilities.
Events happen or they do not. You cannot be 90% alive after exposing yourself to a 1 in 10 risk of death. You are alive or you are not. Better to avoid the exposure than to rely on the odds to keep you safe. Just like the stock market, gold, or bonds. Prices move randomly in the short run, but the long run is based upon complex inter-relationships. You do better when you understand what circumstances create the event not just understand the summarized odds.
Don Shaughnessy is a retired partner in an international accounting firm and is presently with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario. | 822 | 3,699 | {"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} | 3.171875 | 3 | CC-MAIN-2022-05 | latest | en | 0.943232 |
https://www.coursehero.com/file/6397099/problem-set-6-solutions/ | 1,495,793,244,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608652.65/warc/CC-MAIN-20170526090406-20170526110406-00018.warc.gz | 1,069,114,871 | 24,488 | problem-set-6-solutions
# problem-set-6-solutions - Ecn 100 Intermediate...
This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: Ecn 100 - Intermediate Microeconomic Theory University of California - Davis November 27, 2010 John Parman Problem Set 6 - Solutions This problem set will not be graded and does not need to be turned in. It is intended to help you review the material from the last two weeks of lectures. Solutions to the problem set are available on Smartsite. 1. Industry Supply Suppose that there are two types of firms in a perfectly competitive market for widgets ( w ). Firms of type A have costs given by C A ( w ) = 5 w 2 + 2 w + 10. Firms of type B have costs given by C B ( w ) = 3 w 2 + 5. There are 100 firms of type A and 180 firms of type B . (a) What are the individual firm supply functions for each type type of firm ( S A ( p ) and S B ( p )? Are there any prices at which no firms produce? Are there any prices at which some firms produce but others do not? We know that a firms supply curve will be the same as the portion of the marginal cost curve that lies above the average variable cost curve. So to get the supply function we need to find the marginal cost curve and also the price at which the marginal cost curve crosses the average variable cost curve. For firm type A : MC A ( w ) = 10 w + 2 AV C A ( w ) = 5 w + 2 Now we set MC A equal to AV C A to find the shutdown point: MC A ( w ) = AV C A ( w ) 10 w + 2 = 5 w + 2 10 w = 5 w The only value of w that will solve this equation is zero. So the shutdown quantity is zero. To get the shutdown price, we just plug this quantity back into the marginal cost function: MC A (0) = 10 · 0 + 2 = 2. So the shutdown price for firm type A is \$2. Now for firm type B : MC B ( w ) = AV C B ( w ) 6 w = 3 w w = 0 2 Problem Set 6 - Solutions MC B (0) = 6 · 0 = 0 So firm type B will shut down only when price hits zero. At prices in between \$0 and \$2, firms of type B produce but firms of type A do not. Given everything we’ve calculated we can now write out the supply functions: p = 10 S A ( p ) + 2 if p ≥ 2, S A ( p ) = 0 otherwise S A ( p ) = 1 10 p- 1 5 if p ≥ 2, S A ( p ) = 0 otherwise p = 6 S B ( p ) for all p > S B ( p ) = 1 6 p for all p > (b) What is the industry supply function? Graph the industry supply function and be certain to label any kinks and all relevant slopes. For prices less than \$2, industry supply comes entirely from the 180 firms of type B . For prices greater than \$2, both firm types supply widgets. So our supply function has two parts: S ( p ) = 180 S B ( p ) = 30 p if p < 2 S ( p ) = 100 S A ( p ) + 180 S B ( p ) = 40 p- 20 if p ≥ 2 (c) Suppose that in the long run, when firms can adjust all inputs, all firms have the following cost function: C ( w ) = w 3- 20 w 2 + 110 w . The market demand for widgets is still given by D ( p ) = 1000- p . What must the price of widgets be in the long run equilibrium? How many firms will there be producing widgets?...
View Full Document
## This note was uploaded on 09/11/2011 for the course ECON 100 taught by Professor Parman during the Winter '08 term at UC Davis.
### Page1 / 11
problem-set-6-solutions - Ecn 100 Intermediate...
This preview shows document pages 1 - 3. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 991 | 3,562 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2017-22 | longest | en | 0.903592 |
http://www.infouse.com/planemath/activities/pioneerplane/jimmyintro.text.html | 1,516,281,547,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887414.4/warc/CC-MAIN-20180118131245-20180118151245-00273.warc.gz | 475,363,065 | 2,769 | Click here for Graphics Version
Click here to return to the Program Guide.
Click here to return to the PlaneMath activities main page.
Header: Jimmy Doolittle
The name's Doolittle, Lieutenant James Harold Doolittle, but you can call me Jimmy. People say I did a lot of crazy things when I was a pilot, and I suppose they're right.
For a guy who did crazy things, he sure lived a long time - 97 years!
Once I flew a Curtiss P-1 aircraft in Chile with both my ankles in casts. And in 1927, I was the first person to perform the "deadly" outside loop! Some thought I'd fall straight out of the plane. But I didn't, and I'm here to tell about it.
The thing I'm most proud of, though, was being the first person to fly a plane without looking out the window, using just the ol' instrumentation. I even designed a couple of instruments myself.
Can you imagine flying without looking out the window? Pretty radical at the time! Most pilots today can fly using only instruments if they have to, like at night or in a storm. You can thank Jimmy next time you fly to Grandma's house!
Let's take a look inside the cockpit here, and I'll show you a thing or two about "flying under the hood"--that is, flying without looking out the window.
There are a lot of dials and stuff in here that tell you what's going on with your plane. You know, though, when I made that first-ever instrument-only flight, I had only a compass, an altimeter, and a attitude indicator.
The compass tells you whether the plane is heading North, South, East or West. The compass shows letters for the cardinal headings, and numbers for every 30 degree interval, from 0 to 360. To save space, though, it drops the last zero. So what does this compass read? That's right: 0 degrees due north. You can use the compass to help you stay on course.
The attitude indicator shows you the position of your plane in relation to the horizon. (What's that? You thought it told you whether you were in a bad mood? That's a different kind of attitude. Now, listen up...) In fact, the horizontal bar splitting the screen into two parts represents the actual horizon. When you're flying, another bar appears called the banking-scale indicator. Just picture it as a miniature airplane: if its right wing is tilted up, that means it's banking, or turning to the left. And if its left wing is tilted up? That's right, it's the opposite-your plane is banking to the right.
And last, but not least, is the altimeter. This instrument tells you how high your airplane is above the ground, otherwise know as your altitude. To read the altimeter you multiply the shortest hand by 10,000, the medium hand by 1,000, and the longest hand by 100. So how high are you according to this altimeter?
That's right, 4,200 ft. Now's your chance to practice.
The upcoming activity will test your skills with the altimeter. Remember: The little hand stands for the 10,000s, the medium hand stands for the 1,000s, and the big hand stands for the 100s.
Click here to go to the Altimeter activity. Note: This game will open in a new window and only works in graphics mode. It is not accessible to screen-readers.
Click here to return to the Pioneer Plane intro. | 744 | 3,200 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2018-05 | longest | en | 0.955297 |
https://www.teacherspayteachers.com/Product/Math-Task-Boxes-for-Kindergarten-Set-1-3249782 | 1,643,464,261,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306181.43/warc/CC-MAIN-20220129122405-20220129152405-00629.warc.gz | 1,041,086,258 | 33,072 | # Math Task Boxes for Kindergarten Set 1
Katie Roltgen
16.4k Followers
K
Subjects
Standards
Resource Type
Formats Included
• PDF
Pages
86 pages
Katie Roltgen
16.4k Followers
#### Also included in
1. This is a discounted bundle of my Kindergarten Math Task Box Activities! All five of my math task box sets are included in this bundle.What are Math Task Box activities?Each set includes activities that cover four kindergarten math skill areas. There are four activities for each skill area. The b
\$20.00
\$25.00
Save \$5.00
### Description
This is a set of 16 mini math activities that can be used for independent math centers, math groups, partner work, early finishers, morning work, and much more! These hands-on activities are not thematic and can be used any time of year!
This set includes four activities for each of the following skill areas:
1) Numbers to 10
2) Numbers 11-20
3) Writing Numbers to 10
4) Writing Numbers 11-20
Each activity includes: A label card, an instruction card, the activity, and a recording page or practice page.
These activities fit into plastic photo storage boxes, pencil cases/pouches, baggies, plastic bins, etc.
This resource is not editable.
Please remember that your purchase is intended for use in one classroom only. If you intend to share with colleagues, please purchase additional licenses. Contact me for site licensing information.
Thank you!
************************************************************************
Here are more great resources!
************************************************************************
Let’s Connect!
Total Pages
86 pages
N/A
Teaching Duration
N/A
Report this Resource to TpT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TpT’s content guidelines.
### Standards
to see state-specific standards (only available in the US).
Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Understand that each successive number name refers to a quantity that is one larger.
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
Understand the relationship between numbers and quantities; connect counting to cardinality. | 563 | 2,656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-05 | latest | en | 0.865062 |
https://www.experts-exchange.com/questions/20153022/Good-coding-practice-nested-if's.html | 1,481,422,771,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543782.28/warc/CC-MAIN-20161202170903-00121-ip-10-31-129-80.ec2.internal.warc.gz | 923,148,552 | 44,623 | Solved
# Good coding practice - nested if's
Posted on 2001-07-18
268 Views
I dislike the look of nested if statements and I have been recently using a nested loop.
This also seems to me to be a bit of a bodge so I am wondering what would be the 'correct' way of doing this.
I realise that there is probably no one correct answer so the points will go to the suggestion that I like the best (or that makes most sense).
The procedure reads a line from a file and deals with the content of the line.
Then reads the next line and continues until the end of the file.
nested if:
Private Sub Command1_Click()
Dim lin As String
Dim fnum As Integer
fnum = FreeFile
Open filename For Input As #fnum
Do Until EOF(fnum)
Line Input #fnum, lin
If condition1 Then
If condition2 Then
If condition3 Then
If condition4 Then
If condition5 Then
DoStuff lin
End If
End If
End If
End If
End If
Loop
Close (fnum)
End Sub
nested loop:
Private Sub Command2_Click()
Dim lin As String
Dim ra() As String
fnum = FreeFile
Open filename For Input As #fnum
Do Until EOF(fnum)
Do While True
Line Input #1, lin
If Not condition1 Then Exit Do
If Not condition2 Then Exit Do
If Not condition3 Then Exit Do
If Not condition4 Then Exit Do
If Not condition5 Then Exit Do
DoStuff lin
Loop
Loop
Close (fnum)
End Sub
0
• 10
• 9
• 8
• +7
LVL 6
Expert Comment
ID: 6295435
If condition1 Then
If condition2 Then
If condition3 Then
If condition4 Then
If condition5 Then
DoStuff lin
End If
End If
End If
End If
End If
can become:
If (condition1) and (condition2) and (condition3) and (condition4) and (condition5) Then
doStuff lin
End if
0
LVL 5
Expert Comment
ID: 6295443
Depends on exactly what Condition1, etc. are. Sometimes, you can do this:
If condition1 And condition2 And condition3 And condition4 And condition5 Then
0
LVL 6
Expert Comment
ID: 6295445
and this:
If Not condition1 Then Exit Do
If Not condition2 Then Exit Do
If Not condition3 Then Exit Do
If Not condition4 Then Exit Do
If Not condition5 Then Exit Do
can become:
If Not(Condition1) Or Not(Condition2) Or Not(Condition3) Or Not(Condition4) Or Not(Condition5) Then Exit Do
0
LVL 5
Expert Comment
ID: 6295449
<sigh> Too slow again...
0
LVL 5
Expert Comment
ID: 6295460
<<If Not(Condition1) Or Not(Condition2) Or Not(Condition3) Or Not(Condition4) Or Not(Condition5) Then Exit Do>>
Or this:
If Not(condition1 And condition2 And condition3 And condition4 And condition5) Then Exit Do
0
LVL 7
Expert Comment
ID: 6295461
Depending on exactly what you are doing, a select case may work well. Either do a
Select Case variable
Case 1 ' or whatever
case 2
End select
or, if your conditions are more complex:
Select Case True
Case variable > 2 and blnFlag = True
Case ' etc
End select
Just be aware that if you use the second approach, even if more than one case is true, only the first will be evaluated.
Zaphod.
0
LVL 17
Author Comment
ID: 6295482
The conditions are very likely to be function calls which it may be necessary to carry out in order.
eg. if enough data exists an account may be created,if more data exists then an existing account may be updated.
I'm afraid that I find long lines hard to read/debug as well as the nested if.
0
LVL 5
Accepted Solution
ID: 6295499
I'm not really suggesting this, but I tend to use something like:
Line Input #fnum, lin
If Evaluate(line) Then DoStuff lin
Then put all the nasty stuff in a function called Evaluate or whatever's relevant. It doesn't actually get rid of the problem, but tucks it out of sight...
0
LVL 6
Expert Comment
ID: 6295529
Private Sub Command3_Click()
Dim lin As String
Dim ra() As String
fnum = FreeFile
Open FileName For Input As #fnum
Do While Not lin.EOF
Line Input #1, lin
Select Case True
Case condition1, condition2, condition3, condition4, condition5
Exit Do
Case Else
DoStuff lin
End Select
Loop
Close (fnum)
End Sub
0
LVL 28
Expert Comment
ID: 6295549
>>I'm afraid that I find long lines hard to read/debug as well as the nested if
you can put the conditions on separate lines:
If (condition1 _
And condition2 _
And condition3 _
And condition4 _
And condition 5) Then
0
LVL 5
Expert Comment
ID: 6295555
Good point, AzraSound! I always forget about that, since I personally hate it...
0
LVL 22
Expert Comment
ID: 6295694
Sometimes it's worthwhile to relegate such ugly things to the back crevices of another routine as seen below. Obviously the conditions may need to be changed depending on the expression's variables.
Private Sub Command1_Click()
Dim lin As String
Dim fnum As Integer
fnum = FreeFile
Open filename For Input As #fnum
Do Until EOF(fnum)
Line Input #fnum, lin
TryToDoStuff
Loop
Close (fnum)
End Sub
' Shove this off in a corner of the module
Private Sub TryToDoStuff(lin as String)
If condition1 Then
If condition2 Then
If condition3 Then
If condition4 Then
If condition5 Then
DoStuff lin
End If
End If
End If
End If
End If
End Sub
0
LVL 1
Expert Comment
ID: 6295726
i don't think putting all teh condition checks into one long statement is very efficient, like above...
If (condition1 _
And condition2 _
And condition3 _
And condition4 _
And condition 5) Then
as teh function has to evaluate everyone before it can make a decision where as with the nestled if statements the code will run faster cos if the first condition isn't met tehn it exits straight away and doesn't go on checking at the other conditions as above... i remember reading a long article by some guru about writing l33t fast code and this was his explanation which i fully agree with and i've tested it... i think it was from the 101 tips for vb from the vb programmers journal 2000...
so i think that your first one would be the fastest.. what type of conditions are you checking perhaps we coudl clean those up???
0
LVL 1
Expert Comment
ID: 6295730
i don't think putting all teh condition checks into one long statement is very efficient, like above...
If (condition1 _
And condition2 _
And condition3 _
And condition4 _
And condition 5) Then
as teh function has to evaluate everyone before it can make a decision where as with the nestled if statements the code will run faster cos if the first condition isn't met tehn it exits straight away and doesn't go on checking at the other conditions as above... i remember reading a long article by some guru about writing l33t fast code and this was his explanation which i fully agree with and i've tested it... i think it was from the 101 tips for vb from the vb programmers journal 2000...
so i think that your first one would be the fastest.. what type of conditions are you checking perhaps we coudl clean those up???
0
LVL 22
Expert Comment
ID: 6295773
"the function has to evaluate everyone before it can make a decision"
This is true in the current versions of VB. The VB.Net documentation indicates that this will be fixed for the .net version.
0
LVL 15
Expert Comment
ID: 6296503
my \$0.02 :-)
- This piece doesn't need "End If"
- Lines are not long
- Code is efficient (if condition1 fails, other conditions are not evaluated)
- There is no need for fake Do...Loop
If condition1 Then _
If condition2 Then _
If condition3 Then _
If condition4 Then _
If condition5 Then _
DoStuff lin: MsgBox "Hello"
0
LVL 1
Expert Comment
ID: 6296957
Select Case False
Case Condition1, Condition2, condition3, Condition4, Condition5
'Do nothing
Case Else
'do ur stuff here
DoStuff lin
End Select
0
LVL 5
Expert Comment
ID: 6296998
ameba, Nice! Very nice!
0
LVL 17
Author Comment
ID: 6297736
ameba, I think that you've hit the nail right on the head about the fake do loop.
In an old version of some Basic that I once used you were able to re-enter a For loop from any part of the block beneath it.
For c = 1 to 100
if not condition1 then next c
if not condition2 then next c
if not condition3 then next c
if not condition4 then next c
Next c
There is probably something very wrong with this as it is not possible in VB, but I think it's something like this that I am looking for.
Reading the code, if the conditions/functions are named carefully then it becomes very clear what state the program is in at each line (perhaps I should say 'statement').
0
LVL 15
Expert Comment
ID: 6297876
RobinD,
>There is probably something very wrong with this
Yes. But after few VB years you get used to it.
"One statement VB lacks is the Continue statement. There are times in the middle of a loop when you want to stop testing and just go to the next iteration in the loop. One can approximate this with nested Ifs but the logic of the nesting can quickly become quite complicated and obscure to follow."
Note that VB has nice function Switch, but it is not very efficient, since all conditions are evaluated. A workaround to NOT execute all conditions, is to use a flag. Here is the sample, but, now, those nested IFs don't look so bad. :-)
Option Explicit
Dim x As Long
Dim blnDone As Boolean
x = 5
If Switch(Condition1, 1 _
, Condition2, 2 _
, Condition3, 3 _
, Condition4, 4 _
, Condition5, 5 _
) = 5 Then
MsgBox "Hello"
End If
End Sub
Private Function Condition1() As Boolean
If blnDone Then Exit Function ' do not execute the 'meat' of the function
If x > 0 Then Condition1 = True
blnDone = True
End Function
Private Function Condition2() As Boolean
If blnDone Then Exit Function ' do not execute the 'meat' of the function
If x > 10 Then Condition2 = True
blnDone = True
End Function
Private Function Condition3() As Boolean
If blnDone Then Exit Function
If x > 20 Then Condition3 = True
blnDone = True
End Function
Private Function Condition4() As Boolean
If blnDone Then Exit Function
If x > 30 Then Condition4 = True
blnDone = True
End Function
Private Function Condition5() As Boolean
If blnDone Then Exit Function
If x > 40 Then Condition5 = True
blnDone = True
End Function
VB has also nice statements "Select Case" and "Choose", but they cannot be used here.
0
LVL 15
Expert Comment
ID: 6297893
OOPS, sorry, Switch cannot be used here. To strong sun here? :-)
0
LVL 15
Expert Comment
ID: 6298095
> If condition1 Then _
> If condition2 Then _
> If condition3 Then _
> If condition4 Then _
> If condition5 Then _
> DoStuff lin: MsgBox "Hello"
Although this piece of code satisfies all the conditions, you should not use it:
- it is a bit strange to use multiple "If...Then" in a single line (I am surprised that syntax works) and it's hard to read/understand.
0
LVL 17
Author Comment
ID: 6298143
I do feel like I'm changing the rules as I go along, I hope it doesn't look like it.
I quite liked the look of:
If condition1 Then _
If condition2 Then _
If condition3 Then _
If condition4 Then _
If condition5 Then _
DoStuff lin: MsgBox "Hello"
although I don't really like line continuation, it does exit nicely and without executing everything.
but I can't add remarks within the block.
If condition1 Then _'check name and address matches
If condition2 Then _'send emails to all your friends
DoStuff lin: MsgBox "Hello"
I do try to name my functions carefully but sometimes a little extra explanation can help.
It's not the executing of the conditions that I am trying to find an alternative for but the removal of my false do_loop.
Isn't there a limit to the depth of nested loops, I know I only put 5 conditions in there but I am looking for a general case.
I did think there may be a text-book answer as quite often you see statements like 'although this works it is bad programming practice', usually with no explanation as to why. Maybe there is a book of 'good programming practice' but I have yet to find it.
0
LVL 15
Expert Comment
ID: 6298195
> Do Until EOF(fnum)
> Do While True
> Line Input #1, lin
> If Not condition1 Then Exit Do
> If Not condition2 Then Exit Do
> If Not condition3 Then Exit Do
> If Not condition4 Then Exit Do
> If Not condition5 Then Exit Do
> DoStuff lin
> Loop
> Loop
>removal of my false do_loop.
Without Do Loop (note that most programmers don't like GOTOs):
Do Until EOF(fnum)
Line Input #1, lin
If Not Condition1 Then GoTo continue
If Not Condition2 Then GoTo continue
If Not Condition3 Then GoTo continue
If Not Condition4 Then GoTo continue
If Not Condition5 Then GoTo continue
DoStuff lin
continue:
Loop
0
LVL 17
Author Comment
ID: 6298515
aaaarrgghh!!!
0
LVL 17
Author Comment
ID: 6298603
re: aaarrggh
Sorry, you caught me by surprise there.
I suppose I am trying to GoTo without actually using the word.
The procedure's I write that use this type of nested statements are usually robotics that run through a sequence of actions usually performed by a user, the robotic just makes it easier and a lot faster for them.
Maybe I'm trying to hide the fact that it's sequential.
0
LVL 15
Expert Comment
ID: 6298752
>Private Sub Command2_Click()
>Dim lin As String
>Dim ra() As String
> fnum = FreeFile
> Open filename For Input As #fnum
> Do Until EOF(fnum)
> Do While True
> Line Input #1, lin
> If Not condition1 Then Exit Do
> If Not condition2 Then Exit Do
> If Not condition3 Then Exit Do
> If Not condition4 Then Exit Do
> If Not condition5 Then Exit Do
> DoStuff lin
> Loop
> Loop
> Close (fnum)
>End Sub
I think this is a bit better:
Private Sub Command2_Click()
Dim lin As String
Dim ra() As String
fnum = FreeFile
Open filename For Input As #fnum
Do Until EOF(fnum)
Line Input #1, lin
Do
If Not condition1 Then Exit Do
If Not condition2 Then Exit Do
If Not condition3 Then Exit Do
If Not condition4 Then Exit Do
If Not condition5 Then Exit Do
DoStuff lin
Exit Do
Loop
Loop
Close (fnum)
End Sub
0
LVL 15
Expert Comment
ID: 6298795
or something like this (uses For...Next Loop instead of Do...Loop):
Line Input #1, lin
For i = 1 To 5
Select Case i
Case 1
If Not Condition1 Then Exit For
Case 2
If Not Condition2 Then Exit For
Case 3
If Not Condition3 Then Exit For
Case 4
If Not Condition4 Then Exit For
Case 5
If Not Condition5 Then Exit For
DoStuff lin
End Select
Next
0
LVL 17
Author Comment
ID: 6299089
ameba,
re: >I think this is a bit better:
My mistake, I actually do a function call for the outer loop along the lines of:
myObject deals with opening/closing the file, what type of file it is, rem lines etc.
(hiding the nasty stuff)
I just threw the example together without noticing where line input should have gone.
well spotted.
I'm going to have to award some points for this soon and so far I've seen two offers that interest me.
KDivad's >I'm not really suggesting this, but
(hide all the nasty bit's)
but why are you not suggesting it ?
and
ameba's >Although this piece of code satisfies all the conditions, you should not use it:
if _
if _
if _
why shouldn't I use it?
0
LVL 5
Expert Comment
ID: 6299122
<<but why are you not suggesting it ?>>
Because your question seemed to indicate that you wanted to remove that bit of code, not just hide it. And now that you say MyObject hides all the nasty reading stuff, I would have thought you'd have already thought of this.
0
LVL 17
Author Comment
ID: 6299237
Where there is no 'right' answer and I just decide which answer I like best, a suggestion that goes along the lines of the way I tend to code looks like a good one.
MyObject hides some nasty stuff, but you want to see the multitude of sins that lie beneath conditions 1 to n.
Thanks for the reply I just wondered if this was a very bad way of doing things - at least I'm not the only one :7).
0
LVL 22
Expert Comment
ID: 6299252
One thing that should be considered in any "tricky" coding is future readability and maintainability.
Although the single-line multi-IF split at line-breaks looks good, it would initially confuse most programmers. Plus, since you can't add comments, that further enhinders the ability to clear up what you're doing.
The nested IF blocks get complicated, but are at least commonly accepted as an extension of what we already do with simple nested IF blocks.
I re-iterate that if the IF block is that complicated, it may be worthwhile breaking off a chunk and dropping it into a subroutine or maybe even a function.
If condition1 _
And condition2 _
And condition3 _
And condition4 _
And condition5 Then
DoThis
End If
I suppose it's essentially the same as using the If-Then-If-Then except that it includes the endif that gives me a good feeling (confirmation) that I've actually come to the end of this mess.
0
LVL 15
Expert Comment
ID: 6299328
RobinD,
>why shouldn't I use it?
rspahitz wrote >Although the single-line multi-IF split at line-breaks looks good, it would initially confuse most programmers.
Yes, this is the reason. Most projects are reviewed or programmed by more programmers.
And reading is done many, many times (10x) more then writing. It is good idea to invest in readability.
0
LVL 17
Author Comment
ID: 6299362
Thanks ameba,
I quite like the look of your:
For i = 1 To 5
Select Case i
...
although I think it would be a bit of a fright to step through, I'm sure it will come in useful one day. I've never thought of directly generating the case condition like this.
I've decided to award the points to KDivad as it was an early answer and neatly replaces the false loop with a function call.
ameba - thanks for all your suggestions, look out for a 'points for' as soon as I get one in there.
0
LVL 5
Expert Comment
ID: 6299599
<surprised>
I also like the look of ameba's For...Next idea. Not sure I'd ever use it, but it does look ingenius.
0
LVL 6
Expert Comment
ID: 6301195
I have the best solution:
Call DoJob
:-)
0
LVL 5
Expert Comment
ID: 6303225
Short. To the point.
<grin>
0
LVL 22
Expert Comment
ID: 6303376
Yup, but ultimately it comes back to the accepted solution: hide it in a corner somewhere.
0
LVL 5
Expert Comment
ID: 6303403
Sure does. Just depends on how much of the code Robin is willing to (and can) hide.
0
LVL 17
Author Comment
ID: 6307445
The primary purpose of this was to create some readable, easy to step-through code in a 'good coding-practice' way.
The nearest I had got to this was by using my fake do-loop.
It works quite well, you can step through the different procedures and each one does it's own little bit in it's own little way.
The only sore thumb was the do-loop.
KDivad's suggestion placed the contents of the loop in a function - same thing happens, except that you get a perfectly valid 'Exit Function' in place of exit for.
Actually I hadn't thought of this as the procedures that are called are so high level that shoving them down a step just hadn't crossed my mind.
It's not so much about hiding code (It all has to be there for something or I wouldn't have put it in.) as keeping code that does things with other code that does similar things and giving it all access to common procedures where necessary.
I just wondered if there was a 'right' way to do it. If there is this may be it.
0
## Featured Post
Have you ever wanted to restrict the users input in a textbox to numbers, and while doing that make sure that they can't 'cheat' by pasting in non-numeric text? Of course you can do that with code you write yourself but it's tedious and error-prone …
Enums (shorthand for ‘enumerations’) are not often used by programmers but they can be quite valuable when they are.  What are they? An Enum is just a type of variable like a string or an Integer, but in this case one that you create that contains…
Get people started with the process of using Access VBA to control Outlook using automation, Microsoft Access can control other applications. An example is the ability to programmatically talk to Microsoft Outlook. Using automation, an Access applic…
Get people started with the utilization of class modules. Class modules can be a powerful tool in Microsoft Access. They allow you to create self-contained objects that encapsulate functionality. They can easily hide the complexity of a process from… | 5,269 | 20,190 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2016-50 | longest | en | 0.682582 |
https://www.reference.com/math/can-calculator-programmed-list-numbers-least-greatest-bab31d761ef798fd | 1,481,047,102,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541950.13/warc/CC-MAIN-20161202170901-00360-ip-10-31-129-80.ec2.internal.warc.gz | 999,773,526 | 20,360 | Q:
# How can a calculator be programmed to list numbers from the least to the greatest?
A:
In order to sort numbers in ascending order, you first press the calculator's STAT key. You then press the number two on the number pad to select sorting in ascending order.
## Keep Learning
After making your selection, enter the name of the list you want to sort by pressing the "2nd" key and then the number one followed by the right arrow key, the up arrow key and then the enter key. Press the letter "L" before entering the list name so that the calculator knows that it is accessing a list data type. The next step is to enter a right parentheses, and then press the enter key. This sorts the list. To view the sorted list on the viewing screen, press STAT followed by the number one.
This method requires that the lists you are sorting have already been defined and stored in the calculator's memory. If you wish to sort a list in descending or decreasing order, select the number three instead of two after pressing the STAT key the first time. It is also possible to sort multiple lists at the same time by entering each list name separated by a comma instead of just one list name.
Sources:
## Related Questions
• A: A calculator helps people perform tasks that involve adding, multiplying, dividing or subtracting numbers. For example, people use calculators to help them... Full Answer >
Filed Under:
• A: A least common multiple calculator is a calculator that finds the lowest common integer divisible by two or more numbers, shows Calculator Soup. Alcula.com... Full Answer >
Filed Under:
• A: In order to use an online calculator to convert square feet to linear feet, two basic measurements must be known. The first is the width in inches of the m... Full Answer >
Filed Under:
• A: To solve an equation with a calculator that is programmed with the order of operations, enter the exact equation and press the solve or equal button. If th... Full Answer >
Filed Under: | 414 | 1,985 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2016-50 | longest | en | 0.873705 |
https://community.intel.com/t5/FPGA-SoC-And-CPLD-Boards-And/High-speed-precision-ADA-card/td-p/271897 | 1,726,519,870,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651710.86/warc/CC-MAIN-20240916180320-20240916210320-00420.warc.gz | 164,666,206 | 45,447 | FPGA, SoC, And CPLD Boards And Kits
FPGA Evaluation and Development Kits
6098 Discussions
## High speed precision ADA card
Honored Contributor II
1,740 Views
Hello
I'm gonna use "Cyclone V GX starter kit" + "Highspeed AD/DA Card"
http://www.terasic.com.tw/cgi-bin/page/archive.pl?language=english&categoryno=73&no=278
I need to the "Highspeed AD/DA Card" schematic or
How much the input & output impedance of the ADA card?
best regards
9 Replies
Honored Contributor II
923 Views
since I want to design an amplifier to amplify the out of ADA card plz help me!
Honored Contributor II
923 Views
--- Quote Start ---
Hello
I'm gonna use "Cyclone V GX starter kit" + "Highspeed AD/DA Card"
http://www.terasic.com.tw/cgi-bin/page/archive.pl?language=english&categoryno=73&no=278
I need to the "Highspeed AD/DA Card" schematic or
How much the input & output impedance of the ADA card?
best regards
--- Quote End ---
Schematic is not present on documentation on board relative CD you can download from terasic site?
Input output impedance is usually set to 50 Ohm as a standard for all high frequency application and or RF if not specified for a different value.
Regards
Honored Contributor II
923 Views
--- Quote Start ---
since I want to design an amplifier to amplify the out of ADA card plz help me!
--- Quote End ---
Card provide a 2Vpp over 50Ohm so power can be calculated: 1Vpeak is equivalent to RMS sqrt of 2, power is square of voltage divided by impedance so 2/50 or 40mW .
Converting 40mW to dBW get a result of -14dBW
select an amplifier from the one meet the level you need.
regards
Honored Contributor II
923 Views
Hello
How much the minimal voltage sensitivity of the ADA card? logically it should be Vref/(2^14) but practically?
Due to 2 ch 65MSPS ADC on the ADA card, How much time can I record two signals? I know most of Altera FPGA Boards have maximum 1GB RAM capacity...
so what should I do if I want to record two signals for a few seconds?
I really need your help and I want to handle my project with Altera Cyclone V+Terasic Tech ADA card
Regards
Honored Contributor II
923 Views
Hi,
record signals to do what?
Still after long time you ask help without explain what is in your mind so we cannot open to see in it your goal...
Record signals at what speed, what type of analysis is to be performed on and
how fast they are and noise level too are unknown.
about sensitivity again is impossible to answer before all parameter involved in a measure are on desk.
Sorry to be so evasive at your eye but at my side I don't see too many details only you know.
Regards
Honored Contributor II
923 Views
--- Quote Start ---
Hi,
record signals to do what?
Still after long time you ask help without explain what is in your mind so we cannot open to see in it your goal...
Record signals at what speed, what type of analysis is to be performed on and
how fast they are and noise level too are unknown.
about sensitivity again is impossible to answer before all parameter involved in a measure are on desk.
Sorry to be so evasive at your eye but at my side I don't see too many details only you know.
Regards
--- Quote End ---
I asked from Terasic Technical support they told me the minimum voltage sensitivity of the ADA board is Vref/(2^14)
I want to sample two signals at the rate 30MHz or 50Mhz maximum and then apply Sliding FFT or Wavelet on them.
but I know I should design a good interface for the ADA card.
now my main problem is:
I want to save sampled data on the SDRAM and then transfer them and FFT results to my laptop.
How can I do it? I don't want to use Linux. How can I manage the SDRAM and USB and Ethernet connection?
if I want to buy Cyclone V Starter board, can I do all? is there any prepared IP cores for managing SDRAM or USB for Nios soft processor?
thanks
Honored Contributor II
923 Views
Hi, 50MHz on two stream of 14 bit sound as 1.4 Gbps, so it is also difficult to sustained stream data to pc. not in some way compressed GigaLan has not enough bandwidth and also USB3 get saturated too.
If you accept sample some data then do FFT and Wavelet on chunk then you can transfer data to pc to do some postprocessing.
So how long is sample to process from FFT, how many FFT point and how is wavelet applied to?
RAW data has to be transferred to pc also?
Cyclon V can manage this but the best is SOC with dual core ARM, if you wish to manage real time data processing forget Windows ( I HATE due is not real multitask nor SMP) and use task spreading from Linux platform or other embedded OS.
ALso to do multiple transfer you need split process on thread and use one processor core, Nios can be used to manage task on low level as register programming and DMA coordination on FPGA fabric side.
NOt sure this is the best but again too many details are missing.
Regards
Roberto
Honored Contributor II
923 Views
--- Quote Start ---
Hi, 50MHz on two stream of 14 bit sound as 1.4 Gbps, so it is also difficult to sustained stream data to pc. not in some way compressed GigaLan has not enough bandwidth and also USB3 get saturated too.
If you accept sample some data then do FFT and Wavelet on chunk then you can transfer data to pc to do some postprocessing.
So how long is sample to process from FFT, how many FFT point and how is wavelet applied to?
RAW data has to be transferred to pc also?
Cyclon V can manage this but the best is SOC with dual core ARM, if you wish to manage real time data processing forget Windows ( I HATE due is not real multitask nor SMP) and use task spreading from Linux platform or other embedded OS.
ALso to do multiple transfer you need split process on thread and use one processor core, Nios can be used to manage task on low level as register programming and DMA coordination on FPGA fabric side.
NOt sure this is the best but again too many details are missing.
Regards
Roberto
--- Quote End ---
Only 1 sec RAW DATA is enough
I don't want to work with Linux bcoz I'm not expert in Linux.. I think it takes long time to learn it
some experts in Xilinx SOC have told me you can manage the RAM and USB with SOC easily without Linux. also told me SOC is better than Microblaze (is similar to Altera Nios)
I'm a master student, All of my time is 7 month.
DE-1 SOC board has only 512MB DDR3 RAM on the HPS and 64MB on the FPGA side
Arria V GX Starter board has 256MB DDR3 RAM but has lots of resources.
Cyclone V GX Starter board has 512MB LPDDR2
my main problem:
which board is better?.. I need an "USB device port" or "Ethernet port" for transferring data to my laptop
I know transferring the data over them needs IP core or writing some codes in FSM
which one is better and easier? Nios or SOC (without Linux)
ps: if I want to process on the FPGA I have to process 4096 point FFT or Continues Wavelet on the sampled data. Continues Wavelet needs Huge Convolution process.
or I can transfer the RAW DATA to my laptop (2x50Mx2Byte=200Mbyte) and then apply the FFT or wavelet on them by Matlab.
Honored Contributor II
923 Views
Ok, I assume after 1 second sampling all stop there so data chunk is not so large and 64MB of ram are useful as buffer to store on main memory.
Final data is large 50Ms * 4 Byte -> about 200MB
I don't see simple solution other than use Linux to manage data stream and also apply some software, 4096 point can be stored on fast FPGA memory as dual port, then changed to new sample by DMA, output buffer must be transferred away before restart a new FFT computation, this on Cyclon has no trouble and you can allocate multiple buffer then use main memory as storage.
I don't see simple solution only using IP cores and Linux you state is difficult help a lot, program to transfer streaming to network or USB is not so complicated and can be debugged without touching hardware on FPGA fabric.
I am using Linux on PC as main development and is faster on compilation, before Intel acquisition was more than 10 times faster, I am using Linux on SOC due I developed all network communication and software emulation on this platforn, I don't wish use windows is slow and cumbersome to have working software in it.
Again you can simply allocate buffers then transfer by ftp or storage sharing or some other simple way ffrom Linux domain. If you don't have a support managing TCPIP or USB I suspect generate a big nightmare.
You can find a lot of help on Linux, if your data can be transferred with some time try also evaluate interface Raspberry PI to FPGA and avoid use the complexity of DE1-SOC environment.
De1-SOC has 1GB of ram not 512K organized as two devices 16x512 so you can feed both devices with the stream from both channel in parallel as 32 bit.
http://www.terasic.com.tw/cgi-bin/page/archive.pl?language=english&categoryno=205&no=836&partno=2
Regards | 2,106 | 8,841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-38 | latest | en | 0.854232 |
https://aptitudequestions.net/aptitude-questions-indices-surds/ | 1,632,617,029,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057787.63/warc/CC-MAIN-20210925232725-20210926022725-00292.warc.gz | 166,479,803 | 10,454 | Select Page
# Indices & Surds
## GETTING STARTED
### Key properties of Indices are as follows:
1 .
eg. 2 -1 = 1/2
2. am x an = am+n
eg. a =3, m=4, n=2.
[For simplicity, we are considering m and n to be integers. They can be any numbers- negative, irrational]
34 x 32 = 81 x 9
= 729
= 36
34 x 3 = 3 (4+2) = 3 6
3 .
eg. a = 6, m = 2, n=3
= 6 -1 = 1/6
4. (am)n = am.n
eg. a = 3, m = 2, n=3
(32)3 = 93 = 729
= 36
= 32×3
Note: a mn and (am) are not the same.
In a mn power of a is mn ,
whereas for (am)n it is m.n
Eg.
3 23 = 38 whereas
(32)3 = 32 x 32 x 32
= 32+2+2
= 36
In the first case, the power is 2 raised to 3, whereas in the second case is 2 times 3.
5. (a.b)n = an. bn
eg.
Let a =13, b = 12, n =2
(13.12)2 = 132 . 122
= 169 x 144
= 24336
6. ( a b) n = a n b n
Eg. a = 6, b =2, n=3
( 62)3 = 6323
= 216 / 27
= 8
7. a0 = 1
SURDS
We have seen in numbers that the number of form p/q where p and q are integers and q ≠ 0, then p/q is a rational number.
☛ Surds are irrational numbers that are left in root form (√ ) so as to denote the exact value. They are of the form n √a where a is a rational number and n is a positive number.
Eg. √7 , 3√5
☛If bn = a, then n√a = b
n√a denotes nth root of a.
Nth root of a number, a is written as n√a or a1/n
If n is not mentioned, then it is square root of the given number.
Laws of surds:
1. n√a = a1/n
Eg.
√16 = 16 1/2
= 4
2. n√ (a.b) = n√ a x n√ b
eg. 3√ 39 = 3√3 . 3√13
3 .
Eg.
4. (n√a)n = a
Eg. 4√(81)4 = 81
5.
= (a1/n) 1/m
= a1/m.n
eg.
6. (n√a)m = (n√am)
eg. (3√3)4 = (3√81) | 745 | 1,636 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2021-39 | longest | en | 0.64419 |
https://www.jiskha.com/questions/801692/A-student-moves-a-box-of-books-down-the-hall-by-pulling-on-a-rope-attached-to-the | 1,537,841,761,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267160853.60/warc/CC-MAIN-20180925004528-20180925024928-00302.warc.gz | 781,512,608 | 4,659 | # physics
A student moves a box of books down the hall
by pulling on a rope attached to the box. The
student pulls with a force of 173 N at an angle of 27.5 above the horizontal. The box has a
mass of 27 kg, and μk between the box and
the floor is 0.2.
The acceleration of gravity is 9.81 m/s2 .
Find the acceleration of the box.
Answer in units of m/s2
1. Divide the net horizontal forward force by the mass.
[173cos27.5 -(M*g -173sin27.5)*ìk]/M = a
M = 27 kg
ìk = 0.2
g = 9.81
Solve for a.
posted by drwls
2. -0.232 m/s^2
posted by Anonymous
## Similar Questions
1. ### Physics
A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 179 N at an angle of 29.8 ◦ above the horizontal. The box has a mass of 42.2 kg, and µk between the
2. ### Physics
1.A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 181 N at an angle of 20.8◦ above the horizontal. The box has a mass of 40.3 kg, and μk between the box
3. ### physics
A student pulls on a rope attached to a box of books and moves the box down the hall. The student pulls with a force of 182N at an angle of 25° above the horizontal. The box has a mass of 35kg and &mu k between the box and the
4. ### college physics
A student moves a box of books by attaching a rope to the box and pulling with a force of 80.0 N at angle of 45o. The box of books has a mass of 25.0 kg and the coefficient of kinetic friction between the bottom of the box and the
5. ### physics
At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F = 88.9 N at an angle of 56◦ , as shown in the figure. The acceleration of gravity is 9.8 m/s
6. ### physics
At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F=86.4 N at an angle of 64 degree. The acceleration of gravity is 9.8 m/s^2. The box of books has a
7. ### Physics
At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of 92 N at an angle of 30 as shown in the figure below. The box of books has a mass of 22.0 kg, and the
8. ### Physics
At the beginning of a new school term, a student moves a box of books by attaching a rope to the box and pulling with a force of F = 84.4 N at an angle of 64degrees. The acceleration of gravity is 9.8 m/s/s. The box of books has a
9. ### Physics
A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 130 N at an angle of 30.0° above the horizontal. The box has a mass of 24.0 kg, and the
10. ### Physics
A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 100.0 N at an angle of 25.0° above the horizontal. The box has a mass of 25.0 kg, and the
More Similar Questions | 867 | 3,030 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2018-39 | latest | en | 0.91215 |
https://www.answers.com/Q/Write_an_addition_sentence_and_a_multiplication_sentence_to_show_equal_rows | 1,716,358,976,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058531.78/warc/CC-MAIN-20240522040032-20240522070032-00522.warc.gz | 576,204,765 | 48,052 | 0
# Write an addition sentence and a multiplication sentence to show equal rows?
Updated: 9/26/2023
Wiki User
7y ago
Be notified when an answer is posted
Earn +20 pts
Q: Write an addition sentence and a multiplication sentence to show equal rows?
Submit
Still have questions?
Related questions
### Write a multiplication sentence with a product of -18?
As for example the product of -6 and 3 is equal to -18.
### Is multiplication before division in order of operations?
"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction." Therefore multiplication and division are equal.
3+4
181
181
### What 5 numbers equal 200?
There are infinitely many possible answers: Addition: 1,1,1,1,196 1,1,1,2,195 -1,-1,-1,-3,206 and so on. Or multiplication: 1,1,1,1,200 0.1,0.1,0.1,0.1,2000000 and so on. It is also possible to have combinations of addition and multiplication: eg 4*5 + 4*5*9 And then there are functions other than addition and multiplication.
12
### How do you write a multiplication sentence?
Here are some examples: Two multiplied by two has four as its product. Two times two is equal to four. 2*2 = 4. 2 X 2 = 4.
### Does a positive and negative equal a positive?
Mathematically it can vary if addition/subtraction. If it's multiplication/division, then it's always negative.
3 * (2 + 1) = 9
### What does one-fourth one sixth one third equal to?
Addition, subtraction, multiplication or division? If addition, then 1/4 + 1/6 + 1/3 = 3/4
### How do you turn 7 8 into a number sentence?
To turn "7 8" into a number sentence, we need to know the mathematical operation to be performed between the numbers. Depending on the operation, the number sentence could be different. For example, if the operation is addition, the number sentence would be "7 + 8." If the operation is multiplication, it would be "7 * 8." | 508 | 1,900 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-22 | latest | en | 0.922369 |
https://discuss.codechef.com/t/happy-numbers-editorial/99780 | 1,653,607,713,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00529.warc.gz | 265,581,028 | 5,075 | # HAPPY NUMBERS - EDITORIAL
Practice
Author: Siddharth Jha
Tester: Siddharth Jha
Editorialist: Siddharth Jha
CAKEWALK
# PREREQUISITES:
Binary Exponentiation
# PROBLEM:
Find the Nth number of the sequence 1,3,7,15… as the numbers can be very large mod it with 998244353.
# QUICK EXPLANATION:
The Nth number of the sequence would be 2^N - 1
# SOLUTIONS:
Setter's Solution
//Siddharth Jha
#include<bits/stdc++.h>
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/tree_policy.hpp>
//#include <ext/pb_ds/trie_policy.hpp>
//using namespace __gnu_pbds;
using namespace std;
//typedef tree<ll, null_type, less, rb_tree_tag, tree_order_statistics_node_update> pbds;
//typedef trie<string,null_type,trie_string_access_traits<>,pat_trie_tag,trie_prefix_search_node_update> pbtrie;
#define ll long long int
#define mod 998244353
#define inf 1e18
#define pb push_back
#define vi vector
#define vs vector
#define pii pair<ll,ll>
#define ump unordered_map
#define mp make_pair
#define pq_max priority_queue
#define pq_min priority_queue<ll,vi,greater >
#define all(n) n.begin(),n.end()
#define ff first
#define ss second
#define mid(l,r) (l+(r-l)/2)
#define bitc(n) __builtin_popcount(n)
#define SET(a) memset( a, -1, sizeof a )
#define CLR(a) memset( a, 0, sizeof a )
#define Pi 3.141592653589793
#define loop(i,a,b) for(int i=(a);i<=(b);i++)
#define looprev(i,a,b) for(int i=(a);i>=(b);i–)
#define _fast ios_base::sync_with_stdio(0); cin.tie(0);
#define iter(container,it) for(__typeof(container.begin()) it = container.begin(); it != container.end(); it++)
#define log(args…) {string _s = #args; replace(_s.begin(), _s.end(), ‘,’, ’ '); stringstream _ss(_s); istream_iterator _it(_ss); err(_it, args); }
#define logarr(arr,a,b) for(int z=(a);z<=(b);z++) cout<<(arr[z])<<" ";cout<<endl;
template T gcd(T a, T b){if(a%b) return gcd(b,a%b);return b;}
template T lcm(T a, T b){return (a*(b/gcd(a,b)));}
vs tokenizer(string str,char ch) {std::istringstream var((str)); vs v; string t; while(getline((var), t, (ch))) {v.pb(t);} return v;}
void err(istream_iterator it) {}
template<typename T, typename… Args>
void err(istream_iterator it, T a, Args… args) {
cout << *it << " = " << a << endl;
err(++it, args…);
}
ll binpow(ll a, ll b, ll m) {
a %= m;
ll res = 1;
while (b > 0) {
if (b & 1)
res = res * a % m;
a = a * a % m;
b >>= 1;
}
return res;
}
void solve() {
ll n;
cin >> n;
cout << (binpow(2,n,mod) - 1 + mod)%mod << “\n”;
}
int main(int argc, char const *argv[]){
_fast
#ifndef ONLINE_JUDGE
freopen(“input.txt”, “r”, stdin);
freopen(“output.txt”, “w”, stdout);
#endif
ll t; cin>>t;
while(t–){
solve();
}
return 0;
} | 835 | 2,634 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2022-21 | latest | en | 0.317791 |
https://readpaper.com/paper/4852447855700344833 | 1,709,147,273,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474744.31/warc/CC-MAIN-20240228175828-20240228205828-00085.warc.gz | 478,741,467 | 10,576 | This website requires JavaScript.
# Constructive mathematics with the predicate of the current mathematical knowledge
Feb 2024
0被引用
0笔记
We assume that the current mathematical knowledge $K$ is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any formal theorem of any mathematician from past or present forever belongs to $K$. We assume that mathematical sets are atemporal entities. They exist formally in $ZFC$ theory although their properties can be time-dependent (when they depend on $K$) or informal. The true statement "$K$ is non-empty" is outside $K$ because $K$ is not a formal set. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a statement depends on time, but the statement does not refer to time. Thus, every statement in $K$ does not refer to time. Paul Cohen proved in $1963$ that the equality $2^{\aleph_0}=\aleph_1$ is independent of $ZFC$. Before $1963$, the false statement "There is a known constructively defined integer $n \geq 1$ such that $2^{\aleph_0}=\aleph_n$" was outside $K$. Since $1963$, this statement is outside $K$ forever. The true statement "There exists a set $X \subseteq \{1,\ldots,49\}$ such that ${\rm card}(X)=6$ and $X$ never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside $K$. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in $ZFC$ and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets $X \subseteq {\mathbb N}$ that belong to constructive and informal mathematics and refer to the current mathematical knowledge on $X$.
AI理解论文&经典十问 | 447 | 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10 | latest | en | 0.921217 |
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=1081 | 1,561,421,148,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999779.19/warc/CC-MAIN-20190624231501-20190625013501-00311.warc.gz | 5,887,658 | 2,889 | Welcome to ZOJ
Problem Sets Information Select Problem Runs Ranklist
ZOJ Problem Set - 1081
Points Within
Time Limit: 2 Seconds Memory Limit: 65536 KB
Statement of the Problem
Several drawing applications allow us to draw polygons and almost all of them allow us to fill them with some color. The task of filling a polygon reduces to knowing which points are inside it, so programmers have to colour only those points.
You're expected to write a program which tells us if a given point lies inside a given polygon described by the coordinates of its vertices. You can assume that if a point is in the border of the polygon, then it is in fact inside the polygon.
Input Format
The input file may contain several instances of the problem. Each instance consists of: (i) one line containing integers N, 0 < N < 100 and M, respectively the number of vertices of the polygon and the number of points to be tested. (ii) N lines, each containing a pair of integers describing the coordinates of the polygon's vertices; (iii) M lines, each containing a pair of integer coordinates of the points which will be tested for "withinness" in the polygon.
You may assume that: the vertices are all distinct; consecutive vertices in the input are adjacent in the polygon; the last vertex is adjacent to the first one; and the resulting polygon is simple, that is, every vertex is incident with exactly two edges and two edges only intersect at their common endpoint. The last instance is followed by a line with a 0 (zero).
Output Format
For the ith instance in the input, you have to write one line in the output with the phrase "Problem i:", followed by several lines, one for each point tested, in the order they appear in the input. Each of these lines should read "Within" or "Outside", depending on the outcome of the test. The output of two consecutive instances should be separated by a blank line.
Sample Input
3 1
0 0
0 5
5 0
10 2
3 2
4 4
3 1
1 2
1 3
2 2
0
Sample Output
Problem 1:
Outside
Problem 2:
Outside
Within
Source: South America 2001
Submit Status | 484 | 2,074 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-26 | latest | en | 0.897983 |
http://www.freemathhelp.com/forum/archive/index.php/t-43779.html | 1,398,009,344,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00317-ip-10-147-4-33.ec2.internal.warc.gz | 426,544,761 | 1,818 | PDA
View Full Version : Help! (r varies jointly with s and t; r = 180 when...)
oryanzmommy1
05-11-2006, 10:01 PM
i ran into a problem and i couldnt get it...i was clue less...i dont know how the problem is suppose to be set up or anything...HELP!!! here is the problem it gives me...
Suppose r varies jointly with s and t, and r=180 when s=3 and t=12. Find r when s=8 and t=20
tkhunny
05-11-2006, 10:54 PM
r varies jointly with s and tThese words should ring in your head. Whenever you see them, don't even keep reading the problem. Stop! Write down "r = k*s*t". THEN go back and read the rest of the problem statement.
oryanzmommy1
05-11-2006, 11:31 PM
ok thank you
tkhunny
05-12-2006, 12:20 AM
The next step is to find 'k', the "constant of proportionality". This can be done by substituting all the values given in the problem statement. It MUST give you a complete set.
oryanzmommy1
05-12-2006, 01:13 PM
ok thank you | 290 | 927 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2014-15 | latest | en | 0.902002 |
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-17-problems-page-654/39 | 1,568,600,284,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514572471.35/warc/CC-MAIN-20190916015552-20190916041552-00302.warc.gz | 878,439,936 | 12,701 | ## College Physics (4th Edition)
(a) Work is done at the rate of $3600~J/s$ (b) $Work = 5.4~J$
(a) We can find the power delivered by the electric organs: $P = V~I$ $P = (200~J/C)(18~C/s)$ $P = 3600~J/s$ Work is done at the rate of $3600~J/s$ (b) We can find the work done during one pulse: $Work = P \times t$ $Work = (3600~J/s)(1.5\times 10^{-3}~s)$ $Work = 5.4~J$ | 150 | 367 | {"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} | 3.71875 | 4 | CC-MAIN-2019-39 | latest | en | 0.922447 |
http://www.conversion-website.com/speed/micrometer-per-second-to-foot-per-hour.html | 1,716,757,815,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058973.42/warc/CC-MAIN-20240526200821-20240526230821-00859.warc.gz | 38,447,560 | 4,383 | Micrometers per second to feet per hour (μm/s to ft/h)
Convert micrometers per second to feet per hour
Micrometers per second to feet per hour conversion calculator above calculates how many feet per hour are in 'X' micrometers per second (where 'X' is the number of micrometers per second to convert to feet per hour). In order to convert a value from micrometers per second to feet per hour (from μm/s to ft/h) just type the number of μm/s to be converted to ft/h and then click on the 'convert' button.
Micrometers per second to feet per hour conversion factor
1 micrometer per second is equal to 0.011811023617397 feet per hour
Micrometers per second to feet per hour conversion formula
Speed(ft/h) = Speed (μm/s) × 0.011811023617397
Example: 326 micrometers per second equal how many feet per hour? To solve this, multiply 326 micrometers per second with the conversion factor from micrometers per second to feet per hour.
Speed(ft/h) = 326 ( μm/s ) × 0.011811023617397 ( ft/h / μm/s )
Speed(ft/h) = 3.8503936992715 ft/h or
326 μm/s = 3.8503936992715 ft/h
326 micrometers per second equals 3.8503936992715 feet per hour
Micrometers per second to feet per hour conversion table
micrometers per second (μm/s)feet per hour (ft/h)
100.11811023617397
150.17716535426096
200.23622047234794
250.29527559043493
300.35433070852192
350.4133858266089
400.47244094469589
450.53149606278288
micrometers per second (μm/s)feet per hour (ft/h)
2002.3622047234794
2502.9527559043493
3003.5433070852192
3504.133858266089
4004.7244094469589
4505.3149606278288
5005.9055118086986
5506.4960629895685
Versions of the micrometers per second to feet per hour conversion table. To create a micrometers per second to feet per hour conversion table for different values, click on the "Create a customized speed conversion table" button.
Related speed conversions
Back to micrometers per second to feet per hour conversion
TableFormulaFactorConverterTop | 567 | 1,947 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2024-22 | latest | en | 0.556582 |
http://nortonkit.co.in/protrain/digital/timer_555_sequencer.html | 1,516,488,108,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889736.54/warc/CC-MAIN-20180120221621-20180121001621-00196.warc.gz | 262,673,001 | 4,261 | www.nortonkit.com 18 अक्तूबर 2013
Direct Links to Other Digital Pages:
Combinational Logic: [Basic Gates] [Derived Gates] [The XOR Function] [Binary Addition] [Negative Numbers and Binary Subtraction] [Multiplexer] [Decoder/Demultiplexer] [Boolean Algebra]
Sequential Logic: [RS NAND Latch] [RS NOR Latch] [Clocked RS Latch] [RS Flip-Flop] [JK Flip-Flop] [D Latch] [D Flip-Flop] [Flip-Flop Symbols] [Converting Flip-Flop Inputs]
Alternate Flip-Flop Circuits: [D Flip-Flop Using NOR Latches] [CMOS Flip-Flop Construction]
Counters: [Basic 4-Bit Counter] [Synchronous Binary Counter] [Synchronous Decimal Counter] [Frequency Dividers] [Counting in Reverse] [The Johnson Counter]
Registers: [Shift Register (S to P)] [Shift Register (P to S)]
The 555 Timer: [555 Internals and Basic Operation] [555 Application: Pulse Sequencer]
555 Application: Pulse Sequencer
One requirement in certain digital circuits is for the generation of a series of pulses in time sequence, but on different lines. The pulse widths may or may not be the same, but they must occur one after the other, and therefore cannot come from the same source.
Sometimes pulses are required to overlap, or there must be a set delay following the end of one pulse before another pulse begins. Or, One pulse must begin a set time after another begins. The possible variations in timing requirements are almost endless, and many different approaches have been used to provide pulses with the necessary timing relationships. One inexpensive method that is perfectly satisfactory in many applications is to use interconnected 555 timers to generate the necessary timing intervals.
In the circuit shown above, we see three 555 timers, all configured in monostable mode. Each one, from left to right, triggers the next at the end of its timing interval. The resulting pulse timing is shown in the timing diagram to the right.
The sequence starts with the falling edge of the incoming trigger pulse. That edge triggers timer A, causing output A to go high. At this point, the incoming trigger pulse can either stay low or go high; it is no longer important.
Output A will remain high for the duration of its timing interval, and then fall back to its low state. At this time, it triggers timer B. Output B therefore goes high as output A falls. The same thing happens again at the end of the B timing interval; output B falls and triggers timer C.
At the end of the C timing interval, the sequence is over and all timers are quiescent, awaiting the arrival of the next triggering signal.
This time, the circuit is wired so that the incoming trigger signal is applied to both timers A and B. However, B's timing interval is very short, so it triggers timer C while the A output is still high. Depending on the designed timing intervals, C can easily be triggered and finish its timing interval while A is still active. Or, C can remain active after A falls back to its quiescent state.
Any number of 555 timers can be sequentially or jointly triggered with this kind of arrangement, and each timer still has its own individually-controlled timing interval. The possible combinations are endless, and independent pulses can overlap or not according to the needs of the application.
The initial triggering signal can come from any source. It can even be from another 555 timer, operating in astable mode. In that case, this kind of circuit is self-starting and will operate continuously.
It is also possible to trigger this sort of circuit manually, using a momentary-contact pushbutton to provide the triggering pulse. Or it could be some sort of sensor device, triggering the circuit upon recognition of some external condition. Thus, the circuit can be triggered by any kind of event, just as it can be used to control any kind of circuit.
There is one drawback to using daisy-chained 555 timers in this fashion. Once a 555 timer in monostable mode has been triggered, it cannot be re-triggered and the timing interval cannot be changed (at least without the addition of external circuitry to accomplish that). Therefore, if a second trigger pulse arrives while the input timer(s) are still active, it will be ignored. A worse possibility exists for the second example above: If the B interval has been completed but the A interval has not been completed when a new trigger pulse is received, timer B will be triggered but timer A will ignore it. If the timing relationship between the A and C pulses is critical, this could cause problems.
Nevertheless, this type of circuit can be highly versatile and useful, provided appropriate precautions are taken to ensure that such errors will not occur.
All pages on www.nortonkit.com copyright © 1996, 2000-2009 by Er. Rajendra Raj Please address queries and suggestions to: nortonkit@gmail.com | 1,079 | 4,807 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2018-05 | latest | en | 0.750328 |
https://cdn.varsitytutors.com/ap_statistics-help/data-collection/data/census-and-studies | 1,708,865,904,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474595.59/warc/CC-MAIN-20240225103506-20240225133506-00586.warc.gz | 167,240,299 | 40,629 | # AP Statistics : Census And Studies
## Example Questions
### Example Question #1 : How To Conduct An Observational Study
You are conducting the following series of observational studies to determine if generally understood parameters about a local population are accurate:
A. You stand on the sidewalk next to a stop sign to observe and record the number of cyclists and drivers who stop or don't stop.
B. You inform customers at a local fast food restaurant of your study to determine the proportion of healthy food choices from the menu and then observe their choices.
C. From your car in the mall parking lot, you observe the proportion of shoppers who hold the door open for the next person who enters or exits the mall.
D. To estimate the proportion of males and females in the local community, you observe spectators at a hockey match and count and record the gender in a randomly selected area of the crowd.
E. You review the daily sign-in sheets at a local fitness center to estimate the average number of workouts per week for residents of the local community.
Which observational study should yield the most accurate results?
Study C
Study E
Study A
Study B
Study D
Study C
Explanation:
Study C takes a representative sample of local residents, and it does so without affecting the outcomes.
Studies A and B are influenced by the person conducting the survey. Studies D and E are biased samples of the population.
Therefore, C should yield the most accurate results.
### Example Question #1 : How To Conduct An Observational Study
What situation would most warrant the method of observational study to produce accurate results?
Studying the social interactions between groups of baboons.
Testing the effectiveness of a new drug.
None of the above.
Observing how chocolate consumption affects mood.
Studying the relationship between sleep deprivation and cold susceptibility.
Studying the social interactions between groups of baboons.
Explanation:
Obseverational study does not involve any interference with the group being studied, so watching baboons in their natural habit would be best suited for this method.
### Example Question #1 : How To Conduct A Census
Kate would like to determine what flavors of ice cream are most popular among students in her AP Statistics class. In total, there are 100 students in the class. Which of the following would be an appropriate sampling methodology?
Randomly select several of the most popular students in the class to answer questions about their favorite ice cream flavor
There is no effective way to obtain a representative sample from the target population
Ask every fifth person that walks through the door what their favorite flavor of ice cream is before class starts
Group students into several homogeneous groups and choose one group to survey in order to determine the class's favorite ice cream flavor
Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream
Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream
Explanation:
In this situation, it is best to conduct a census in order to determine what the class's favorite flavor of ice cream is. Since there are only 100 students in the class, a sample of the class would be very small and may not be representative of the class as a whole.
### Example Question #1 : How To Conduct A Census
Census is to __________ as survey is to __________.
sample; population
There are no similarities between these two.
population; group
population; sample
cluster; stratum | 706 | 3,640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-10 | latest | en | 0.899627 |
https://metanumbers.com/23025 | 1,601,425,898,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402093104.90/warc/CC-MAIN-20200929221433-20200930011433-00619.warc.gz | 510,198,247 | 7,435 | ## 23025
23,025 (twenty-three thousand twenty-five) is an odd five-digits composite number following 23024 and preceding 23026. In scientific notation, it is written as 2.3025 × 104. The sum of its digits is 12. It has a total of 4 prime factors and 12 positive divisors. There are 12,240 positive integers (up to 23025) that are relatively prime to 23025.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 12
• Digital Root 3
## Name
Short name 23 thousand 25 twenty-three thousand twenty-five
## Notation
Scientific notation 2.3025 × 104 23.025 × 103
## Prime Factorization of 23025
Prime Factorization 3 × 52 × 307
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 4605 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 23,025 is 3 × 52 × 307. Since it has a total of 4 prime factors, 23,025 is a composite number.
## Divisors of 23025
1, 3, 5, 15, 25, 75, 307, 921, 1535, 4605, 7675, 23025
12 divisors
Even divisors 0 12 6 6
Total Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 38192 Sum of all the positive divisors of n s(n) 15167 Sum of the proper positive divisors of n A(n) 3182.67 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 151.74 Returns the nth root of the product of n divisors H(n) 7.2345 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 23,025 can be divided by 12 positive divisors (out of which 0 are even, and 12 are odd). The sum of these divisors (counting 23,025) is 38,192, the average is 31,82.,666.
## Other Arithmetic Functions (n = 23025)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 12240 Total number of positive integers not greater than n that are coprime to n λ(n) 3060 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2568 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 12,240 positive integers (less than 23,025) that are coprime with 23,025. And there are approximately 2,568 prime numbers less than or equal to 23,025.
## Divisibility of 23025
m n mod m 2 3 4 5 6 7 8 9 1 0 1 0 3 2 1 3
The number 23,025 is divisible by 3 and 5.
• Deficient
• Polite
## Base conversion (23025)
Base System Value
2 Binary 101100111110001
3 Ternary 1011120210
4 Quaternary 11213301
5 Quinary 1214100
6 Senary 254333
8 Octal 54761
10 Decimal 23025
12 Duodecimal 113a9
20 Vigesimal 2hb5
36 Base36 hrl
## Basic calculations (n = 23025)
### Multiplication
n×i
n×2 46050 69075 92100 115125
### Division
ni
n⁄2 11512.5 7675 5756.25 4605
### Exponentiation
ni
n2 530150625 12206718140625 281059685187890625 6471399251451181640625
### Nth Root
i√n
2√n 151.74 28.449 12.3183 7.45487
## 23025 as geometric shapes
### Circle
Diameter 46050 144670 1.66552e+09
### Sphere
Volume 5.11314e+13 6.66207e+09 144670
### Square
Length = n
Perimeter 92100 5.30151e+08 32562.3
### Cube
Length = n
Surface area 3.1809e+09 1.22067e+13 39880.5
### Equilateral Triangle
Length = n
Perimeter 69075 2.29562e+08 19940.2
### Triangular Pyramid
Length = n
Surface area 9.18248e+08 1.43858e+12 18799.8
## Cryptographic Hash Functions
md5 c4c98da153c360c232e1494b9cdd8cea 11985332d3ae05911b86ab48c4070a53e3e0fe11 74a8aea068e352ac5dfc2b54628c1b7478429607bbd8bbba20dd410e8ccc3e67 ec00e5d851fc7c3b7da1333f685bf0e02d028009346aafa8fba074a7495db0a18a671bdea517adfca7dc32d478d94c4b53600b92634de152cbd0c9755fa4b1b7 eaa054ecfa0d230e751fc5dd0c698746f0c15e2b | 1,447 | 4,049 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2020-40 | latest | en | 0.811664 |
https://metanumbers.com/63717 | 1,638,058,335,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358323.91/warc/CC-MAIN-20211127223710-20211128013710-00601.warc.gz | 446,988,984 | 7,401 | # 63717 (number)
63,717 (sixty-three thousand seven hundred seventeen) is an odd five-digits composite number following 63716 and preceding 63718. In scientific notation, it is written as 6.3717 × 104. The sum of its digits is 24. It has a total of 3 prime factors and 8 positive divisors. There are 41,712 positive integers (up to 63717) that are relatively prime to 63717.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 24
• Digital Root 6
## Name
Short name 63 thousand 717 sixty-three thousand seven hundred seventeen
## Notation
Scientific notation 6.3717 × 104 63.717 × 103
## Prime Factorization of 63717
Prime Factorization 3 × 67 × 317
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 63717 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 63,717 is 3 × 67 × 317. Since it has a total of 3 prime factors, 63,717 is a composite number.
## Divisors of 63717
1, 3, 67, 201, 317, 951, 21239, 63717
8 divisors
Even divisors 0 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 86496 Sum of all the positive divisors of n s(n) 22779 Sum of the proper positive divisors of n A(n) 10812 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 252.422 Returns the nth root of the product of n divisors H(n) 5.89317 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 63,717 can be divided by 8 positive divisors (out of which 0 are even, and 8 are odd). The sum of these divisors (counting 63,717) is 86,496, the average is 10,812.
## Other Arithmetic Functions (n = 63717)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 41712 Total number of positive integers not greater than n that are coprime to n λ(n) 10428 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 6379 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 41,712 positive integers (less than 63,717) that are coprime with 63,717. And there are approximately 6,379 prime numbers less than or equal to 63,717.
## Divisibility of 63717
m n mod m 2 3 4 5 6 7 8 9 1 0 1 2 3 3 5 6
The number 63,717 is divisible by 3.
## Classification of 63717
• Arithmetic
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
• Sphenic
## Base conversion (63717)
Base System Value
2 Binary 1111100011100101
3 Ternary 10020101220
4 Quaternary 33203211
5 Quinary 4014332
6 Senary 1210553
8 Octal 174345
10 Decimal 63717
12 Duodecimal 30a59
20 Vigesimal 7j5h
36 Base36 1d5x
## Basic calculations (n = 63717)
### Multiplication
n×y
n×2 127434 191151 254868 318585
### Division
n÷y
n÷2 31858.5 21239 15929.2 12743.4
### Exponentiation
ny
n2 4059856089 258681850422813 16482431463390375921 1050211085552844582558357
### Nth Root
y√n
2√n 252.422 39.941 15.8878 9.138
## 63717 as geometric shapes
### Circle
Diameter 127434 400346 1.27544e+10
### Sphere
Volume 1.08356e+15 5.10177e+10 400346
### Square
Length = n
Perimeter 254868 4.05986e+09 90109.4
### Cube
Length = n
Surface area 2.43591e+10 2.58682e+14 110361
### Equilateral Triangle
Length = n
Perimeter 191151 1.75797e+09 55180.5
### Triangular Pyramid
Length = n
Surface area 7.03188e+09 3.04859e+13 52024.7
## Cryptographic Hash Functions
md5 ee600797ef18eabe7f2ebb7d864a0df2 0a8d9df6818704210fcd8b70f70a03c64ce80203 991957b275c8ba58651183f7d0d9ff1ebb55d2aa8f72dad945dfa69b597ccd5d 46e7faf71dea7c0547b4411ac8b85ac87b8ef62b52af5df5a5403ca20849166b66693486246bba2ca7e12faa3fe1fbe099c1cf642c8322edebaced3deaf40ef5 f9236716b5d1aa22e01962a83d657ae72baaf219 | 1,465 | 4,177 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2021-49 | latest | en | 0.806487 |
https://www.jiskha.com/questions/93736/Bryan-owns-an-orchard-behind-johns-house-and-property-The-only-access-to-the-orchard | 1,555,874,055,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578532050.7/warc/CC-MAIN-20190421180010-20190421202010-00333.warc.gz | 715,385,329 | 4,611 | Bryan owns an orchard behind john's house and property. The only access to the orchard is john's driveway, which Bryan uses to get to his land. Bryan sells the orchard to Tom. Can Tom use the right-of-way across Kay's property?
1. 👍 0
2. 👎 0
3. 👁 42
## Similar Questions
1. ### Math
An orchard has enough space to plant 21 rows with y trees in each row, or 18 rows with y+7 trees in each row. If each orchard plan contains the same number of trees, how many trees can each orchard contain? *I know the answer is
asked by Katie on January 12, 2016
2. ### Calculus
There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number
asked by Q on March 25, 2014
3. ### math
There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number
asked by tye on April 4, 2011
4. ### statistics
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 6.45 inches and a standard deviation of 0.45 inches. Show all work. (A) What percentage of the grapefruits in this orchard have diameters
asked by Laynette on August 28, 2011
5. ### microeconomics
A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard owner since the bees pollinate the apple trees: one beehive pollinates one acre of orchard. Unfortunately, there are not enough bees
asked by Alex on November 27, 2015
6. ### Statistics
The table list the sugar content of two types of apples from three different orchards. At a=0.05, test the claim that the sugar content of the apples and the orchard where they were grown are not related. Sugar
asked by Lea on May 7, 2012
7. ### math
An orchard produces 720 liters of maple syrup per year. How many kiloliters of maple syrup does the orchard produce in a year?
asked by josselin on March 1, 2017
8. ### math
An orchard produces 720 liters of maple syrup per year. How many kiloliters of maple syrup does the orchard produce in a year?
asked by carol on March 1, 2017
9. ### statistics
The diameters of apples in a certain orchard are normally distributed with a mean of 4.77 inches and a standard deviation of 0.43 inches. Show all work. (A) What percentage of the apples in this orchard is larger than 4.71 inches?
asked by Laynette on September 2, 2011
10. ### statistics
The diameters of apples in a certain orchard are normally distributed with a mean of 4.77 inches and a standard deviation of 0.43 inches. Show all work. (A) What percentage of the apples in this orchard is larger than 4.71 inches?
asked by Valerie on November 2, 2010
More Similar Questions | 767 | 2,885 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2019-18 | latest | en | 0.947042 |
https://pegaswitch.com/lifehacks/what-is-a-field-book-in-surveying/ | 1,669,724,832,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710691.77/warc/CC-MAIN-20221129100233-20221129130233-00614.warc.gz | 480,598,642 | 39,055 | Lifehacks
# What is a field book in surveying?
## What is a field book in surveying?
: a notebook used for keeping field notes in surveying.
## How do field books work in surveying?
B. Precautions to be Taken While Entering the Field book
1. All measurements should be noted as soon as they are taken.
2. Each chain line should be recorded on a separate page.
3. Over –writing should be avoided.
4. Figures and hand-writing should be neat and legible.
5. Index-sketch, object-sketch and notes should be clear.
What is the size of field book in surveying?
Explanation: The book in which the chain or tape measurements are entered is called the field book. It is an oblong book of size about 20 cm x 20 cm and opens lengthwise.
### What is the basic principle of surveying?
Two basic principles of surveying are: • Always work from whole to the part, and • To locate a new station by at least two measurements ( Linear or angular) from fixed reference points. area is first enclosed by main stations (i.e.. Control stations) and main survey lines.
### What is M book?
Mbook is the short form of the Measurement Book. It is used for making payments to the contractor. The payment to the work done by a contractor is made based on the Measurements of work done by the contractor. It basically consists of 3 main terms length, breadth, depth.
What is Rise and Fall method?
The rise and fall method is the method of calculating the difference in elevation between consecutive points in levelling work. Some of the points you have to know before starting numerical are: Back sights: The first reading after seeing the instrument is called back sights.
## What is single line field book?
Single-line field book In this type of field book a single red line is drawn through the middle of each page. The line represents the chain line, and the chainages are written on it. The offsets are recorded, with the sketches, to the left or right of the chain line.
## What is the first principle of surveying?
What is the first principle of surveying? Explanation: The first principle of surveying is to work from whole to part. Before starting the actual survey measurements, the surveying is to work from around the area to fix the best positions of survey lines and survey stations.
How important is a field book?
Importance and challenges of field books They provide rich data for researchers to understand how biodiversity has changed over time and space. They enhance information associated with specimens by providing details regarding dates, localities (for geo-referencing), and associated event data.
### What is a field book used for?
Surveyors use Field Books to record both survey data and notes as surveys were carried out. They often contain notes about buildings and topography, astronomical observations for charting coordinates, boundary marks and other details. Field books are durable and water-resistant to withstand the harshest job sites.
### What are the three basic principles of surveying?
Basic Principles of Surveying
• BASIC PRINCIPLES IN SURVEYING.
• PRINCIPLE OF WORKING FROM WHOLE TO PART.
• IMPORTANCE OF SCIENTIFIC HONESTY.
• CHECK ON MEASUREMENTS.
• ACCURACY AND PRECISION.
• Horizontal Distance Measurement.
What do surveyors record in a field book?
Surveyors use Field Books to record both survey data and notes as surveys were carried out. They often contain notes about buildings and topography, astronomical observations for charting coordinates, boundary marks and other details.
## Is the survey Field Procedures Manual a textbook?
It is not a textbook or a contract document. Nor is it a substitute for surveying knowledge, experience or judgment. Although portions include textbook material, this MANUAL does not attempt to completely cover any facet of surveying.
## What do you need to know about surveying?
This manual provides basic concepts about surveying and is intended for use in the training course Surveying Methods for Local Highway Agencies. The manual and course are intended for town, village, city, and county personnel who have field responsibilities related to highway construction and maintenance.
What are the different types of land surveys?
Surveying encompasses the following categories: 1. Geodetic Surveys – Surveys, which establish control networks on a mathematical datum so that measurements will reflect the curved (ellipsoidal) shape of the earth. 2. Land Surveys – Surveys which include retracement of existing land ownership boundaries or the creation of new boundaries. 3. | 942 | 4,565 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-49 | latest | en | 0.961307 |
https://docs.qgis.org/1.8/pt_PT/docs/user_manual/working_with_vector/field_calculator.html | 1,611,552,667,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703564029.59/warc/CC-MAIN-20210125030118-20210125060118-00578.warc.gz | 314,125,246 | 7,629 | # Field Calculator¶
The Field Calculator button in the attribute table allows to perform calculations on basis of existing attribute values or defined functions, e.g to calculate length or area of geometry features. The results can be written to a new attribute column or it can be used to update values in an already existing column.
You have to bring the vector layer in editing mode, before you can click on the field calculator icon to open the dialog (see figure_attributes_3). In the dialog you first have to select whether you want to only update selected features, create a new attribute field where the results of the calculation will be added or update an existing field.
Figure Attributes 3:
Field Calculator
If you choose to add a new field, you need to enter a field name, a field type (integer, real or string), the total field width, and the field precision (see figure_attributes_3). For example, if you choose a field width of 10 and a field precision of 3 it means you have 6 signs before the dot, then the dot and another 3 signs for the precision.
The Function List contains functions as well as fields and values. View the help function in the Selected Function Help. In Expression you see the calculation expressions you create with the Function List. The most commonly used operators, see Operators.
In the Function List, click on Fields and Values to view all attributes of the attribute table to be searched. To add an attribute to the Field calculator Expression field, double click its name in the Fields and Values list. Generally you can use the various fields, values and functions to construct the calculation expression or you can just type it into the box. To display the values of a field, you just right click on the appropriate field. You can choose between Load top 10 unique values and Load all unique values. On the right side opens the Field Values list with the unique values. To add a value to the Field calculator Expression box, double click its name in the Field Values list.
The Operators, Math, Conversions, String, Geometry and Record groups provides several functions. In Operators you find mathematical operators. Find Math for mathematical functions. The Conversions group contains functions that convert one data type to another. The String group provides functions for data strings. In the Geometry group you find functions for geometry objects. With Record group functions you can add a numeration to your data set. To add a function to the Field calculator Expression box, click on the > and then doubleclick the function.
A short example illustrates how the field calculator works. We want to calculate the length of the railroads layer from the QGIS sample dataset:
1. Load the Shapefile railroads.shp in QGIS and press Open Attribute Table.
2. Click on Toggle editing mode and open the Field Calculator dialog.
3. Select the Create a new field checkbox to safe the calculations into a new field.
4. Add length as Output field name, real as Output field type and define Output field width 10 and a Precision of 3.
5. Now click on function length in the Geometry group to add it as \$length into the Field calculator expression box and click [Ok].
6. You can now find a new column length in the attribute table.
The available functions are listed below.
```column name "column name" value of the field column name
'string' a string value
NULL null value
a IS NULL a has no value
a IS NOT NULL a has a value
a IN (value[,value]) a is below the values listed
a NOT IN (value[,value]) a is not below the values listed
a OR b a or *b* is true
a AND b a and *b* is true
NOT a inverted truth value of a
sqrt(a) square root of a
sin(a) sinus of a
cos(a) cosinus of b
tan(a) tangens of a
asin(a) arcussinus of a
acos(a) arcuscosinus of a
atan(a) arcustangens of a
to int(a) convert string a to integer
to real(a) convert string a to real
to string(a) convert number a to string
lower(a) convert string a to lower case
upper(a) convert string a to upper case
length(a) length of string a
atan2(y,x) arcustangens of y/x using the signs of the two
arguments to determine the quadrant of the result
replace(*a*, replacethis, withthat) replace this with that in string a
regexp_replace(a,this,that) replace the regular expression this with that
substr(*a*,from,len) len characters of string *a* starting from from
(first character index is 1)
a || b concatenate strings a and b
\$rownum number current row
\$area area of polygon
\$perimeter perimeter of polygon
\$length length of line
\$id feature id
\$x x coordinate of point
\$y y coordinate of point
xat(n) X coordinate of the point of an n-th line (indeces
start at 0; negative values refer to the line end)
yat(n) y coordinate of the point of an n-th line (indeces
start at 0; negative values refer to the line end)
a = b a and b are equal
a != b and a <> b a and b are not equal
a >= b a is larger than or equal to b
a <= b a is less than or equal to b
a > b a is larger than b
a < b a is smaller than b
a ~ b a matches the regular expression b
a LIKE b a equals b
a ILIKE b a equals b (without regard to case-sensitive)
a |wedge| b a raised to the power of b
a * b a multiplied by b
a / b a divided by b
a + b a plus b
a - b a minus b
+ a positive sign
- a negative value of a```
The field calculator Function list with the Selected Function Help , Operators and Expression menu are also available through the rule-based rendering in the Style tab of the Layer properties and the expression based labeling in the Labeling core application. | 1,339 | 6,991 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-04 | latest | en | 0.773715 |
https://www.i-inox.ru/how-to-solve-a-trigonometry-problem-6491.html | 1,624,451,811,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00367.warc.gz | 718,995,866 | 9,697 | # How To Solve A Trigonometry Problem
Tags: Write In PaperEssays By E. A. PoeEastern And Western Cultures EssayRomeo And Juliet Characterization EssayOutline For Literature ReviewOutline For Cloning Research PaperSandra Cisneros The House On Mango Street EssayNon Performing Assets Research Paper
We first need to get the trig function on one side by itself.
To do this all we need to do is divide both sides by 2.
Likewise, the angle in the fourth quadrant will $$\frac$$ below the $$x$$-axis.
So, we could use $$- \frac$$ or $$2\pi - \frac = \frac$$.
One way to remember how to get the positive form of the second angle is to think of making one full revolution from the positive $$x$$-axis ( subtracting) $$\frac$$. As the discussion about finding the second angle has shown there are many ways to write any given angle on the unit circle.
## How To Solve A Trigonometry Problem Research Papers On Grief And Loss
Sometimes it will be $$- \frac$$ that we want for the solution and sometimes we will want both (or neither) of the listed angles.So, the solutions are : $$\frac,\;\frac,\; - \frac,\; - \frac$$.This problem is very similar to the other problems in this section with a very important difference. Due to the nature of the mathematics on this site it is best views in landscape mode.If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.In a calculus class we are often more interested in only the solutions to a trig equation that fall in a certain interval.The first step in this kind of problem is to find all possible solutions. $\begin\frac 2\pi \,n\,,\;\;n = 0,\, \pm 1,\, \pm 2,\, \pm 3,\, \ldots \ \frac 2\pi \,n\,,\;\;n = 0,\, \pm 1,\, \pm 2,\, \pm 3,\, \ldots \end$ Now, to find the solutions in the interval all we need to do is start picking values of $$n$$, plugging them in and getting the solutions that will fall into the interval that we’ve been given. $\begin& \frac 2\pi \,\left( 0 \right)\, = \frac use $$n = - 2$$) we will once again be outside of the interval so we’ve found all the possible solutions that lie inside the interval $$[ - 2\pi ,2\pi ]$$.Now we come to the very important difference between this problem and the previous problems in this section.The solution is NOT \[\beginx & = \frac 2\pi n,\quad n = 0, \pm 1, \pm 2, \ldots \ x & = \frac 2\pi n,\quad n = 0, \pm 1, \pm 2, \ldots \end$ This is not the set of solutions because we are NOT looking for values of $$x$$ for which $$\sin \left( x \right) = - \frac$$, but instead we are looking for values of $$x$$ for which $$\sin \left( \right) = - \frac$$.Note the difference in the arguments of the sine function! This makes all the difference in the world in finding the solution! $\beginx & = \frac \frac = \frac 2\pi \end$ Okay, so we finally got past the right endpoint of our interval so we don’t need any more positive n.Therefore, the set of solutions is $\begin5x & = \frac 2\pi n,\quad n = 0, \pm 1, \pm 2, \ldots \ 5x & = \frac 2\pi n,\quad n = 0, \pm 1, \pm 2, \ldots \end$ Well, actually, that’s not quite the solution. $\beginx & = \frac \frac = \frac = \frac & \hspace & \Rightarrow \hspace\sin \left( \right) = \sin \left( \right) = - \frac\ x & = \frac \frac = \frac & \hspace & \Rightarrow \hspace\sin \left( \right) = \sin \left( \right) = - \frac\end$ We’ll leave it to you to verify our work showing they are solutions. If you didn’t divide the $$2\pi n$$ by 5 you would have missed these solutions! Now let’s take a look at the negative $$n$$ and see what we’ve got. \[\beginx & = \frac \frac = - \frac This problem is a little different from the previous ones.
## Comments How To Solve A Trigonometry Problem
• ###### Trigonometry and Right Triangles Boundless Algebra
Trigonometric functions can be used to solve for missing side lengths in right. Recognize how trigonometric functions are used for solving problems about right.…
Apr 16, 2019. This online Trigonometry solver can tell you the answer for your math problem, and even show you the steps for a fee.…
• ###### Trigonometry Word Problems and How to Solve Them - Udemy Blog
Apr 25, 2014. Trigonometry word problems can feel intimidating but there are some tried and tested means of solving these problems. This step by step guide.…
• ###### How to Solve Trigonometry Word Problems - Onlinemath4all
Understanding the question and drawing the appropriate diagram are the two most important things to be done in solving word problems in trigonometry.…
• ###### Sine, Cosine, Tangent Real World Applications. How to use.
Problem 2. The angle of elevation from a point 43 feet from the base of a tree on level ground to the top of the tree is 30°. What is the height of the tree?…
• ###### Trigonometric Equation Calculator - Symbolab
Free trigonometric equation calculator - solve trigonometric equations step-by-step.… | 1,347 | 4,975 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2021-25 | latest | en | 0.865442 |
https://jp.mathworks.com/matlabcentral/cody/problems/628-book-club/solutions/700595 | 1,590,874,909,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347410352.47/warc/CC-MAIN-20200530200643-20200530230643-00099.warc.gz | 411,359,074 | 15,623 | Cody
# Problem 628. Book Club
Solution 700595
Submitted on 14 Jul 2015 by Jan Orwat
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
%% n = 4; k = 6; y_correct = 1560; assert(isequal(bookclub(n,k),y_correct))
2 Pass
%% n = 3; k = 6; y_correct = 540; assert(isequal(bookclub(n,k),y_correct))
3 Pass
%% n = 3; k = 5; y_correct = 150; assert(isequal(bookclub(n,k),y_correct)) | 164 | 500 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-24 | latest | en | 0.614899 |
https://en.m.wikibooks.org/wiki/Scheme_Programming/List_Operations | 1,726,772,832,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00383.warc.gz | 209,228,226 | 10,196 | # Scheme Programming/List Operations
Scheme Programming ← Further Maths List Operations Vector Operations →
Lists are a fundamental data structure in Scheme, as they are in many other functional languages. While among the simplest of structures, they have a rich set of operations and an amazing variety of uses. In this section, we'll cover the basics of creating and using lists.
## Scheme Lists
A list is a sequence of elements ending with `()`, sometimes called the "empty list" or "nil". We can build up lists with `cons`, which attaches a new element to the head of a list:
```> '() ; The empty list must be quoted.
()
> (cons 3 '())
(3)
> (cons 2 (cons 3 '()))
(2 3)
> (cons #t (cons 2 (cons 3 '())))
(#t 2 3)
```
The first argument of `cons` may be any Scheme object, and the second is a list; the value of `(cons x xs)` is a new list which contains `x` followed by the elements of `xs`.[1] (Scheme's way of printing lists uses a shorthand which hides the final `()`. In the responses above, we simply see the elements of a list enclosed in parentheses.) It's important to note that we must always quote `()`, in order to prevent Scheme from trying to interpret it as an (invalid) expression.
Two predicates define the Scheme list type. `null?`, is true for `()` (the empty list) and is false otherwise, while `pair?` returns true only for objects constructed with `cons`.[2]
There are two basic functions for accessing the elements of lists. The first, `car`, extracts the first element of a list:
```> (car (cons 1 '()))
1
> (car (cons 2 (cons 3 '())))
2
> (car '())
; Error!
```
Applying `car` to the empty list causes an error.
The second function, `cdr`, gives us the tail of a list: that is, the list without its leading element:
```> (cdr (cons 1 '()))
()
> (cdr (cons 2 (cons 3 '())))
(3)
> (cdr '())
; Error!
```
As with `car`, trying to apply `cdr` to the empty list causes an error.
The three functions `cons`, `car`, and `cdr` satisfy some useful identities. For any Scheme object x and list xs, we have
```(car (cons x xs)) = x
(cdr (cons x xs)) = xs
```
For any non-empty list ys, we also have
```(cons (car ys) (cdr ys)) = ys
```
Clearly, building a list through successive `cons` operations is clumsy. Scheme provides the built-in function `list` which returns a list of its arguments:
```> (list 1 2 3 4)
(1 2 3 4)
> (cons 1 (cons 2 (cons 3 (cons 4 '())))) ; equivalent, but tedious
(1 2 3 4)
```
`list` can take any number of arguments.
We can write a range of useful functions using just `cons`, `car`, and `cdr`. For example, we can define a function to compute the length of a list:
```(define (length xs)
(if (null? xs)
0
(+ 1 (length (cdr xs)))))
```
This definition, like the definitions of most list operations, closely follows the recursive structure of a list. There is a case for the empty list (which is assigned the length 0), and a case for a non-empty list (the length of the tail of the list, plus one). In practice, Scheme provides `length` as a built-in function.
Here's another simple example:
```(define (find-number n xs)
(if (null? xs)
#f
(if (= n (car xs))
#t
(find-number n (cdr xs)))))
```
`find-number` returns `#t` if the argument n occurs in the list xs, and returns `#f` otherwise. Once again, this definition follows the structure of the list argument. The empty list has no elements, so `(find-number n '())` is always false. If `xs` is non-empty, then n could be the first element, or it could be somewhere in the tail. In the former case, `find-number` returns true immediately. In the latter, the return value should be true if n appears in `(cdr xs)` and false otherwise. But since this is the definition of `find-number` itself, we have a recursive call with the new argument `(cdr xs)`.
## Notes
1. This is a simplified account which is correct for our current purposes. In fact, `cons` constructs pairs of its arguments, both of which may be arbitrary Scheme objects. A pair whose second element is `()` or another pair is called a list; all other pairs are called improper.
2. The definition of the Scheme list type is looser than that of numbers, booleans, etc. While the (scheme list) library provides a true `list?` function, this function is defined in terms of `null?` and `pair?`. See the previous note. | 1,125 | 4,307 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2024-38 | latest | en | 0.82927 |
http://compilers.iecc.com/comparch/article/97-11-051 | 1,493,152,573,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917120878.96/warc/CC-MAIN-20170423031200-00565-ip-10-145-167-34.ec2.internal.warc.gz | 91,956,630 | 2,338 | Re: Multiply by a constant --> shift-and-adds algorithm?
Sergey Solyanik <ssolyanik@icdc.com>9 Nov 1997 12:06:15 -0500
From comp.compilers
Related articles
Multiply by a constant --> shift-and-adds algorithm? Vincent.Lefevre@ens-lyon.fr (Vincent Lefevre) (1997-11-07)
Re: Multiply by a constant --> shift-and-adds algorithm? rweaver@ix.netcom.com (1997-11-09)
Re: Multiply by a constant --> shift-and-adds algorithm? preston@cs.rice.edu (1997-11-09)
Re: Multiply by a constant --> shift-and-adds algorithm? ssolyanik@icdc.com (Sergey Solyanik) (1997-11-09)
Multiply by a constant --> shift-and-adds algorithm? txr@alumni.caltech.edu (Tim Rentsch) (1997-11-09)
Re: Multiply by a constant --> shift-and-adds algorithm? n8tm@aol.com (1997-11-11)
Re: Multiply by a constant --> shift-and-adds algorithm? dube@brachio.IRO.UMontreal.CA (Danny Dube) (1997-11-11)
Re: Multiply by a constant --> shift-and-adds algorithm? cdg@nullstone.com (Christopher Glaeser) (1997-11-13)
Re: Multiply by a constant --> shift-and-adds algorithm? ssolyanik@icdc.com (Sergey Solyanik) (1997-11-14)
Re: Multiply by a constant --> shift-and-adds algorithm? shankar@powertelglobal.com (Shankar Unni) (1997-11-15)
[2 later articles]
| List of all articles for this month |
From: Sergey Solyanik Newsgroups: comp.compilers Date: 9 Nov 1997 12:06:15 -0500 Organization: Bentley Systems, Inc. References: 97-11-038 Keywords: arithmetic, optimize
Vincent Lefevre wrote:
>
> Some compilers (including gcc) are able to convert a "multiply by a
> constant" operation into a sequence of shifts and adds/subtracts.
The method I am using for our JIT compiler is memoizing dynamic
algorithm that uses a dag of best match sequences. I cannot share the
source code because it is commercial product, but I've put algorithm
description and compiled program (win32) that uses it at:
http://w3.icdc.com/~solyanik/decomp.html
This algorithm is a "smart brute force" (as any dynamic algorithm),
but it seems to work and it turned out to be fast enough for JIT
environment.
I would be very interested to seem smarter implementation.
Regards -
Sergey Solyanik
Software Developer
Bentley Systems, Inc
--
Post a followup to this message | 636 | 2,197 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2017-17 | latest | en | 0.730157 |
https://philoid.com/question/4886-what-are-the-advantages-of-connecting-electrical-devices-in-parallel-with-the-battery-instead-of-connecting-them-in-series | 1,696,052,114,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510603.89/warc/CC-MAIN-20230930050118-20230930080118-00033.warc.gz | 491,351,777 | 11,060 | ## Book: NCERT - Science
### Chapter: 12. Electricity
#### Subject: Physics - Class 10th
##### Q. No. 3 of In Text Questions-Pg-216
Listen NCERT Audio Books - Kitabein Ab Bolengi
3
##### What are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?
The advantages of connecting electrical devices in parallel rather than series are as follows:
a) The voltage is same across all the elements in case of parallel circuits. Even if any one of the electrical devices stop working, it will not affect other electrical appliances and they will work normally. On the other hand, in series circuit, the current through all devices is same. If one electrical appliance stops, Then the whole circuit is broken and no current flows. As a result, all other appliances also stop working.
b) In case of parallel circuits, each electrical appliance works independently, i.e. it has its own switch. Each device can be turned on or turned off independently, without affecting other appliances. In series circuit, all the electrical appliances have only one switch due to which they cannot be turned on or turned off independently.
c) In parallel circuits, each electrical appliance gets the same voltage as that of the battery due to which all the appliances work properly. In series circuit, the appliances do not get the same voltage but get the same current. Each appliance has a different voltage.
d) In a parallel connection, the overall resistance of the circuit is reduced due to which the current from the battery is high and hence each electrical appliance can draw the required amount of current. In the series connection of electrical appliances, the net resistance is the sum of all the resistances, thereby increasing the overall resistance of the circuit. Due to this current formulation from the battery is low an all the electrical appliances cannot draw sufficient amount of current for their proper working.
3
1
2
3
4
5 | 400 | 1,994 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2023-40 | longest | en | 0.930711 |
https://budgetlightforum.com/t/resistor-mod-question/38619 | 1,716,321,121,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058512.80/warc/CC-MAIN-20240521183800-20240521213800-00300.warc.gz | 119,448,287 | 5,894 | # Resistor mod question
When modding a light. I want to bridge the R100 resister with an R220, but I would like to know what the value on the resistors are. I am going to purchase a standard resistor and need to get the correct value.
How do I know the correct value??
The light is a t50 clone.
TIA
R100 = 0.1 Ohm = 100 mOhm
R200 = 0.2 Ohm = 200 mOhm
From the website, :220 = 22 × 100 (1) = 22Ω
Which one is correct??
Both are correct.
Quote from that website:
``````Resistances of less than 100 ohms are marked with the help of the letter 'R',
indicating the position of the decimal point.
``````
3R3 = 3.3 Ohm = 3300 mOhm
R100 = 0.1 Ohm = 100 mOhm
R200 = 0.2 Ohm = 200 mOhm
Happy modding
HQ
When you bridge a resistor with another, the inverses add, because the currents add.
1 / 0.1 = 10 Mho
1 / 0.2 = 5 Mho
1 / 15 Mho = 0.07 Ohm
That should read 220=22x 10^0 (1)=22
10^0=1 | 314 | 892 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2024-22 | latest | en | 0.8743 |
https://doc.sagemath.org/html/en/prep/Intro-Tutorial.html | 1,725,762,337,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650958.30/warc/CC-MAIN-20240908020844-20240908050844-00385.warc.gz | 196,845,035 | 14,489 | # Introductory Sage Tutorial#
This Sage document is the first in a series of tutorials developed for the MAA PREP Workshop “Sage: Using Open-Source Mathematics Software with Undergraduates” (funding provided by NSF DUE 0817071). It is licensed under the Creative Commons Attribution-ShareAlike 3.0 license (CC BY-SA).
If you are unsure how to log on to a Sage server, start using a local installation, or to create a new worksheet, you might find the prelude on logging in helpful.
Otherwise, you can continue with this tutorial, which has the following sections:
This tutorial only introduces the most basic level of functionality. Later tutorials address topics such as calculus, advanced plotting, and a wide variety of specific mathematical topics.
## Evaluating Sage Commands#
Or, How do I get Sage to do some math?
### Evaluating in the Jupyter notebook#
In a Jupyter worksheet, there are little boxes called input cells or code cells. They should be about the width of your browser.
To do math in a Jupyter cell, one must do two things.
• First, click inside the cell so that the cell is active (i.e., has a bright green border). This was already the case in the first cell above. (If it is blue, the Jupyter notebook is in “command mode”). Type some math in it.
• Then, there are two options. A not-very-evident icon that looks like the “play” symbol on a recording device can be clicked:
Or one can use the keyboard shortcut of holding down the Shift key while you press the Enter key. We call this Shift + Enter.
Sage prints out its response just below the cell (that’s the 4 below, so Sage confirms that $$2+2=4$$). Note also that Sage has automatically made a new cell, and made it active, after you evaluated your first cell.
To do more mathematics, just do the same thing with more cells!
One has to learn a variety of keyboard shortcuts or click on various menu items to manipulate cells. There is a help menu to get you started on this; the Jupyter developers also maintain an example notebook which may assist you.
## Functions in Sage#
To start out, let’s explore how to define and use functions in Sage.
For a typical mathematical function, it’s pretty straightforward to define it. Below, we define a function.
$f(x)=x^2$
sage: f(x)=x^2
>>> from sage.all import *
>>> __tmp__=var("x"); f = symbolic_expression(x**Integer(2)).function(x)
Since all we wanted was to create the function $$f(x)$$, Sage just does this and doesn’t print anything out back to us.
We can check the definition by asking Sage what f(x) is:
sage: f(x)
x^2
>>> from sage.all import *
>>> f(x)
x^2
If we just ask Sage what f is (as opposed to f(x)), Sage prints out the standard mathematical notation for a function that maps a variable $$x$$ to the value $$x^2$$ (with the “maps to” arrow $$\mapsto$$ as |-->).
sage: f
x |--> x^2
>>> from sage.all import *
>>> f
x |--> x^2
We can evaluate $$f$$ at various values.
sage: f(3)
9
>>> from sage.all import *
>>> f(Integer(3))
9
sage: f(3.1)
9.61000000000000
>>> from sage.all import *
>>> f(RealNumber('3.1'))
9.61000000000000
sage: f(31/10)
961/100
>>> from sage.all import *
>>> f(Integer(31)/Integer(10))
961/100
Notice that the output type changes depending on whether the input had a decimal; we’ll see that again below.
Naturally, we are not restricted to $$x$$ as a variable. In the next cell, we define the function $$g(y)=2y-1$$.
sage: g(y)=2*y-1
>>> from sage.all import *
>>> __tmp__=var("y"); g = symbolic_expression(Integer(2)*y-Integer(1)).function(y)
However, we need to make sure we do define a function if we use a new variable. In the next cell, we see what happens if we try to use a random input by itself.
sage: z^2
Traceback (most recent call last):
...
NameError: name 'z' is not defined
>>> from sage.all import *
>>> z**Integer(2)
Traceback (most recent call last):
...
NameError: name 'z' is not defined
This is explained in some detail in following tutorials. At this point, it suffices to know using the function notation (like g(y)) tells Sage you are serious about y being a variable.
One can also do this with the var('z') notation below.
sage: var('z')
z
sage: z^2
z^2
>>> from sage.all import *
>>> var('z')
z
>>> z**Integer(2)
z^2
This also demonstrates that we can put several commands in one cell, each on a separate line. The output of the last command (if any) is printed as the output of the cell.
Sage knows various common mathematical constants, like $$\pi$$ (pi) and $$e$$.
sage: f(pi)
pi^2
>>> from sage.all import *
>>> f(pi)
pi^2
sage: f(e^-1)
e^(-2)
>>> from sage.all import *
>>> f(e**-Integer(1))
e^(-2)
In order to see a numeric approximation for an expression, just type the expression inside the parentheses of N().
sage: N(f(pi))
9.86960440108936
>>> from sage.all import *
>>> N(f(pi))
9.86960440108936
Another option, often more useful in practice, is having the expression immediately followed by .n() (note the dot).
sage: f(pi).n()
9.86960440108936
>>> from sage.all import *
>>> f(pi).n()
9.86960440108936
For now, we won’t go in great depth explaining the reasons behind this syntax, which may be new to you. For those who are interested, Sage often uses this type of syntax (known as “object-oriented”) because…
• Sage uses the Python programming language, which uses this syntax, ‘under the hood’, and
• Because it makes it easier to distinguish among
• The mathematical object,
• The thing you are doing to it, and
• Any ancillary arguments.
For example, the following numerically evaluates (n) the constant $$\pi$$ (pi) to twenty digits (digits=20).
sage: pi.n(digits=20)
3.1415926535897932385
>>> from sage.all import *
>>> pi.n(digits=Integer(20))
3.1415926535897932385
Sage has lots of common mathematical functions built in, like $$\sqrt{x}$$ (sqrt(x)) and $$\ln(x)$$ (ln(x) or log(x)).
sage: log(3)
log(3)
>>> from sage.all import *
>>> log(Integer(3))
log(3)
Notice that there is no reason to numerically evaluate $$\log(3)$$, so Sage keeps it symbolic. The same is true in the next cell - $$2\log(3)=\log(9)$$, but there isn’t any reason to do that; after all, depending on what you want, $$\log(9)$$ may be simpler or less simple than you need.
sage: log(3)+log(3)
2*log(3)
>>> from sage.all import *
>>> log(Integer(3))+log(Integer(3))
2*log(3)
sage: log(3).n()
1.09861228866811
>>> from sage.all import *
>>> log(Integer(3)).n()
1.09861228866811
Notice again that Sage tries to respect the type of input as much as possible; adding the decimal tells Sage that we have approximate input and want a more approximate answer. (Full details are a little too complicated for this introduction.)
sage: log(3.)
1.09861228866811
>>> from sage.all import *
>>> log(RealNumber('3.'))
1.09861228866811
sage: sqrt(2)
sqrt(2)
>>> from sage.all import *
>>> sqrt(Integer(2))
sqrt(2)
If we want this to look nicer, we can use the show command. We’ll see more of this sort of thing below.
sage: show(sqrt(2))
>>> from sage.all import *
>>> show(sqrt(Integer(2)))
$\sqrt{2}$
sage: sqrt(2).n()
1.41421356237310
>>> from sage.all import *
>>> sqrt(Integer(2)).n()
1.41421356237310
Do you remember what $$f$$ does?
sage: f(sqrt(2))
2
>>> from sage.all import *
>>> f(sqrt(Integer(2)))
2
We can also plot functions easily.
sage: plot(f, (x,-3,3))
Graphics object consisting of 1 graphics primitive
>>> from sage.all import *
>>> plot(f, (x,-Integer(3),Integer(3)))
Graphics object consisting of 1 graphics primitive
In another tutorial, we will go more in depth with plotting. Here, note that the preferred syntax has the variable and endpoints for the plotting domain in parentheses, separated by commas.
If you are feeling bold, plot the sqrt function in the next cell between 0 and 100.
## Help inside Sage#
There are various ways to get help for doing things in Sage. Here are several common ways to get help as you are working in a Sage worksheet.
### Documentation#
Sage includes extensive documentation covering thousands of functions, with many examples, tutorials, and other helps.
• One way to access these is to click the “Help” link at the top right of any worksheet, then click your preferred option at the top of the help page.
• They are also available any time online at the Sage website, which has many other links, like video introductions.
• The Quick Reference cards are another useful tool once you get more familiar with Sage.
Our main focus in this tutorial, though, is help you can immediately access from within a worksheet, where you don’t have to do any of those things.
### Tab completion#
The most useful help available in the notebook is “tab completion”. The idea is that even if you aren’t one hundred percent sure of the name of a command, the first few letters should still be enough to help find it. Here’s an example.
• Suppose you want to do a specific type of plot - maybe a slope field plot - but aren’t quite sure what will do it.
• Still, it seems reasonable that the command might start with pl.
• Then one can type pl in an input cell, and then press the Tab key to see all the commands that start with the letters pl.
Try tabbing after the pl in the following cell to see all the commands that start with the letters pl. You should see that plot_slope_field is one of them.
sage: pl
>>> from sage.all import *
>>> pl
To pick one, just click on it; to stop viewing them, press the Escape key.
You can also use this to see what you can do to an expression or mathematical object.
• Assuming your expression has a name, type it;
• Then type a period after it,
• Then press tab.
You will see a list pop up of all the things you can do to the expression.
To try this, evaluate the following cell, just to make sure $$f$$ is defined.
sage: f(x)=x^2
>>> from sage.all import *
>>> __tmp__=var("x"); f = symbolic_expression(x**Integer(2)).function(x)
Now put your cursor after the period and press your Tab key.
sage: f.
>>> from sage.all import *
>>> f.
Again, Escape should remove the list.
One of the things in that list above was integrate. Let’s try it.
sage: f.integrate(x)
x |--> 1/3*x^3
>>> from sage.all import *
>>> f.integrate(x)
x |--> 1/3*x^3
### Finding documentation#
Or, Why all the question marks?
In the previous example, you might have wondered why I needed to put f.integrate(x) rather than just f.integrate(), by analogy with sqrt(2).n().
To find out, there is another help tool one can use from right inside the notebook. Almost all documentation in Sage has extensive examples that can illustrate how to use the function.
• As with tab completion, type the expression, period, and the name of the function.
• Then type a question mark.
• Press tab or evaluate to see the documentation.
To see how this help works, move your cursor after the question mark below and press Tab.
sage: f.integrate?
>>> from sage.all import *
>>> f.integrate?
The examples illustrate that the syntax requires f.integrate(x) and not just f.integrate(). (After all, the latter could be ambiguous if several variables had already been defined).
To stop viewing the documentation after pressing Tab, you can press the Escape key, just like with the completion of options.
If you would like the documentation to be visible longer-term, you can evaluate a command with the question mark (like below) to access the documentation, rather than just tabbing. Then it will stay there until you remove the input cell.
sage: binomial?
>>> from sage.all import *
>>> binomial?
Try this with another function!
### Finding the source#
There is one more source of help you may find useful in the long run, though perhaps not immediately.
• One can use two question marks after a function name to pull up the documentation and the source code for the function.
• Again, to see this help, you can either evaluate a cell like below, or just move your cursor after the question mark and press tab.
The ability to see the code (the underlying instructions to the computer) is one of Sage’s great strengths. You can see all the code to everything .
This means:
• You can see what Sage is doing.
• Your curious students can see what is going on.
• And if you find a better way to do something, then you can see how to change it!
sage: binomial??
>>> from sage.all import *
>>> binomial??
## Annotating with Sage#
Whether one uses Sage in the classroom or in research, it is usually helpful to describe to the reader what is being done, such as in the description you are now reading.
### Jupyter Annotation#
Thanks to a styling language called Markdown and the TeX rendering engine called MathJax, you can type much more in Sage than just Sage commands. This math-aware setup makes Sage perfect for annotating computations.
Jupyter notebook can function as a word processor. To use this functionality, we create a Markdown cell (as opposed to a input cell that contains Sage commands that Sage evaluates).
To do this without the keyboard shortcut, there is a menu for each cell; select “Markdown”.
Now you can type in whatever you want, including mathematics using LaTeX.
Then evaluate the cell (for instance, with “Shift-Enter”):
Markdown supports a fair amount of basic formatting, such as bold, underline, basic lists, and so forth.
It can be fun to type in fairly complicated math, like this:
$\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}=\prod_p \left(\frac{1}{1-p^{-s}}\right)\; .$
One just types things like:
$$\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}=\prod_p \left(\frac{1}{1-p^{-s}}\right)$$
in a Markdown cell.
Of course, one can do much more, since Sage can execute arbitrary commands in the Python programming language, as well as output nicely formatted HTML, and so on. If you have enough programming experience to do things like this, go for it!
sage: html("Sage is <a style='text-decoration:line-through'>somewhat</a> <b>really</b> cool! <p style='color:red'>(It even does HTML.)</p>")
>>> from sage.all import *
>>> html("Sage is <a style='text-decoration:line-through'>somewhat</a> <b>really</b> cool! <p style='color:red'>(It even does HTML.)</p>")
## Conclusion#
This concludes the introductory tutorial. Our hope is that now you can try finding and using simple commands and functions in Sage. Remember, help is as close as the notebook, or at the Sage website. | 3,575 | 14,380 | {"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": 2, "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} | 3.5625 | 4 | CC-MAIN-2024-38 | latest | en | 0.914018 |
http://mathhelpforum.com/calculus/67865-completing-square-center-radius.html | 1,481,137,271,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542244.4/warc/CC-MAIN-20161202170902-00207-ip-10-31-129-80.ec2.internal.warc.gz | 171,359,327 | 10,462 | 1. ## Completing the Square: Center and Radius
Thank for the help.
2. Hi,
Just bring the 4 from Left Hand Side to the right
The term on RHS is the square of radius
ie; $\sqrt{\frac{21}{4}}$ is the radius
and the center coordinates are (1,-2,0)..
Hi,
ie; $\sqrt{\frac{21}{4}}$ is the radius | 91 | 294 | {"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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-50 | longest | en | 0.791709 |
https://ch.mathworks.com/matlabcentral/answers/1591274-euler-s-method | 1,642,878,201,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303868.98/warc/CC-MAIN-20220122164421-20220122194421-00437.warc.gz | 234,311,148 | 25,302 | # euler's method
2 views (last 30 days)
taojian li on 20 Nov 2021
Edited: James Tursa on 20 Nov 2021
I am trying to solve a equation but the dydt is wrong I guess? The original equation is y''+0.1y'+siny=0
h = 0.01;
x = 0:h:10;
y = zeros(size(x));
y(1) = 1;
n = numel(y);
for i = 1:n-1
dy = -0.1*y(2)+siny(1);
y(i+1) = y(i) + dy*h;
end
Yongjian Feng on 20 Nov 2021
What is siny? Is it sin(y)?
Also you dy is a constant in the loop, only depends on y(2) and y(1). Maybe it should depend on y(i) instead?
##### 2 CommentsShowHide 1 older comment
taojian li on 20 Nov 2021
thank you I already know how to solve it
James Tursa on 20 Nov 2021
Edited: James Tursa on 20 Nov 2021
Your code does not have enough states. You have a 2nd order ODE (the highest derivative present is 2), so the state vector needs to be two elements, not one element as you have it. You will need to carry both y and y' at each step. To keep with your outline, let's make the state a column vector, and then have the result in a matrix where the columns are the states at each time point. I.e., y(1,i) is the y at time x(i), and y(2,i) is the y' at time x(i). Then take your code and everywhere you see y you need to replace it with a column vector. E.g.,
h = 0.01;
x = 0:h:10;
y = zeros(2,numel(x)); % y is a matrix composed of 2-element column vector states
y(:,1) = [1;yprime_initial]; % the first column is the initial state for y and y'
n = numel(x); % changed argument to x
for i = 1:n-1
dy = [ y' at time x(i); y'' at time x(i) ]; % A 2-element column vector, you need to fill this in
y(:,i+1) = y(:,i) + dy*h; % changed the y to column vectors
end
I modified almost everything in your code to account for the 2-element column vector states. I even included the outline of what the 2-element column vector dy needs to be in terms of y' and y''. You simply need to fill in the values for these. It will be a function of the current column vector state y(:,i) and time x(i). Give it a shot and let us know if you have problems. I have arbitrarily given the inital y' value as yprime_initial, but you should change this to the actual value. | 656 | 2,118 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2022-05 | latest | en | 0.892217 |
https://www.infinity-cdma.com/p/154820221257523/ | 1,556,216,263,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578732961.78/warc/CC-MAIN-20190425173951-20190425195951-00330.warc.gz | 712,148,617 | 4,896 | ### Series Circuit Diagram
Series Circuit Diagram
## Series Circuit Definition Series Circuit Examples Electrical Academia
A final way of describing an electric circuit is by usage of conventional circuit logos to offer a schematic structure of this circuit and its elements. A few circuit symbols used in schematic diagrams are shown below.
An electric circuit is commonly explained with words. On many occasions in Courses 1 through 3words are used to refer to circuits. But another way of describing that the circuit is to simply draw on it. Such drawings supply a faster mental picture of the real circuit. Circuit drawings like the one below are used many times in Courses 1 through 3.
The above circuits presumed that the three light bulbs were attached in such a way that the rate flowing through the circuit would pass through each of the three light bulbs in sequential mode. The path of a positive test rate leaving the positive terminal of the battery and also traversing the external circuit would involve a passage through every one of the 3 joined light bulbs before returning into the negative terminal of the battery life. But is this the sole solution that three light bulbs can be connected? Do they must be connected in sequential fashion as shown above? Absolutely not! In reality, example 2 below contains the exact verbal description together with the drawing along with the schematic diagrams being attracted otherwise.
Both of these examples illustrate both common kinds of connections made in electrical circuits. When two or more resistors exist in a circuit, they may be linked in series or in parallel. The rest of 4 will be dedicated to a report on both of these types of connections and also the impact that they have upon electrical quantities like current, resistance and electric potential. The next part of Lesson 4 can introduce the distinction between parallel and series connections.
So far, this unit of The Physics Classroom tutorial has concentrated on the vital components of an electrical circuit and upon the notions of electric potential difference, current and resistance. Conceptual meaning of phrases have been introduced and implemented to simple circuits. Mathematical connections between electrical quantities have been discussed and their use in resolving problems has been mimicked. Lesson 4 will concentrate on the way by which a couple of electric apparatus can be linked to form an electrical circuit. Our discussion will advance from simple circuits to somewhat complex circuits. Former fundamentals of electrical potential difference, current and resistance is going to be applied to those complex circuits and exactly the exact mathematical formulas are utilized to examine them.
Using the verbal outline, an individual can acquire a mental picture of this circuit being clarified. This informative article can then be represented by a drawing of 3 cells and three light bulbs attached by cables. The circuit symbols introduced above might be used to represent exactly the circuit. Note that three sets of long and short parallel lines are utilized to symbolize the battery pack with its three D-cells. And note that each light bulb is represented by its own personal resistor symbol. Straight lines are utilized to connect both terminals of the battery into some resistors and the resistors to one another.
One cell or other power source is represented with a long and a brief parallel line. A collection of cells or battery is represented by a collection of short and long parallel lines. In both circumstances, the long line is representative of the positive terminal of this energy supply and the brief line represents the terminal. A straight line is used to symbolize a connecting wire between any two components of this circuit. An electric device that delivers resistance to the flow of charge is generically known as a resistor and is symbolized by a zigzag line. An open button is generally represented by supplying a break in a straight line by lifting some of the lineup at a diagonal. These circuit logos are frequently used during the rest of 4 as electrical circuits have been represented by schematic diagrams. It will be significant to memorize these symbols to refer to this short listing regularly till you are accustomed to their own usage.
Utilizing the verbal outline, one can acquire a mental image of the circuit being clarified. But this moment, the relations of light bulbs is done in a manner such that there is a point on the circuit where the cables branch away from each other. The branching location is known as a node. Every bulb is set in its own division. These branch wires finally connect to each other to produce a second node. A single wire is used to connect this second node to the negative terminal of battery. | 883 | 4,819 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-18 | latest | en | 0.947284 |
https://oeis.org/A065906 | 1,624,339,368,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488507640.82/warc/CC-MAIN-20210622033023-20210622063023-00488.warc.gz | 395,871,975 | 3,914 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065906 Integers i > 1 for which there are three primes p such that i is a solution mod p of x^4 = 2. 5
15, 48, 55, 197, 206, 221, 235, 283, 297, 408, 444, 472, 489, 577, 578, 623, 641, 677, 701, 703, 763, 854, 930, 1049, 1081, 1134, 1140, 1159, 1160, 1201, 1253, 1303, 1311, 1328, 1374, 1385, 1415, 1458, 1459, 1495, 1501, 1517, 1557, 1585, 1714, 1723, 1726 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Solutions mod p are represented by integers from 0 to p-1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^4 = 2 iff i^4 - 2 has a prime factor > i; i is a solution mod p of x^4 = 2 iff p is a prime factor of i^4 - 2 and p > i. i^4 - 2 has at most three prime factors > i. For i such that i^4 - 2 has no resp. one resp. two prime factors > i cf. A065903 resp. A065904 resp. A065905. LINKS FORMULA a(n) = n-th integer i such that i^4 - 2 has three prime factors > i. EXAMPLE a(3) = 55, since 55 is (after 15 and 48) the third integer i for which there are three primes p > i (viz. 73, 103 and 1217) such that i is a solution mod p of x^4 = 2, or equivalently, 55^4 - 2 = 9150623 = 73*103*1217 has three prime factors > 4. (cf. A065902). PROG (PARI): a065906(m) = local(c, n, f, a, s, j); c = 0; n = 2; while(cn, s = concat(s, f[j, 1]))); if(matsize(s)[2] == 3, print1(n, ", "); c++); n++) a065906(50) CROSSREFS Cf. A040028, A065902, A065903, A065904, A065905. Sequence in context: A236401 A000813 A156205 * A154060 A168305 A208155 Adjacent sequences: A065903 A065904 A065905 * A065907 A065908 A065909 KEYWORD nonn AUTHOR Klaus Brockhaus, Nov 28 2001 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified June 22 01:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.) | 791 | 2,173 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2021-25 | latest | en | 0.771222 |
https://solvedlib.com/n/consicerthe-gaseous-reaction-below-nzlgl-hzclg-nordl-hz,5373002 | 1,685,632,046,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647895.20/warc/CC-MAIN-20230601143134-20230601173134-00014.warc.gz | 571,013,685 | 20,407 | # Consicerthe gaseous reaction below:Nzlgl + = HzClg) ~ Nordl Hz(g)Kc-1.0 x 10*9 at 10 "CIf initially;concentnaion of N2 1.3 M
###### Question:
Consicerthe gaseous reaction below: Nzlgl + = HzClg) ~ Nordl Hz(g) Kc-1.0 x 10*9 at 10 "C If initially; concentnaion of N2 1.3 M and 2. forwate vapor; what is the [Hz] equilbrium? Give your ans ver with signilicant figures either as numerce bnswer Orin Scentiic catation (e-g. 5.0E-20; note that 5.0e-20 ungcceotable -
#### Similar Solved Questions
##### 3.(15 pts) In each case, find the missing AH (kJ/mole) (a) If 2Al(s) + Fe2O3(s) -...
3.(15 pts) In each case, find the missing AH (kJ/mole) (a) If 2Al(s) + Fe2O3(s) - > Al2O3(s) + 2 Fe(s) AH -851.5kJ/mol then 1/8 Al2O3(s) + 1/4 Fe(s) ---> 1/4 Al(s) + 1/8 Fe2O3(s) AHan = ? (b) If Cao(s) + 3 C(s) --> CaC(s) + CO(g) AH -464.8 kJ/mol then 6 CaO(s) + 18 C(s) -> 6 CaC2(s) +6 C...
##### 6. (20 points) Let W be a plane spanned by the vectors ői = [1, 2,...
6. (20 points) Let W be a plane spanned by the vectors ői = [1, 2, 2)", T2 = (-1,1,2) (a). Find an orthonormal basis for W. (b). Extend it to an orthonormal basis of R3....
##### 346 3409 3372 3336 3300 3821 3783 3745 3707 3669 4207 4168 4129 4090 4052 4602 4562 4522 4483 4) ~Scoo 4960 4920 4SSO 4840 SCoo 5040 S0SO 5120 5160 5398 5438 5478 5517 5557 5793 5832 '5871 5910 '5948 ; 6179 6217 6255 6293 6331 6554 6591 6628 6664 6700 6915 6950 6985 7019 '705 4 47257 7291 '7344 7357 '7359 .7580 ~7611 7642 ~7673 47704 .78S1 '7910 7939 7967 7995 8159 8186 8212 8238 8264 8413 8438 8461 8485 S508 8643 8665 8636 S708 8729 8849 8869 '8S8 8907 S925
346 3409 3372 3336 3300 3821 3783 3745 3707 3669 4207 4168 4129 4090 4052 4602 4562 4522 4483 4) ~Scoo 4960 4920 4SSO 4840 SCoo 5040 S0SO 5120 5160 5398 5438 5478 5517 5557 5793 5832 '5871 5910 '5948 ; 6179 6217 6255 6293 6331 6554 6591 6628 6664 6700 6915 6950 6985 7019 '705 4 47257 ...
##### 77 pointe SOrPSEI0 24OpuuzmiMy NotesAak Youn Teachot(a) Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 128 V: m/s(b) Calculate the speed of an electron that is accelerated through the same potential difference_ m/sNeed Help?
77 pointe SOrPSEI0 24 Opuuzmi My Notes Aak Youn Teachot (a) Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 128 V: m/s (b) Calculate the speed of an electron that is accelerated through the same potential difference_ m/s Need Help?...
##### SOLVE THE PH PROBLEMSThe pH of rainwater is about 5.6. Is rainwater acidic, basic, or neutral? acidicThe pH of Coke is 2_ What is the hydrogen ion concentration of the solution?What is the hydroxide ion concentration of Coke (pH 2)? Solution has pH of 3 and solution B has pH of 5 This means solution A is more acidic means that solution A has more hydrogen ions than solution B.than solution B. This alsoSolution has pH of 12 and solution B has pH of 7 This means solution A is more Select means th
SOLVE THE PH PROBLEMS The pH of rainwater is about 5.6. Is rainwater acidic, basic, or neutral? acidic The pH of Coke is 2_ What is the hydrogen ion concentration of the solution? What is the hydroxide ion concentration of Coke (pH 2)? Solution has pH of 3 and solution B has pH of 5 This means solu...
##### Cabinaire Inc. is one of the largest manufacturers of office furniture in the United States. In...
Cabinaire Inc. is one of the largest manufacturers of office furniture in the United States. In Grand Rapids, Michigan, it assembles filing cabinets in an Assembly Department. Assume the following information for the Assembly Department: Direct labor per filing cabinet 30 minutes Supervisor sal...
##### P21-2B The management of Gill Corporation is trying to decide whether to continue manufacturing a part...
P21-2B The management of Gill Corporation is trying to decide whether to continue manufacturing a part or to buy it from an outside supplier. The part, called FIZBE. is a component of the company's finished product. This information was collected for the year ending December 31, 2017 1. 5,000 un...
##### We have the survey data on the body mass index (BMI) of 645 young women. The...
We have the survey data on the body mass index (BMI) of 645 young women. The mean BMI in the sample was X = 28.5. We treated these data as an SRS from a Normally distributed population with standard deviation o = 7.5. Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, ...
##### (1)J_oo (2+1)(2+9) dx (2)_o: dx sinhx
(1)J_oo (2+1)(2+9) dx (2)_o: dx sinhx...
##### Therapist Would . like to determinc if acknowledging positive statements and ignoring negative statements that patient makes will have an effect of future statements. Before trcatment the therapist intervicws patients and records the number of positive remarks made. During Ihe next se'ssion; the therapist uses her therapy. Then during the session after the treatment; the therapist records the number of positive statements The data are as followsBeforc_AllerConduct OXO- tailed related mtatni
therapist Would . like to determinc if acknowledging positive statements and ignoring negative statements that patient makes will have an effect of future statements. Before trcatment the therapist intervicws patients and records the number of positive remarks made. During Ihe next se'ssion; th...
##### Need Help?Re2d[L7. [0/1 Points]DETAILSPREVIOUS ANSWERSSPRECALC7 3.3.013.Two polynomlals P and D are given: Use eitner synthetic or Iong dlvisian to dlvlde P(x)by P(x) 84 4 642, D(x) 2x2P(X)Naad Help?Submi An5nec8. [~/1 Points]DETAILSSPRECALC7 3.3.014.Two polynomials P and D are given. Use either synthetic or long division to divide Pr) by P(x) 64x5 16x" D(x) 4x2 4* + 1
Need Help? Re2d[L 7. [0/1 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 3.3.013. Two polynomlals P and D are given: Use eitner synthetic or Iong dlvisian to dlvlde P(x)by P(x) 84 4 642, D(x) 2x2 P(X) Naad Help? Submi An5nec 8. [~/1 Points] DETAILS SPRECALC7 3.3.014. Two polynomials P and D are given. U...
##### 2. 1.024 grams of a sugar was dissolved in 50.00 mL of water using a volumetric flask. The optical rotation was observed as 1.38* when placed in a 0.50 dMcell What is the specific rotation of this sugar? Show work for credit: 2 pt 1.0244 0.02049 M 1. 28 J 24 12.6 5u WUi (0.0209) (0.5) 0.01024 f+ byIo
2. 1.024 grams of a sugar was dissolved in 50.00 mL of water using a volumetric flask. The optical rotation was observed as 1.38* when placed in a 0.50 dMcell What is the specific rotation of this sugar? Show work for credit: 2 pt 1.0244 0.02049 M 1. 28 J 24 12.6 5u WUi (0.0209) (0.5) 0.01024 f+ byI...
##### Score: 0 of 1 pt 6 of 18 (1 complete) HW Score: 5.56%, 1 of 18...
Score: 0 of 1 pt 6 of 18 (1 complete) HW Score: 5.56%, 1 of 18 pts 6.1.5 is Question Help Find the critical value ze necessary to form a confidence interval at the level of confidence shown below. c=0.82 (Round to two decimal places as needed.)...
##### According to an article the bottled water you are drinking may contain more bacteria and other...
According to an article the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. Of the more than 1500 bottles studied, nearly one-third exceeded government levels. Suppose that a department wants an ...
##### Hi, Please let me know my T-account Hi, I am trying to show up solution (1.)...
Hi, Please let me know my T-account Hi, I am trying to show up solution (1.) into T-account for this problem please help if any wrong as well as give me explain for remaining questions. Thanks Pr. 3-134—Adjusting entries. Data relating to the balances of various accounts affected by adjusting ...
##### You are working on skin preparation for a patient and before you know it, you've run...
You are working on skin preparation for a patient and before you know it, you've run out of prep sponges. You see some surgical sponges nearby. Can you use those to finish prep? Why or why not?... | 2,597 | 8,068 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-23 | latest | en | 0.394882 |
https://discourse.mc-stan.org/t/missing-data-latent-variable-problem/21620 | 1,652,717,712,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662510138.6/warc/CC-MAIN-20220516140911-20220516170911-00541.warc.gz | 275,790,878 | 8,638 | # Missing data/latent variable problem
Hi,
I am evaulating a screening programme, where there is a two-stage process:
• `test`: gives a continous score from 0 to 1. If `test` score is >=0.88, then the participant progresses to a definitive test to ascertain disease status
• `disease`: based on another test, the person is classifed as having the disease or not.
We also have covariates and tests that are associated with disease status (e.g. `test2`).
We are interested in the overall accuracy of `test` for predicting `Disease`, but our sample is biased because we only know `disease` status for those with a “positive” `test`.
Here are some simulated data to demonstrate:
``````library(copula)
library(tidyverse)
#Simulate some correlated data
set.seed(123)
myCop <- normalCopula(param = c(0.46, 0.27, 0.18),
dim = 3, dispstr = "un")
out <- rCopula(1e5, myCop)
out[, 1] <- qbeta(out[, 1], 8,2)
out[, 2] <- qbinom(out[, 2], size = 1, prob = 0.05)
out[, 3] <- qbinom(out[, 3], size = 1, prob = 0.226)
#prepare the data for modelling
d <- as.data.frame(out) %>%
rename(test=V1, disease=V2, test2=V3) %>%
mutate_at(.vars = vars(disease, test2),
.funs = funs(factor))
#> Warning: `funs()` was deprecated in dplyr 0.8.0.
#> Please use a list of either functions or lambdas:
#>
#> # Simple named list:
#> list(mean = mean, median = median)
#>
#> # Auto named with `tibble::lst()`:
#> tibble::lst(mean, median)
#>
#> # Using lambdas
#> list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
head(d)
#> test disease test2
#> 1 0.7686354 0 1
#> 2 0.8574327 0 1
#> 3 0.8278272 0 0
#> 4 0.8080611 0 0
#> 5 0.8596687 0 0
#> 6 0.9560706 0 0
#distributions of the data
d %>%
ggplot() +
geom_density(aes(test, fill=disease), alpha=0.3) +
facet_grid(test2~.)
``````
``````#Now change disease status to missing for all with test score >=0.88
#i.e. disease status only ascertained for those with a high test1 score
d2 <- d %>%
mutate(disease = case_when(test>=0.88 ~ disease,
TRUE ~ NA_integer_))
head(d2)
#> test disease test2
#> 1 0.7686354 <NA> 1
#> 2 0.8574327 <NA> 1
#> 3 0.8278272 <NA> 0
#> 4 0.8080611 <NA> 0
#> 5 0.8596687 <NA> 0
#> 6 0.9560706 0 0
``````
Created on 2021-03-31 by the reprex package (v0.3.0)
Now we want to estimate the overall acuracy of `test`, but recognising that disease status is missing in a biased manner, and that we potentially have additional information from `test2`. This where I am struggling. It seems like this could be either be a “missing data” problem, or an problem that could be addressed through latent class analysis.
I understand `Stan` does not support discrete parameters for estimation of count missing values (see `m2` example below). But I am hopeful that someone will have a suggestion for an alternative approach!
``````library(brms)
#> Loading required package: Rcpp
#> Loading 'brms' package (version 2.14.4). Useful instructions
#> can be found by typing help('brms'). A more detailed introduction
#> to the package is available through vignette('brms_overview').
#>
#> Attaching package: 'brms'
#> The following object is masked from 'package:stats':
#>
#> ar
#Fit a model to the data
#this ignores the missing disease status
m1 <- brm(disease ~ test + test2,
data=d2,
chains=1,
family=bernoulli())
#> Warning: Rows containing NAs were excluded from the model.
#> Compiling Stan program...
#> Trying to compile a simple C file
#> Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
#> clang -mmacosx-version-min=10.13 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
#> In file included from <built-in>:1:
#> In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
#> In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
#> In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
#> /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:628:1: error: unknown type name 'namespace'
#> namespace Eigen {
#> ^
#> /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:628:16: error: expected ';' after top level declarator
#> namespace Eigen {
#> ^
#> ;
#> In file included from <built-in>:1:
#> In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
#> In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
#> /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
#> #include <complex>
#> ^~~~~~~~~
#> 3 errors generated.
#> make: *** [foo.o] Error 1
#> Start sampling
#>
#> SAMPLING FOR MODEL 'fc5c5b8a5161ca9226ca5d50c5c16cee' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000717 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 7.17 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 1: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 1: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 1: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 5.08442 seconds (Warm-up)
#> Chain 1: 3.76533 seconds (Sampling)
#> Chain 1: 8.84975 seconds (Total)
#> Chain 1:
conditional_effects(m1)
``````
``````#Now try to fit a model imputing missing disease status
m2 <- brm(disease | mi() ~ test + test2,
data=d2,
chains=1,
family=bernoulli())
#> Error: Argument 'mi' is not supported for family 'bernoulli(logit)'.
``````
Created on 2021-03-31 by the reprex package (v0.3.0)
1 Like
Hi, sorry for not getting to you earlier, your question is relevant and well written.
Unfortunately this seems to me like a very tough problem that lies mostly in the design of the data collection. If you had at least some data on how `disease` looks like for people with lower test scores, the whole thing would be reasonably easy. Even incoroporating such data from different studies/populations/… might be easier than trying to answer the question from the data you have. Or if you have some idea on what the expected total prevalence in your population would be (which we could then use to infer the number of cases we missed).
Without additional data, I think you will need to bring a lot of untestable assumptions to the table to be able to do anything. You basically need to somehow extrapolate the relationship between `test` and `disease` (and potentially `test2`) from cases where `test >= 0.88` to the rest of the cases. And extrapolations are tough. E.g. even if there was a clean linear relationship between log odds of `disease` and `test` for high test values, how can we justify extrapolating this line all the way towards say `test = 0.25`?
If you can consult the knowledge of the particular disease and test to constrain the possible form of the relationships that might help.
It seems to me that your case is very similar to that discussed at: MICE missing values on the response If that is right than the best you can do is to fit the model to the cases where you have the response and hope they generalize, but as I said above, I don’t think such hope would be easy to justify.
Best of luck with your model!
Hi, thanks for the reply.
I had feared that this was the case.
We are trying some alternative approaches, so I will post back here if any success.
All the best.
1 Like
I realized that I worded my reply a bit too strongly - all what I wrote is my opinion and understanding, but it is quite possible I am missing something. I don’t have expertise in this kinds of problems and was just trying to use some statistical common sense - which is definitely fallible, so please double check that what I wrote makes sense to you and ask if you feel like there are potential holes/mistakes in the argument.
1 Like
Could this help?
2 Likes
Not at all - very helpful to think through these issues, and very grateful for the insights.
1 Like
Thank you - that is exactly the way our thinking is evolving. ONce we have ironed out some of the code, I will post back with how we get on. Thanks!
1 Like | 2,995 | 10,127 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-21 | latest | en | 0.728219 |
https://en.academic.ru/dic.nsf/enwiki/1439072/Cartan%27s_criterion | 1,611,616,649,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704792131.69/warc/CC-MAIN-20210125220722-20210126010722-00515.warc.gz | 309,420,633 | 11,738 | # Cartan's criterion
Cartan's criterion
Cartan's criterion is an important mathematical theorem in the foundations of Lie algebra theory that gives conditions for a Lie agebra to be nilpotent, solvable, or semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on $mathfrak\left\{g\right\}$ defined by the formula: $K\left(u,v\right)=operatorname\left\{tr\right\}\left(operatorname\left\{ad\right\}\left(u\right)operatorname\left\{ad\right\}\left(v\right)\right),$where tr denotes the trace of a linear operator. The criterion is named after Élie Cartan.
Formulation
Cartan's criterion states: : "A finite-dimensional Lie algebra $mathfrak\left\{g\right\}$ over a field of characteristic zero is semisimple if and only if the Killing form is nondegenerate. A Lie algebra $mathfrak\left\{g\right\}$ is solvable if and only if $K\left(mathfrak\left\{g\right\}, \left[mathfrak\left\{g\right\},mathfrak\left\{g\right\}\right] \right)=0.$"
More generally, a finite-dimensional Lie algebra $mathfrak\left\{g\right\}$ is reductive if and only if it admits a nondegenerate invariant bilinear form.
References
* Jean-Pierre Serre, "Lie algebras and Lie groups." 1964 lectures given at Harvard University. Second edition. Lecture Notes in Mathematics, 1500. Springer-Verlag, Berlin, 1992. viii+168 pp. ISBN 3-540-55008-9
* Modular Lie algebra
Wikimedia Foundation. 2010.
### См. также в других словарях:
• List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
• Trace (algèbre) — Pour les articles homonymes, voir Trace. En algèbre linéaire, la trace d une matrice carrée A est définie comme la somme de ses coefficients diagonaux et notée Tr(A). La trace peut être vue comme une forme linéaire sur l espace vectoriel des… … Wikipédia en Français
• Killing form — In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. In an example of Stigler s law of eponymy, the Killing form was actually invented… … Wikipedia
• Real form (Lie theory) — Lie groups … Wikipedia
• List of Lie groups topics — This is a list of Lie group topics, by Wikipedia page. Contents 1 Examples 2 Lie algebras 3 Foundational results 4 Semisimple theory … Wikipedia
• Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… … Wikipedia
• Solvable Lie algebra — In mathematics, a Lie algebra g is solvable if its derived series terminates in the zero subalgebra. That is, writing for the derived Lie algebra of g, generated by the set of values [x,y] for x and y in g, the derived series … Wikipedia
• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… … Wikipedia
• Tychonoff's theorem — For other theorems named after Tychonoff, see Tychonoff s theorem (disambiguation). In mathematics, Tychonoff s theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey… … Wikipedia
• Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… … Wikipedia
### Поделиться ссылкой на выделенное
##### Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку» | 1,033 | 4,044 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-04 | latest | en | 0.394318 |
https://math.stackexchange.com/questions/173400/solving-for-x-the-following-linear-equation-is-the-solution-a-unique-rectangu | 1,718,840,263,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861853.72/warc/CC-MAIN-20240619220908-20240620010908-00552.warc.gz | 331,448,177 | 37,007 | solving for $X$ the following linear equation, is the solution a unique rectangular matrix?
I have an invertible matrix $A$ of size $n \times n$ and a matrix $U$ of size $n \times m$, for $m < n$. Matrix $U$ is orthonormal, meaning, the rows are orthonormal vectors. I also have an $m \times m$ diagonal matrix $\Sigma$ with positive values on the diagonal.
I want to find the solution for the equation
$$X A U = \Sigma.$$
Since $U$ is orthonormal, then $U^T U = I$, and therefore, for $X = \Sigma U^T A^{-1}$, we have:
$$X A U = \Sigma U^T A^{-1} A U = \Sigma.$$
I would like to know if this is the only solution, and if so, how to show it.
• Is $U$ in the first line the same as $B$? Is $\Sigma$ the $m \times m$ diagonal matrix and you are solving for $X$? Commented Jul 20, 2012 at 21:40
• @Ross, terribly sorry. I fixed the question. Yes to both of your questions. Commented Jul 20, 2012 at 21:45
• @copper, I am confused by your answer. I stared a bit at the equation and guessed the solution. My problem is that even though $U'U = I$, we don't have $UU' = I$ because $m < n$. So we can't multiply both sides by $U'$. Commented Jul 20, 2012 at 21:48
• @kloop: OOps, sorry, I didn't check your calculation. I will delete my comment momentarily. Commented Jul 20, 2012 at 21:51
• The title is rather extraordinary in that it's so general that it could be the title for almost any question, but it doesn't actually fit this particular question, since you're not in fact asking how to find a solution; you've already found one and want to know whether it's unique. Please try to choose titles that summarize the question. Commented Jul 20, 2012 at 21:55
Since $\Sigma$ and $A$ are invertible, from $\Sigma^{-1}XAU=I$, we can characterize the solution set as the set of all matrices $X$ of the form $\Sigma VA^{-1}$, where $V$ is any matrix with $VU=I$. For $m\lt n$ there are matrices other than $U'$ with this property.
• thanks. that seems correct. but why can we "characterize the solution set as the set of all matrices $X$ of the form ..." ? Commented Jul 20, 2012 at 22:22
• Write $V=\Sigma^{-1}XA$. Then your equation is $VU=I$. Since $\Sigma$ and $A$ are invertible, there's a one-to-one correspondence between $V$ and $X$; being invertible, $\Sigma$ and $A$ merely "translate" between the two. So for any $V$ with $VU=I$, there's exactly one solution $X=\Sigma VA^{-1}$, and conversely, for every solution $X$, your equation requires $VU=\Sigma^{-1}XAU=I$. Commented Jul 20, 2012 at 22:35
Take $\Sigma = \begin{bmatrix} 1 \end{bmatrix}$, $A=\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$, $U = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$. Then the equation above becomes $$\begin{bmatrix} x_1 & x_2 \end{bmatrix} A U = \Sigma$$ and all solutions satisfy $x_1+x_2 = 1$. So the solution is not, in general, unique. | 874 | 2,824 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-26 | latest | en | 0.946801 |
http://us.metamath.org/ileuni/rexeqi.html | 1,652,708,082,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662510117.12/warc/CC-MAIN-20220516104933-20220516134933-00589.warc.gz | 64,759,143 | 3,340 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > rexeqi GIF version
Theorem rexeqi 2555
Description: Equality inference for restricted existential qualifier. (Contributed by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
raleq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
rexeqi (∃𝑥𝐴 𝜑 ↔ ∃𝑥𝐵 𝜑)
Distinct variable groups: 𝑥,𝐴 𝑥,𝐵
Allowed substitution hint: 𝜑(𝑥)
Proof of Theorem rexeqi
StepHypRef Expression
1 raleq1i.1 . 2 𝐴 = 𝐵
2 rexeq 2551 . 2 (𝐴 = 𝐵 → (∃𝑥𝐴 𝜑 ↔ ∃𝑥𝐵 𝜑))
31, 2ax-mp 7 1 (∃𝑥𝐴 𝜑 ↔ ∃𝑥𝐵 𝜑)
Colors of variables: wff set class Syntax hints: ↔ wb 103 = wceq 1285 ∃wrex 2350 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-cleq 2075 df-clel 2078 df-nfc 2209 df-rex 2355 This theorem is referenced by: rexrab2 2760 rexprg 3446 rextpg 3448 rexxp 4502 rexrnmpt2 5641 arch 8341 infssuzex 10478 gcdsupex 10482 gcdsupcl 10483
Copyright terms: Public domain W3C validator | 666 | 1,320 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2022-21 | latest | en | 0.171565 |
teytaud.over-blog.com | 1,506,131,453,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689413.52/warc/CC-MAIN-20170923014525-20170923034525-00476.warc.gz | 332,814,784 | 48,765 | 19 juin 2012 2 19 /06 /juin /2012 10:11
## Monte-Carlo Tree Search in one page
MCTS algorithm
Input: a state S
Output: a decision D
Global variable: a tree T, each node having nbSims
initiliazed at a single node with state S and nbSims=0 and totalReward=0
While (I have time)
{
Do one simulation from state S until a game is over
==> we get a sequence s(0), s(1), s(2), s(3),..., s(k) (with s(0)=S and s(k) a final state)
==> we get a reward r
Consider i minimal such that s(i) is not in T
If such an i exists, then add s(i) in T, with an edge from s(i-1) to s(i)
For each i such that s(i) is in T:
s(i).nbSims++
s(i).totalReward+=r
}
Procedure for doing one simulation from state S until a game is over:
s=S
while (s it not terminal)
{
choose child s' of s such that UCB(s') is maximum
s=s'
}
Procedure for computing the UCB score of a node s':
{
meanReward=s'.totalReward / s'.nbSims
fatherSims=s'.father.nbSims
UCB = meanReward + sqrt( log(fatherSims) / s'.nbSims)
}
Based on research in the TAO team
Repost 0
## commentaires
BASTARDI CRIMINALI MASSIMO DORIS ED ENNIO DORIS DI BANCA MEDIOLANUM MAFIOLANUM NAZISTANUM! 17/09/2017 03:37
FIGLIO DI PUTTANONA ANGELO LIETTI DI MEDIOLANUM, NAZISTANUM, NDRANGOLANUM, MAFIOLANUM! TENEVA I RAPPORTI CON GLI IMPRENDITORI ASSASSINI DI COSA NOSTRA: IGNAZIO ZUMMO E FRANCESCO ZUMMO! AI TEMPI DELL'ARRESTO DELL'AVVOCATO PEDOFILO E NEONAZISTA PAOLO SCIUME'!
IL TUTTO IN CONNESSIONE COL RAZZISTA, KU KLUK KLANISTA, MAFIOSO, MEGA RICICLA CASH MAFIOSO, LADRO, TRUFFATORE, PEDERASTA, CORROTTISSIMO, SEMPRE FALSO, ESTORTORE DI SOLDI, MEGA STALKER SU INTERNET, GIA' 3 VOLTE IN CARCERE, CACCIATO A SBERLE DA CITIBANK, INDAGATO DA 7 PROCURE ITALIANE E DALLA PROCURA DI LUGANO, MEGA MULTATO DALLA CONSOB, ORGANIZZANTE L'OMIDICIO DI DAVID ROSSI DI MONTE PASCHI: CRIMINALE, TRUFFATORE, ASSASSINO PAOLO PIETRO BARRAI NATO A MILANO IL 28.6.1965!
E' DAVVERO DA ARRESTARE SUBITO ( PRIMA CHE FACCIA AMMAZZARE ANCORA), IL TERRORISTA NAZIRAZZISTA ED ASSASSINO, PAOLO BARRAI, NATO A MILANO IL 28.6.1965. NONCHE' MEGA RICICLA SOLDI MAFIOSI E POLITI-C-RIMINALI, OSSIA FRUTTO DI MEGA RUBERIE E MEGA MAZZETTE, RICEVUTE DA LEGA LADRONA E STRAGISTA SPAPPOLA MAGISTRATI, NONCHE', TANTO QUANTO, NAZIFASCISTA DITTATORE E PEDOFILO: SILVIO BERLUSCONI! DICEVO, E' DAVVERO DA ARRESTARE UNA QUARTA VOLTA, E SUBITO, IL TERRORISTA NAZISTA ED ASSASSINO, PAOLO BARRAI. NON PER NIENTE, GIA' STATO IN GALERA 3 VOLTE. OPINIONI TUTTE TERRIFICANTI SU DI LUI! MEGA TRUFFATORE E MEGA RICICLA CASH ASSASSINO VIA CRIMINALISSIMA BLOCKCHAIN INVEST O VIA CRIMINALISSIMA BLOCKCHAININVEST CHE SIA, OLTRE CHE VIA CRIMINALISSIMA WMO SAGL LUGANO, CRIMINALISSIMA WORLD MAN OPPORTUNITIES LUGANO, CRIMINALISSIMA WMO SA PANAMA E CRIMINALISSIMA BSI ITALIA SRL DI VIA SOCRATE 26 MILANO! NOTO PEDOFIL-O-MOSESSUALE SODOMIZZA BAMBINI E RAGAZZINI! CACCIATO DA CITIBANK A SBERLE, PER MEGA FRODI CHE LI FACEVA! SBAGLIA SEMPRE IN BORSA! AZZERA I RISPARMI DI TANTISSIME PERSONE! FALSO&LADRO&TRUFFATORE! DIFFAMA SUL WEB A FINI NAZI-RAZZISTI! FONDATORE DEI NUOVI MEGASSASSINI TERRORISTI DI ESTREMISSIMA DESTRA: "NUOVI NAR"! FONDATORE DEL, PROSSIMAMENTE, DI FREQUENTE, OMICIDA: KU KLUK KLAN PADANO! CONDANNATO AL CARCERE A MILANO ED IN BRASILE ( 8 ANNI E PURE PER PEDERASTIA OMOSESSUALE, RIPETO, PURE PER PEDERASTIA OMOSESSUALE)! MULTATO DA CONSOB 70.000 €! DESTABILIZZA L'ITALIA PER FILO NAZISTI SERVIZI SEGRETI SVIZZERI ( ITALIA, DICEVAMO, DA 30 ANNI, GIUSTISSIMAMENTE, NAZIONE SCHIFATA IN TUTTO IL MONDO, IN QUANTO FASCIOMAFIOSA DITTATURA DI BERLUSCONIA.. NON PER NIENTE, TUTTE LE PIU' GRANDI INDUSTRIE, IN ITALIA DA SECOLI, DALLA TIRANNIASSASSINA DI BERLUSCONIA SON SCAPPATE, VEDI FIAT, PIRELLI, LUXOTTICA, MERLONI E MIGLIAIA E MIGLIAIA DI ALTRE... E CHE SIA CHIARO, PLS, CHE IDDIO BENEDICA I GRANDI PM CHE NON SOPPORTANTO IL CANCRO DEL MONDO INTERO, SILVIO BERLUSCONI, COME HENRY WOODCOCK, ILDA BOCASSINI E CHIUNQUE ALTRO DI QUESTA AMMIREVOLISSIMA CATEGORIA)! FA CRIMINI SU CRIMINI E NAZI-ST-ALKING, SU INTERNET, SU ORDINE DEI PUZZONI CRIMINALISSIM SILVIO BERLUSCONI, PAOLO BERLUSCONI ED UBALDO LIVOLSI DI FININVEST ( CHE DA ANNI FANNO GLI ADOLPH HITLER MISTI AD AL CAPONE, DEL WEB, ANCHE, MA DI CERTO, NON SOLO, CON QUEL VERME SCHIFOSAMENTE TERRORISTA DI GIULIO OCCHIONERO). INNEGGIANTE ALLO SPAPPOLAMENTO DI MAGISTRATI SCOMODI "COME BERLUSCONI GRANDISSIMAMENTE FECE CON FALCONE E BORSELLINO"! PAROLE SUE, DETTE SPESSISSIMO! ORGANIZZANTE OMICIDIO DI DAVID ROSSI DI MONTE PASCHI!
Ho tantissimo da scrivere sul gia' 3 volte finito in galera, accertatissimo pedofilo omosessuale, ladro, truffatore, sempre falso, nazi-st-alker, mandante di omicidi ( spesso, ma non sempre, mascherati da finti incidenti, malori o "suicidate"... come quando fece ammazzare David Rossi di Monte Paschi, ma ne scrivero' in dettagli molto presto), mega ricicla soldi mafiosi e/o politico-criminali (piu' tanto di orrido altro), arrestato gia' 3 volte, Paolo Barrai, nato a Milano il 28.6.1965 e gia' residente a Milano in Via Ippodromo 105! Come presto meglio sottolineeremo, multato dalla Consob ben 70.000 euro!
http://www.consob.it/main/documenti/hide/afflittivi/pec/mercati/2013/d18579.htm
http://www.bluerating.com/banche-e-reti/33345/qmultaq-da-70mila-euro-per-un-ex-promotore-che-ha-violato-gli-obblighi-informativi
Ho tantissimo da scrivere su sto Renato Vallanzasca ( in quanto ad indole malavitosa) misto ad Ugo Fantozzi ( in quanto ad essere il piu' grande ciula, perdente, cane in Borsa, brucia risparmi di tutti e sempre, sia esso su azioni, criptovalute, valute, obbligazioni, materie prime, case, diamanti, oro fisico, qualsiasi tipo di investimento... con la differenza che Ugo Fantozzi era simpatico e per bene a sua nettissima differenza) della finanza piu' filo mafiosa e ricicla soldi mafiosi che esista. In criminalissima Fineco, con arrogantissimo e delinquente promotore finanziario Luca Morelli (o arrogantissimo e delinquente promotore finanziario Luca Giovanni Morelli che sia).
Attraverso il pezzo di merda, promotore finanziario tutt'uno con la Ndrangheta, noto pedofilo Rocco Tripodi di criminalissima Hypo tirol bank Parma.
http://www.misterimprese.it/emilia-romagna/parma/parma/consulenza-finanziaria-e-commerciale/984184.html
Unitissimo agli assassini Massimo Colosimo e Antonio Bianco della sanguinarissima cosca dei Trapasso.
http://parma.repubblica.it/cronaca/2016/11/29/news/_ndrangheta_maxioperazione_contro_cosca_3_arresti_a_parma-153088843/
Oltre a lavare cash assassino ed essere noto pederasta, il criminamissimo promotore finanziario di Parma, Rocco Tripodi, e' un bastardo nazista, proprio come Paolo Barrai. Ciuccia i cazzi dei massoni Hitleriani di Casa Pound. Anche questo provabilissimo.
Non solo nel Parmense ma anche a Bolzano. A Bolzano in quanto e' tutt'uno anche con la nota lavatrice finanziaria di soldi della cosca immensamente assassina dei Pesce ( a little joke, please... Rocco Tripodi di criminalissima Hypo tirol bank Parma e' un noto pedofil-o-mosessuale, da sempre... gli piace "lu pesce", da qui che lava specialmente, ma non solo, per gli efferati assassini della cosca ndranghetista Pesce di Gioia Tauro) . Ossia Claudio Lucia a cui hanno effettuato un importante sequestro in Austria
http://www.ilfattoquotidiano.it/2015/04/27/ndrangheta-la-cosca-investe-in-austria-sequestrata-villa-al-tesoriere-del-clan-pesce/1627159/
L'avanzo di galera Paolo Barrai, lava cash assassino a gogo anche in Credit Suisse. Attraverso porco puzzolente, amatissimo sia da Cosa Nostra, che dalla Camorra, che dalla Ndrangheta ( per malavitosi riciclaggi di cash killer che fa a lor pro): Aldo Acquistapace, ben appunto, di Credit Suisse.
Residente in Via Lipari 7 a Milano, come anche in via Savona 23 a Milano e nato a Milano l'8.6.1960 ( fratello di criminalissimo Marco Acquistapace di Londra, presso Synergy Global Management Limited,
http://www.synglobal.com/lasocieta.html
un altro mega pezzo di merda super riciclante soldi mafiosi provenienti da killer di Puglia, Sicilia, Calabria, Campania, ma anche di Colombia, Romania ed Albania... da anni ed anni al centro di centinaia e centinaia di scandali, truffe e ruberie di ogni..
http://corrieredelmezzogiorno.corriere.it/bari/notizie/cronaca/2013/20-giugno-2013/soldi-fisco-finiti-uno-yacht-lussoa-processo-evasione-11-milioni-2221769688150.shtml
http://www.brindisireport.it/economia/aerotecsys-unoperazione-contestata.html
... ovviamente, scandali, truffe e ruberie tutte targate, ^neopiduistissimamente^, ^ occultissimamente^, fasciomafioso, stragista spappola magistrati, depravato lecca fighe di zoccole 14 enni marocchine: Silvio Berlusconi).
Lava, lava e stra lava cash mafioso In malavitosissima Banca Simetica di Via Costantino Crosa, 3c - 13900 BIELLA, dei porci mega ricicla soldi mafiosi PierLuigi Barbera e Giorgio Mello Rella.
http://www.bancasimetica.it/news.php
Mega ricicla cash assasino, di Mafia, Camorra, Ndrangheta, Sacra Corona Unita, in malavitosissima Banca Mediolanum dei banchieri criminalissimi Carlo Secchi ( puzzone schifoso, sempre a tramare a morte, via Trilaterale) Oscar di Montigny, Ennio Doris, Massimo Doris e Giovanni Pirovano!
http://www.mediolanum.com/ITA/12231_profili-manageriali.html
In malavitosissima IwBank delle merde criminalissime Massimo Capuano ed Andrea Pennacchia!
https://www.iwbank.it/governance
In malavitosissima Arner Bank Lugano dei colletti lerci stile "topi di fogna" Giovanni Schraemli, Gabriele Gandolfi e Roland Müller-Ineichen.
http://www.arnerbank.ch/?view=2242
In malavitosissima BancaStato Lugano dei verminosi delinquenti Bernardino Bulla, Fabrizio Cieslakiewicz, Daniele Albisetti e Claudio Genasci!
https://www.bancastato.ch/bancastato/chi-siamo/Corporate-Governance/Direzione-generale.html.
Attraverso criminalissima Tax and Finance Lugano, di quel porco schifoso, lurido, puzzone, mega ricicla cash mafioso che e' Gerardo Segat
https://pbs.twimg.com/media/CIB3862WcAA8F7c.png
http://www.moneyhouse.ch/it/p/gerardo-segat
( a cui era unito, un altro porco schifoso, lurido, puzzone, mega ricicla cash mafioso, Andrea Baroni, ex Tax and Finance, non per niente finito in galera
Come attraverso malavitosissima InvestireOggi.it del topo di fogna albanese Bogdan Bultrini, mega ricicla cash assassino di Mala, ben appunto, Albanese, ma anche Bulgara, Rumena, Turca e Russa!
COME ATTRAVERSO IL NOTO CRIMINALISSIMO PEDOFIL-O-MOSESSUALE STEFANO BASSI DE IL GRANDE BLUFF
E DI TORINO. TUTT'UNO CON LA NDRANGHETA E DA ANNI. CINTURA FRA ASSASSINI CALABRESI BASATI IN PIEMONTE, BEN NOTO SPAPPOLA MAGISTRATI E PEDOFILO SILVIO BERLUSCONI E LEGA LADRONA. LAVATRICE FINANZIARIA DEI KILLER NDRANGHETISTI CROTONESI DELLE FAMIGLIE OMICIDA VRENNA E MEGNA, VERI E PROPRI PADRONI DI MEZZO PIEMONTE.
PER NON PARLARE DELL'ALTRETTANTO PEDOFILO OMOSESSUALE PAOLO CARDENÀ DI CRIMINALISSIMO BLOG VINCITORI E VINTI ( SEMPRE A LAVARE CASH ASSASSINO, SPECIE DEI MAFIOSI IMMENSAMENTE ASSASSINO CRISAFULLI DI MILANO, MA NON SOLO)
PER NON DIRE, POI, DEL BASTARDO NAZIRAZZISTA E MEGA RICICLA SOLDI MAFIOSI: GIACOMO ZUCCO DI CRIMINALISSIMA BHB-BLOCKCHAINLAB, BLOCKCHAINLABIT, ASSOB.IT E WMO SA PANAMA ( NONCHE' DI HITLERIANI TEA PARTIES).
SCHIFOSO KU KLUK KLANISTA. CIUCCIA CAZZI MORTI DI SILVIO BERLUSCONI DA MATTINA A SERA. E, PER LO STESSO PEDOFILO SPAPPOLA MAGISTRATI SILVIO BERLUSCONI, LA MERDA MALAVITOSA GIACOMO ZUCCO, MEGA RICICLA SOLDI ASSASSINI DI BEN 7 NDRINE BASATE NEL MILANESE ( FRA CUI LA MEGA SANGUINARIA NDRINA DI SANTO PASQUALE MORABITO). COME DELL'EFFERATO KILLER CAMORRISTA SALVATORE POTENZA!
PER NON AGGIUNGERE DEL PARI PEDERASTA ED AZZERA RISPARMI FEDERICO IZZI, DETTO ZIO ROMOLO
( MEGA RICICLA CASH MALAVITOSISSIMO DEI GIRI LERCI DI MAFIA CAPITALE E DI CAMORRISTI PRESENTI NEL BASSO LAZIO
https://meloniclaudio.wordpress.com/2016/12/30/la-camorra-a-roma-e-nel-lazio/
http://www.iltempo.it/cronache/2013/11/02/gallery/i-veleni-della-camorra-nel-basso-lazio-913245/ ).
O DEL PARI PEDERASTA MAURIZIO BARBERO DI TECHNOSKY MONTESETTEPANI
SEMPRE IN THAILANDIA A STUPRARE BAMBINI SU BAMBINI
( ED IL NOTO PEDOFILO MAURIZIO BARBERO DI TECHNOSKY MONTESETTEPANI ERA CIO' CHE UNIVA I CREATORI DI NUOVE OVRA E GESTAPO, I BASTARDI CRIMINALI UBALDO LIVOLSI, FRANCESCA OCCHIONERO E GIULIO OCCHIONERO AD ENAV
http://www.ilfattoquotidiano.it/2017/01/13/giulio-occhionero-un-cyberspione-che-piu-maldestro-non-si-puo/3312745/
http://www.repubblica.it/cronaca/2017/01/10/news/cyberspionaggio_inchiesta-155753314/
DI CUI, NON PER NIENTE, TECHNOSKY MONTESETTEPANI, SOCIETA' CONTROLLATA DA SERVIZI SEGRETI DI ESTREMA DESTRA, SPESSISSIMO ASSASSINI, E' IN PIENO, PARTE).
E a proposito del pregiudicato, gia' stra condannato a galera Ubaldo Livolsi di criminalissima Livolsi - Iaquinta and partners e di Fininvest, nota in tutto il mondo come (Ma)Fi(a)Ninvest... Trattasi anche lui di viscidissimo pedofilo che paga ragazzini perche' lo inculino ( i Berlusconiani stanno ai pedofili, come il sole sta ad Habana Cuba a luglio... e da sempre..ad iniziare dal pedofilo dei pedofili numero uno al mondo: Silvio Berlusconi
http://www.elmundo.es/elmundo/2010/11/03/internacional/1288770719.html
http://www.huffingtonpost.it/2015/03/26/intervista-gianni-boncompagni_n_6945522.html
Pure assassino. Proprio cosi': pure assassino! Organizzava tanti omicidi fra il 2001 ed il 2006, omicidi mascherati da finti suicidi, malori ed incidenti. Il tutto targato "disarticolazioni attraverso mezzi traumatici (ossia killer)".
http://forum.enti.it/viewtopic.php?t=66625
http://www.ariannaeditrice.it/articolo.php?id_articolo=6352
http://www.omniauto.it/forum/index.php?showtopic=17113
http://www.grnet.it/news/95-news/852-segreto-di-stato-sulle-schedature-illegali-berlusconi-salva-pollari-a-pompa
http://ferdinandoimposimato.blogspot.pt/2007/07/il-sismi-gate-il-caso-pollari.html
http://penlib.blogspot.pt/2009/12/spiare-e-colpire-i-dossier-e-la-regia.html
Non siamo comunisti, ma anche questo link dice cose interessantissime
http://www.pmli.it/sismicolpivanemiciberlusconi.htm
Schifezze mega omicida che il pezzo di merda assassino Ubaldo Livolsi prima faceva col suo amante omosessuale Pio Pompa, noto in tutto il mondo come "er pompinaro" Pio Pompa ( cuginetto de "er nuovo pompinaro" Mike Pompeo dei prima citati, ku kluk klanisti Tea Parties e della nazifascista e nazimafiosa Cia attuale). E con lo schifoso verme, anche lui noto pederasta, Giulio Occhionero ( massone sata-n-azista del Goi). Fra l'altro sto verme viscidissimo di Ubaldo Livolsi da decenni mega ricicla cash assassino di Matteo Messina Denaro. E di certo non solo. E' gia' stato condannato al carcere per il caso Finpart http://www.repubblica.it/economia/finanza/2012/04/03/news/crac_finpart_livolsi_condannato-32697350/ Era dietro le piu' lercie puzzone trame dei furbetti del quartierino. Fa pedinare abusivamente. Intecetta telefonate abusivamente. Come detto, organizza nuove Ovra e Gestapo assassine. Sia pubbliche che private. Dovrebbe essere in carcere, ora, a spompinarsi col noto "er pompinaro" Pio Pompa ed il suo partner gay, nonche' terrorista nazifascista killer, Giulio Occhionero!
STA BESTIA SCHIFOSA DI PAOLO BARRAI RICICLA CASH KILLER ANCHE ATTRAVERSO UN'ALTRA SOCIETA' CRIMINALISSIMA: LA FRUIMEX DI TORINO, ALBA ... E "BLOGSPOT". SOCIETA' ESTREMAMENTE MALAVITOSA CHE RICICLA TANTI SOLDI MAFIOSI, ESATTAMENTE DELLA NDRANGHETA ( VIA FAMIGLIE MEGASSASSINE CALABRESI BELFIORE E CREA, NOTORIAMENTE, CONTROLLANTI TUTTA TORINO), MA ANCHE DI COSA NOSTRA E CAMORRA (SOCIETA' CRIMINALISSIMA, MEGA RICICLA SOLDI MAFIOSI FRUIMEX DI VIA NICOLA FABRIZI 44 10145 TORINO Tel: 011746342 COME ANCHE SOCIETA' CRIMINALISSIMA, MEGA RICICLA SOLDI MAFIOSI FRUIMEX DI ALBA: LOCALITA' SAN CASSIANO 15 - 12051).
https://www.guidamonaci.it/gmbig/main.php?p=comp_prof01&id=154326093763838
BASTARDAMENTE MALAVITOSA FRUIMEX "KAPEGGIATA" DA DUE SCHIFOSE PROSTITUTE DI ESTREMISSIMA DESTRA, SEMPRE AD ARCORE-HARDCORE A FARE SESSO ANALE. E DA ANNI ( VANNO A FARE SESSO ANALE AD HARDCORE-ARCORE DA TANTI ANNI... E PURE DA "TANTI ANI"). NOTA MIGNOTTONA NAZIFASCISTA PIERA CLERICO, BEN APPUNTO, DELLA FRUIMEX ( MADRE)
http://jenkins-ci.361315.n4.nabble.com/BASTARDISSIMA-TROIA-PIERA-CLERICO-FRUIMEX-A-CAPO-ANZI-A-quot-KAPO-quot-DI-TANTE-SETTE-SATANISTE-ANZI-td4897000.html
E NOTA MEGA TROIA, SEMPRE NAZIFASCISTA, ELISA COGNO, PURE DELLA FRUIMEX ( FIGLIA)
http://www.jlaforums.com/viewtopic.php?t=251058941
http://www.impresaitalia.info/mstdb80753147/fruimex-di-cogno-elisa-e-c-sas/alba.aspx
COME SAPETE, IL MONDO DEL BITCOIN E DELLA BLOCKCHAIN SERVE, AL 99,99999%, SOLO A RICICLARE SOLDI ASSASSINI! DI MAFIE DI TUTTO IL MONDO! E DI TERRORISTI KILLER DI ESTREMA DESTRA ( QUALE E' DA SEMPRE PAOLO BARRAI E TUTTI I VERMI SOPRA QUI CITATI)!
http://www.ilsole24ore.com/art/commenti-e-idee/2017-01-24/bitcoin-riciclaggio-invisibile-mafie-e-terrorismo-internazionale-164825.shtml?uuid=AEISiAH
http://fortune.com/2012/12/18/bitcoin-looks-primed-for-money-laundering/
https://www.bloomberg.com/news/articles/2016-11-11/hong-kong-central-bank-flags-blockchain-money-laundering-risk
DA QUI CHE ALTRI CRIMINI SU CRIMINI A LIVELLO DI RICICLAGGIO VENGONO EFFETTUATI FRA IL GIA' TRE VOLTE IN GALERA, PAOLO BARRAI ED IL DELINQUENTE SCHIFOSO RICCARDO CASATTA DI MALAVITOSE ETERNITY WALLS E GIA' CITATA BLOCKCHAINLAB!
COME FRA IL NOTO PEDOFIL-O-MOSESSUALE, TRUFFATORE, BRUCIANTE O LADRANTE I RISPARMI DI TUTTI E SEMPRE, PAOLO BARRAI E L'AL CAPONE DI LONDRA, CHIAMATO DA TUTTI "THE CRIMINAL BEAST": THOMAS BERTANI FROM ORACLIZE. ONE OF WORST MAFIA MONEY LAUNDERERS PRESENT IN THE CITY. PROPRIO COSI', A LONDRA LO CHIAMANO TUTTI " LA BESTIA CRIMINALE" A THOMAS BERTANI DI ORACLIZE. UNO DEI MASSIMI RICICLATORI DI CASH DEI MAFIE DI MEZZO MONDO DELLA CITY (INSIEME AL MEGA VERME, PARIMENTI CRIMINALISSIMO, DAVIDE SERRA DI ALGEBRIS, TWITTER E FACEBOOK... NON PER NIENTE SOCIO DEI PORCI DI COSA NOSTRA PRIMA CITATI DI BANCA MEDIOLANUM, MAFIOLANUM, CAMORRANUM, NDRANGOLANUM, NAZISTANUM... COME VEDETE, QUADRIAMO OGNI COSA E SEMPRE.. MA NON METTIAMO ORA, TROPPA CARNE A FUOCO, PLEASE.. TROPPA CARNE PUO' ANCHE DIVENIRE INDIGESTA... OGNI COSA LA DESCRIVEREMO SU DIVERSI TESTI AND REAL SOON).
Io, Gianni Panni, sono uno dei tantissimi da lui truffato. L'efferato criminale Paolo Barrai nato a Milano il 28.6.1965 mi ha azzerato tutti i risparmi. Come accaduto anche a centinaia e centinaia di altre persone come me.
http://www.today.it/user/profile/truffati/16094703496099/
https://www.rockit.it/user/pippo.lippo6
Si. Sono Gianni Panni di Modena (dovuto nick name per ovvi motivi di auto protezione). Manager della Maserati ( in questo caso per davvero: nessuna " nick profession"). giannipanni@gmx.com
Come tutti sanno, sto verme malavitoso di Paolo Barrai, e' stato condannato da Consob a pagare ben 70.000 euro di multa per mega truffa fatta da sto verminoso, vi assicuro, pure pederasta sodomizza bambini (ne scrivero' molto presto), che e' Paolo Barrai di criminalissima Bsi Italia srl di Via Socrate 26 Milano, criminalissima Blochain Invest o criminalissima Blockchainininvest che sia ( che controlla insieme ad un altro schifoso verme mega ricicla soldi mafiosi, via bitcoins, Natale Ferrara di Naters o verme mega ricicla soldi mafiosi, via bitcoins, Natale Massimiliano Ferrara di Naters, o verme mega ricicla soldi mafiosi, via bitcoins, Natale M. Ferrara di Naters che sia
unito poi, al citato, sempre mega ricicla cash assassino di Cosa Nostra, Camorra e Ndrangheta, Giacomo Zucco
http://jenkins-ci.361315.n4.nabble.com/CRIMINALISSIMA-BLOCKCHAINLABIT-DI-FIGLIO-DI-PUTTANA-GIACOMO-ZUCCO-VIA-GIA-3-VOLTE-IN-GALERA-PAOLO-BA-td4895904.html
che lava capitali assassini tanto quanto, via criminalissime BHB-Blockchainlabit e AssoB.it
Non per niente, noto nazista, razzista, mega kuklukklanista, rappresentante i terroristi assasini di estremissima destra, Tea Parties, nel verminaio swastikato di "loro" Berlusconia-Renzusconia-Gentilusconia-Salvinusconia-Calendusconia or whatever disgusting and horrid you may wanna call it). Per non parlare della criminalissima World Man Opportunities di Via Mazzini 14, 6900 Lugano, criminalissima WMO Sagl Lugano alias criminalissima Wmo Sa Panama e criminalissimo blog Mercato "Merdato" Libero. Multa connessa a sua mega frode sul fotovoltaico.
http://www.consob.it/main/documenti/hide/afflittivi/pec/mercati/2013/d18579.htm
Come e' stato condannato al carcere in Brasile, otto anni di galera sentenziatissimi. Per pedofilia omosessuale, furto, truffa, minacce di morte, tentativi di estorsione uniti a stalking via internet, riciclaggio di soldi mafiosi, propaganda razzista, propaganda nazifascista. Ecco i links di inizio indagine. Ora vi e' la sentenza. E' scappato da Porto Seguro, di notte, in pieno carnevale 2011, per fuggire a processo e galera ( ed ovviamente, da allora, di piedi in Brasile non ne ha mai piu' messi: perbacco che coincidenzuzza bedda). Fate voi di che schifoso topo di fogna parliamo quando parliamo di sto colerico ratto criminale che da sempre e' Paolo Barrai (o ratto criminalissimo "Paolo Pietro Barrai" nato a Milano il 28.6.1965..... come si fa chiamare all'estero, truffaldinamente, e quindi, come da suo solito... per vigliaccamente depistare Google)
http://4.bp.blogspot.com/-aqbT4KlYsmw/TcLbvUUpkeI/AAAAAAAAAe4/TiDPLR0LH_U/s1600/barrai+ind-pag01.jpg
http://noticiasdeportoseguro.blogspot.be/2011/03/quem-e-pietro-paolo-barrai.html
http://www.geraldojose.com.br/mobile/?sessao=noticia&cod_noticia=13950
http://www.jornalgrandebahia.com.br/2011/03/policia-civil-de-porto-seguro-investiga-blogueiro-italiano-suspeito-de-estelionato/
http://www.devsuperpage.com/search/Articles.aspx?hl=en&G=23&ArtID=301216
---
Condannato al carcere a Milano ad inizio anni 2000.
"Il funzionario di Citibank che faceva criminalissimi finti conti bancari e criminalissime finte transazioni bancarie" come da finale del seguente articolo, era assolutissimamente lui.
http://ricerca.repubblica.it/repubblica/archivio/repubblica/2001/02/19/maxi-evasione-da-400-miliardi-terenzio-sotto-torchio.html
Cacciato a sberle, poi, da Citibank e fatto condannare al carcere da stessa Citibank.
Il, vi assicuro, pure frequentissimo mandante di omicidi ( mascherati da finti suicidi, malori, incidenti, o meno), Paolo Barrai, e' uno degli assolutissimi killer di David Rossi di Monte Paschi. Unito in questo ai criminali, assassini, mega ricicla soldi mafiosi Silvio Berlusconi, Paolo Berlusconi, Marina Berlusconi, Fedele Confalonieri, Pasquale Cannatelli (noto come "o Ndranghetista pazzo", in quanto unitissimo alla cosca del noto assassino Sebastiano Romeo detto " U Staccu", per via delle tante teste che ha decapitato in vita sua), Yves "bastardo nazi" Confalonieri, Ennio Doris, Massimo Doris, Edoardo Lombardi, Ettore Parlato Spadafora, Luigi Del Fabbro, Annalisa Sara Doris, Luigi Berlusconi, Bruno Bianchi, Paolo Gualtieri ( indagato da mille procure), Angelo Renoldi, Carlos Javier Tusquets, Francesca Meneghel, Adriano Alberto Angeli, Marco Giuliani, Gianluca Bosisio, Angelo Lietti, Luca Maria Rovere, Carlo Secchi ed Oscar di Montigny ( parecchi di questi ultimi in Banca Mediolanum Mafiolanum Camorranum Ndrangolanum Lavapercocakaleroscolombianum Nazistanum Mediolanum), Giuliano Adreani, Franco Bruni, Mauro Crippa, Bruno Ermolli, Fernando Napolitano, Gina Nieri, Marco Giordani, Niccolò Querci, Stefano Sala, Carlo Secchi ( questi altri in Mafiaset, Camorraset, Ndangaset, MalaRussaset, TriadeCineseset, Nazistset, Mediaset), Ubaldo Livolsi (gia' condannato al carcere), Roberto Poli, Barbara Berlusconi e Salvatore Sciascia (questi altri, invece, in Fininvest, alias, ^Ma^Fi^a^ninvest), Adriano Galliani ( del dopatissimo, sempre compra partite e compra arbitri, Milan... ahahah... che non vuole mai nessuno, non per niente), Giuseppe Sabato, Andrea Cingoli, Vittorio Volpi ed Edoardo Lombardi ( questi altri ancora, in nazimafiosissima Banca Esperia). Aggiungendo al tutto, il verme piu' Berlus-corrotto del mondo, lo ripeto, verme Berlus-corrottissimo senza pari: Alberto Nagel di Mediobanca. I fatti, ora, a proposito della "suicidata Berlusconiana", ossia dell'assoluto ennesimo omcidio ordinato da Silvio Berlusconi e sua megassassina gang, in piccola parte, appena sopra citata. Fra il Giugno 2010 ed il Marzo 2011 ( allorche' David Rossi fu prima ferito a morte nel suo ufficio, a, tagliandogli le vene, b, colpendolo al cranio con un aggeggio in ferro, massonico, con punta triangolare, giungente direttamente dalla loggia massonica personale di proprieta' di Arcore-Hardcore di Al Capone misto ad Adolf Hitler, Silvio Berlusconi......
per solo poi, far volare David Rossi stesso dalla finestra
http://www.ilfattoquotidiano.it/2016/06/17/mps-morte-david-rossi-nessun-mistero-nel-video-choc-i-due-uomini-gia-sentiti-e-identificati-dai-pm/2838155/
http://www.lastampa.it/2016/06/17/italia/mps-video-shock-sulla-la-morte-del-banchiere-david-rossi-uBxB453zC6kiCascoy7w4I/pagina.html
) vi era una furibonda guerra di Seo, Search Engine Optimization, fra i bastardi, malavitosi, killer vertici di Fininvest, Mediaset e Banca Mediolanum ( che da dieci anni usano come loro mega ricicla soldi omicida e gangster via internet, questo verme davvero cattivo, davvero bastardo, davvero sata-n-azista di Paolo Barrai .... vero e proprio sicario sangunario di assolute Ovra e Gestapo, sia pubbliche che private, del nazimafioso, stragista, pedofilo Silvio Berlusconi) e David Rossi ( ovviamente, lui, per conto della sua banca). Ho varie testimonianze, a proposito, di come sto frequente mandante di omicidi di Paolo Barrai, dicesse spessissimo, ben appunto, fra il Giugno 2010 ed il Marzo 2011, al telefono e di persona: " abbiamo due persone da far ammazzare al piu' presto, David Rossi di Monte Paschi, che stiam cercando di distruggere via internet, e quel genio borsistico, pero' troppo intelligente ed anti Berlusconiano per i nostri gusti, Michele Nista, che da Londra, avendo mollato il mio blog, avendolo privato delle sue vincentissime previsioni borsistiche, lo sta facendo sprofondare in audience, qualita', da ogni punto di vista". David Rossi di Monte Paschi fu assolutissimamente fatto ammazzare dagli assassini Silvio Berlusconi, Marina Berlusconi, Oscar di Montigny, Ennio Doris, Massimo Doris di Banca Mediolanum, piu' altra parte di gang in cravatta, prima citata, insieme a loro killer Paolo Barrai di criminalissima Bsi Italia srl di via Socrate 26 a Milano, criminalissima World Man Opportunities Sagl di via Mazzini 14 a Lugano, alias criminalissima Wmo sa Panama. Leggete qui a seguito, con quale crudelta', sto ratto di fogna killer di Paolo Barrai stesso, festeggia la loro "suicidatassassina" di David Rossi. Urlando che fu "giusta cosa che David Rossi morisse ed in detta maniera ( firmando il loro omicidio, di fatto)" e spingendo disumanissimamente, financo, a non partecipare, ai di lui, funerali. E/o di come odiava e ridicolizzava David Rossi stesso, da vivo:
http://ilpunto-borsainvestimenti.blogspot.com.es/2013/03/andare-al-funerale-di-david-rossi.html
http://ilpunto-borsainvestimenti.blogspot.pt/2013/03/david-rossi-si-e-suicidato-o-cosi.html
http://ilpunto-borsainvestimenti.blogspot.pt/2016/06/si-scrive-david-rossi-si-legge-truffa.html
http://ilpunto-borsainvestimenti.blogspot.pt/2013/03/david-rossifesteggiamento-macabro-mps.html
http://ilpunto-borsainvestimenti.blogspot.pt/2016/09/defenestrato-viola-dal-terzo-piano-di.html
(vi sono ancora tantissimi agghiacchianti links, a proposito, che potrete trovare smanettando su internet.. io, piu' di 16-20 ore di lavoro al giorno, 24/7, purtroppo, ripeto, purtroppo, non riesco a fare )
In possesso della tessera di ... tenetevi forte, pls, and stra pls "ORGOGLIO PEDOFILO".
https://it.wikipedia.org/wiki/NAMBLA
STO SCHIFOSO DEPRAVATO ... LO DEVO DIRE... IN QUANTO VERO... SODOMIZZA BAMBINI, SODOMIZZA ZINGARELLI DI 8-10-12 ANNI, CHE E' L'ACCLARATISSIMO PEDOFIL-O-MOSESSUALE PAOLO BARRAI ( CHE IN VITA SUA HA FATTO ANCHE FILM PEDOPORN-O-MOSESSUALI, COME ANCHE, TENETEVI FORTISSIMO, PLS, CIUCCIANDO FALLI DI CAVALLI PER BERNE "EQUINO SPERMA".. DA QUI IL SUO ESSERE NOTISSIMO COME "CCC: CIUCCIA CAZZI DI CAVALLO PAOLO BARRAI"
http://rbnsn.com/pipermail/info-vax_rbnsn.com/2015-May/077000.html
ACCADETTE IN GERMANIA, UNGHERIA E ROMANIA! COME DA LUI STESSO DETTOCI! PAOLO BARRAI CIUCCIAVA FALLI EQUINI, BEVEVA SPERMA EQUINO E PRENDEVA NEL SUO INFINTO ANO, FALLI EQUINI.... AD INIZIO ANNI 2000, APPENA CACCIATO DA CITIBANK, PER POI VENIR CONDANNATO AL CARCERE SU DENUNCIA DI CITIBANK, PER VIA DELLE TERRIFICANTI FRODI PRIMA CITATE CHE PAOLO BARRAI, IVI VI FACEVA...
http://newsgroups.derkeiler.com/Archive/Comp/comp.soft-sys.matlab/2013-06/msg00535.html
IL TUTTO GIUSTO PRIMA DEL SUO INIZIARE A SPENNARE POLLI VIA WEB. L'ACCLARATISSIMO PEDOFIL-O-MOSESSUALE PAOLO BARRAI, GIA' ABITANTE A MILANO IN VIA IPPODROMO 105 ( LO CITO PER LA SICUREZZA DEI BAMBINI CHE ABITANO LI), NATO A MILANO IL 28.06.1965, RAGLIA SPESSISSIMO IN PRIVATO: " SIA NELLA THAILANDIA CHE TANTO AMO
http://ilpunto-borsainvestimenti.blogspot.pt/2015/11/bangkok-serata-allopus.html
COME NEL LATIN AMERICA
http://www.mercatolibero.info/panama-mercato-libero/
CHE PURE TANTO AMO, E' FACILE FARE SESSO CON RAGAZZINI DI 8-10-12 ANNI... TANTE BAMBINE DI 12-14 ANNI RIMANGONO IN CINTA.. QUINDI, QUANDO VIAGGIO LI, PAGO ED INCULO BAMBINI O POCO PIU' CHE BAMBINI, BEVO IL LORO PRIMO SPERMA... SON CONVINTISSIMO PEDERASTA, SON PER LA PEDOFILIA LIBERA E ME NE VANTO". HO SENTITO QUESTI SUOI DISCORSI DA VOMITO ANCHE IO, DI PERSONA, QUANDO VENNE A TROVARCI A MODENA.
http://ilpunto-borsainvestimenti.blogspot.be/2013/03/lunedi-11-marzo-cena-modena-per-parlare.html
PAOLO BARRAI ORGANIZZA, IN TUTTA SUA "TERRA PADANA", COME IN CANTON TICINO, CENTINAIA E CENTINAIA E CENTINAIA DI ORGE "PEDOFILESC-O-MOSESSUALI"! PIENE DI SESSO OMOSESSUALE DEPRAVATISSIMO! SENZA PROTEZIONE! FRA CENTINAIA E CENTINAIA DI FOLLI DROGHE! PAOLO BARRAI E' ORMAI UN DECEREBRATO MEGA COCAINOMANE, PIENO DI HIV, GONORREA, SIFILIDE E CENTOMILA INFEZIONI ANALI. A LUGANO E MILANO E' IL RAS DI QUESTO SESSO FRA PERVERTITI PEDOFILI, SEMPRE, COME DETTO, STRETTAMENTE OMOSESSUALI
http://www.corriere.it/cronache/17_febbraio_26/ecco-via-quanti-siete-sigle-codici-eccessi-feste-sesso-estremo-gay-grindr-iene-9b38d840-fba2-11e6-8df2-f7ebe5fcea94.shtml
http://it.aleteia.org/2016/03/08/sesso-perverso-e-voglia-di-forti-emozioni-dietro-lomicidio-di-luca-varani/
( E NONOSTANTE SIA SPOSATO CON UNA NOTA EX PROSTITUTA MILANESE, BARBARA BORGONOVO, NATA A MILANO IL 26.6.1966.. ED ABBIA DUE FIGLI, CHE, DA PERICOLOSISSIMO PEDOFILO CHE PAOLO BARRAI DA SEMPRE E', SODOMIZZA O STUPRA IN GENERE, DA QUANDO POCO PIU' CHE NEONATI... OSSIA, LA DA SEMPRE SODOMIZZATA COSTANZA BARRAI NATA A MILANO IL 1.1.1999 ED IL DA SEMPRE SODOMIZZATO RICCARDO BARRAI NATO A MILANO IL 26.11.1996, QUEST'ULTIMO, ORMAI, PIU' CHE VENTENNE, ANCHE LUI GAY DI TIPO PERVERTITISSIMO, SEMPRE AD ORGE DROGATISSIME E DEPRAVATE, SOPRA CITATE). HO MILLE TESTIMONI A PROPOSITO DI QUESTO E SONO PRONTO A DEPORNE IN QUALSIASI TRIBUNALE ( TESTIMONI, TUTTI COME ME, EX FORZA ITALIA O EX LEGA NORD O EX CASA POUND O EX FIAMMA TRICOLORE O EX FORZA NUOVA O EX GRAN LOGGIA D'ITALIA, CHE, COME TUTTI SANNO, DA SEMPRE SIGNIFICA MASSONERIA DI ESTREMISSIMA DESTRA). IO, GIANNI PANNI, MANAGER DELLA MASERATI DI MODENA ( PUR SE IL MIO NOME E COGNOME, PER PROTEGGERLO, E' QUI, ORA, PER OVVI MOTIVI, UN NICK... MA NON LO E' LA MIA PROFESSIONE), NON HO NULLA CONTRO I GAYS ONESTI E NON PERICOLOSI ( PER SE ED ALTRI), SIA CHIARO, MA CHIAMO LE COSE SEMPRE COL LORO NOME E LO FARO' HASTA L'ULTIMO SECONDO DE MI VIDA.. HASTA LA VISTORIA SIEMPRE ( DETTO APPOSTA ALLA CHE GUEVARA, PROPRIO PER PROVOCARE TUTTI STI BASTARDI NAZIFASCISTI ASSASSINI PRIMA CITATI, PUR SE COMUNISTA NON SONO E NON SONO MAI STATO)!!
Fa sempre, il pure verminoso stalker e criminale informatico in genere, Paolo Barrai, via Hitleriano e mafioso Gruppo Fininvest di criminalissimi Marina Berlusconi e Silvio Berlusconi che lo proteggono, hackerare miei Facebook, Linkedin o Google accounts ( da sempre delinquenzialissimo Gruppo Fininvest, che gli "gira" tonnellate di soldi assassini da lavare per conto di loro spietati omicida di Cosa Nostra, Camorra, Ndrangheta, Mala russa, Triade cinese, Mala messicana, Mala colombiana, come soldi rubati o frutto di mega mazzette da parte di verminosi Gruppi come Finmeccanica, o Partiti immensamente malavitosi, a cui ero iscritto, e da cui, proprio per i loro tantissimi crimini che ho visto, sono scappato, tipo l'ex Pdl, "Popolo di Ladroni" ora Forza Italia "mafiosa" e LL "Lega Ladrona" ... detto cash criminalissimo, prima veniva riciclato con l'ausilio della famiglia nazirazzista dei Pesenti, presso loro Finter Bank Zurich e Bahamas, guidate da noti banchieri di Cosa Nostra, Camorra e Ndrangheta, Filippo Crippa e Giovanni Dei Cas.... ora che le autorita' svizzere han imposto a sti bastardi nazirazzisti Ku Kluk Klanisti dei Pesenti di vendere Finter Bank, la stessa e' passata a Bank Vontobel...
http://www.repubblica.it/economia/finanza/2015/09/04/news/i_pesenti_vendono_la_banca_svizzera_finter_per_74_milioni-122187737/
e la stessa Bank Vontobel, "sempre non per niente", come primissima decicione, ha cacciato LETTERALISSIMAMENTE A CALCI IN CULO, IL TOPO DI FOGNA, GIA' 3 VOLTE IN GALERA, PAOLO BARRAI... CHE ORA EFFETTUA SUOI CRIMINALISSIMI RICICLAGGI DI CASH ASSASSINO, PRESSO PUZZOLENTE SCHIFOSO PORCO CLAUDIO GENASCI DI BANCA STATO LUGANO E LURIDO TOPO DI FOGNA BERNARDINO BULLA, PURE DI BANCA DELLO STATO DEL CANTON TICINO DI LUGANO.. NE SCRIVE, DI TUTTO QUESTO, UN LORO MANAGER, ANDREAS NIGG, QUI
https://plus.google.com/100971124804472238998 ). Ovvissimamente, in quanto svelo assolute verita' che li imbarazzano. Ma appena mi faran hackerare un altro solo account, ne riapriro' centoventisei: fra Facebook, Linkedin, Blogger, Google Plus, You Tube, e migliaia e stra migliaia di Blogs.
But let's go ahead now, pls, let's go ahead. Iamm bell, ia'.
Il sempre azzerante risparmi di tutti, cagnaccio in Borsa come nessun altro al mondo, Paolo Barrai di criminalissima World Man Opportunities di Via Mazzini 14, 6900 Lugano o criminalissima Wmo Sa Panama che sia, e criminalissima Bsi Italia srl via Socrate 26 Milano, fece comprare il Bitcoin a 700\$, dicendo che in un baleno sarebbe andato a 70.000\$.. lo stesso scese, a seguito, "appena appena", fino a sotto 250\$
( http://ilpunto-borsainvestimenti.blogspot.be/2014/03/bitcoin-con-giacomo-zucco-stiamo-ridendo.html)
Come suo idiotissimo e perdentissimo solito, quando il Bitcoin, poi, ad inizio 2015, raggiunse quota 250 ( con l'asino azzera risparmi Paolo Barrai che aveva causato ai ciucci come lui, una perdita, "appena appena" del 75%), questo Al Capone misto ad Ugo Fantozzi della finanza, disse che lo steso Bitcoin era da shortare, in quanto sarebbe andato a zero... E cosa e' accaduto? " Iamm e stra iamm bell, ia'". Che lo stesso e' tornato a 700 dollari. Gia' tre volte in galera Paolo Pietro Barrai nato a Milano il 28.5.1965: siamo di fronte al piu' grande cesso, al piu' grande idiota, al piu' grande perdentissimo imbecille della finanza, mai venuto al mondo, " y de stra verdad ( come leggo, in tanti, scrivono in giro)"! Ma non e' finita. No babies. No, no, no e stra no. In data 16.6.2016, l'azzera risparmi di tutti e sempre, Paolo Barrai, il, pure noto pedofil-o-mosessuale, nonche' mandante di "suicidate" come fatto con David Rossi di Monte Paschi, l'assassino Paolo Barrai, raglio' che il Bitcoin a 740 dollari ( ove era, more or less, in data 16.6.2016) era da stracomprare. Che a pochissimi giorni lo si sarebbe visto oltre i 1000 dollari.
http://ilpunto-borsainvestimenti.blogspot.pt/2016/06/bitcoin-ultimi-giorni-per-comprarlo.html
Cosa e' successo? Iamm bell, ia', che e' successo a seguito? Che 45 giorni dopo il Bitcoin fini' a 580 dollari. Il brucia risparmi altrui a gogo, Paolo Barrai, anche in questo caso, fece perdere a tutti i ca-n-azisti che lo seguono, un altro 35% dei propri risparmi! I fatti parlan molto meglio che miliardi di parole. Action speaks louder than words!
IN DATA 6 AGOSTO 2017, IL MANDANTE DI OMICIDI, MEGA LAVA CASH MAFIOSO E BASTARDO TRUFFATORE RAGLIAVA " BITCOINS VOLERA' SU FINO A 6000 DOLLARI IN UN BALENO"
http://ilpunto-borsainvestimenti.blogspot.pt/2017/08/bitcoin-la-nuova-era.html
MA AD INIZIO SETTEMBRE 2017, APPENA UN MESE DOPO, LO STESSO BRUCIA RISPARMI DI TUTTI E SEMPRE, RI RAGLIAVA CHE LO STESSO BITCOINS ERA LI PER PRECIPITARE, GIU, A ZERO
http://ilpunto-borsainvestimenti.blogspot.pt/2017/09/settembre-bero-per-bitcoin-e.html
SIAMO A CHE FARE CON UN COCAINOMANE PAZZO, CHE DOVREBBE MARCIRE IN GALERA FOR EVER AND EVER. UNA PROVA? ECCOLA QUI. UN ALTRO UOMO CHE CON LUI HA PERSO TUTTI, TUTTI, TUTTI I PROPRI RISPARMI!
" SONO ANCHE IO APPENA STATO TRUFFATO A MORTE DALLA CAROGNA CRIMINALISSIMA PAOLO BARRAI!
MI FECE COMPRARE IL BITOCOIN A 2980 DOLLARI. ATTORNO AL 12.6.2017. ASSICURANDOMI CHE SAREBBE ANDATO A 10.000 DOLLARI, DI CERTISSIMO, ENTRO FINE 2017. MI FACEVA LEGGERE SEMPRE QUESTO SUO POST SUPER IDIOTA, INCOMPETENTE ED ANCOR PIU' TRUFFALDINO
http://ilpunto-borsainvestimenti.blogspot.com.es/2016/12/they-love-bitcoin-10000-usd-per-bitcoin.html
PER VIA DEI MARGINI IL BROKER ME LO HA VENDUTO A 2.380 IL 10.7.2017. MENO CHE UN MESE DOPO. HO PERSO 35.000 EURO, TUTTI I MIEI RISPARMI ( SONO UN NEOLAUREATO DELLA BOCCONI, FIGLIO DI UN DIRETTORE CENTRALE DI UN IMPORTANTE ISTITUTO BANCARIO). ERO IN LEVA. SU SPINTA DI STO CRIMINALE BASTARDO DI PAOLO BARRAI. UNA VOLTA CHE HO PERSO TUTTO, MI HA PURE DETTO AL TELEFONO "CAZZI TUOI, FIGLIO DI PUTTANA, VAI A FANCULO, E NON MI CHIAMARE MAI PIU', TANTO, SU INTERNET, DI COGLIONI COME TE NE TROVO SEMPRE"! LO HO QUERELATO. SPERIAMO CHE I BASTARDI MAFIOSI E NAZISTI MATTEO SALVINI, ENNIO DORIS E SILVIO BERLUSCONI CHE PROTEGGONO QUESTO PURE NOTO PEDOFILO OMOSESSUALE DI PAOLO BARRAI, NON FACCIANO SOTTERRARE IL TUTTO, IN TRIBUNALE, A MILANO. MAI AVERE A CHE FARE CON STA CAROGNA MEGA COCAINOMANE, ARROGANTE E BRUCIANTE TUTTI I TUOI RISPARMI, CHE E' PAOLO BARRAI. E' DAVVERO IL RENATO VALLANZASCA DELLA FINANZA, COME GIUSTAMENTE, CITATO QUI!
http://jenkins-ci.361315.n4.nabble.com/VERME-TRUFFATORE-PAOLO-BARRAI-GIA-IN-MANETTE-NON-IN-WIKIPEDIA-INDAGATO-DA-PROCURA-DI-LUGANO-COME-DA--td4897021.html "
VISTO CHE TESTIMONIANZA SHOCK. UNA SU MILIARDI E MILIARDI, ORMAI, DI CHI HA PERSO TUTTO CON PAOLO BARRAI. NE VOLETE ALTRE, NE TROVATE A BIZZEFFE E STRA BIZZEFFE QUI!
Ma andiamo avanti. Avanti, avanti, iamm bell ia', iamm bell! In data 20.7.2015 fece comprare Ftse Mib ragliando che sarebbe andanto subito a 40.000, e lo stesso, sempre a seguito... e' sempre solo sceso, sceso...sceso.. "appena appena".. fino a 16.000
( http://ilpunto-borsainvestimenti.blogspot.be/2015/07/la-borsa-italiana-e-sui-massimi.html )
Volete ridere istericamente per tirarvi su un po' su, ora, please? Il mega cocainomane, l'auto proclamantesi pedofil-o-mosessuale, il tre volte condannato al carcere fra Milano, Brasile e non solo, il notissimo avanzo di galera Paolo Barrai, scrisse che l'inizio del 2016 sarebbe stato esagerato, opulento, ricco... Ahahhaha: ovviamente tutto e' precipitato, ed anche molto piu' del 50%. In un solo mese e mezzo di inizio 2016 (non per niente, il genio borsistico e direi anche eroe civile, Michele Nista di Londra, che taglio' ogni rapporto professionale, ed anche solo di conoscenza, con la bestia criminalissima Paolo Barrai, nel 8.2009, notando che ricicla soldi mafiosi egli fosse .. e che per questo riceve il di lui stalking assassino.... scrisse a suoi clienti ed amici, e dal Giugno 2015, di disatri borsistici in arrivo, sia nell'Agosto 2015, che ad inizio 2016, come accaduto poi con microchirurgica perfezione.. come disse poi di andare lunghissimi di azioni, prevendendo mega rialzi delle stesse, come poi ri accaduto con microchirurgica perfezione). Leggete qui, please. Giusto per piegarsi in tre dalle risate, por please and stra please...
http://ilpunto-borsainvestimenti.blogspot.com.es/2015/10/il-nuovo-rinascimento-italiano-del-2016.html
MAI VISTO UN IDIOTISSIMO REVERSAL INDICATOR COME IL SEMPRE PEREDENTE PAOLO BARRAI.... COME IL CIUCCIA PENI DI BAMBINI, ACCLARATO PEDOFILOMOSESSUALE PAOLO BARRAI DI CRIMINALISSIMA WORLD MAN OPPORTUNITIES LUGANO, CRIMINALISSIMA WMO SA PANAMA E CRIMINALISSIMA BSI ITALIA SRL DI VIA SOCRATE 26 MILANO.... QUANDO FA COMPRARE, OGNI VOLTA, TUTTO CROLLA... QUANDO FA VENDERE, SENZA ECCEZIONE ALCUNA, TUTTO SCHIZZA VERSO L'ALTO
http://ilpunto-borsainvestimenti.blogspot.com.es/2015/10/il-nuovo-rinascimento-italiano-del-2016.html
Non basta??? Iamm nnanz. Iam bell, ia'. Fece vendere il Dow Jones, ragliando che sarebbe crollato a 15.000 ed in un mese lo stesso volo' su a a 18.000.
( http://ilpunto-borsainvestimenti.blogspot.be/2014/10/dow-jones-atteso-in-area-15000.html)
Ragliava in data 18.2.2015, che i suoi mandanti (a livello di stalking assassino che il verme criminale Paolo Barrai fa da sempre su internet), ossia i nazimafiosi, spappolatori di Giovanni Falcone e Paolo Borsellino, mandanti di centinaia di omicidi mascherati (da finti suicidi, malori ed incidenti), ladri, truffatori, dittatori, por-co-rruttori, mega cocainomani e pedofili, ossia i Berlusconi e Doris, avrebbero visto la loro Camorraset Ndrangaset Mediaset, volare fino a 5,8 euro
http://ilpunto-borsainvestimenti.blogspot.com.es/2015/02/mediaset-quando-e-non-sesuperera-i-410.html
Et voila'... fai l'opposto di quel che raglia l'asino fallitissimo Paolo Barrai e divieni ricchissimo. All the times, again and again and again. Non per niente, nel frattempo, questo monnezzaio di Camorraset Ndrangaset Mafiset Nazistset Mediaset ha perso "solo" un 60% ( e valeva 25 euro, quindi, dai veri massimi, ha perso il 97% circa). In data 30.7.2016, la stessa fini' a 2,70 euro ( per non parlare del Milan che schifa a tutti, e non lo compra mai nessuno... ovviamente, nessuno, tranne il pedofilo spappola magistrati Silvio Berlusconi stesso, via suoi porci prestanome della Triade http://www.calciomercato.com/news/tre-scatole-cinesi-per-il-milan-284579 ) . Ed il grandissimo Vincent Bollore', che visto che razza di sarcofago pieno di ossa di morti e vermi e' Mediaset Premium ( che fa perdite record su perdite record di continuo), della stessa non vuole piu' nulla. E giustissimamente! GRANDE VINCENT BOLLORE, GRANDISSIMO. ALLA FRANCESE: CHAPEAU!
Ma ancora... again and again and again... Fece comprare il Gas Naturale a 12 \$, 10\$, 8\$, 6\$, 4\$ e lo stesso precipito' "appena appena", a seguito, fino a 2\$ ( perdita secca del 90%.. da infarto... fate voi, pls)
http://ilpunto-borsainvestimenti.blogspot.com.es/2010/06/natural-gas.html
http://www.infomine.com/investment/metal-prices/natural-gas/5-year/
Fece vendere o non sottoscrivere i Btp e da quel momento son divenuti oro misto a platino.
http://www.tempi.it/barrai-btp-day-assurdo-conviene-cercare-protezione-svizzera#.WLLi0lU1-po
Fece comprare a Mafia, Camorra e Ndrangheta ( come prima citato, suoi veri e soli clienti.. che se ne fregano delle performances, volendo solo lavare capitali assassini), case, in Brasile, nel Marzo 2011, e da allora il Real Brasiliano ha perso "solo" il 73% per cento.
http://www.forexinfo.it/Real-brasiliano-rischia-il-tracollo-tra-crisi-economica-e-politica
http://www.xe.com/currencycharts/?from=BRL&to=EUR
A seguito venne condannato al carcere in Brasile, otto anni di galera sentenziatissimi. Per pedofilia omosessuale, furto, truffa, minacce di morte, tentativi di estorsione uniti a stalking via internet, riciclaggio di soldi mafiosi, propaganda razzista, propaganda nazifascista. Ecco i links di inizio indagine. Ora vi e' la sentenza. E' scappato da Porto Seguro, di notte, in pieno carnevale 2011, per fuggire a processo e galera ( ed ovviamente, da allora, di piedi in Brasile non ne ha mai piu' messi: perbacco che coincidenzuzza bedda). Fate voi di che schifoso topo di fogna parliamo quando parliamo di sto colerico ratto criminale che da sempre e' Paolo Barrai (o ratto criminalissimo "Paolo Pietro Barrai" nato a Milano il 28.6.1965..... come si fa chiamare all'estero, truffaldinamente, e quindi, come da suo solito... per vigliaccamente depistare Google)
http://4.bp.blogspot.com/-aqbT4KlYsmw/TcLbvUUpkeI/AAAAAAAAAe4/TiDPLR0LH_U/s1600/barrai+ind-pag01.jpg
http://noticiasdeportoseguro.blogspot.be/2011/03/quem-e-pietro-paolo-barrai.html
http://www.geraldojose.com.br/mobile/?sessao=noticia&cod_noticia=13950
http://www.jornalgrandebahia.com.br/2011/03/policia-civil-de-porto-seguro-investiga-blogueiro-italiano-suspeito-de-estelionato/
http://www.devsuperpage.com/search/Articles.aspx?hl=en&G=23&ArtID=301216
.....COME CANTAVA LA GRANDE LYNN COLLINS... "AGAIN AND AGAIN AND AGAIN AND AGAIN"....
Fece comprare l'oro a 1800 dollari, nell'Estate 2011, ed a seguire, lo stesso, e' "solo" precipitato fino a 1160 dollari.
http://www.nasdaq.com/markets/gold.aspx?timeframe=10y
Fece comprare il petrolio a 105 dollari e passa, nella primavera 2014, e lo stesso e' caduto in un baratro: giu fino a 27 dollari!
http://www.nasdaq.com/markets/crude-oil.aspx?timeframe=10y
Raglio' di "de dollarizzazione", a fine 2011, mentre l'euro valeva 1,40 contro un dollaro, e lo stesso dollaro ha poi guadagnato un 30% e passa contro l'euro.
http://www.xe.com/currencycharts/?from=EUR&to=USD&view=10Y
POTREI RIPORTARE ALTRI MILLE ESEMPI QUI. MILLE. COME MINIMO. COMPROVANDOLI COI LINKS DI "MERDATO" LIBERO! SUPER STRA DIMOSTRANTI CHE CA-N-AZISTA BRUCIA RISPARMI DI TUTTI E SEMPRE SIA PAOLO BARRAI! MA PER POTERLO FARE, LA MIA GIORNATA LAVORATIVA DOVREBBE ESSERE DI MILLE ORE AL DI' E NON 24. MA ESSENDO CHE MI CHIAMANO DA SEMPRE "IL MASTINO NAPOLETANO DELLA MASERATI", NON MOLLERO' MAI E STRA MAI, ED IL TEMPO LO TROVERO' DI CERTO. GRADUALMENTE, MA LO TROVERO'. DOVESSI CREPARE SU UN COMPUTER, DI INFARTO, ANCHE OGGI STESSO.
Ora, please... vi rendete conto di quanto perdereste tutti i vostri risparmi e vi sputtanereste in tutto il mondo, ad affidarvi o anche solo ad accostarvi a... parole sue.. sto " bevitore di primo sperma di dodicenni", quale e' e stra e' il gia' tre volte in galera, verminoso pedofilomosessuale Paolo Barrai di criminalissima Wold Man Opportuinities di Via Mazzini 14, 6900 Lugano, alias criminalissima Wmo sa Panama e criminalissima Bsi Italia srl di via Socrate 26 a Milano ( indagato al momento in Svizzera.... a rischio di arresto a Lugano.... come in mezza Italia pure... misero in carcere suoi compari di mega riciclaggi di cash assassino e/o Berluscriminale come di Lega Ladrona, imboscatisi, non per niente, come lui, in Canton Ticino, quale il finito in carcere Alessandro Proto
http://www.caffe.ch/stories/Economia/37256_spregiudicati_affaristi_di_frontiera/
http://www.ilfattoquotidiano.it/2013/02/14/manipolazione-del-mercato-arrestato-a-milano-finanziere-alessandro-proto/500117/
ed il finito in carcere Andrea Baroni di criminalissima Tax and Finance Lugano con cui Paolo Barrai lavava soldi assassini, assassini, di mafie di mezzo mondo, a go go
https://pbs.twimg.com/media/CIB3862WcAA8F7c.png
http://www.repubblica.it/sport/calcio/2015/10/10/news/diritti_tv_baroni_arresto-124762513/
speriamo che in galera finisca per la quarta volta, pure il frequentisismo mandante di omicidi Paolo Barrai nato a Milano il 28.6,1965.. ovvero .. speriamo che in galera finisca per la quarta volta, pure il frequentisismo mandante di omicidi Paolo Pietro Barrai nato a Milano il 28.6,1965, ed al piu' presto possibile)? Scritto per mero vostro bene. Questo e' solo un antipastino su chi e' davvero sto mega truffatore e mega avanzo di galera di Paolo Barrai. Fra poco mi stra scatenero' giorno e notte per farlo sapere anche su Marte e Venere, non solo su questo pianeta, sempre... piu' piccino. A fra non molto. Gianni Panni. Modena. giannipanni@gmx.com
PS
A prescindere dai gusti politici di ognuno ( io ero di destra, come citato, mentre ora sono piu' di centro, ma son sempre stato e sempre rimarro' assolutissimamente d-e-m-o-c-r-a-t-i-c-o), per terminare, guardate questo nazista, questo kukluklanista, questo razzist-a-ssassino di Paolo Barrai, come diede ad Obama Barack, del "BASTARDO NERO"
http://ilpunto-borsainvestimenti.blogspot.nl/2013/01/ecco-limpatto-fiscale-che-ha-fatto.html
O DELLA "CHECCA ISTERICA"
( la cosa totalmente demente, totalmente decerebrata, e' che Paolo Barrai, e', come citato prima, un noto, autodichiarantesi, pedofil-o-mosessuale, ossia un pederasta che fa sesso a pagamento, o usando violenza, con poco piu' che bambini...CHE FA SESSO DA SEMPRE COI PROPRI FIGLI, DA QUANDO ERANO POCO PIU' CHE NEONATI.... e da' della checca isterica ad Obama Barack... questo Renato Vallanzasca depravato della finanza mondiale che e' Paolo Barrai e' da internare per un venti anni, in galera, e se gli rimane, poi, tempo da vivere, detto tempo deve venir fattogli passare totalmente in manicomio criminale... ed a partir da subito... o, il pure assassino Paolo Barrai, fara' ammazzare ancora, come fatto con David Rossi di Monte Paschi e di certo non solo)!
ED ORA UNA SCIOCCANTISSIMA TESTIMONIANZA DA PARTE DI ANTONELLA COHEN, SENIOR CONSULTANT DI GOLDMAN SACHS LONDON, PLS.
Gruppo di risparmiatori truffati da criminale Paolo Barrai di mlavitosissime societa' Bsi Italia srl, Wmo Sa Panama, World man opportunities Lugano. Gruppo di risparmiatori truffati da incapace, delinquente, ladro, nazista, antisemita, vigliacchissimo, truffatore, azzerarisparmi di una vita, Paolo Barrai del blog Mercato Libero, non per niente, nickato da tutti, nel mondo: Merdato Libero. Colletto malavitoso Paolo Barrai nato a Milano il 28.6.1965. Facente suoi crimini su crimini da Via Ippodromo 105, Milano ( tel 02.4521842).
Ciao, sono Antonella Cohen di Londra e Milano e faccio parte di un foltissimo gruppo di clienti truffati dall'assolutamente criminale Paolo Barrai di Mercato Libero.
http://www.consob.it/main/documenti/hide/afflittivi/pec/mercati/2013/d18579.htm
Costui è davvero uno spietato delinquente. A tutti noi, uniti ora in una associazione " risparmiatori truffati dal criminalissimo Paolo Barrai di Mercato Libero " e siamo gia’ in centocinquanta, dico, centocinquanta", di tutta Italia ed anche mezza Europa, ci fece andare corti ( al ribasso) sul mercato azionario italiano a inizio marzo 2009. Abbiam perso quasi tutti tra il 50 e il 90 per cento dei nostri investimenti. E quando lo telefonavamo per chiedere semplicemente che fare, mentre il mercato saliva rapidissimamente, egli, come un vile ratto, scappava, si faceva sempre negare al telefono. Mandavamo e mails, nessuna risposta. Citofanavamo agli uffici di ultra truffatrice, ultra malavitosa, ultra ladrona Bsi Italia Srl di Via Socrate 26 a Milano di suo padre, noto criminale tanto quanto, Vincenzo Barrai, ci vedeva dalla telecamera e nemmeno ci rispondeva. Nemmeno ci apriva il cancello di entrata. Io non sto offendendo, sto dicendo la mera verità. E fra poco la faremo sapere a fior fior di Tribunali di mezza Italia. Che i delinquenti ti debbano fare fessa, e pure non permettano replica, no eeeee. Il neofascismo e la mafia del criminale, del delinquente, del ladro, del truffatore, del professionalmente incapacissimo Paolo Barrai di Mercato Libero alias Mer-d-ato Libero, a noi non fa nessuna paura. Una truffata dal malavitoso falso e vigliacco Paolo Barrai di Mercato Libero. Antonella di Milano. PS Mi ha bruciato 700.000 euro. Tutto quello che avevo al momento. Ma a tanti altri ha bruciato 1, 2, 3, 10 milioni di euro. Facendo comprare il gas naturale a 5\$ e passa, che in poche settimane crollava a 2 \$. Senza che lui prendesse telefonate, rispondesse ad emails. Senza dare indicazione alcuna a noi clienti terrorizzati! Come uno struzzo, che dalla paura e coscienza di essere incapacissimo a livello di fiuto per investimenti, mette la testa sotto la sabbia. Paolo Barrai, oltre ad essere il peggiore consulente per investimenti borsistici o di qualsiasi altro tipo, ove, inesorabilmente, sbaglia sempre, ove mai, mai e ri mai ne azzecca mezza, è un irresponsabile, codardo, ladro, truffatore, criminale, falsissimo. E mi dicono che ha pregressi, pure, vari patteggiamenti di condanne al carcere. Aaa, ad averlo saputo prima e non essermi fidata della Lega Nord, di cui ero parte, e che mi ha messo in contatto con sto brucia risparmi e super truffatore. Ora mi son sfogata qui. Presto lo ri faró in fronte a polizia, carabinieri, magistrati, giudici! E con me, almeno altre 150 persone! Oooo!! Non cascateci, ne scrivo proprio per questo, via dal criminale, delinquente, ladro, truffatore, professionalmente incapacissimo Paolo Barrai di Mercato Libero.
PS
Guardate, ora, pls, che emails manda in giro il nazista, antisemita, assassino Paolo Barrai ( nato a Milano il 28.06.1965). In questo caso ad un grandissimo genio borsistico ed eroe civile chiamantesi Michele Nista, residente a Londra, dopo che lo stesso, con l'agosto 2009, con un criminale efferato, mega ricicla soldi mafiosi e mandante di omicidi, come Paolo Barrai, decise di non voler mai piu' avere a che fare. Le seguente emails partirono tutte da sue criminalissima mercatiliberi@gmail.com e criminalissima paolobarrai@gmail.com. Ora affiancate da criminalissima tanto quanto info@wmogroup.com
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" Oggi sono andato a pisciare sulla tomba di tuo padre, piu' tardi ci vado a cagare pure. Ha fatto bene Berlusconi a farlo ammazzare, ahahahah. Grazie per farti scroccare su euro, gas naturale e caffe robusta. Io sbaglio sempre nei mercati, ma grazie a te, riesco ancora a sopravvivere, ahahaha".
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
"Presto Berlusconi e il mio Bossi, manderanno sicari mafiosi o dei servizi segreti, a Londra, a farti sparare, ahahaha. Ti scrocchiamo e poi ti spariamo pure, come si fa con un ciupa ciupa usato, ahahah. L'Italia e' nostra, e' nazifascista. A morte gli ebrei. A noi!!!"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" Speriamo che ti venga una trombosi alla gamba, ho fatto un post di solidarieta' su di te, per fingermi corretto, in realta', non vedo l'ora che ti ammazzano. Voi bastardi ebrei, o amici di ebrei, dovrete tutti crepare soffrendo"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" Ti ho fatto infiltrare da Filati del Piemonte, da Angelo Pegli, da Gianluca Gualandri, da Stelvio Callimaci, sei pieno di mie spie. Io prendo un po' di prestanome, e ti infiltro. E intanto, faccio passare per mie, idee che sono tue. E fra poco ti faro' pure sparare a Londra, ahahahah. Crepa bastardo, chi lavora con gli ebrei, deve bruciare nei forni".
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" Stelvio Callimaci sta facendo un ottimo lavoro, mi passa tutti i tuoi inputs e io li faccio passare per miei, ahahahahaah; manda inputs, manda, e io vi faccio i soldi, ahahahah; presto ti spariamo in faccia, Nista comunista di merda, Berlusconi e Bossi non si criticano, si adorano, ahahahaha; noi della Lega, presto faremo migliaia di morti"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" bravo ottimi post continua cosi'.. presto ti spariamo in faccia... Nista, sei il primo della lista, la Lega spara, ammazza, non perdona, il mondo e' nostro, della destra... Paolo Barrai ammazza, la Lega ammazza, ahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" sei troppo dolce
ti sta forse leccando il culo tua ma-re!!! hahahaha, vai vai....
ma non perdere lucidita'’ per i tuoi clienti....attendono impazienti gli inputs"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" di infiltrati come stelvio e filati ne abbiamo tanti ahahahaah, e presto ti verremo a trovare a Londra, io e Michele Milla, e come facemmo con Ubaldo Gaggio, ti ammazzeremo, ahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" non correre...la gamba potrebbe non seguirti... Nista, presto saliremo a Londra e ti spareremo in bocca.... la mia Lega non perdona, la Lega uccide, ahhaha.. e' vero, abbiamo ammazzato noi Giorgio Panto e Paolo Alberti, perche' andarono con Prodi, e presto ammazzeremo anche a te, la Lega non perdona, la Lega ammazza tantissimo... ahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" credo che stai per finire...ahahahaha.. fra poco ti spariamo in bocca, Nista bastardo, Nista primo della lista, anzi no...abbiamo bisogno dei tuoi articoli da esaltato.. ti diamo ancora 15 giorni e poi ti spariamo in faccia, la Lega ammazza, Bossi fa ammazzare, prepara il testamento, sei morto, ahah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" mi dicono che a londra stanno predisponendo un forno .....e gli manca materiale!!! vi ficchiamo dentro te e William Levi... voglio un nuovo nazismo.. voglio vedere tutti gli ebrei e chi lavora con gli ebrei, come fai te, bruciare... evviva il nazismo.. evviva la Lega, che e' il nuovo nazismo, Berlusconi muove la mafia, noi i nazisti, ahahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" buona trombosi.. Nista ti ammazziamo noi, se vuoi.. crepa presto o noi del Pdl e della Lega ti ammazziamo.. come gia' abbiamo fatto con tuo padre.. Berlusconi e Bossi ammazzano, e presto lo vedrai.. Heil Hitler, Heil Mussolini, Heil Bossi, Heil Berlusconi, Heil Barrai, ahahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" ahahahahaha, presto ti spareremo in faccia...Nista sei morto, Nista ti ammazzeremo, Nista sei condannato a crepare... Nista, divieni Berlusconiano, come ti volevo fare diventare un anno fa, o ti ammazziamo, Nista morto, ahaah"
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" grazie per la fantastica azzeccata su dow jones, gas naturale e per il tantissimo resto..
ahahahaha, vamos siamo forti!
come mi ha detto Don...non mi morire per strada...perche' fra poco salgo io a Londra, a scaricarti una p38 in bocca... Stefano Bassi de il Grande Bluff e io siamo assassini, terroristi neri, e presto ti ammazzeremo, ahahah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" sempre nemici... ognuno persegue i suoi obbiettivi.... tanto tu sei condannato a morte... Berlusconi e Bossi han gia deciso: Nista come Falcone e Borsellino, Nista sparato in bocca, ahahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" non ti deconcentro, scusa
devi preparar i report che cosi' ci dai gli inputs vincentissimi come sempre, scusami... dai impegnati, impegnati, che presto io, Berlusconi e Bossi, ti faremo sparare dritto in faccia, ahahaha"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" Marina Berlusconi ha gia' messo il pollice verso, Marina Berlusconi ti ha condannato a morte..ha gia' avvertito la mafia di eseguire, di ammazzarti.. e se non esegue la mafia, eseguono i servizi segreti di destra, fascisti come me, della Lega ... Nista sei un morto ormai, ahahahahah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" ahahahah, passa ancora un po' di dritte che qui si fanno soldi a palate...lavora schiavo... lavora, che fra poco, Berlusconi e Bossi ti fanno sparare in bocca.. via nostre Mafia e Servizi Segreti.... non criticare mai piu' Berlusconi o ti ammazziamo, bastardo.. Berlusconi e Bossi non si criticano, si adorano.. il problema e' che Marina Berlusconi ha gia' ordinato di ammazzarti, e quella non perdona, la Lega e' il nuovo nazismo e tappa le bocche ammazzando, Nista, ormai sei morto, ahahahhah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" salutami william levi ...lo sento bruciare...come legna sul fuoco....o meglio ...il suo cadavere puo' essere usato per il sapone, ahahahahah..presto sara' nuovo nazismo, e chiunque lavora con gli ebrei come fai te... diverra' legna per i forni, ahahahah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" fammi qualche articolo come nel passato .....ti prego tantissimo. A natale ti regalo un forno crematorio per William... Nista, noi Berlusconiani siamo la mafia, siamo la camorra, siamo la ndrangheta.. e tu sei condannato a morte, cosi' impari a non divenire uno dei nostri, ahahaaaahah"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" attento a chi incontri a londra....ahahaah... dai, sei bravo, azzecchi sempre, e' vero, voglio scroccarti un po' di piu', prima di ammazzarti... Nista e Levi nei forni di Auschwitz, si, nei forni di Auschwitz, w la Lega, w il Nazismo"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" POVERO BASTARDO CHE SI PERMETTE DI ESSERE DI CENTRO/SINISTRA: PRESTO TI SCHIACCEREMO, LA LEGA UCCIDE, BERLUSCONI UCCIDE, IO, PAOLO BARRAI, UCCIDO, W LA LEGA, W IL NAZISMO, W LA MAFIA, E INTANTO TI SCROCCO SEMPRE"
---
da criminalissima mercatiliberi@gmail.com
(ora anche criminalissima info@wmogroup.com)
e criminalissima paolobarrai@gmail.com
" MI DICONO CHE DI NOTTE SULLA TOMBA DI TUO PADRE CI VANNO A CAGARE I VERMI... E ANCHE CHE PRESTO TI AMMAZZERANNO A LONDRA...FATTI SCROCCARE IN SILENZIO O IO E STEFANO BASSI DE IL GRANDE BLUFF TI FAREMO AMMAZZARE... ANCHE STEFANO BAGNOLI E' UN ASSASSINO COME NOI... NISTA, LA SENTENZA C'E', PRESTO TI UCCIDEREMO, W IL NAZISMO, W IL PDL, W LA MAFIA, W LA RAZZISTA LEGA NORD, W LA CAMORRA, W LA LEGHISTISSIMA NDRANGHETA, AHA"
---
da criminalissima mercatiliberi@gmail.com
(ora anche crimina
ewe 17/10/2012 13:34
Voir Blog(fermaton.over-blog.com)No.22- THÉORÈME ÉTAT. - La base des mathématiques de l'Esprit. | 21,536 | 62,867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-39 | longest | en | 0.514902 |
http://nzmaths.co.nz/resource/even-more-pizzas-and-things | 1,369,488,204,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705955434/warc/CC-MAIN-20130516120555-00004-ip-10-60-113-184.ec2.internal.warc.gz | 197,155,922 | 10,754 | Te Kete Ipurangi
Communities
Schools
### Te Kete Ipurangi user options:
Level Three > Number and Algebra
# Even More Pizzas And Things
Achievement Objectives:
Specific Learning Outcomes:
Solve problems involving fractions
Devise and use problem solving strategies (draw a picture, use equipment, guess and check, be systematic, think)
Interpret information and results in context.
Description of mathematics:
This problem is a multi-step one that involves fractions and the four arithmetic operations. It also requires a careful analysis if what is known, what is unknown and what can be obtained from what with what sequence of operations.
Like a number of similar problems that have a lot of inter-related information, this problem can be handled by algebra. So algebra is a natural follow on from this type of problem. However, like a number of so-called algebra problems, this one can be sorted out by careful reasoning.
The students should be asked – what do you know? and what can you find out from this?
Required Resource Materials:
Copymaster of the problem (English)
Copymaster of the problem (Māori)
Activity:
### The Problem
The pizza place has three tables. The biggest one seats three times as many people as the smallest one. The middle sized table seats twice as many people as the smallest one.
On Tuesday night three-quarters of the seats were taken. Then twelve more people arrived. Unfortunately there were only enough seats for half of them.
How many people can sit at the smallest table?
### Teaching Sequence
1. Introduce the problem by posing fraction questions to be solved mentally. Ask that the students explain the mental strategies that they used.
I am ¾ of 16, what number am I?
I am 2/3 of 30, what number am I?
I am 4/6, what other names could I be called?
2. Pose the problem to the class. Check that they understand what is required by asking volunteers to retell the problem.
3. As the students solve the problem ask questions that focus on their understanding of fractions.
How are you solving the problem?
Why are you using those numbers?
Are you convinced that your answer is correct? Why?
Can you convince me that you have the correct answer?
How would you describe what a fraction was to a friend who had forgotten what they were?
4. Remind the students to record their work so that it can be shared with others.
5. Display and discuss solutions.
#### Other Contexts
Letting the tables be containers and the people, sand or water can turn the problem into one relating to measurement.
#### Extension to the problem
The number of tables or the number of people that can be seated at the smaller table can be increased.
### Solution
What do we know? There are three tables and they are of different sizes. We even know the number that the two bigger tables will seat with respect to the first one. But at the moment we have no information to be able to work out the size of any table.
We know that The Pizza Place is three-quarters full. But again this is no use to us at the moment.
We know that 12 people arrive and half of them are turned away. So we know how many are turned away. A half of 12 is 6. So that means too that 6 people can be seated.
How can we tie that in with the fact that the Pizza Place is three-quarters full? If it is three-quarters full, then it is one-quarter empty. So 6 people is a quarter of a full house. So the full house must be 4 times 6 = 24.
Now we can go back to the tables. At this stage we could guess that the smallest table seats 3. In that case the next table seats 6 and the biggest table seats 9. Since 3 + 6 + 9 = 18, our guess is a bit low. So guess 5. Then we get 10 and 15 for the other tables. Now 5 + 10 + 15 = 30 and that’s too high. So the smallest table must seat 4. That can be easily checked.
Another way to tackle the last part is to suppose that the smallest table seats some. Then the next table seats two lots of some. Altogether, this is three lots of some. The biggest table seats three lots of some. So now we have six lots of some in total. Now six lots of some is 24. So some is 4 and that’s the number of people that can suit at the smaller table.
(If you think that this problem is too hard for your class, then tell them that the smaller table holds 4 people and ask them how many people The Pizza Place has to turn away when 12 new people arrive. Remember that by reversing what is known we can make a problem harder or easier. In this case it can be made easier. Try doing this with some of the other problems that we have on the site.)
AttachmentSize
EvenMorePizzas.pdf58.34 KB
EvenMorePizzasMaori.pdf63.12 KB
## Lollies, Lollies, Lollies
Solve problems that involve multiplication and division
Use equations to express a problem
## Darts Game
Apply the number operations to single digit numbers.
Use a problem solving strategy to identify all the possible outcomes.
## Super Darts
Apply number operations in combination to single digit numbers.
Work systematically to find the possible outcomes.
## Make Up Your Own
Use their mathematical knowledge to invent problems;
Solve other students' problems.
Devise and use problem solving strategies to explore situations mathematically.
## More Pizzas and Things
Solve problems that involve halves and thirds
Devise and use problem solving strategies (draw a picture, use equipment, guess and check, be systematic, think). | 1,210 | 5,421 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2013-20 | longest | en | 0.958065 |
http://pari.math.u-bordeaux.fr/archives/pari-dev-0603/msg00000.html | 1,417,215,161,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416931011032.12/warc/CC-MAIN-20141125155651-00131-ip-10-235-23-156.ec2.internal.warc.gz | 230,286,161 | 2,665 | Karim Belabas on Thu, 02 Mar 2006 22:04:22 +0100
Re: qflllgram
```* Gonzalo Tornaria [2006-02-27 18:47]:
> Strange behaviour:
>
> ? qflllgram([1,0;0,-1],0)
> *** qflllgram: the PARI stack overflows !
> current stack size: 128000000 (122.070 Mbytes)
> [hint] you can increase GP stack with allocatemem()
>
> ? allocatemem()
> *** allocatemem: Warning: doubling stack size; new stack = 256000000
> (244.141 Mbytes).
> ? qflllgram([1,0;0,-1],0)
> *** qflllgram: length (lg) overflow
Junk in, junk out: the function is undefined on indefinite matrices.
More precisely:
For flag = 0, the implementation uses floating point computations and
increases the internal precision when incremental Gram-Schmidt fails
(basis vector with non-positive square norm).
When the input is exact, we enter an infinite loop, and eventually
overflow the capacities of the implementation. When the input is
inexact, we give up relatively quickly.
> It /does/ work with flag=1 (lllgramint):
>
> ? qflllgram([1,0;0,-1],1)
> *** qflllgram: not a definite matrix in lllgram
For flag = 1, we use the atrociously slow all-integer algorithm. But a
negative vector length in Gram-Schmidt is immediately flagged as an error:
since all computations are exact, it can't be due to roundoff errors.
I don't see why we should clutter the code and slow down the floating
point code to check the input in case the user would be playing tricks
on us. Try it at \g4 and a non trivial computation, like
\g4
\p300
algdep(3^(1/5)+2^(1/6), 30)
Quite a number of precision changes, heh ? [ This could be performed
much more efficiently, but I haven't had time to implement Phong &
Stehle's L^2 algorithm yet ]
Cheers,
K.B.
--
Karim Belabas Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation http://www.math.u-bordeaux.fr/~belabas/
F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]
``` | 604 | 1,971 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2014-49 | longest | en | 0.723584 |
https://gmatclub.com/forum/hardy-and-andy-start-a-two-length-swimming-race-at-the-same-moment-but-91380-20.html?sort_by_oldest=true | 1,586,189,369,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371637684.76/warc/CC-MAIN-20200406133533-20200406164033-00271.warc.gz | 487,567,673 | 151,636 | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 06 Apr 2020, 08:09
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Hardy and Andy start a two-length swimming race at the same moment but
Author Message
TAGS:
### Hide Tags
Current Student
Joined: 03 Apr 2013
Posts: 258
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
25 May 2017, 02:21
VeritasPrepKarishma wrote:
Hussain15 wrote:
Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
A. 55.5 m
B. 45 m
C. 66 m
D. 49 m
E. 54 m
Let length of the pool be L.
Deep
A —————————————><———————————----———————————— H
.................(18.5m)
H ——————————————————————————-———><————————- A
..............................................................................................................(10.5)
In same time, Andy covers 18.5 and Hardy covers L - 18.5.
In same time, Andy covers L - 18.5 + 10.5 while Hardy covers 18.5 + L - 10.5
The ratio of these distances covered would be the same since the speeds of both people are constant.
18.5/(L - 18.5) = (L - 8)/(L + 8)
Plug in the options to find that L = 45 works.
How do you say that the 45 seconds wait time does not matter?
And can something of this sort be expected on the GMAT?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10248
Location: Pune, India
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
25 May 2017, 02:48
ShashankDave wrote:
VeritasPrepKarishma wrote:
Hussain15 wrote:
Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
A. 55.5 m
B. 45 m
C. 66 m
D. 49 m
E. 54 m
Let length of the pool be L.
Deep
A —————————————><———————————----———————————— H
.................(18.5m)
H ——————————————————————————-———><————————- A
..............................................................................................................(10.5)
In same time, Andy covers 18.5 and Hardy covers L - 18.5.
In same time, Andy covers L - 18.5 + 10.5 while Hardy covers 18.5 + L - 10.5
The ratio of these distances covered would be the same since the speeds of both people are constant.
18.5/(L - 18.5) = (L - 8)/(L + 8)
Plug in the options to find that L = 45 works.
How do you say that the 45 seconds wait time does not matter?
And can something of this sort be expected on the GMAT?
The wait time doesn't matter since after their first meet, they both rest for 45 secs and then meet again.
Say, they meet again in 2 mins. But actually both swam for only 1 min 15 secs. Doesn't matter to us either way. Time for which they swam is still the same. So ratio of distance covered will still be the same as the ratio of their speeds.
_________________
Karishma
Veritas Prep GMAT Instructor
Current Student
Joined: 03 Apr 2013
Posts: 258
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
25 May 2017, 03:23
VeritasPrepKarishma wrote:
ShashankDave wrote:
VeritasPrepKarishma wrote:
[quote="Hussain15"]Hardy and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
A. 55.5 m
B. 45 m
C. 66 m
D. 49 m
E. 54 m
Let length of the pool be L.
Deep
A —————————————><———————————----———————————— H
.................(18.5m)
H ——————————————————————————-———><————————- A
..............................................................................................................(10.5)
In same time, Andy covers 18.5 and Hardy covers L - 18.5.
In same time, Andy covers L - 18.5 + 10.5 while Hardy covers 18.5 + L - 10.5
The ratio of these distances covered would be the same since the speeds of both people are constant.
18.5/(L - 18.5) = (L - 8)/(L + 8)
Plug in the options to find that L = 45 works.
How do you say that the 45 seconds wait time does not matter?
And can something of this sort be expected on the GMAT?
The wait time doesn't matter since after their first meet, they both rest for 45 secs and then meet again.
Say, they meet again in 2 mins. But actually both swam for only 1 min 15 secs. Doesn't matter to us either way. Time for which they swam is still the same. So ratio of distance covered will still be the same as the ratio of their speeds.[/quote]
Okay..I took example numbers for time and understood the same..but as this concept is completely new..it couldn't have struck in the test under pressure..is it honestly a GMAT problem?
Sent from my Pixel XL using GMAT Club Forum mobile app
Intern
Joined: 24 Feb 2017
Posts: 34
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
15 Jul 2017, 02:55
VeritasPrepKarishma wrote:
In same time, Andy covers L - 18.5 + 10.5 while Hardy covers 18.5 + L - 10.5
Just to highlight - For this equation to be formed, the underlying criteria that they both complete 1 Length of the pool (given in the question) is important.
I got confused with the fact that, Andy needn't have completed his 1 full length yet before meeting for the second time. I need to read the question prompt carefully.
Intern
Joined: 12 Nov 2016
Posts: 3
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
16 Jul 2017, 00:54
I am stilling struggling to understand the question since I'm not english native speaker. Could anyone help explain the meaning of "deep end" and "shallow end" mentioned in the question? Without understanding correctly, I cannot depict the question....
Intern
Joined: 24 Feb 2017
Posts: 34
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
16 Jul 2017, 01:51
1
JoPha wrote:
I am stilling struggling to understand the question since I'm not english native speaker. Could anyone help explain the meaning of "deep end" and "shallow end" mentioned in the question? Without understanding correctly, I cannot depict the question....
A swimming pool is typically constructed in a rectangular fashion (L X B). It doesn't really matter what the deep and shallow ends actually are, other than the fact that they are opposite ends of a swimming pool.
Shallow end (4ft depth) Deep end (17ft)
_____________________________________________
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
<---------------Length of the pool---------------------->
The question indicates the race length as 2-length, which means the swimmer:
- goes from one end to and another
- and returns to that end to finish the race
Hope this helps.
Intern
Joined: 12 Nov 2016
Posts: 3
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
17 Jul 2017, 04:01
rbramkumar wrote:
JoPha wrote:
I am stilling struggling to understand the question since I'm not english native speaker. Could anyone help explain the meaning of "deep end" and "shallow end" mentioned in the question? Without understanding correctly, I cannot depict the question....
A swimming pool is typically constructed in a rectangular fashion (L X B). It doesn't really matter what the deep and shallow ends actually are, other than the fact that they are opposite ends of a swimming pool.
Shallow end (4ft depth) Deep end (17ft)
_____________________________________________
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
|-------------------------------------------------------------|
<---------------Length of the pool---------------------->
The question indicates the race length as 2-length, which means the swimmer:
- goes from one end to and another
- and returns to that end to finish the race
Hope this helps.
Now I'm clear. Thank you very much.
Non-Human User
Joined: 09 Sep 2013
Posts: 14467
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink]
### Show Tags
20 Oct 2018, 20:58
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Hardy and Andy start a two-length swimming race at the same moment but [#permalink] 20 Oct 2018, 20:58
Go to page Previous 1 2 [ 28 posts ]
Display posts from previous: Sort by | 2,692 | 10,746 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-16 | latest | en | 0.873678 |
http://acm.scu.edu.cn/soj/problem/3499/ | 1,571,897,337,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987841291.79/warc/CC-MAIN-20191024040131-20191024063631-00350.warc.gz | 7,036,083 | 1,058 | Time Limit:1000ms Memory Limit:65536KB
## Description
```When the cildren's day comes, the God-Like Cow(GLC) wants to celebrate the festival.
So he buys many cards with digit '1' or '6' and gives them to girls in memory of "6.1".
But the girls join the cards together to form a number.
What the k-th(1-based) large number?
```
## Input
```Mutiple test cases.
Each line is a integer k(1<=k<=10000).
```
## Output
```For each test case, output the answer in a single line.
```
```1
2
4
```
```1
6
11
```
## Hint
```1 6 9 11 16 19 61 66 69 91 96 99
```
baihacker | 187 | 570 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-43 | latest | en | 0.800236 |
https://www.traditionaloven.com/metal/precious-metals/platinum/convert-fluid-ounce-fl-oz-to-troy-ounce-tr-oz-platinum.html | 1,544,598,434,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823785.24/warc/CC-MAIN-20181212065445-20181212090945-00404.warc.gz | 1,067,816,697 | 13,946 | Platinum fluid ounce to troy ounces of platinum converter
# platinum conversion
## Amount: fluid ounce (fl oz) of platinum volume Equals: 20.42 troy ounces (oz t) in platinum mass
Calculate troy ounces of platinum per fluid ounce unit. The platinum converter.
TOGGLE : from troy ounces into fluid ounces in the other way around.
### Enter a New fluid ounce Amount of platinum to Convert From
* Enter whole numbers, decimals or fractions (ie: 6, 5.33, 17 3/8)
## platinum from fluid ounce to ounce (troy) Conversion Results :
Amount : fluid ounce (fl oz) of platinum
Equals: 20.42 troy ounces (oz t) in platinum
Fractions: 20 21/50 troy ounces (oz t) in platinum
CONVERT : between other platinum measuring units - complete list.
## Platinum Amounts (solid platinum)
Here the calculator is for platinum amounts (solid platinum volume; dense, precious, gray to white metal rare in abundance on the planet earth. Its annual production is only a very few hundred tons. It is a very highly valuable metal. Platinum performs real well in resisting corrosion. Not only beautiful jewellery is made out of platinum, this metal enjoys quite a wide variety of uses. For instance in electronics, chemical industries and also in chemotherapy applications against certain cancers. Traders invest money in platinum on commodity markets, in commodity future trading as this material is also one of the major precious commodity metals. Thinking of going into investing in stocks? It would be a wise idea to start learning at least basics at a commodity trading school first, to get used to the markets, then start with small investments. Only after sell and buy platinum.)
Is it possible to manage numerous units calculations, in relation to how heavy other volumes of platinum are, all on one page? The all in one Pt multiunit calculation tool makes it possible to manage just that.
Convert platinum measuring units between fluid ounce (fl oz) and troy ounces (oz t) of platinum but in the other direction from troy ounces into fluid ounces.
conversion result for platinum: From Symbol Equals Result To Symbol 1 fluid ounce fl oz = 20.42 troy ounces oz t
# Precious metals: platinum conversion
This online platinum from fl oz into oz t (precious metal) converter is a handy tool not just for certified or experienced professionals. It can help when selling scrap metals for recycling.
## Other applications of this platinum calculator are ...
With the above mentioned units calculating service it provides, this platinum converter proved to be useful also as a teaching tool:
1. in practicing fluid ounces and troy ounces ( fl oz vs. oz t ) exchange.
2. for conversion factors training exercises with converting mass/weights units vs. liquid/fluid volume units measures.
3. work with platinum's density values including other physical properties this metal has.
International unit symbols for these two platinum measurements are:
Abbreviation or prefix ( abbr. short brevis ), unit symbol, for fluid ounce is: fl oz
Abbreviation or prefix ( abbr. ) brevis - short unit symbol for ounce (troy) is: oz t
### One fluid ounce of platinum converted to ounce (troy) equals to 20.42 oz t
How many troy ounces of platinum are in 1 fluid ounce? The answer is: The change of 1 fl oz ( fluid ounce ) unit of a platinum amount equals = to 20.42 oz t ( ounce (troy) ) as the equivalent measure for the same platinum type.
In principle with any measuring task, switched on professional people always ensure, and their success depends on, they get the most precise conversion results everywhere and every-time. Not only whenever possible, it's always so. Often having only a good idea ( or more ideas ) might not be perfect nor good enough solutions. Subjects of high economic value such as stocks, foreign exchange market and various units in precious metals trading, money, financing ( to list just several of all kinds of investments ), are way too important. Different matters seek an accurate financial advice first, with a plan. Especially precise prices-versus-sizes of platinum can have a crucial/pivotal role in investments. If there is an exact known measure in fl oz - fluid ounces for platinum amount, the rule is that the fluid ounce number gets converted into oz t - troy ounces or any other unit of platinum absolutely exactly. It's like an insurance for a trader or investor who is buying. And a saving calculator for having a peace of mind by knowing more about the quantity of e.g. how much industrial commodities is being bought well before it is payed for. It is also a part of savings to my superannuation funds. "Super funds" as we call them in this country.
Conversion for how many troy ounces ( oz t ) of platinum are contained in a fluid ounce ( 1 fl oz ). Or, how much in troy ounces of platinum is in 1 fluid ounce? To link to this platinum - fluid ounce to troy ounces online precious metal converter for the answer, simply cut and paste the following.
The link to this tool will appear as: platinum from fluid ounce (fl oz) to troy ounces (oz t) metal conversion.
I've done my best to build this site for you- Please send feedback to let me know how you enjoyed visiting. | 1,118 | 5,200 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-51 | longest | en | 0.860049 |
https://www.physicsforums.com/threads/moment-of-forces-about-the-axes.990747/ | 1,721,913,443,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763858305.84/warc/CC-MAIN-20240725114544-20240725144544-00260.warc.gz | 806,949,571 | 17,040 | # Moment of forces about the axes
• Engineering
• mingyz0403
In summary, to determine the sign of Ma and Mb for their y and z component, use the right-hand rule to find the direction of the moment vector and then determine the projection and signage of the vector components onto the y and z axes. The A-torque is negative when looked at in the +y direction, while the B-torque is positive when looked at in the +y direction. The couple about the x-axis is negative because it points in the negative x direction.
mingyz0403
Homework Statement
Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x axis. Replace the couples applied to the shafts by a single equivalent couple, specifying its magnitude and the direction of its axis.
Relevant Equations
M=RXF
I reslove Ma and Mb into y and z component.
Ma=1200sin(20)j+1200cos(20)k
Mb=900sin(20)j+1200cos(20)k
Mc=-840i
I looked at the solution and it states that the y component of Ma is negative (-1200sin(20)j+1200cos(20)k). I understand that Mc is -840i because it is Clockwise. How do you determine the sign of Ma and Mb for their y and z component.
#### Attachments
• 1.jpg
21.5 KB · Views: 205
It is best to forget about sign conventions for clockwise and counterclockwise. Rather, show the couple in its vector form using the right hand rule , and the moment vector will point in the direction of your thumb. Then you should be able to more easily find the projection and signage of the vector Components onto the y and z axes. Hint: the couple about the x-axis is negative because it points in the negative x direction.
FactChecker
The A-torque is tilted slightly down, in the -y direction. Using the right-hand rule, it is positive when looked at in the -y direction. That is the same as negative in the +y direction. The B-torque is tilted slightly up in the +y direction.
## 1. What is a moment of force?
A moment of force, also known as torque, is the measure of the tendency of a force to rotate an object about an axis. It is calculated by multiplying the force by the perpendicular distance from the axis of rotation to the line of action of the force.
## 2. What are the different types of moments of force?
There are two types of moments of force: clockwise and counterclockwise. A clockwise moment of force causes an object to rotate in a clockwise direction, while a counterclockwise moment of force causes an object to rotate in a counterclockwise direction.
## 3. How is the moment of force calculated?
The moment of force is calculated by multiplying the force vector by the perpendicular distance from the axis of rotation to the line of action of the force. This can be represented by the formula: M = F x d, where M is the moment of force, F is the force vector, and d is the distance from the axis of rotation to the line of action of the force.
## 4. What is the importance of moments of force in physics?
Moments of force are important in physics because they play a crucial role in understanding the motion and stability of objects. They are used to describe the rotational motion of objects and are essential in engineering and design applications, such as building structures and machines.
## 5. How do moments of force affect the equilibrium of an object?
Moments of force can cause an object to be in equilibrium, meaning that it is not moving or rotating. This occurs when the sum of all the clockwise moments equals the sum of all the counterclockwise moments. If the moments are not balanced, the object will experience a rotational motion.
• Engineering and Comp Sci Homework Help
Replies
22
Views
2K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
25
Views
466
• Engineering and Comp Sci Homework Help
Replies
5
Views
6K
• Engineering and Comp Sci Homework Help
Replies
1
Views
6K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
4K
• Engineering and Comp Sci Homework Help
Replies
5
Views
3K
• Engineering and Comp Sci Homework Help
Replies
4
Views
2K
• Engineering and Comp Sci Homework Help
Replies
6
Views
1K | 1,025 | 4,281 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-30 | latest | en | 0.914134 |
https://github.polettix.it/ETOOBUSY/2021/09/30/pwc132-hash-join/ | 1,726,515,982,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651710.86/warc/CC-MAIN-20240916180320-20240916210320-00760.warc.gz | 242,251,982 | 5,206 | TL;DR
On with TASK #2 from The Weekly Challenge #132. Enjoy!
# The challenge
Write a script to implement Hash Join algorithm as suggested by wikipedia.
(In the challenge there is a part that is actually ignored in this post)
Example
Input:
@player_ages = (
[20, "Alex" ],
[28, "Joe" ],
[38, "Mike" ],
[18, "Alex" ],
[25, "David" ],
[18, "Simon" ],
);
@player_names = (
["Alex", "Stewart"],
["Joe", "Root" ],
["Mike", "Gatting"],
["Joe", "Blog" ],
["Alex", "Jones" ],
["Simon","Duane" ],
);
Output:
Based on index = 1 of @players_age and index = 0 of @players_name.
20, "Alex", "Stewart"
20, "Alex", "Jones"
18, "Alex", "Stewart"
18, "Alex", "Jones"
28, "Joe", "Root"
28, "Joe", "Blog"
38, "Mike", "Gatting"
18, "Simon", "Duane"
# The questions
I admit to have been puzzled by this challenge.
The original text seems to include a part that is very relevant in the actual implementation of a database engine, where e.g. not all data can fit in memory at the same time and strategies have to be thought to address this:
1. For each tuple $r$ in the build input $R$
1. Add $r$ to the in-memory hash table
2. If the size of the hash table equals the maximum in-memory size:
1. Scan the probe input $S$, and add matching join tuples to the output relation
2. Reset the hash table, and continue scanning the build input $R$
2. Do a final scan of the probe input $S$ and add the resulting join tuples to the output relation
So… what is this challenge requesting, actually? I opted to ignore that part, and concentrate on the basic algorithm description in wikipedia, i.e.:
• one of the two input relations is transformed into a hash, where keys point to lists (arrays, in our case) of records matching the selected key, implementing the hash phase;
• the other is used for the scan phase.
The resulting function might then be used in the memory-aware mechanism.
Is this a deal?
Oh… another thing: we’re going to consider only single-column keys.
Is this still a deal?
# The solution
With the simplifications laid out in The questions section, here’s how we can address the challenge in Perl:
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
use Data::Dumper;
sub hash_join ($one,$kone, $two,$ktwo) {
# make sure ($one,$kone) deal with the shorter of the two relations
($one,$kone, $two,$ktwo) = ($two,$ktwo, $one,$kone)
if $one->@* >$two->@*;
# hash phase, build a hash from ($one,$kone)
my %hash_one;
push $hash_one{$_->[$kone]}->@*,$_ for $one->@*; # scan phase return map { my @record =$_->@*;
my $key = splice @record,$ktwo, 1;
next unless exists $hash_one{$key};
map { [$_->@*, @record] }$hash_one{$key}->@*; }$two->@*;
}
my @player_ages = (
[20, "Alex" ],
[28, "Joe" ],
[38, "Mike" ],
[18, "Alex" ],
[25, "David" ],
[18, "Simon" ],
);
my @player_names = (
["Alex", "Stewart"],
["Joe", "Root" ],
["Mike", "Gatting"],
["Joe", "Blog" ],
["Alex", "Jones" ],
["Simon","Duane" ],
);
say join ', ', $_->@* for hash_join(\@player_ages, 1, \@player_names, 0); Our only concession to optimizations is to (possibly) swap the two input relations to make sure that the hash is built starting from the smaller one. Although this should not change anything from the point of view of complexity (it should be somewhere between$O(N + M)$and$O(N \cdot M)$, where$N$and$M$are the number of records and depending on their contents), it makes sense to use that as a base for building the hash so that collisions and re-arrangements will be less probable. Here is how that can be translated in Perlish Raku: #!/usr/bin/env raku use v6; sub hash-join (@one,$kone is copy, @two, $ktwo is copy) { # make sure ($one, $kone) deal with the shorter of the two relations (@one,$kone, @two, $ktwo) = (@two,$ktwo, @one, $kone) if @one > @two; # hash phase, build a hash from (@one,$kone)
my %hash_one;
(%hash_one{$_[$kone]} //= []).push($_) for @one; # scan phase gather for @two ->$record {
my @record = |$record; my$key = @record.splice($ktwo, 1); next unless %hash_one{$key}:exists;
take [($_, @record).flat] for %hash_one{$key}.List;
}
}
my @player_ages =
[20, "Alex" ],
[28, "Joe" ],
[38, "Mike" ],
[18, "Alex" ],
[25, "David" ],
[18, "Simon" ],
;
my @player_names =
["Alex", "Stewart"],
["Joe", "Root" ],
["Mike", "Gatting"],
["Joe", "Blog" ],
["Alex", "Jones" ],
["Simon","Duane" ],
;
.join(', ').say for hash-join(@player_ages, 1, @player_names, 0);
I can definitely feel my Raku teeth growing, because I got most of the changes needed to translate from Perl from the get go. Like using different sigils and the .flat in the right place. Alas… most is not all, because I had to also add the .List for iterating over the array in %hash_one{\$key}. All in all I was happy that this was the only change needed!
And yes, I know. There’s a performance hit with gather/take, which is probably something we should not accept while mimicking a database engine. But it’s such a lovely idiom that I can hardly avoid it in these challenges. Heck, these are supposed to be fun!
OK, enough for today… stay safe folks!
Comments? Octodon, , GitHub, Reddit, or drop me a line! | 1,541 | 5,204 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2024-38 | latest | en | 0.852306 |
https://im.kendallhunt.com/k5_es/teachers/grade-4/unit-2/lesson-5/lesson.html | 1,721,792,261,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518154.91/warc/CC-MAIN-20240724014956-20240724044956-00151.warc.gz | 282,228,108 | 22,496 | # Lesson 5
Fracciones en rectas numéricas
## Warm-up: Conversación numérica: Un número por doce (10 minutes)
### Narrative
The purpose of this warm-up is to remind students of doubling as a strategy for multiplication in which a factor in one product is twice a factor in another product. The reasoning that students do here with the factors 2, 4, 8, and 16 will support them as they reason about equivalent fractions and find multiples of numerators and denominators.
### Launch
• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time
### Activity
• Keep problems and work displayed.
• Repeat with each expression.
### Student Facing
Encuentra mentalmente el valor de cada expresión.
• $$2\times12$$
• $$4\times12$$
• $$8\times12$$
• $$16\times12$$
### Activity Synthesis
• “¿Cómo les ayudaron las tres primeras expresiones a encontrar el valor de la última expresión?” // “How did the first three expressions help you find the value of the last expression?”
## Activity 1: Todas alineadas (20 minutes)
### Narrative
The purpose of this activity is to remind students of a key insight from grade 3—that the same point on the number line can be named with fractions that don’t look alike. Students see that those fractions are equivalent, even though their numerators and denominators may be different.
Students have multiple opportunities to look for regularity in repeated reasoning (MP8). For instance, they are likely to notice that:
• Fractions that have the same number for the numerator and denominator all represent 1.
• In fractions that describe the halfway point between 0 and 1, the numerator is always half the denominator, or the denominator twice the numerator.
• In fractions that describe $$\frac{1}{4}$$, the denominator is 4 times the numerator.
These observations will help students to identify and generate equivalent fractions later in the unit.
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were most important to solve the problem. Display the sentence frame, “La próxima vez que los puntos estén en el mismo lugar de varias rectas numéricas, voy a . . .” // “The next time points are in the same place on different number lines, I will . . . .“
Supports accessibility for: Language, Attention
### Required Materials
Materials to Gather
### Launch
• Groups of 2
• Give students access to straightedges. Display the first set of number lines.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (I notice each number line has different fractions represented. The first number line has a point that is half-way between 0 and 1 labeled $$\frac{1}{2}$$, but if you label all the tick marks you won't have 2 in the denominator for all of them. I wonder what fraction goes on each mark? Can you have a number line with both halves and fourths? How many fourths are at the $$\frac{1}{2}$$ line?)
• 1 minute: quiet think time
• “Compartan con su pareja lo que observaron y se preguntaron” // “Share what you noticed and wondered with your partner.”
• 1 minute: partner discussion
### Activity
• “Trabajen individualmente en la tarea por un momento. Después, discutan su trabajo con su pareja” // “Take a moment to work independently on the task. Then, discuss your work with your partner.”
• “En los puntos que estén en rectas numéricas diferentes deben escribir fracciones con números diferentes” // “The labels that you write for the points on different number lines should be different.”
• 7–8 minutes: independent work time
• Monitor for students who:
• partition each number line into as many parts as the denominator before naming a fraction for the point on the number line
• use multiplicative relationships between denominators to name a fraction (for instance, $$4 \times 3 = 12$$, so the line showing twelfths has 3 times as many parts as the one showing fourths)
### Student Facing
1. Estas rectas numéricas tienen fracciones con números diferentes en la marca de más a la derecha.
1. Explícale a tu compañero por qué en la marca de más a la derecha se pueden escribir fracciones con números diferentes.
2. En cada punto, escribe una fracción que lo represente (no escribas $$\frac{1}{2}$$).
3. Explícale a tu compañero por qué las fracciones que escribiste son equivalentes.
2. En cada recta numérica, escribe un número que represente al punto. Prepárate para explicar tu razonamiento.
a.
b.
c.
### Activity Synthesis
• Select students to share their responses and reasoning for the first set of questions. Highlight explanations that convey that:
• Any fraction with the same number for the numerator and denominator has a value of 1.
• Equivalent fractions share the same location or are the same distance from 0 on the number line.
• Select students to share their responses for the second set of questions.
MLR3 Clarify, Critique, Correct
• If students show the following partially correct idea, display this explanation:
“Para saber la fracción que representa un punto, conté las marcas que había después del 0. Luego, usé el denominador de la fracción que representaba 1. Por ejemplo, en la pregunta 2, parte b, el punto está en la primera marca después del 0 y la etiqueta de 1 es $$\frac{10}{10}$$, entonces escribí $$\frac{1}{10}$$ en el punto” // “To know what fraction a point represents, I counted the tick marks from 0. Then, I used the denominator of the fraction for 1. For example, for question 2 part b, the point is on the first tick mark from 0 and the label for 1 says $$\frac{10}{10}$$, so I’d label the point $$\frac{1}{10}$$.”
• “¿Qué creen que entiende bien el estudiante? ¿Con qué creen que puede estar confundido?” // “What do you think the student understands well? What do you think they might have misunderstood?”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• “Con su pareja, escriban una explicación ajustada” // “With your partner, work together to write a revised explanation.”
• Display and review the following criteria:
• Explain: How would one know what numerator and denominator the fraction can have?
• Write in complete sentences.
• Use words such as: “primero” // “first,” “después” // “next,” or “luego” // “then.”
• Include the number line diagram.
• 3–5 minutes: partner work time
• Select 1–2 groups to share their revised explanation with the class. To facilitate their explanation, display blank number lines for students to annotate. Record responses.
• “¿En qué se parecen y en qué son diferentes las explicaciones?” // “What is the same and what is different about the explanations?”
## Activity 2: ¿Cuánto vamos a correr? (15 minutes)
### Narrative
In this activity, students reason about whether two fractions are equivalent in the context of distance. To support their reasoning, students use number lines and their understanding of fractions with related denominators (where one number is a multiple of the other). The given number lines each have only one tick mark between 0 and 1, so students need to partition each line strategically to represent two fractions with different denominators on the diagram.
To help students intuit the distance of 1 mile, consider preparing a neighborhood map that shows the school and some points that are a mile away. Display the map during the launch.
### Launch
• Groups of 2
• “¿Quién ha caminado una milla? ¿Quién ha corrido una milla?” // “Who has walked a mile? Who has run a mile?”
• “¿Cuánta distancia es 1 milla? ¿Cómo la describirían?” // “How far is 1 mile? How would you describe it?”
• Consider showing a map of the school and some landmarks or points on the map that are a mile away.
### Activity
• 6–8 minutes: independent work time
• Monitor for the different ways students reason about the equivalence of $$\frac{9}{12}$$ and $$\frac{3}{4}$$. For instance, they may:
• know that 1 fourth is equivalent to 3 twelfths and reason that 3 fourths must be 9 twelfths
• note that $$\frac{3}{4}$$ and $$\frac{9}{12}$$ are both halfway between $$\frac{1}{2}$$ and 1 on the number line
• locate $$\frac{3}{4}$$ and $$\frac{9}{12}$$ on the same number line (or separate ones) and show that they are in the same location
• 2–3 minutes: partner discussion
### Student Facing
1. Han y Kiran planean ir a correr después de la escuela. Están decidiendo qué tan lejos van a correr.
• Han dice: “Corramos $$\frac{3}{4}$$ de milla. Es lo mismo que corro hasta mi entrenamiento de fútbol”.
• Kiran dice: “Yo solo puedo correr $$\frac{9}{12}$$ de milla”.
¿Qué distancia deberían correr? Explica tu razonamiento. Usa una o más rectas numéricas para mostrar tu razonamiento.
2. Tyler quiere ir a correr con Han y Kiran. Él dice: “¿Qué tal si corremos $$\frac{7}{8}$$ de milla?”.
¿La distancia que propuso Tyler es la misma que la que sus amigos querían correr? Explica o muestra tu razonamiento.
### Activity Synthesis
• Select students to share their responses and how they knew that $$\frac{9}{12}$$ is equivalent to $$\frac{3}{4}$$ but $$\frac{7}{8}$$ is not.
• To facilitate their explanation, ask them to display their work, or display blank number lines for them to annotate.
• “¿Alguien pensó de la misma forma, pero lo explicaría de otra manera?” // “Who reasoned the same way but would explain it differently?”
• “¿Alguien lo pensó de otra forma y aun así llegó a la misma conclusión?” // “Who thought about it differently but arrived at the same conclusion?”
## Lesson Synthesis
### Lesson Synthesis
“Hoy representamos fracciones en rectas numéricas y razonamos sobre fracciones equivalentes” // “Today we represented fractions on number lines and reasoned about equivalent fractions.”
Display a labeled diagram of fraction strips and the labeled number lines from today’s activity.
“¿Dónde vemos fracciones equivalentes en el diagrama de tiras de fracciones?” // “Where in the diagram of fraction strips do we see equivalent fractions?” (Parts that have the same length are equivalent.)
“¿Dónde vemos fracciones equivalentes en las rectas numéricas?” // “Where on the number lines do we see equivalent fractions?” (Points that are in the same location on the number line, or are the same distance from 0, are equivalent.)
“Supongamos que quieren ayudarle a alguien a entender que $$\frac{1}{5}$$ es equivalente a $$\frac{10}{50}$$. ¿Usarían una recta numérica o una tira de fracciones? ¿Por qué?” // “Suppose you’d like to help someone see that $$\frac{1}{5}$$ is equivalent to $$\frac{10}{50}$$. Would you use a number line or a fraction strip? Why?” (Sample response: Use a number line, because it’s not necessary to show all the tick marks. If using fraction strips, it would mean partitioning each fifth into 10 fiftieths, which is cumbersome.) | 2,737 | 10,895 | {"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} | 4.78125 | 5 | CC-MAIN-2024-30 | latest | en | 0.716228 |
http://windowssecrets.com/forums/showthread.php/86540-Words-to-numbers-function-%282000%29 | 1,484,757,594,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280308.24/warc/CC-MAIN-20170116095120-00327-ip-10-171-10-70.ec2.internal.warc.gz | 303,382,958 | 14,792 | # Thread: Words to numbers function (2000)
1. ## Words to numbers function (2000)
I have the following function in the db, but on 100000 it lists one hundred and thousand
We are usign it to convert a price to number , any ideaS?
2. ## Re: Words to numbers function (2000)
"the following function"? <img src=/S/scratch.gif border=0 alt=scratch width=25 height=29>
3. ## Re: Words to numbers function (2000)
'Declare some general working variables.
Dim English, strNum, Chunk, Pennies As String
Dim Hundreds, Tens, Ones As Integer
Dim StartVal, LoopCount As Integer
Dim TensDone As Boolean
Dim varword As Variable
'Make array of number words called EngNum.
Dim EngNum(90) As String
EngNum(0) = ""
EngNum(1) = "One"
EngNum(2) = "Two"
EngNum(3) = "Three"
EngNum(4) = "Four"
EngNum(5) = "Five"
EngNum(6) = "Six"
EngNum(7) = "Seven"
EngNum(8) = "Eight"
EngNum(9) = "Nine"
EngNum(10) = "Ten"
EngNum(11) = "Eleven"
EngNum(12) = "Twelve"
EngNum(13) = "Thirteen"
EngNum(14) = "Fourteen"
EngNum(15) = "Fifteen"
EngNum(16) = "Sixteen"
EngNum(17) = "Seventeen"
EngNum(18) = "Eighteen"
EngNum(19) = "Nineteen"
EngNum(20) = "Twenty"
EngNum(30) = "Thirty"
EngNum(40) = "Forty"
EngNum(50) = "Fifty"
EngNum(60) = "Sixty"
EngNum(70) = "Seventy"
EngNum(80) = "Eighty"
EngNum(90) = "Ninety"
'** If xero or null passed, just return "VOID"
If Nz(AmountPassed) = 0 Then
NumWord = "VOID"
Exit Function
End If
'** strNum is the passed number converted to a string.
strNum = Format(AmountPassed, "000000000.00")
'Pennies variable contains last two digits of strNum
Pennies = Mid(strNum, 11, 2)
'Prep other variables for storage.
English = ""
LoopCount = 1
StartVal = 1
'** Now do each 3-digit section of number.
Do While LoopCount <= 3
Chunk = Mid(strNum, StartVal, 3) '3-digit chunk
Hundreds = Val(Mid(Chunk, 1, 1)) 'Hundreds portion
Tens = Val(Mid(Chunk, 2, 2)) 'Tens portion
Ones = Val(Mid(Chunk, 3, 1)) 'Ones portion
'** Do the hundreds portion of 3-digit number
If Val(Chunk) > 99 Then
English = English & EngNum(Hundreds) & " Hundred and "
End If
'** Do the tens & ones portion of 3-digit number
TensDone = False
'** Is it less than 10?
If Tens < 10 Then
English = English & " " & EngNum(Ones)
TensDone = True
End If
'** Is it a teen?
If (Tens >= 11 And Tens <= 19) Then
English = English & EngNum(Tens)
TensDone = True
End If
'** Is it evenly divisible by 10?
If (Tens / 10) = Int(Tens / 10) Then
English = English & EngNum(Tens)
TensDone = True
End If
'** Or is it none of the above?
If Not TensDone Then
English = English & EngNum((Int(Tens / 10)) * 10)
English = English & " " & EngNum(Ones)
End If
'** Add the word "Million" if necessary
If AmountPassed > 999999.99 And LoopCount = 1 Then
English = English + " Million "
End If
'** Add the word "Thousand" if necessary
If AmountPassed > 999.99 And LoopCount = 2 Then
English = English & " Thousand "
End If
'** Do pass through next three digits
LoopCount = LoopCount + 1
StartVal = StartVal + 3
Loop
'** Done: Return English with Pennies/100 tacked on
NumWord = Trim(English) & " pounds"
End Function
4. ## Re: Words to numbers function (2000)
Hi Luke
I seem to have this bookmarked, obviously some project that never got off the ground. It seems to work along the same lines as you are running and is broken down into 1's, 10's, 100's and 1000's. may help you
Convert numbers to words
5. ## Re: Words to numbers function (2000)
Try the attached version. I have done the following:
<UL><LI>Corrected the declarations - in a line such as
Dim Hundreds, Tens, Ones As Integer
Hundreds and Tens are *not* declared as integers, but as variants. It should be
Dim Hundreds As integer, Tens as Integer, Ones As Integer
The declaration
Dim varword As Variable
is incorrect and superfluous, as this variable is never used.
<LI>Applied consistent indentation. Code is hard to read if indentation is absent or applied haphazardly.
<LI>Removed the references to Pennies since they were ignored anyway.
<LI>Added a few lines to add " and " only when needed.[/list]
6. ## Re: Words to numbers function (2000)
thanks
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 1,325 | 4,219 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2017-04 | longest | en | 0.662536 |
https://www.physicsforums.com/threads/zero-group-refractive-index.871177/ | 1,508,327,168,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187822930.13/warc/CC-MAIN-20171018104813-20171018124813-00647.warc.gz | 972,013,649 | 15,914 | Zero group refractive index
Tags:
1. May 10, 2016
jsea-7
1. The problem statement, all variables and given/known data.
I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency.
2. Relevant equations.
\begin{align*}
\frac{2\omega n L}{c} &= 2m\pi
\end{align*}
\begin{align*}
n_g &= n + \omega \frac{dn}{d\omega}
\end{align*}
3. The attempt at the solution.
I have considered a uniform plane wave propagating within the cavity satisfying the following relation
\begin{align*}
\frac{2\omega n L}{c} &= 2m\pi
\end{align*}
where ω is the angular frequency, n is the effective refractive index and L is the length of the laser cavity. I have derived the group refractive index as follows
\begin{align*}
n_g &= n + \omega \frac{dn}{d\omega} \\
&= \frac{c m \pi}{\omega L} - \frac{c m \pi}{ \omega L}\\
&= 0
\end{align*}
If this is correct, I don't understand what this is physically entailing. Any insight would be much appreciated! Thank you.
2. May 11, 2016
blue_leaf77
You are calculating the group index of refraction for a monochromatic wave, which is of course zero. | 335 | 1,120 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2017-43 | longest | en | 0.840381 |
https://www.astronomyclub.xyz/hole-argument/what-is-an-observable-in-general-relativity.html | 1,566,134,201,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00281.warc.gz | 721,924,466 | 11,176 | ## What Is an Observable in General Relativity
It is a curious fact about the hole argument that the indeterminism is not an observable feature; it is not an empirical kind of indeterminism that we could in any way detect. Even if it was true that general relativity was indeterministic in the sense that Earman and Norton say the manifold substantivalist is committed to, it is of such a strange kind that we could never tell one way or the other whether we lived in a world that ran according to such a scheme. For example, Hoefer writes:
Note that this indeterminism is just about what individual points will underlie what material processes (matter and metric fields). It does not entail a failure of determinism in terms of the nonindividualistically-expressed happenings in space and time, that is, nothing observable is made indeterminate by the hole argument. ([Hoefer, 1996], p. 9)
Why is this so? It clearly depends on what we take 'observable' to mean. Recall the two fields, g and \$*g, that resulted from an active diffeomorphism.187 The fields are mathematically distinct: they are spread differently over the manifold, such that g(x) = 0*g(x). But this is the only way they are distinct, only by their localization relative to the manifold—i.e. with respect to their absolute location. The crucial question is: do they represent the same physical situation, the same possible world? As Norton explains, "It would be very odd if they did not. Both systems of fields agree completely in all invariants; they are just spread differently on the manifold. Since observables are given by invariants, they agree in everything observable" ([2003], p. 114). But what things are observable? According to Einstein, following Kretschmann's bashing, only spacetime coincidences of fields and particles. This rather narrows down the space of observables, perhaps far too much, but it avoids the indeterminism and the unmeasurability of the quantities defined with respect to the manifold's points (by simply doing away with such quanti
187 By active diffeomorphism here I mean a mapping of the manifold to itself that preserves the topological and differential structure of the manifold. We made use of the carrying along (by the diffeomorphism) of geometric object fields on the manifold, such that if our diffeomorphism sends the point x to the point y then field values at y (post-diffeomorphism) look the same as they did at x (pre-diffeomorphism). Or, as Rovelli puts it, "[a] field theory is formulated in manner invariant under passive diffs (or change of co-ordinates), if we can change the coordinates of the manifold, re-express all the geometric quantities (dynamical and non-dynamical) in the new co-ordinates, and the form of the equations of motion does not change. A theory is invariant under active diffs, when a smooth displacement of the dynamical fields (the dynamical fields alone) over the manifold, sends solutions of the equations of motion into solutions of the equations of motion" ([Rovelli, 2001], p. 122).
ties). But the modern answer is pretty close: not necessarily coincidences between particles and fields, but correlations between field-values (one of which will be the gravitational field)—the latter presumably include the former.
This, or something analogous, was the case with the Leibniz-shift argument, permutations of indistinguishable quantum particles, and the indeterminism of Maxwell's theory. All agree that the theories are indeed deterministic or unprob-lematic at the level of empirically observable ontology—putting aside quantum indeterminism of course—and that we can make well confirmed predictions within each theoretical framework. The same goes for general relativity too; it has yet to be disconfirmed in any of its predictions about the behaviour of empirically observable objects. The equations of motion of the theory of general relativity are sufficient to propagate all empirically observable components of that theory. The problem concerns the empirically unobservable (unmeasurable188) ontology (if, indeed, we take there to be such): which individuals play which roles in the structure? If we chose as our motto 'what we cannot see cannot hurt us', there would be no problem with any of the cases I have examined so far. But surely we have progressed beyond such straight-jacketed empiricism? Perhaps, but any interpretation that takes a stand with respect to the ontological status of these "individual" elements—such as spacetime points and absolute location with respect to them—on the basis of physics will have the spectre of the Quine-Duhem problem to deal with: there will be multiple incompatible interpretations compatible with the theory and the evidence.
Observables are generally understood to be those quantities described by physical theories that are measured in physical interactions between systems; but they go beyond the empirically observable, for is no necessity that we can observe them. They encode information about the state of a system, and their values should be able to be predicted by the theory. Clearly, some of the candidates for observable ontology cannot be predicted, for one has at best a range of possible values connected by symmetry; one cannot determine the unique value from within this range. What I have been pushing for is an indifference or insensitivity of the laws of physics (specifically concerning observables) to certain kinds of unobservable ontology (qualitatively indistinguishable individuals). Specifically, those involving elements (objects) connected by gauge-type symmetries, such that if those elements were to appear permuted in different scenarios then the scenarios would be indistinguishable. In other words, the observables should not register haecceitistic differences—but this does not imply that there are none, simply that the physics is, or ought to be, a qualitative enterprise. This is borne out by gauge invariance principles, where this condition is built-in: in gauge theories, the observables give the same value on such elements, so that for some observable O and elements x and y related by a gauge transformation, i.e. x ~ y, we have O(x) = O(y). General relativity is a gauge theory, with the gauge freedom given by the dif-
188 Recall that the unmeasurability stems from the fact that the local values of certain fields are underdetermined by the theory and the world's qualitative properties and relations; since there will be many assignments of values to the fields that are compatible with the equations of the theory and the empirical structure (e.g. the electromagnetic field in the case of Maxwell's theory). Thus, one will not know whether one has measured A^ or A^ + df in the electromagnetic case, so one cannot view measurement as possible in this case: what is the result of the measurement? No measurement (observable) could ever distinguish between these cases.
feomorphisms of spacetime; a diffeomorphism's action on the fields amounts to a gauge transformation. However, in order to make proper sense of this proposal, we need to know what the observables are. I have dealt with the case of elec-tromagnetism already, and showed that there were a number of candidates; if we wanted to escape the indeterminism we had to make them gauge invariant (invariant under U(1)-transformations of the fields). In this section I discuss the much more complicated problem of observables in general relativity.189 In this case the observables will have to be diffeomorphism-invariant if the theory is to avoid the indeterminism. Since the diffeomorphisms comprise the gauge part of the theory, such observables will be thereby classed as gauge invariant as well. Any fields related by diffeomorphism will thus be understood as the same as far as the observables of the theory are concerned (i.e. as far as the physics goes). Since the observables will be the same in such cases, and since just such cases comprise the problem cases of the hole argument (namely metrics painted differently, yet diffeomorphically, on to the points of M), the hole argument is avoided. Let us discuss this resolution further, before considering its philosophical consequences.
One of the first things we notice about when we consider general relativity as a gauge theory is that the metric variables with respect to which the hole argument is defined do not class as observables, and so any local (i.e. defined with respect to manifold points190) quantity constructed from the metric cannot be observable either.191 Why not? Because the observables must be indifferent to permutations of the points, for such permutations (invertible ones) comprise the gauge freedom in the theory. The diffeomorphisms underlie the general covariance of general relativity, and this tells us that the models that are thus related will be indistinguishable as far as quantities not connected to the pointwise location of the fields are concerned. Therefore, the hole argument fails to get a grip: general relativity isn't meant to predict values for these quantities, nor for any quantities localized to points of the (bare) manifold regardless of how well we can specify them in connected regions of spacetime. The kinds of quantity that do class as observables in general relativity are relational (or highly non-local), much as Einstein argued, though not quite so narrowly defined. (I agree with this classification, but below I tame the view of many physicists that this implies relationalism about spacetime.) Let us say a little more about these observables, and give some examples that connect with measurements.
189 I only discuss the problem briefly here, focusing specifically on how the problem relates to the hole argument. In the next chapter I discuss the relations between the observables, the hole argument and the problem of time. This section can be seen as a bridge connecting the hole argument with the problems of time since those problems result from the application of the resolution of the hole argument presented in this section. In the final chapter I home in on ontological issues.
190 There is a proof (for the case of closed vacuum solutions of general relativity) that there can be no local observables at all [Torre, 1993]—'local' here means that the observable is constructed as a spatial integral of local functions of the initial data and their derivatives.
191 Though, you will recall, the metric does contain invariant components. However, these are best used to define local events and coordinates, rather than functioning as self-contained observables. One localizes observables with respect to these invariants.
0 0 | 2,197 | 10,681 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2019-35 | longest | en | 0.942348 |
https://discourse.quantecon.org/t/estimate-markovchain-from-data-using-ml/239 | 1,653,253,654,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662546071.13/warc/CC-MAIN-20220522190453-20220522220453-00685.warc.gz | 266,200,619 | 5,853 | # Estimate MarkovChain from data using ML
It would be nice to have routines to construct the MarkovChain type / class in QuantEcon.jl / QuantEcon.py (which can be found here or here) from data. That is, the user provides a time series that shows transitions from across a finite number of states, and the routine returns a MarkovChain instance with transition probabilities corresponding to the empirical transition probabilities in the data. The standard estimation routine is max likelihood. See
1 Like
This would be great.
Relatedly, I would be keen on having a routine that takes continuous data and estimates a Markov Chain. You could rely on the assumption that there are N states (specified by the user) and that each observation is a “true state” plus (normally distributed) noise. This would be in the spirit of the the Hamilton QE example (I also think there is a famous example where he does a similar exercise for GDP growth) and other Hidden Markov models (some related calculations are worked out in appendix 2 of RMT 3).
I was actually thinking of exactly this
One use would be as an alternative to methods like Tauchen’s method. You could take a specification of an arbitrary continuous state stochastic process (not just linear AR1!) and simulate it, and then estimate a corresponding discrete state Markov chain from the data.
Now you have a way to discretize any time homogeneous Markov process.
Assuming that this specified process is stationary and ergodic, it would be natural to somehow estimate the ergodic distribution from the simulated data, and then choose the state values for the Markov chain so that they concentrate in the region where the ergodic distribution puts most of its mass…
1 Like
Do you have some papers in mind that do something like this?
EDIT: I thought this had come up recently… One is linked in the discussion from a couple weeks ago (Alternative method for discretizing general state Markov processes).
Right, thanks for making the connection. The method used in that paper is different again. It looks neat and we should probably start there first. But it would be good nonetheless to add an estimation routine to these MarkovChain objects that allows transition probabilities to be recovered from data, as discussed above. | 472 | 2,296 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-21 | latest | en | 0.93442 |
https://lists.mcs.anl.gov/pipermail/petsc-users/2020-December/042795.html | 1,709,609,525,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707948217723.97/warc/CC-MAIN-20240305024700-20240305054700-00348.warc.gz | 379,449,068 | 3,376 | # [petsc-users] How do constraint dofs work?
Matthew Knepley knepley at gmail.com
Mon Dec 7 14:06:46 CST 2020
```On Mon, Dec 7, 2020 at 2:25 PM Alexis Marboeuf <alexis.marboeuf at hotmail.fr>
wrote:
> Hi Matt,
>
> I don't understand how unconstrained dofs in the neighborhood of a
> Dirichlet boundary can see non-zero constrained dofs in a finite element
> framework. To me, known non-zero terms due to non-zero imposed dofs are
> added in the RHS of the unconstrained dofs system?
>
I see now. I never do this, so I misunderstood your question. Yes, if you
are assembling A and b separately, then you need the terms you constrained
in b. You can
do that, but I think it is needlessly complex and error prone. I phrase
everything as a nonlinear system, forming the residual and Jacobian
F(u) = A u - b
J(u) = A
Since you have the boundary values in u, your residual will automatically
create the correct RHS for the Newton equation, which you only solve once.
There is no
overhead relative to the linear case, it is simpler, and you can
automatically do things like iterative refinement.
Thanks,
Matt
> Or the proper terms are automatically added in the RHS and no modification
> of the system is necessary? But, in that case, I don't know how to set
> imposed non-zero values to tell Petsc what terms to include?
> Thank you again for your time and I apologize if I miss something.
>
> Regards,
> Alexis
>
> ------------------------------
> *De :* Matthew Knepley <knepley at gmail.com>
> *Envoyé :* lundi 7 décembre 2020 02:02
> *À :* Alexis Marboeuf <alexis.marboeuf at hotmail.fr>
> *Cc :* petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Objet :* Re: [petsc-users] How do constraint dofs work?
>
> On Sun, Dec 6, 2020 at 1:46 PM Alexis Marboeuf <alexis.marboeuf at hotmail.fr>
> wrote:
>
> Hello,
>
> I intend to contribute to the Petsc documentation, especially on PetscSF
> and PetscSection objects. I'm writing an example where I solve a linear
> elasticity problem in parallel on unstructured meshes. I discretize the
> system with a finite element method and P1 Lagrange base functions. I only
> use Petsc basics such as PetscSF, PetscSection, Mat, Vec and SNES objects
> and I need to implement Dirichlet and/or Neuman boundary conditions.
> PetscSectionSetConstraintDof and related routines allow to define which
> dofs are removed from the global system but are kept in local Vec. I don't
> how it works? In particular, do I have to manually add terms related to
> inhomogeneous Dirichlet boundary condition in the RHS? Am I missing
> something?
>
>
> The way this mechanism is intended to work is to support removal of
> constrained dofs from the global system. This means it solves for only
> unconstrained dofs and no modification of the system is necessary.
> However, you would be responsible for putting the correct boundary values
> into
> any local vector you use. Note that this mechanism is really only
> effective when you can constrain a dof itself, not a linear combination.
> For that, we
> do something more involved.
>
> Operationally, SetConstraintDof() keeps track of how many dofs are
> constrained on each point. Then SetConstraintIndices() tells us which dofs
> on that
> point are constrained, where the indices are in [0, n) if there are n dofs
> on that point. If you make a global Section, constrained dofs have negative
> offsets,
> just like ghost dofs.
>
> Thanks,
>
> Matt
>
>
> Regards,
> Alexis Marboeuf
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20201207/eb15abd5/attachment.html>
``` | 1,094 | 4,149 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10 | latest | en | 0.848883 |
http://dict.cnki.net/h_1891377000.html | 1,596,575,150,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735882.86/warc/CC-MAIN-20200804191142-20200804221142-00198.warc.gz | 29,311,459 | 12,207 | 全文文献 工具书 数字 学术定义 翻译助手 学术趋势 更多
basic程序 的翻译结果: 查询用时：1.426秒
历史查询
basic程序
basic program
Analysis from BASIC Program to Visual BASIC Program BASIC程序改写为Visual BASIC程序的分析 短句来源 FILES TRANSMISSION OF BASIC PROGRAM BETWEEN EG3200 AND MC-176 MICROCOMPUTER EG3200微机与MC-176微机之间BASIC程序文件的传送 短句来源 A BASIC Program Computing LD_(50) with Figure by Bliss Method 一种带作图的Bliss法计算LD_(50)的BASIC程序 短句来源 Analysing BASIC Program of Failure Tree 故障树的BASIC程序分析——PC—1500的应用 短句来源 BASIC Program of Gradual Regression 逐步回归BASIC程序 短句来源 更多
basic programme
This paper introduced the basic constantmathematical modelcomputational method and basic programme of pregnant model of NRC 1998 for pregnant sow． 详细介绍了NRC（1998）妊娠母猪营养需要模型的基本常数、数学公式和计算方法，编制出了计算妊娠母猪营养需要的Basic程序。 短句来源 The BASIC programme made out is applicable in 7 modes making regression and analysis of the shearing rate, stress and test Value of various Newtonian and non-Newtonian fluid oil. 编制的BASIC程序,可用于七种常见的模式,对各种牛顿、非牛顿体原油的剪切速率、剪切应力的实验值进行回归分析。 短句来源 The whole calculation process is completed by PB—700 microcom-puter with selfdefined BASIC programme. 整个数值计算过程采用自编 BASIC 程序由 PB—700微型计算机完成。 短句来源 BASIC PROGRAMME OF THE ANALYSING COMPLEX STATE OF STRESS 复杂应力状态分析的BASIC程序 短句来源 In this paper is made an approach to the county population model, population control and population forecast of 2000 year in Xinjiang, and is worked out the BASIC programme of the population forecast according to the characteristics of the population risiug in the area inhabited by many nationalities of the region. 本文根据新疆多民族杂居地区人口发展的特点,探讨了该地区县级人口模型、人口控制及2000年人口予测,编制了人口予测的BASIC程序。 短句来源 更多
basic programs
BASIC Programs for Variance Analysis 方差分析的BASIC程序 短句来源 This paper is mainly discussed with a method that how Microsoft Visual Basic programs create a Microsoft Excel Object and transfer the database to Excel Worksheet for outputting,and some VB codes are given. 本文主要讨论如何利用Microsoft Visual Basic程序来调用Microsoft Excel对象,把数据库文件转换为Microsoft Excel电子表格进行打印输出的方法,并给出部份源代码。 短句来源 FORTRAN and BASIC programs were worked out by using simplex optimization. 编成FORTRAN和BASIC程序,在长城0520或IBM微机上应用均获得成功。 短句来源 BASIC programs are presented, showing the problems in designing respectively the rigid body guidance and function generator. 文中附有BASIC程序,并各举一例分别阐明刚体导引和再现函数两类设计课题. 短句来源 A method for storing and reading of chromatographic data on the disk of C-R3A microprocessor and the corresponding BASIC programs are described. Using this method users can reprocess the chromatographic data in data file on the disk with other data processing method which they choose. 本文介绍了在C－R3A微处理机上对色谱数据进行磁盘存储和读取的方法及相应的BASIC程序，用户可以采用原有功能以外的自行数据处理方法，对磁盘上数据文件中的色谱数据进行再处理。 短句来源 更多
basic programm
COMPILING AND APPLICATION OF BASIC PROGRAMM FOR H_2 CONTENT CALCULATION 氢气自动差减计算BASIC程序的编制及应用 短句来源 A BASIC programm of Monte Carlo Simulation of binary copolymerization was made according to the Terminal Model . 本文根据蒙特卡罗方法的原理,编写了微机用BASIC程序,供模拟末端模型二元共聚反应使用。 短句来源 This paper, based on the graphical function, proposed a new method, by means of which the TRUE BASIC programm menu can be conveniently designed. 通过分析TRUEBASIC的图形功能,找出制作TRUE BASIC程序菜单的新方法。 短句来源
我想查看译文中含有：的双语例句
basic program
A graph for the evaluation of the CSF-protein profile is presented as a basic program for the clinical-neurochemical laboratory. A basic program for direkt calculation of important By using visual basic program to communicate and program, the centralized management and automatic control of the lime furnace are realized. A Q-basic program was designed to calculate K and n values. Estimates derived from the spreadsheet program may be used in a BASIC program to arrive at the optimal fit. 更多
basic programme
The Swedish Medical Association's basic programme regarding psychiatric care in Sweden Another possibility is to join the Ecoprofit Club, a union of companies that participated at least in the basic programme. An extra treatment can be added after the basic programme has finished if signs of parasitism should appear. Because of the great amount of new information and also of new tasks, there is not enough time in the basic programme for extensive innovative ideas. Experience shows, that the shorter the basic programme, the more difficult becomes the implementation in companies. 更多
basic programs
All the options tested can be applied by correctly programming the spectrometer with BASIC programs, within reach of any use who has even a small understanding of programming. The results were evaluated by BASIC programs for one dimensional data evaluation, by principal components plot and by multidimensional analysis of variance. A high flexibility is achieved, as the BASIC programs can readily be modified for specific purposes. In this paper the fundamental aspects that unify the basic programs for locomotion generation in both vertebrates and invertebrates are examined. The computer system is user-friendly and consists of several Visual Basic programs while the geographical information system is incorporated to facilitate input and output interface and database management. 更多
其他
The least square method of fitting the testing data of gear life is dealt with and the functional relation representing the gear fatigue curve is established. The ALGOL and BASIC programs for the fatigue curve are set up and the experimental fatigue curve of the gear is plotted with the aid of a computer. The method proposed, the relation established and the program of computation and plotting can be extended in use to the fatigue testing of common metals or V belts. 本文探讨应用最小二乘法拟合齿轮疲劳试验数据,建立齿轮疲劳曲线的函数关系式。文中编制了求解疲劳曲线的ALGOL程序和BASIC程序。并利用电子计算机绘制出齿轮的试验疲劳曲线。本文探讨的方法、建立的函数式以及计算和绘图程序可以推广用于一般金属疲劳试件或三角胶带。 This treatise investigates and analyses the geometrical relationship ofparts of runaway-escapement of the starwheel-pinpallet type. It sets up thefunctional relationships between the principal characteristic dimensions(such as distance between centers of escapement wheel and balance, dis-tance between the centers of pallet pins, diameter of the addendum circleof starwheel etc.) and period of oscil1ation of the balance (oscillatingmass). Through the medium of these relationships, we can analyse theinfluences... This treatise investigates and analyses the geometrical relationship ofparts of runaway-escapement of the starwheel-pinpallet type. It sets up thefunctional relationships between the principal characteristic dimensions(such as distance between centers of escapement wheel and balance, dis-tance between the centers of pallet pins, diameter of the addendum circleof starwheel etc.) and period of oscil1ation of the balance (oscillatingmass). Through the medium of these relationships, we can analyse theinfluences of the constructional dimensions of the present escapements tothe periods of oscillaton and can also employ these functional relationshipsto decide rational constructional dimensions and to assign rationaltolerance in dimensions. This treatise also introduce the BASIC program tocalculate the period of oscillation of the pinpallet-starwheel type runawayescapement, with little modification we can also calculate the influencesof every geometrical dimensions of the mechanism to the period ofoscillation. 本文分析研究了直齿销式无返回力矩擒纵调速器的几何关系,把调速器的主要性能尺寸(如中心距、擒齿直径、擒轮齿顶角、卡摆销心距等)同卡摆的振动周期建立了函数关系。通过它,我们可以分析现有调速器机构的结构尺寸对周期的影响,在设计新调速器时可以用它合理决定结构尺寸,合理决定尺寸公差。 本文还介绍了这理论所用的计算周期的BASIC程序,应用它可以求解销式调速器的振动周期,稍加变化还可计算各几何尺寸对周期的影响 The TRS-80 microcomputer is a general purpose personal computersystem without stand-by interface, and the MCS-052/10 is a specialmicrocomputer system designed for the data acquisition and industrial processcontrol. If these two microcomputers are connected on-line working,the performance of utility for the system will be upgraded. This paper introduces basal construction and performance of previousmicrocomputers. The hardware connection of serial interface expandedon the TRS-80 system bus, and the programming... The TRS-80 microcomputer is a general purpose personal computersystem without stand-by interface, and the MCS-052/10 is a specialmicrocomputer system designed for the data acquisition and industrial processcontrol. If these two microcomputers are connected on-line working,the performance of utility for the system will be upgraded. This paper introduces basal construction and performance of previousmicrocomputers. The hardware connection of serial interface expandedon the TRS-80 system bus, and the programming used for on-lineoperation by format of MCS-052/10 monitor commands are described indetail. In addition, the operation way of this system is introduced. Fin-ally, a list of online routine written by BASIC program language is givenin the appendix. TRS—80是一种未配置备用接口的通用个人计算机,而MCS—052/10则是一台专为数据采集与工业过程控制而设计的微型计算机系统。连接两台微型计算机使之联机工作将会提高系统的使用特性。本文介绍了上述两类微型计算机的基本结构与特性,详细阐述了在TRS—80系统总线上扩充串行接口的硬件连接,以及按MCS—052/10机监控命令格式编制的联机操作程序。此外,还介绍了该系统的操作使用方法,并在附录中给出了以BASIC程序语言编写的程序单。 << 更多相关文摘
相关查询
CNKI小工具 在英文学术搜索中查有关basic程序的内容 在知识搜索中查有关basic程序的内容 在数字搜索中查有关basic程序的内容 在概念知识元中查有关basic程序的内容 在学术趋势中查有关basic程序的内容
CNKI主页 | 设CNKI翻译助手为主页 | 收藏CNKI翻译助手 | 广告服务 | 英文学术搜索
2008 CNKI－中国知网
2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社 | 2,614 | 9,145 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-34 | latest | en | 0.379681 |
http://groups.google.com/group/sci.physics/msg/164f42a9b9faee0a | 1,369,202,320,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368701409268/warc/CC-MAIN-20130516105009-00049-ip-10-60-113-184.ec2.internal.warc.gz | 130,195,236 | 22,988 | The old Google Groups will be going away soon, but your browser is incompatible with the new version.
Message from discussion first counterexamples in Riemann Hypothesis because Euler encoding is not viable #1349 Correcting Math
From:
To:
Cc:
Followup To:
Subject:
Validation: For verification purposes please type the characters you see in the picture below or the numbers you hear by clicking the accessibility icon.
More options Dec 30 2010, 9:44 pm
Newsgroups: sci.math, sci.physics, sci.logic
From: David Bernier <david...@videotron.ca>
Date: Thu, 30 Dec 2010 21:44:53 -0500
Local: Thurs, Dec 30 2010 9:44 pm
Subject: Re: first counterexamples in Riemann Hypothesis because Euler encoding is not viable #1349 Correcting Math
Archimedes Plutonium wrote:
> On Dec 30, 11:38 am, Archimedes Plutonium
> <plutonium.archime...@gmail.com> wrote:
>> On Dec 30, 5:09 am, Archimedes Plutonium
>> <plutonium.archime...@gmail.com> wrote:
>>> On Dec 30, 1:03 am, Archimedes Plutonium
>>> <plutonium.archime...@gmail.com> wrote:
>>>> On Dec 29, 2:22 am, Archimedes Plutonium
>>>> <plutonium.archime...@gmail.com>
>>>> wrote:
>>>> (snipped to save space)
>>>>> In Circumferencing the Perimeter we start with a square-side and find
>>>>> its perimeter and then
>>>>> we pi-twiddle and see if we can match it with a circumference. We have
>>>>> truncations also.
>>>>> 215.50
>>>>> 2152.050
>>>>> Here is an example of on square side in the Circumferencing the
>>>>> Perimeter:
>>>>> Let me try 2152.550 as more suitable
>>>>> side of square = 2152.550
>>>>>
perimeter = 4xside = 8610.200
>>>>>
8610.200/3.141 = 2741.228 = diameter
>>>>>
start pi twiddling 1/(B^2)twiddle 8610.200/2741.228 = 3.1410010
>>>>> pi twiddle = 3.141002
>>>>>
3.141002 x 2741.228 = 8610.202 mismatch
>>>>> 3.141001 x 2741.228 = 8610.199 mismatch
>>>>> Can someone set up a computer program that incorporates the above
>>>>> example and find that
>>>>> accurate table of first breakdowns in B matrices from 100 to 10^8?
>>>>> Is 215.50 the first square-side to have a breakdown in the 100 B
>>>>> matrix? Please fill in the
>>>>> first breakdowns all the way out to 10^8.
>>>>> P.S. Can someone set up a computer program to tell me all of the even
>>>>> cube roots of integerized pi lie? 314 is integerized pi to three
>>>>> places and 3141 is integerized pi to
>>>>> four places and neither are evenly cube rootable. I want to know along
>>>>> the integerized pi
>>>>> string of digits, where it is evenly cube rootable. I suspect that pi
>>>>> is cube rootable only
>>>>> at the 603rd digits where pi has those three zeroes in a row. The
>>>>> reason I want this information is because pi could tell us where the
>>>>> first counterexamples to FLT exist when
>>>>> we have infinity as imprecisely defined. In other words, pi could lead
>>>>> us to how large of a
>>>>> large number we have to go to in order to engineer the counterexample.
>>>>> Or, pi may tell us that 10^603 is the counterexample of FLT for
>>>>> exponent 3.
>>>> So are those accurate?
>>>> 215.50 first breakdown in 100 B matrix
>>>> 2152.050 first breakdown in 1000 B matrix of Circumferencing the
>>>> Perimeter
>>>> And can someone fill in the table out to 10^8 B matrix?
>>> 215.50
>>>
2152.050
>>> 21521.5000
>>> Circumferencing the
Perimeter:
>>> for B matrix 10^4
>>> side of square = 21521.5000
>>>
perimeter = 4xside = 86086.0000
>>> 86086.0000/3.1415 = 27402.8330 = diameter
>>> start pi twiddling 1/(B^2)twiddle 86086.0000/27402.8330 = 3.141500004
>>> pi twiddle = 3.14150001
>>> 3.14150001 x 27402.8330 = 86086.0001 mismatch
>>> 3.14150000 x 27402.8330 = 86085.9998 mismatch
>>> Apparently the digit pattern arrangement of 215---- leads to
>>> breakdowns in Circumferencing, but whether they are the
>>> first breakdowns for those B matrices is not yet established.
>> I think I may have spotted where the Riemann Hypothesis has its first
>> breakdown in
>> counterexamples of nontrivial zeroes on the 1/2 Real strip. The
>> question being, as in
>> FLT, whether the breakdown is before 10^603 or long after the 10^603
>> as the border between
>> Finite and Infinity.
> Reading from the book Prime Obsession by John Derbyshire on page 104.
> What I am trying to resolve is whether the Euler encoding of the
> multiplication of primes is really and truly equal to that of the zeta
> function of the addition series.
The Riemann-von Mangoldt formula for psi(x) is a truly marvelous thing.
First, the definition of the von Mangoldt function Lambda(n),
for an integer n >=1:
If n has no prime factors, Lambda(n) = 0.
If n has two or more distinct prime factors, Lambda(n) = 0.
The remaining case is where n has just one prime factor, p.
Then n could be p, p^2, p^3, ...
Then Lambda(p) = Lambda(p^2) = Lambda(p^3) = ... = log(p) [base 'e' ].
psi(x) := sum_{1 <= n <= x} Lambda(n) .
[ This is the summatory von Mangoldt function, or Chebyshev function,
according to Wikipedia].
There is an expression for psi(x) in terms of the non-trivial zeta zeros
that is referred to as the "Riemann-von Mangoldt explicit formula"
or "von Mangoldt explicit formula". You can find it here,
following the text "Von Mangoldt's formula for psi(x):"
< http://web.viu.ca/pughg/Psi/ > .
There is also an applet there. As more zeta zeros are included,
the graph changes less and less. I think there are jump
discontinuities in psi(x) at primes and prime powers,
and I'm not sure how the "explicit formula" behaves point-wise
at the jump discontinuities.
David Bernier
> Here is what we do know for sure, is that pi is a series involving
> primes and this series allows us to
> fetch three zeroes in a row in the 10^-603 place value.
> But that a multiplication of primes as the Euler Encoding would not
> possibly be able to fetch 3 zero digits in a row
> in multiplication. So that the Euler multiplication encoding is not
> equal to the Riemann Zeta Function and that all this huff puff
> hallyballoo about the primes being as perfectly spaced as possible was
> just a fanciful wish.
> What I have to do here, is see if I can analyze where RH has its first
> counterexample, whether it is below the 10^603 mark or smack dab on
> the mark of 10^603 where Circumferencing the Perimeter breaks down
> also, or whether RH breaksdown some distance beyond the 10^603 mark.
> Archimedes Plutonium
> http://www.iw.net/~a_plutonium/
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies
--
\$ gpg --fingerprint david...@videotron.ca
pub 2048D/653721FF 2010-09-16
Key fingerprint = D85C 4B36 AF9D 6838 CC64 20DF CF37 7BEF 6537 21FF
uid David Bernier (Biggy) <david...@videotron.ca> | 1,993 | 6,713 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2013-20 | latest | en | 0.740089 |
https://www.theunitconverter.com/knot-to-foot-second-conversion/ | 1,718,204,041,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861173.16/warc/CC-MAIN-20240612140424-20240612170424-00208.warc.gz | 961,311,083 | 7,842 | # Knot to Foot/Second Conversion
## Knot to Foot/Second Conversion - Convert Knot to Foot/Second (kn to ft/s)
### You are currently converting Velocity and Speed units from Knot to Foot/Second
1 Knot (kn)
=
1.68781 Foot/Second (ft/s)
Knot : The knot is a non-SI unit for speed. It is equal to one nautical mile(1.852 km) per hour, and approximately equal to 1.151 mph (full name: mile per hour). Without standard abbreviation, the commonly used is kn, but kt and NMPH are also used. In the worldwide, the knot is popularly used in meteorology, and in maritime and air navigation.
Foot/Second : Feet per second is a unit for both speed and velocity. It is defined as the distance in feet traveled or displaced, divided by the time in seconds. Its abbreviations are ft/s, ft/sec and fps, and the scientific notation ft s-1. 1 ft/s = 0.3048 m/s.
### Velocity and Speed Conversion Calculator
1 Knot = 1.68781 Foot/Second
### FAQ about Knot to Foot/Second Conversion
1 knot (kn) is equal to 1.68781 foot/second (ft/s).
1kn = 1.68781ft/s
The speed v in foot/second (ft/s) is equal to the speed v in knot (kn) times 1.68781, that conversion formula:
v(ft/s) = v(kn) × 1.68781
One Knot is equal to 1.68781 Foot/Second:
1kn = 1kn × 1.68781 = 1.68781ft/s
One Foot/Second is equal to 0.59248 Knot:
1ft/s = 1ft/s × 0.59248 = 0.59248kn
v(ft/s) = 5(kn) × 1.68781 = 8.43905ft/s | 424 | 1,381 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2024-26 | latest | en | 0.884362 |
https://www.physicsforums.com/threads/algorithm-for-change-making-problem.547456/ | 1,627,908,216,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154320.56/warc/CC-MAIN-20210802110046-20210802140046-00716.warc.gz | 964,708,423 | 14,671 | # Algorithm for change-making problem
Ok, so I found this article that presents an algorithm for deciding whether or not a set of coins allows for use of a greedy algorithm when making change:
http://ecommons.cornell.edu/bitstream/1813/6219/1/94-1433.pdf
But I'm not quite sure if I've understood it. The way I see it you do the following:
-choose i and j
-compute G(ci-1 -1)
-from G(ci-1 -1), find M(w)
-from M(w) find w
-compute G(w)
-if |M(w)| < |G(w)| there is a counterexample and the coin set does not allow for a
greedy algorithm
-repeat for different combinations of i and j until you find a counterexample or until all
combinations have been tried, in which case the coin set allows for use of a greedy
algorithm | 192 | 725 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2021-31 | latest | en | 0.842084 |
https://mrburkemath.blogspot.com/2021/07/ | 1,726,797,163,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652073.91/warc/CC-MAIN-20240919230146-20240920020146-00308.warc.gz | 375,298,308 | 59,661 | ## Friday, July 30, 2021
### (x, why?) Mini: Nonlinear Partial Differential Equations
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
What it says is what you get.
Dedicated to Dr. Anna Kiesenhofer, a mathematician researching non-linear partial differential equations, and who won an Olympic gold medal in the Women's Individual Road Race in Cycling.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part II: Each correct answer will receive 2 credits. Partial credit is possible.
31. State the value of the expression (4.1 X 102)(2.4 X 103) / (1.5 X 107) in scientific notation.
Answer:
Remember the rules for exponents. Having base 10 is no different from having base x.
You can regroup them if you want to. Use your calculator to solve the first part. Remember to put the final answer back into scientific notation with the coefficient between 1 and 9.9999...
(4.1 X 102)(2.4 X 103) / (1.5 X 107)
(4.1)(2.4)/(1.5) X (102)(103) / (107)
6.56 X 102 + 3 - 7
6.56 X 10-2
I'm a little surprised that they didn't form the problem so that the coefficient was 10 or greater or less than one.
32. Express the product of (x + 2)/2 and (4x + 20)/(x2 + 6x + 8) in simplest form.
Answer:
With problems like this, factor whatever you can, and then cancel out common factors in the numerator and denominator which form a multiplicative identity.
(x + 2) / 2 * (4x + 20) / (x2 + 6x + 8)
(x + 2) / 2 * ( (4)(x + 5) ) / ( (x + 4)(x + 2) )
1 / 1 * ( (2)(x + 5) ) / ( (x + 4)(1) )
( (2)(x + 5) ) / (x + 4)
(2)(x + 5)
x + 4
Either (2)(x + 5) or 2x + 10 were acceptable in the numerator.
33. On the set of axes below, graph y = 3x over the interval -1 < x < 2.
Answer:
It is very important that you ONLY graph the domain that they gave you. Do NOT go beyond it. Do NOT draw arrows indicating the directions the line is going in. You CAN pick whatever scale you want for the x-axis. If you wanted, say, to count two boxes for every 1, that's fine.
Your graph should look like this:
At x = -1, the point should be at about 1/3 of the distance between 0 and 1. Do the best you can. Do NOT make a point on the x-axis.
More to come. Comments and questions welcome.
More Regents problems.
## Thursday, July 29, 2021
### New Improbolympic Events
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
It can add a new dimension to the games ... or take one away.
I don't think I could've done better with those hurdles, even with infinite time.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
26. What is the solution of 2 / (x + 1) = (x + 1) / 2
1) -1 and -3
2) -1 and 3
3) 1 and - 3
4) 1 and 3
Answer: 3) 1 and - 3
Cross-multiply and solve the resulting quadratic equation.
2 / (x + 1) = (x + 1) / 2
(x + 1)(x + 1) = 4
x2 + 2x + 1 = 4
x2 + 2x - 3 = 0
(x - 1)(x + 3) = 0
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
27. The total score in a football game was 72 points. The winning team scored 12 points more than the losing team. How many points did the winning team score?
1) 30
2) 42
3) 54
4) 60
Answer: 2) 42
As much as I'd like to say that 42 is the Ultimate Answer to the Question of Life, the Universe and Everything, we still have to solve this problem to see if it's the solution to this problem.
If x is the number of points the losing team scored, then x + 12 is the number of points the winning team scored because they scored 12 more points. The sum of those two expressions is x + x + 12.
x + x + 12 = 72
2x + 12 = 72
2x = 60
x = 30
The losing team scored 30. The winning team scored 30 + 12 = 42.
28. What is the perimeter of the figure shown below, which consists of an isosceles trapezoid and a semicircle?
1) 20 + 3π
2) 20 + 6π
3) 26 + 3π
4) 26 + 6π
Answer: 1) 20 + 3π
Add the three sides of the trapezoid that are shown. Do not add the dotted line because it is not part of the perimeter. It is inside. Then calculate the circumference of the semicircle.
The trapezoid sides are 4 + 6 + 10 = 20. Eliminate Choices (3) and (4).
The semicircle has a diameter of 6 because the trapezoid is isosceles. The Circumference of a circle is πd or 2πr, so the circumference of a semicircle (1/2 of a circle) is half as much: 1/2 πd or πr.
We know the diameter is 6, so the circumference is 3π. Choice (1).
29. The probability that it will rain tomorrow is 1/2. The probability that our team will win tomorrow’s basketball game is 3/5. Which expression represents the probability that it will rain and that our team will not win the game?
1) 1/2 + 3/5
2) 1/2 + 2/5
3) 1/2 * 3/5
4) 1/2 * 2/5
Answer: 4) 1/2 * 2/5
The most important word here is not. You were given the probability that the team will win. We need the probability that they will NOT win. Since there are only two possiblities, winning and not winning, and because those two probabilities must add up to 1, the probability of not winning is 1 - 3/5, which is 2/5.
The probability of two independent events occurring is the product of the two individual events happening separately.
30. The formula for the volume of a pyramid is V = 1/3 Bh. What is h expressed in terms of B and V?
1) h = 1/3 VB
2) h = V / (3B)
3) h = (3V)/B
4) h = 3VB
Answer: 3) -2 or 2
Use inverse operations to isolate the h.
V = 1/3 Bh
3V = Bh
3V/B = h
End of Part I.
More to come. Comments and questions welcome.
More Regents problems.
## Wednesday, July 28, 2021
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
21. Given:
A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {2, 3, 5, 7}
D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Which statement is false?
1) A ∪ B ∪ C = D
2) A ∩ B ∩ C = { }
3) A ∪ C = {1, 2, 3, 5, 7}
4) A ∩ C = {3, 5, 7}
Answer: 3) A ∪ C = {1, 2, 3, 5, 7}
1) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, which is set D.
(1) is True.
2) A ∩ B ∩ C = {1, 3, 5, 7, 9} ∩ {2, 4, 6, 8, 10} ∩ {2, 3, 5, 7}
= { } ∩ {2, 3, 5, 7} = { }.
(2) is True.
3) A ∪ C = {1, 3, 5, 7, 9} ∪ {2, 3, 5, 7}
= {1, 2, 3, 5, 7, 9} =/= {1, 2, 3, 5, 7, 9}.
(3) is False.
4) A ∩ C = {1, 3, 5, 7, 9} ∩ {2, 3, 5, 7} = {3, 5, 7}.
(4) is True.
22. Which expression is equivalent to ( 2x6 - 18x4 + 2x2 ) / 2x2
1) x3 - 9x2
2) x4 - 9x2
3) x3 - 9x2 + 1
4) x4 - 9x2 + 1
Answer: 4) x4 - 9x2 + 1
Divide the coefficient of each term in the numerator by 2, and reduce the exponent of the variable by 2. The rule for dividing variables with exponents is to keep the base and subtract the exponent. In this case, each term will have two fewer factors of x.
2x6 / 2x2 = x4. Eliminate Choices (1) and (3).
18x4 / 2x2 = 9x2.
2x2 / 2x2 = 1. Eliminate Choice (2).
23. In a given linear equation, the value of the independent variable decreases at a constant rate while the value of the dependent variable increases at a constant rate. The slope of this line is
1) positve
2) negative
3) zero
4) undefined
Answer: 2) negative
If one variable is increasing while the other is decreasing, the slope is negative.
If the slope were positive, both variables would be increasing or both variables would be decreasing.
A zero slope would require that the dependent variable NOT change at all but instead remain constant. For example, y = 3.
An undefined slope would require that the independent variable NOT change at all but instead remain constant. For example, x = 2.
24. The volume of a cylindrical can is 32π cubic inches. If the height of the can is 2 inches, what is its radius, in inches?
1) 8
2) 2
3) 16
4) 4
Answer: 4) 4
The Volume of a cylinder uses the formula V = π r2 h.
V = π r2 h = 32π
π r2 (2) = 32π
r2 = 16
r = 4
25. The expression ( 14 + x ) / ( x2 - 4 ) is undefined when x is
1) -14, only
2) 2, only
3) -2 or 2
4) -14, -2, or 2
Answer: 3) -2 or 2
A fraction is undefined if its denominator is equal to zero. You cannot divide by 0.
The numerator can be zero, and you can divide 0 as many ways as you want. The quotient will always be 0, unless you are divide by zero.
For what values of x is the denominator equal to 0?
x2 - 4 = 0
(x - 2)(x + 2) = 0
x - 2 = 0 or x + 2 = 0
x = 2 or x = -2
More to come. Comments and questions welcome.
More Regents problems.
## Tuesday, July 27, 2021
### Math!
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Math * (Math - 1) * (Math - 2) * ... * 1
It depends on the value of Math. And some people give Math more value than others!
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
16. The rectangular prism shown below has a length of 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm.
What is the surface area, in square centimeters?
1) 45.6
2) 49.5
3) 78.0
4) 91.2
Answer: 4) 91.2
The surface area is the sum of the areas of the six sides of the prism. Since it is a rectangular prism, the opposite sides have the same area.
You have find the L * W, L * H, and W * H, double each of those, and find the sum.
L * W = 3 * 2.2 = 6.6
L * H = 3 * 7.5 = 22.5
W * H = 2.2 * 7.5 = 16.5
2 * (6.6 + 22.5 + 16.5) = 91.2
17. Which set of coordinates is a solution of the equation 2x - y = 11?
1) (-6, -1)
2) (-1, 9)
3) (0, 11)
4) (2, -7)
Answer: 4) (2, -7)
You can try each of the choices to see which makes a true statement, or you can rewrite the equation, solving for y, and put that into your graphing calculator and look at the Table of Values for the correct entry.
2x - y = 11
2x - 11 = y, or y = 2x - 11
Ironically, it wasn't until I typed the above equation just now that I noticed that the first three choices are all solutions to y = 2x + 11. I would've just did the mental math.
18. The graph of a parabola is represented by the equation y = ax2 where a is a positive integer. If a is multiplied by 2, the new parabola will become
1) narrower and open downward
2) narrower and open upward
3) wider and open downward
4) wider and open upward
Answer: 2) narrower and open upward
Since a is positive, it opens upward. Eliminate Choices (1) and (3).
If you double a, then the y values will increase more rapidly. That will cause the parabola to become thinner, or narrower.
19. Which equation represents a line that has a slope of 3/4 and passes through the point (2,1)?
1) 3y = 4x - 5
2) 3y = 4x + 2
3) 4y = 3x - 2
4) 4y = 3x + 5
Answer: 3) 4y = 3x - 2
The choices given are not in any familar form. However, they could easily be put into slope-intercept form by dividing by the coefficient of y to get y = mx + b.
If you divide Choices (1) and (2) by 3, then the value of m will be 4/3 instead of 3/4. Eliminate choices (1) and (2).
Next, substitute x = 2 into Choices (3) and (4).
4y = 3(2) - 2 = 6 - 2 = 4; 4y = 4, y = 1. This is the solution we are looking for.
4y = 3(2) + 5 = 6 + 5 = 11; 4y = 11, y = 11/4. This is NOT the solution we are looking for.
20. What is the value of | ( 4(-6) + 18 ) / 4! | ?
1) 1/4
2) - 1/4
3) 12
4) -12
Answer: 1) 1/4
I hate questions like this. I had a student come up to me after the exam and ask me, "Mr. Burke, what does an exclamation point in a math problem mean?" That's not to say that he shouldn't have known it, but the notation wasn't used as much as the concept it stands for. However, the reason I hate this problem is because it's meaningless and bizarre. There is no reason to put a factorial symbol in an equation like this other than to see if students were paying attention. It's a meaningless Order of Operations question with an added twist to it that only makes it longer, but not more challenging or interesting.
Order of Operations: Evaluate the numerator, multiply and add. Then evaluate the factorial, 4!, which is 4*3*2*1. Then simplify the fraction. Finally, take the absolute value.
Note that the Absolute Value is the final step, so the answer cannot be negative. Eliminate Choices (2) and (4).
| ( 4(-6) + 18 ) / 4! |
= | ( -24 + 18 ) / 4! |
= | -6 / 4! |
= | - 6/24 |
= | -1/4 |
= 1/4
I'm a little curious where they got 12 from. That should come from an "obvious" mistake, but I'm not seeing it.
More to come. Comments and questions welcome.
More Regents problems.
## Monday, July 26, 2021
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
11. Is the equation A 21000(1 - 0.12)t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?
1) exponential growth and 12%
2) exponential growth and 88%
3) exponential decay and 12%
4) exponential decay and 88%
Answer: 3) exponential decay and 12%
There is 12% decay, which will leave you with 88% of the original amount.
You know it is decay because of the minus sign, telling you that you will have less than 100% (the full amount) after the first time period.
12. The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used to find the longest possible width?
1) 30 + 2w < 50
2) 30 + 2w < 50
3) 30 + 2w > 50
4) 30 + 2w > 50
Answer: 2) 30 + 2w < 50
We are looking for the longest, meaning that there is a maximum number. All of the possibilities have to be LESS THAN that amount. Eliminate Choices (3) and (4).
The words "at most" 50 tell you that it can equal 50, so you want LESS THAN OR EQUAL TO.
13. Craig sees an advertisement for a car in a newspaper. Which information would not be classified as quantitative?
1) the cost of the car
2) the car's mileage
3) the model of the car
4) the weight of the car
Answer: 3) the model of the car
If you were unsure about quantitative vs qualitative, then this would be a good time to play "One of these things is NOT like the others".
Three of the four choices are numerical data and things that can be measured in dollars, miles and pounds. One of them is an arbitrary name given to the car, which is a description for the car.
14. What are the coordinates of the vertex and the equation of the axis of symmetry of the parabola shown in the graph below?
1) (0,2) and y = 2
2) (0,2) and x = 2
3) (-2, 6) and y = -2
4) (-2, 6) and x = -2
Answer: 4) (-2, 6) and x = -2
The vertex of a parabola is the turning point. It is either the maximum or the minimum point (and a parabola will only have one of those). In this example, the topmost point occurs at (-2, 6).
The axis of symmetry is a vertical line that, if drawn, would cut the parabola in half, creating two mirror images. The axis goes through the vertex.
The equation for all vertical lines is x = a, and every point on that line will be (a, y) for whatever value of y. The x coordinate of the vertex is -2.
15. A correct translation of “six less than twice the value of x” is
1) 2x < 6
2) 2x - 6
3) 6 < 2x
4) 6 - 2x
Answer: 2) 2x - 6
Do NOT confuse "less than" (subtraction) with "IS less than" (inequality).
Eliminate Choices (1) and (3) for using the < symbol instead of subtraction.
If my height is three inches less than your height, and your height is 68 inches, would you find my height by doing 68 - 3 or 3 - 68? The latter choice is ridiculous because it would give me a negative height.
"Six less than" something means "take six away from" something, and the something has to be there first to take something away from it.
More to come. Comments and questions welcome.
More Regents problems.
## Sunday, July 25, 2021
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
6. Jason’s part-time job pays him \$155 a week. If he has already saved \$375, what is the minimum number of weeks he needs to work in order to have enough money to buy a dirt bike for \$900?
1) 8
2) 9
3) 3
4) 4
Answer: 4) 4
You can set up an equation, or you can start with 375 and keeping adding 155 to it until you are over 900.
Set up an inequality in the form ax + b > c. The b represents the starting amount that he has, which is 375. This isn't repeated, so it doesn't get a variable. The a is the rate of change (the slope), which is the amount that occurs repeated, which is why it goes before the x. This is the 155.
155x + 375 > 900
155x > 525
x > 3.387...
Do NOT round down. He would have enough money after only three weeks. The first integer GREATER THAN 3.387... is 4. Jason will have money left over.
7. The expression 9a2 - 64b2 is equivalent to
1) (9a - 8b)(a + 8b)
2) (9a - 8b)(a - 8b)
3) (3a - 8b)(3a + 8b)
4) (3a - 8b)(3a - 8b)
Answer: 3) (3a - 8b)(3a + 8b)
The expression 9a2 - 64b2 is the difference of two perfect squares. Each part of it is a perfect square (which means you can take a square root of each component) and the two terms are separated by a minus sign.
When we have this, it means that the polynomial can be factored into two conjugates. Conjugates are two binomials that are identical, except that one has a plus and one has a minus separating them. When you multiply the two conjugates, you will get a zero pair with the two "middle" terms. (That is, the "OI" in "FOIL" will cancel out and become zero.)
9a2 - 64b2 = (3a - 8b)(3a + 8b). Note that the order of the two binomials doesn't matter.
Note that if you have two minus signs, then the middle terms, when combined, will not have a sum of zero.
8. The scatter plot below shows the profit, by month, for a new company for the first year of operation. Kate drew a line of best fit, as shown in the diagram.
Using this line, what is the best estimate for profit in the 18th month?
1) \$35,000
2) \$37,750
3) \$42,500
4) \$45,000
Answer: 3) \$42,500
Interesting that there were two scatter plot questions so close together. (If you missed the previous post, question 4 was about correlation.)
Look at the line of best fit. Then go to 18 on the x-axis and move up to that line. You will see that the y-coordinate is between 40,000 and 45,000. So Choice 3 is the best estimate.
9. Which statement illustrates the additive identity property?
1) 6 + 0 = 6
2) -6 + 6 = 0
3) 4(6 + 3) = 4(6) + 4(3)
4) (4 + 6) + 3 = 4 + (6 + 3)
Answer: 1) 6 + 0 = 6
The identity property for addition states that adding 0 to a number doesn't change the number. It stays the same. (Multiplying by 1 for multiplication identity.)
Choice (2) shows an example of the Inverse Property of Addition, where adding two additive inverses yields a sum of zero. These two numbers are a zero pair.
Choice (3) is the Distributive Property of Multiplication over Addition.
Choice (4) is the Associative Property.
10. Peter walked 8,900 feet from home to school.
1 mile 5,280 feet
How far, to the nearest tenth of a mile, did he walk?
1) 0.5
2) 0.6
3) 1.6
4) 1.7
Answer: 4) 1.7
To change feet into miles, divide by 5,280.
8900 / 5200 = 1.71...
The sum of the leading coefficients 3 and -1 is 2, so eliminate Choice (4).
Since 8900 is greater than 5280, it's obvious that he walked more than a mile, so Choices (1) and (2) should be eliminated immediately.
More to come. Comments and questions welcome.
More Regents problems.
## Friday, July 23, 2021
### Algebra Problems of the Day (Integrated Algebra Regents, August 2012)
Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
### August 2012
Part I: Each correct answer will receive 2 credits.
1. A system of equations is graphed on the set of axes below.
The solution of this system is
1) (0, 4)
2) (2, 4)
3) (4, 2)
4) (8, 0)
Answer: 3) (4, 2)
The solution to a system of equations is the point where the two lines intersect. That point is (4, 2). If you thought it was (2, 4), then you need to review which is the x coordinate and which is the y coordinate. Hint: the x comes first.
2. A cell phone can receive 120 messages per minute. At this rate, how many messages can the phone receive in 150 seconds?
1) 48
2) 75
3) 300
4) 18,000
Answer: 3) 300
Change minutes to seconds by dividing by 60 and then multiplying by 150 seconds.
120 / 60 * 150 = 300
If you multiplied by 60 and then divided by 150, you would've gotten 48. If you did 60 times 150 and then divided by 120 (I don't know why you would do that), you would get 75. If you just multiplied 120 by 150, you would have gotten 18,000. (It's rarely that easy when there's so much going on in a problem.)
3. The value of y in the equation 0.06y + 200 = 0.03y + 350 is
1) 500
2) 1,666.666...
3) 5,000
4) 18,333.333...
Answer: 3) 5,000
Note: On the actual exam, they used the repeater bar to indicate the repeating decimal.
0.06y + 200 = 0.03y + 350
0.03y + 200 = 350
0.03y = 150
y = 150/0.03 = 5,000
You can check your answer by substituting 5000 for y:
0.06(5000) + 200 = 0.03(5000) + 350
500 = 500 (check)
4. The scatter plot shown below represents a relationship between x and y.
This type of relationship is
1) a positive correlation
2) a negative correlation
3) a zero correlation
4) not able to be determined
Answer: 1) a positive correlation
First of all, we wouldn't say a "zero correlation". We'd say that there was no correlation. Is this splitting hairs? Maybe, but consider the difference between a zero slope and no slope. Words have meanings.
As the x values increase, the y values generally increase. So it is a positive correlation.
5. The sum of 3x2 + 5x - 6 and -x2 + 3x + 9 is
1) 2x2 + 8x - 15
2) 2x2 + 8x + 3
3) 2x4 + 8x2 + 3
4) 4x2 + 2x - 15
Answer: 2) 2x2 + 8x + 3
When you add polynomials, you combine like terms. The variables and their exponents do not change. Eliminate Choice (3).
The sum of the leading coefficients 3 and -1 is 2, so eliminate Choice (4).
5x + 3x = 8x and -6 + 9 = +3, so Choice (2) is the answer.
As the x values increase, the y values generally increase. So it is a positive correlation.
More to come. Comments and questions welcome.
More Regents problems.
### Olympic Venn-ue
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Games, Sets, Matches
Not that we play with matches...
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Tuesday, July 20, 2021
### Math+
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
More math content would be A+, right?
I could crack a few jokes here, or discuss possibilities. Or I could save that for future comics.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Monday, July 19, 2021
### School Life #22: Getting Closer
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Sometimes you need to retreat and regroup before you face the next level.
One for the Hal-Daisy fans.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Friday, July 16, 2021
### Argument of a Complex Number
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
They're not out of line here. Well, maybe above the line.
That's one problem with Algebra: there's always a lot of arguments!
The mathematical definition of Argument of a Complex Number is left as an exercise for the reader. But it's 3π/4 in this example.
It wasn't my intention to take a week off. It just worked out that way between life and the heat. Likewise, I considered doing something special for Comic #1750 (if I haven't started misnumbering again), but I settled for not doing a "mini" or a "quickie".
Final note: some of you might remember Negative Kitt from the other universe that was Through a Window, Darkly.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Friday, July 09, 2021
### Coordinate Hustlers
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Those who will not learn from Geometry will lose a lot of money to Geometry.
And as improbable as it may seem, whichever points are selected, the altitude in this problem will also be 3. The base AB is shown to be 3, so the area will always be 4.5 of those square boxes.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Thursday, July 08, 2021
### June 2021 Algebra 1 Regents (v202), Part I (multiple choice)
This exam was adminstered in June 2021. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.
Part II is located here.
### Part I
Each correct answer will receive 2 credits.
1. A high school club is researching a tour package offered by the Island Kayak Company. The company charges \$35 per person and \$245 for the tour guide. Which function represents the total cost, C(x), of this kayak tour package for x club members?
(1) C(x) = 35x
(2) C(x) = 35x + 245
(3) C(x) = 35(x + 245)
(4) C(x) = 35 + (x + 245)
Answer: (2) C(x) = 35x + 245
\$35 per person is the cost that is multiplied by the x number of people going on the tour. The \$245 is paid one time before anyone has even signed up for the tour, which makes it the y-intercept.
2. The expression 3(x + 4) - (2x + 7) is equivalent to
(1) x + 5
(2) x - 10
(3) x - 3
(4) x + 11
Answer: (1) x + 5
Distribute the 3 and distribute the minus sign (-1).
3(x + 4) - (2x + 7) = 3x + 12 - 2x - 7 = x + 5
3. A function is defined as K(x) = 2x2 - 5x + 3. The value of K(-3) is
(1) 54
(2) 36
(3) 0
(4) -18
Answer: (2) 36
K(-3) = 2(-3)2 - 5(-3) + 3 = 2(9) - (-15) + 3 = 18 + 15 + 3 = 36
4. Which relation is not a function?
Answer: (4)
In a function map, each member of the domain (on the left) can only have one arrow coming out of it because each input can only can associated with one output.
In Choice (4), there are two arrows coming out of the number six, meaning that (6, 10) and (6, 12) are in the same relation. This would cause it to fail the vertical line test.
5. The value of Tony's investment was \$1140 on January 1st. On this date three years later, his investment was worth \$1824. The average rate of change for this investment was \$19 per
(1) day
(2) month
(3) quarter
(4) year
Answer: (4) -6
1824 - 1140 = 684, which is 684 / 3 = 228 per year, which is 228 / 12 = 19 per month.
This was an interesting question in that you had to work through the choices. However, number sense should tell you that "per month" was the most likely, so you could have tried 684 / 36 first.
6. The solution to 3(x - 8) + 4x = 8x + 4 is
(1) 12
(2) 28
(3) -12
(4) -28
Answer: (4) -28
Use the Distributive Property, and then solve the equation for x.
3(x - 8) + 4x = 8x + 4
3x - 24 + 4x = 8x + 4
7x - 24 = 8x + 4
-28 = x
7. An ice cream shop sells ice cream cones, c, and milkshakes, m. Each ice cream cone costs \$1.50 and each milkshake costs \$2.00. Donna has \$19.00 to spend on ice cream cones and milkshakes. If she must buy 5 ice cream cones, which inequality could be used to determine the maximum number of milkshakes she can buy?
(1) 1.50(5) + 2.00m > 19.00
(2) 1.50(5) + 2.00m < 19.00
(3) l.50c + 2.00(5) > 19.00
(4) l.50c + 2.00(5) < 19.00
Answer: (1) 1.50(5) + 2.00m > 19.00
If she must buy 5 ice cream cones, then substitute c = 5, not m = 5. If she can't spend more than \$19, than you need to have a < symbol.
8. When written in standard form, the product of (3 + x) and (2x - 5) is
(1) 3x - 2
(2) 2x2 + x - 15
(3) 2x2 - llx - 15
(4) 6x - 15 + 2x2 - 5x
Answer: (2) 2x2 + x - 15
First of all, you know that the answer will be a quadratic expression, so Choice (1) is out. And Choice (4) is NOT is standard form, so eliminate that.
(x + 3)(2x - 5) = 2x2 + 6x - 5x - 15 = 2x2 + x - 15
9. If x = 2, y = 3 SQRT(2), and w = 2 SQRT(8), which expression results in a rational number?
(1) x + y
(2) y - w
(3) (w)(y)
(4) y / x
Answer: (3) (w)(y)
The product of SQRT(2) and SQRT(8) is SQRT((2)(8)) = SQRT(16) = 4, which is a rational number. When that result is multiplied by 3 and 2, it will still be rational. (24)
10. Which product is equivalent to 4x2 - 3x - 27?
(1) (2x + 9)(2x - 3)
(2) (2x - 9)(2x + 3)
(3) (4x + 9)(x - 3)
(4) (4x - 9)(x + 3)
Answer: (3) (4x + 9)(x - 3)
You can multiply these or graph them or factor the given expression.
If you "borrow & payback" then (4)(-27) = -108. What two factors of -108 have a sum of -3? Running through the list of factors will get you to (9)(-12). You have to "pay back" the 4.
Write out 4x2 - 12x + 9x - 27, and factor by grouping: 4x(x - 3) + 9(x - 3) = (4x + 9)(x - 3)
11. Given: f(x) = 2/3 x - 4 and g(x) = 1/4x + 1
Four statements about this system are written below.
I. f(4) = g(4)
II. When x = 12,f(x) = g(x).
III. The graphs of f(x) and g(x) intersect at (12,4).
IV. The graphs of f(x) and g(x) intersect at (4,12).
Which statement(s) are true?
(1) II, only
(2) IV, only
(3) I and IV
(4) II and III
Answer: (4) II and III
Statement I says that f(4) = 2/3(4) - 4 = -4/3 = g(4) = 1/4(4) + 1 = 2. This is not true.
Statement II says that f(12) = 2/3 (12) - 4 = 8 - 4 = 4 = g(12) = 1/4 (12) + 1 = 4. This is true.
Statement III restates statement II with extra information, which if that not only is f(12) = g(12) but they both equal 4.
Statement IV is not true because statement I is not true.
12. Which sketch represents the polynomial function f(x) = x(x + 6)(x + 3)?
Answer: Choice (1)
Choices (3) and (4) are not functions. They fail the vertical line test.
If f(x) = x(x + 6)(x + 3) then there are zeroes at x = 0, x + 6 = 0 and x + 3 = 0, or x = 0, x = -6 and x = -3.
That's Choice (1).
13. If the parent function of f(x) is p (x) = x2, then the graph of the function f(x) = (x - k)2 + 5, where k > 0, would be a shift of
(1) k units to the left and a move of 5 units up
(2) k units to the left and a move of 5 units down
(3) k units to the right and a move of 5 units up
(4) k units to the right and a move of 5 units down
Answer: (3) k units to the right and a move of 5 units up
Basic definition. You can try it in your graphing calculator by picking any value (e.g. 2) for k and observing how the graph changes.
14. Which expression is equivalent to (-4x2)3?
(1) -12x6
(2) -12x5
(3) -64x6
(4) -64x5
Answer: (3) -64x6
The exponent of 2 in (-4x2)3 goes only with the x. Everything in the parentheses gets the 3 exponent.
(-4)3 x2 * 3 = -64x6. Notice that when you take a power to another power, you have to multiply.
15. Which function has the smallest y-intercept?
Answer: Choice (1)
The y-intercept in Choice (1) is -6, as you can see from y = mx + b.
The y-intercept in Choice (2) is 1, as you can see from the row where x = 0.
The y-intercept in Choice (3) is -2, as you can see if you calculate f(0).
The y-intercept in Choice (4) is -2, as you can see on the graph at the y-axis.
16. Which domain would be the most appropriate to use for a function that compares the number of emails sent (x) to the amount of data used for a cell phone plan (y)?
(1) integers
(2) whole numbers
(3) rational numbers
(4) irrational numbers
Answer: (3) rational numbers
If you are comparing two whole numbers, you will have a ratio, and you would want rational numbers.
Answer: (2) whole numbers
The domain refers to the x values. The number of emails is a countable number, so whole numbers would be the most appropriate.
17. Eric deposits \$500 in a bank account that pays 3.5% interest, compounded yearly. Which type of function should he use to determine how much money he will have in the account at the end of 10 years?
(1) linear
(2) quadratic
(3) absolute value
(4) exponential
Answer: (4) exponential
If it is compounded interest, then you need an exponential function. Simple interest is linear.
18. Given: the sequence 4, 7, 10, 13,. ..
When using the arithmetic sequence formula an = a1 + (n - 1)d to determine the 10th term, which variable would be replaced with the number 3?
(1) a1
(2) n
(3) an
(4) d
Answer: (4) d
The common difference, d, is 3 from term to term.
19. Below are two representations of data.
A: 2,5,5,6,6,6,7,8,9
Which statement about A and B is true?
(1) median of A > median of B
(2) range of A < range of B
(3) upper quartile of A < upper quartile of B
(4) lower quartile of A > lower quartile of B
Answer:
The medians of A and B are both 6, so eliminate Choice (1).
The range of A is 7 and the range of B is 6, so eliminate Choice (2).
The upper quartile of A is 7.5 and the upper quartile of B is 9. This is the correct statement.
The lower quartile of A and B are both 5.
20. Which system has the same solution as the system below?
x + 3y = 10
-2x - 2y = 4
(1) -x + y = 6, 2x + 6y = 20
(2) -x + y = 14, 2x + 6y = 20
(3) x + y = 6, 2x + 6y = 20
(4) x + y = 14, 2x + 6y = 20
Answer: (2) -x + y = 14, 2x + 6y = 20
This was an interesting question. Uusually when they ask something like this, the choices are multiples of the given equation (although 3 of the choices will not be multiplied correctly). This question, however, is just which two separate systems of equations happen to have the same solution, totally by coincidence.
Put these all in your graphing calulcator to find which ones intersect at the same point.
The given system has a solution of (-8, 6). Now you can graph the others, or you can plug in the values to see which gives you a true statement.
-(-8) + (6) = 14, which is =/= 6. Eliminate Choice (1).
-(8) + 6 = 14, (check), and 2(-8) + 6(6) = -16 + 36 = 20 (check). This is the solution.
If you wanted to solve the original system of equations algebraically
x + 3y = 10
-2x - 2y = 4
2x + 6y = 20
-2x - 2y = 4
4y = 24
y = 6
x + 3(6) = 10
x + 18 = 10 x = -8
21. Given the pattern below, which recursive formula represents the number of triangles in this sequence?
(1) y = 2x + 3
(2) y = 3x + 2
(3) a1 = 2, an = an - 1 + 3
(4) a1 = 3, an = an - 1 + 2
Answer: (4) a1 = 3, an = an - 1 + 2
Notice that Choices (1) and (2) are not recursive formulas, so both can be eliminated.
The first term has 3 triangles and each term after adds 2 more. This is Choice (4).
22. Students were asked to write an expression which had a leading coefficient of 3 and a constant term of -4. Which response is correct?
(1) 3 - 2x3 - 4x
(2) 7x3 - 3x5 - 4
(3) 4 - 7x + 3x3
(4) -4x2 + 3x4 - 4
Answer: (4) -4x2 + 3x4 - 4
Were my students to give me any of these answers, I'd have a problem. None of these is in standard form, which I might not care about in some instances, but if I'm asking for a specific leading coefficient, write it first!
The leading coefficient of (1) is 2. The leading coefficient of (2) is -3. The leading coefficient of (3) is 3, but the constant is 4, not -4. The leading coefficient of (4) is 3, and the constant is -4.
23. Sarah travels on her bicycle at a speed of 22.7 miles per hour. What is Sarah's approximate speed, in kilometers per minute?
(1) 0.2
(2) 0.6
(3) 36.5
(4) 36.6
Answer: (2) 0.6
Common sense should tell you that Choices (3) and (4) might be approximate answers in kilometers per hour, not minute.
To change from miles to kilometers, multiply by 1.609 (as per the back of the booklet). To change hours to minutes, divide by 60.
22.7 * 1.609 / 60 = 0.608..., which is approximately 0.6.
24. Which ordered pair does not fall on the line formed by the other three?
(1) (16,18)
(2) (12,12)
(3) (9,10)
(4) (3,6)
Answer:
Another interesting problem in that you are required to look at all for points to see with one doesn't belong.
The easiest thing to do is plot the four points on graph paper and see which one doesn't line up.
If you checked the slopes, you would have seen that lines from (16, 18) to the other three all would have different slopes.
(18 - 12) / (16 - 12) = 6/4 or 3/2, (18 - 10) / (16 - 9) = 8/7, (18 - 6) / (16 - 3) = 12 / 13. Since all three are different, you can be sure that (16, 18) is the odd point out.
More to come. Comments and questions welcome.
More Regents problems.
## Wednesday, July 07, 2021
### Why Did I -- ?
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Neither one was me this morning, but I was closer to the second guy.
I don't know what possesses people to stop in doorways and at the tops and bottoms of escalators, thinking that these are the best places to evaluate their surroundings.
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Tuesday, July 06, 2021
### June 2021 Algebra 1 Regents (v202), Parts III & IV
This exam was adminstered in June 2021. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.
Part II is located here.
### Part III
Each correct answer will receive 3 credits. Partial credit can be earned. It is usually possible to get 1 point for a correct answer with no correct work shown.
33. Joey recorded his heartbeats, in beats per minute (bpm), after doing different numbers of jumping jacks. His results are shown in the table below.
[TABLE COMING]
(x, y), (0, 68), (10, 84), (15, 104), (20, 100), (30, 120)
State the linear regression equation that estimates the heart rate per number of jumping jacks
State the correlation coefficient of the linear regression equation, roudned to the nearest hundredth
Explain what the correlation coefficient suggest in the context of this problem.
Answer:
Put the data into a table in your graphing calculator. Then go to Stats and perform a linear regression.
You will get the a = 1.72 and b = 69.4. Written in the form y = ax + b, that gives you y = 1.72x + 69.4
The correlation coefficient is 0.967..., which is 0.97 to the nearest hundredth.
In the context of this problem, this suggests a very strong positive correlation between the number of jumping jacks and heartbeats per minute.
34. Hannah went to the school store to buy supplies and spent \$16.00. She bought four more penciels than pens and two fewer erasers than pens. Pens cost \$1.25 each, pencils cost \$0.55 each, and erasers are 0.75 each.
If x represents the number of pens Hannah bought, write an equation in terms of x than can be used to find how many of each item she bought.
Use your equation to determin algebraically how many pens Hannah bought.
Answer:
x = the number of pens Hannah bought
(x + 4) = the number of pencils Hannah bought
(x - 2) = the number of erasers Hannah bought
The equation to solve would be 1.25x + 0.55(x + 4) + 0.75(x - 2) = 16
1.25x + 0.55(x + 4) + 0.75(x - 2) = 16.00
1.25x + 0.55x + 4 * 0.55 + 0.75x - 2 * 0.75 = 16.00
1.25x + 0.55x + 2.20 + 0.75x - 1.50 = 16.00
1.25x + 0.55x + 0.75x = 15.30
2.55x = 15.30
x = 6
Note: if you didn't get a Whole Number, you know that you must've made a mistake. You can't buy part of a pen or pencil or eraser.
x = the number of pens Hannah bought = 6
(x + 4) = the number of pencils Hannah bought = 6 + 4 = 10
(x - 2) = the number of erasers Hannah bought = 6 - 2 = 4
You can check your work: 1.25(6) + 0.55(6 + 4) + 0.75(6 - 2) = 1.25(6) + 0.55(10) + 0.75(4) = 16 (check!)
35. Graph the given set of inequalities on the set of axes below:
y < -3/4 x + 5
3x - 2y > 4
Is (6, 3) a solution to the system of inequalities? Explain your answer.
Answer:
Remember: when answering the final question, answer it based on YOUR graph, even if you made a mistake on your graph. The graph is your justification. As long as you are consistent, you will get a point for your answer. If you did not do the graph, you cannot get a point for "Yes" or "No" unless you back it up with some work, such as substitution into both inequalaities.
The first inequality can be graphed as is because you have a slope and a y-intercept. Since it has a "<" sign, it will be a solid line with shading beneath it. All points on the line and below it are solutions to the inequality.
The second inequality needs to be rewritten into a more useful form. (Standard form can be useful, too, but in this case the x-intercept is (4/3, 0), which would be difficult to graph.)
Do the following:
3x - 2y > 4
-2y > -3x + 4
y < 3/2x - 2
The "<" symbol means it will be a broken or dashed line with shading beneath it. The line itself is a boundary and none of those points are solutions.
Put a captial "S" in the section of the graph with double-shading (the criss-cross pattern shown below). That is the section that is the solution to the system. Be sure to label the lines.
According to the graph, (6, 3) is not a solution because it is not in the double-shaded section of the graph.
36. A ball is projected up into the air from the surface of a platform to the ground below. The height of the ball above the ground, in feet, is modeled by the function f(t) = -16t2 + 96t + 112, where t is the time, in seconds, after the ball is projected.
State the height of the platform in feet.
State the coordinates of the vertex. Explain what it means in the context of this problem.
State the entire interval over which the ball's height is decreasing.
Answer:
This is a problem of projectile motion that uses gravity (the -16 leading coefficient is a giveaway!). It's a quadratic function and will follow the path of a parabola with the following limitations: the independent variable cannot be negative because that would be negative time, and the dependent variable cannot be negative because that would be below the ground. In reality, the ball will bounce when it strikes the ground, and the function does not model this.
The height of the platform is 112, which is the y-intercept. When t = 0, the ball has not left the platform yet, so the platform is 112 feet.
The cooridinates of the vertex can be found in your calculaor, or you can use the formula for the Axis of Symmetry:
x = -b / (2a)
x = -96 / (2(-16)) = -96 / -32 = 3
h(3) = -16(3)2 + 96(3) + 112 = 256
The vertex is (3, 256) which is the ball will reach its highest point of 256 feet at 3 seconds.
The ball will be decreasing after t = 3 until it hits the ground. The ground has a height = 0. We have to find the zeroes of the equation.
-16t2 + 96t + 112 = 0
t2 - 6t + 7 = 0
(t - 7)(t + 1) = 0
t = 7 or t = -1
Discard t = -1 because time cannot be negative.
The ball is decreasing over the interval 3 < t < 7.
### Part IV
Each correct answer will receive 4 credits. Partial credit can be earned. It is usually possible to get 1 point for a correct answer with no correct work shown.
37. At a local shop, the price of plants includes sales tax.
The cost of 4 large plants and 8 medium plants is \$40. The cost of 5 large plants and 2 medium plants is \$28.
If L is the cost of a large plant and M is the cost of a medium plant, write a system of equatios that models this situation.
Could the cost of one large plant be \$5.50 and the cost of one medium plants be \$2.25? Justify your answer.
Determine algebraically both the cost of a lare planst and the cost of a medium plant.
Answer:
Note that the problem actually used l and m (lower case). However, on this blog it would be difficult to distinguish the l from a 1 (one). To avoid confusion, you should either use a capital L or a script l that doesn't look like a 1.
Translate the two sentences into a system of equations.
4L + 8M = 40
5L + 2M = 28
To find if (5.50, 2.25) is a solution, substitute these numbers into BOTH equations. If they do not work for both equations, then it isn't a possible solution.
4(5.50) + 8(2.25) = 40 (check!)
5(5.50) + 2(2.25) = 32, not 28. This is not a solution.
To solve the system, multiply the second equation by 4, then subtract the equations:
4L + 8M = 40
5L + 2M = 28
4L + 8M = 40
20L + 8M = 112
16L = 72
L = 4.50
4L + 8M = 40
4(4.50) + 8M = 40
18 + 8M = 40
8M = 22
M = 2.75
The cost of a Large plant is \$4.50 and the cost of a Medium plant is \$2.75.
End of Exam
Comments and questions welcome.
More Regents problems.
## Monday, July 05, 2021
### June 2021 Algebra 1 Regents (v202), Part II
This exam was adminstered in June 2021. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.
More Regents problems.
### June 2021 (v202)
Part II: Each correct answer will receive 2 credits. Partial credit can be earned. One mistake (computational or conceptual) will lose 1 point. A second mistake will lose the other point. It is sometimes possible to get 1 point for a correct answer with no correct work shown.
25. Solve algebraically for y:
4(y - 3) < 4(2y + 1)
Answer:
The Distributive property is unnecessary but not incorrect if you use it. Since both sides have a multiplier of 4, the inequality can be divided by 4.
4(y - 3) < 4(2y + 1)
y - 3 < 2y + 1
-3 < y + 1
-4 < y
or y > -4
(rewriting to put the y on the left is not necessary, however, if you do, you must flip the inequality symbol)
26. Graph the function f(x) = | (1/2)x + 3 | over the invertal -8 < x < 0.
Answer:
If you are given an interval, DO NOT go beyond it, DO NOT use arrows. You should include solid (closed) circles at the two endpoints.
An absolute value graph is V-shaped. This one will have a slope on -1/2 on the left side of the vertex and +1/2 on the right side.
The vertex is (-6, 0) because the function can be written as f(x) = -1/2 |x + 6| + 0, with vertex (h, k) being (-6, 0).
You can use your graphing calculator, or you can just make a Table of Values by plugging in -8, -7, -6, -5, etc. Make sure you keep going until you hit the vertex.
27. The table below shows the height in feet, h(t), of a hot-air balloon and the number of minutes, t, the balloon is in the air.
[TABLE TO BE ADDED]
The function h(t) = 30.5t + 8.7 can be used to model this table.
Explain the measning of the slope in the context of the problem.
Explain the meaning of the y-intercept in the context of the problem.
Answer:
The table is actually unnecessary for answering the questions because you already have the function that models it.
The slope, 30.5, represents how many feet the balloon is rising each minute.
The y-intercept, 8.7. represents the ballon's height from the ground before it started rising.
28. Factor x4 - 1 completely.
Answer:
Any time you see "factor completely", you can be pretty sure that there will be more than one step. Likewise, if you see an exponent of 4 (or generally anything above 2), you should suspect that there will be an extra step.
x4 - 1
= (x2 + 1)(x2 - 1)
= (x2 + 1)(x + 1)(x - 1)
As you can see, the original expression was the Difference of Two Sqaures, which could be factored into two conjugates (such as (x+a)(x-a)). The square root of x4 is x2 because 2 is half of 4, and (x2)2 = x2 * x2 = x4.
However, x2 - 1 is also the Difference of Two Squares and can also be factored the same way. On the other hand, x2 + 1 has no real roots.
29. Mike knows that (3, 6.5) and (4, 17.55) are points on the graph of an exponential function, g(x), andhe wants to find another point on the graph of this function.
Fist, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5, 28.6) is a point on g(x).
Is he correct? Explain your reasoning.
Answer:
This is one of those times where if you say "Yes" or "No" without any explanation, you will not get any credit. You can't get a point for a 50-50 guess.
If you have the correct answer but answer but your reasoning isn't completely correct, you may only get one credit. And if you make a conceptual error (see below), you could get one credit as long as you are consistent.
No, Mike is not correct because he was trying to find slope of a straight line between the two points he had, but it is a linear function. This gives you 2 credits.
If you said, "Yes because Mike correctly calculated the slope between the two points and used that to find another point on the line", then you may have been awarded one point for the conceptual error of confusing a linear and an exponential function.
30. Use the method of completing the square to determine the vertex of f(x) = x2 - 14x - 15.
State the coordinates of the vertex.
Answer:
You can graph this to find the vertex in advance, or use the formula for the Axis of Symmetry. It may be easier to do if you already find the answer another way. You can get a point for stating the coordinates of the vertex if you find it using a different method than Completing the Square.
To Complete the square, keep in mind that the Axis of Symmetry is x = -b/(2a). You want to cut that middle coefficient in half. If you recall, (x + 1)2 = x2 + 2x + 1, and (x + 4)2 is x2 + 8x + 16. The middle term is always double and the last term must be a perfect square.
f(x) = x2 - 14x - 15
half of -14 is -7, so (x - 7) will be in our answer; (-7)2 = 49
f(x) + 49 = x2 - 14x + 49 - 15
f(x) + 49 = (x - 7)2 - 15
f(x) = (x - 7)2 - 64
The vertex is (7, -64)
31. The temperature inside a cooling unit is measured in defrees Celsius, C. Josh wants to find out how cold it is in degrees Fahrenheit, F.
Solve the formula C = 5/9 (F - 32) for F so that Josh can convert Celsius to Fahrenheit.
Answer:
Seriously, everyone should be able to do this, even outside of a math class. This is one of the most common examples given in math text books, and it's useful to know if you ever travel outside the U.S., or if you are from outside the U.S. and travel here.
C = 5/9 (F - 32)
9C = 5(F - 32)
9/5 C = F - 32
9/5 C + 32 = F
F = 9/5 C + 32
32. Solve 4w2 + 12w - 44 = 0 algebraically for w, to the nearest hundredth.
Answer:
Since they are asking for the nearest hundredth, you know that the equation isn't going to factor "nicely" and that you will have to use the quadratic formula. At least in this case, they didn't ask you to simplify the radical, which would have made it a more complicated problem.
There are two approaches you can take, and I will show them both because I am so Awesome, and modest, too.
4w2 + 12w - 44 = 0
w2 + 3w - 11 = 0
w = ( -3 + ( (-3)2 - 4(1)(-11) )(1/2) ) / (2(1))
w = ( -3 + ( 9 + 44 )(1/2) ) / 2
w = ( -3 + ( 53 )(1/2) ) / 2
w = 2.1400... or w = -5.1400...
w = 2.14 or w = -5.14
End of Part II
More to come. Comments and questions welcome.
More Regents problems.
## Sunday, July 04, 2021
### Happy Independence Day 2021!
(Click on the comic if you can't see the full image.)
(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).
Celebrating our Independent Variables Everywhere with a Liberty Bell Curve!
### I also write Fiction!
Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.
If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.
Thank you.
Come back often for more funny math and geeky comics.
## Friday, July 02, 2021
### Algebra Problems of the Day (Integrated Algebra Regents, January 2013)
While I'm waiting for new Regents exams to come along (AND THEY ARE COMING SOON!), I'm revisiting some of the older NY Regents exams.
More Regents problems.
Administered January 2013
Part IV: Each correct answer will receive 4 credits. Partial credit can be earned.
37. Using the line provided, construct a box-and-whisker plot for the 12 scores below.
26, 32, 19, 65, 57, 16, 28, 42, 40, 21, 38, 10
Determine the number of scores that lie above the 75th percentile.
Answer:
Before you do anything else, PUT THE NUMBERS IN ORDER!
There are 12 scores, so the median is between the sixth and seventh (which is the sixth from the back). That means Q1 is between the third and fourth, and Q3 is between the ninth and tenth. You don't need to "take the average", just find the number in between them. In each case, it's only 1 or 2 away. No need to "add them and divide by 2".
The minimum is the first (lowest) number, and the maximum is the last (highest) number. You should label all five of these numbers so that they are somewhere on the page. In particular, there is no obvious way from the number line to know that Q3 is 41.
Pick a scale for the number line. It is big enough to count by fives. You DO NOT have to start at 0. I did, but there isn't any particular reason to. You could have started with 5 or 10.
Do NOT label the number line with the scores. What I mean here: don't write 10, 16, 19, etc. under the tick marks. That's not how a number line works. And I've seen it written by students who didn't understand what they were supposed to do.
Since the third-quartile (Q3) is 41, there are THREE numbers greater than it. To get this credit, you need to have Q3 stated somewhere on the page, and you should identify those three numbers. You can write the three numbers, or where you wrote them in order, you can circle them and write that they are above the Q3.
The image below shows the box-and-whisker plot.
38. A metal pipe is used to hold up a 9-foot fence, as shown in the diagram below. The pipe makes an angle of 48° with the ground.
Determine, to the nearest foot, how far the bottom of the pipe is from the base of the fence.
Determine, to the nearest foot, the length of the metal pipe.
Answer:
You are given an angle and the length of the opposite side. That means that you have two trigonometric functions avaiable to you:
sin (48°) = opposite / hypotenuse
tan (48°) = opposite / adjacent
Use the sine function to find the length of the metal pipe, and the tangent function to find the distance on the ground. You will get half credit if you reverse these. You will lose points if you cosine in place of one of the other two functions.
Some common sense: the metal pipe MUST be longer than 9 feet because it's the hypotenuse. It you get a number smaller than 9, you made a mistake. Since the angle is greater than 45, that means that the adjacent side will be smaller than opposite side, but since it is 48 degrees, it will not be shorter by a lot.
Finally, make sure your calculator is in DEGREE mode not RADIAN mode or you will get crazy results. Conversely, if you get crazy results, check if your calculator is in RADIAN mode.
tan (48°) = 9 / x
x = 9 / tan (48°) = 8.1...
The bottom is approximately 8 feet from the fence.
sin (48°) = 9 / x
x = 9 / sin (48°) = 12.1...
The metal pipe is approximately 12 feet long.
39. On the set of axes below, graph the following system of equations.
y + 2x = x2 + 4
y - x = 4
Using the graph, determine and state the coordinates of all points in the solution set for the system of equations.
Answer:
You are graphing a parabola and a line. They may intersect at one point, two points or zero points. Note that even if you make graphing errors, you can get points for stating the solutions (even if you have to approximate a decimal) that are shown ON YOUR GRAPH. If your two lines don't intersect, then you must state that there are No Solutions to the system.
The first mistake that might be made usually happen when rewriting the equations to isolate the y on the left. This will allow you to use your graphing calculator to help you create a Table of Values.
y + 2x = x2 + 4
y = x2 - 2x + 4
This will have its Axis of Symmetry at x = 1.
y - x = 4
y = x + 4
Slope = 1, y-int = 4
Since the parabola is symmetrical, if you start with x = 1, 2, 3, 4, you will get the results for x = 0, -1, -2 as well.
As you can see in the image below, there are two points of intersection, (0, 4) and (3, 7). You can label these points on the graph. However, if you identify any other points on the graph, then you need to label these as your solutions.
Also, AT LEAST ONE of the two lines must be labeled with the original equation from the problem, not the rewritten one. Yes, it may be "obvious" to you which line is the quadratic and which is linear, but it must be stated. Not doing this is a graphing error and you will lose a point.
End of Part IV
End of Exam.
How'd you do?
More to come. Comments and questions welcome.
More Regents problems. | 18,305 | 59,991 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2024-38 | latest | en | 0.901975 |
https://modcanyon.com/5-words-letter-containing-o-hints-in-the-puzzle/ | 1,718,295,253,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861480.87/warc/CC-MAIN-20240613154645-20240613184645-00218.warc.gz | 374,314,051 | 29,627 | Wordle players who are looking for the list of 5 Words letters containing O should read this article.
Are you frustrated with your daily wordle puzzles Is the O letter related to your puzzle? What are your final answers to the wordle puzzle? This article will provide all the solutions to readers who are unsure about their wordle puzzle.
Wordle is a global hit word game and has been attracting the attention of numerous players. Every day there are new puzzles. You must find the correct word in your grid. For more rewards points, please read this article about 5 Words Letter Containing.
## List Of Five Letter Words Containing O:
If the wordle puzzle shows O, this word might help you get the correct answers.
Adobe, abode. Along, alone, aroma.
### 5 letters words that start with O:
Aside from words with O in the middle, people are also searching for words that start with O. Here are some possible five-letter word ideas that start with O.
Oaked and oaers, operes and oboli, obeysb.
There is an endless number of words that either start with O, or have O in between. To shorten the list of possible words, players must find a string hint. By doing this, players will be able place the letters in the grid within the allowed time.
### 5 Words – End:
Now that we have the word list with O in the middle of start, let us go and find the five-letter words ending in End. These words are:
Abaco. Addio. Although, Bacco.
### Hints in the Puzzle:
We have already mentioned the list with all possible words we could find for the given hint. However, before we continue with the 5 Word Words Starting with O puzzle, it is important that readers bring more clues in order to help them find the answers.
This is because wordle puzzle words contain five letters, of which two or three are vowels. You will find it more confusing if you try to solve the puzzle using just one vowel.
### Final Verdict:
We have included all the words possible for your clarity. We advise our readers that they read their hints for final answers to 5 Words Letter Containing o. There can be thousands of words. A 40% chance is that a word will contain O. | 489 | 2,147 | {"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} | 2.5625 | 3 | CC-MAIN-2024-26 | latest | en | 0.920014 |
https://www.assignmentexpert.com/homework-answers/chemistry/other/question-199773 | 1,623,530,052,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487586390.4/warc/CC-MAIN-20210612193058-20210612223058-00006.warc.gz | 601,305,641 | 288,470 | 99 718
Assignments Done
98.3%
Successfully Done
In May 2021
# Answer to Question #199773 in Chemistry for Francine Jean
Question #199773
. Select the warmer temperature in each pair (Show the conversions):
a) 10°C or 10°F b) 30°C or 15°F c) -10°C or 32°F d) 200°C or 200°K
1
2021-05-31T02:26:03-0400
T(°F) = T(°C) × 1.8 + 32
T(K) = T(°C) + 273.15
Solution:
a) 10°C or 10°F
10°C: T(°F) = 10°C × 1.8 + 32 = 50°F
Thus: 10°C warmer than 10°F
b) 30°C or 15°F
30°C: T(°F) = 30°C × 1.8 + 32 = 86°F
Thus: 30°C warmer than 15°F
c) -10°C or 32°F
-10°C: T(°F) = -10°C × 1.8 + 32 = 14°F
Thus: 32°F warmer than -10°C
d) 200°C or 200 K
200°C: T(K) = 200°C + 273.15 = 473.15 K
Thus: 200°C warmer than 200 K
Need a fast expert's response?
Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS! | 372 | 859 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-25 | latest | en | 0.480478 |
https://goprep.co/q31-the-vertices-of-a-triangle-are-6-0-0-6-and-6-6-the-i-1nl7jz | 1,656,973,774,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104496688.78/warc/CC-MAIN-20220704202455-20220704232455-00096.warc.gz | 321,051,607 | 46,710 | Q. 315.0( 1 Vote )
# The vertices of a
Let A(0, 6), B(6, 0) and C(6, 6) be the vertices of the given triangle.
Diagram:
Coordinates of N
= (6, 3)
Coordinates of P = (3, 6)
Equation of MN is y = 3
Equation of MP is x = 3
As we know that circumcentre of a triangle is the intersection of the perpendicular bisectors of any two sides .Therefore, coordinates of circumcentre is (3,3)
Thus, the coordinates of the circumcentre are (3, 3) and the centroid of the triangle is (4,4).
Let d be the distance between the circumcentre and the centroid.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :
Find the values oRD Sharma - Mathematics
The vertices of aRD Sharma - Mathematics
For specifying a Mathematics - Exemplar
If the line <spanMathematics - Exemplar
Equations of diagMathematics - Exemplar
If the coordinateMathematics - Exemplar | 309 | 1,182 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2022-27 | latest | en | 0.815603 |
https://easierwithpractice.com/what-is-the-meaning-of-the-greek-word-for-atom-atomos/ | 1,713,642,166,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817674.12/warc/CC-MAIN-20240420184033-20240420214033-00204.warc.gz | 195,196,460 | 40,453 | # What is the meaning of the Greek word for atom atomos?
uncuttable
## What did John Dalton describe atoms as?
Dalton hypothesized that the law of conservation of mass and the law of definite proportions could be explained using the idea of atoms. He proposed that all matter is made of tiny indivisible particles called atoms, which he imagined as “solid, massy, hard, impenetrable, movable particle(s)”.
Does the word atom mean invisible?
The word atom is derived from the Greek ‘atomos’ – “indivisible.” But the word ‘atom’ itself just means the smallest particle, not necessarily invisible.
Is Amu equal to g mol?
The mass of a single atom of an element [amu] is numerically equal to the mass [g] of 1 mol of that element, regardless of the element. 1 atom of 12 C has a mass of 12 amu 1 mol 12 C has a mass of 12 g. Q: How many moles of water are in a liter of water, if 1 liter = 1 kilogram water.
### What is 1 amu or 1u?
1 amu or 1 atomic mass unit is equals to the 1/12 of the mass of a carbon atom. U is the standard unit of measure for designating the vertical usable space, or height of racks (metal frame designed to hold hardware devices) and cabinets (enclosures with one or more doors).
### What 1u means?
U is the standard unit of measure for designating the vertical usable space, or height of racks (metal frame designed to hold hardware devices) and cabinets (enclosures with one or more doors). This unit of measurement refers to the space between shelves on a rack. 1U is equal to 1.75 inches.
Why do we use amu?
An atomic mass unit (symbolized AMU or amu) is defined as precisely 1/12 the mass of an atom of carbon-12. The AMU is used to express the relative masses of, and thereby differentiate between, various isotopes of elements.
Is Amu the same as U?
In chemistry, an atomic mass unit or AMU is a physical constant equal to one-twelfth of the mass of an unbound atom of carbon-12. It is a unit of mass used to express atomic masses and molecular masses. The symbol for the unit is u (unified atomic mass unit) or Da (Dalton), although AMU may still be used.
## Why can’t you see an atom with the naked eye?
Hint: There are some microscopic particles that can’t be seen from our vision because they are very tiny or smaller in size. Atoms can’t be seen from our naked eyes because of the same reason and also, they do not exist independently.
## Is Dalton same as AMU?
The atomic mass constant, denoted mu is defined identically, giving mu = m(12C)/12 = 1 Da. A unit dalton is also approximately numerically equal to the molar mass of the same expressed in g / mol (1 Da ≈ 1 g/mol)….Dalton (unit)
dalton (unified atomic mass unit)
Unit of mass
Symbol Da or u
Named after John Dalton
Conversions
Is Dalton equal to grams per mole?
Measure of molecular weight or molecular mass. One molecular hydrogen molecular atom has molecular mass of 1 Da, so 1 Da = 1 g/mol.
What is the numerical value of mole?
1 mole = 6.022×1023 particles (atoms or molecules) 1 mole=6.02214179*1023 atoms or molecules present in it.
### What is Dalton size?
A very small unit of mass, about the mass of a hydrogen atom. Presently taken as an alternative name for the unified atomic mass unit, that is, one-twelfth of the mass of a carbon-12 atom, about 1.660 538 86 × 10⁻²⁷ kilogram. Symbol, Da, and previously sometimes D or d.
### What is the 500 Dalton Rule?
The 500-Dalton rule states that for a substance to be able to cross the skin barrier, it must have a molecular weight of fewer than 500 Daltons. Though there are certain exceptions to this rule, it is generally considered as a standard rule of thumb for cosmetic manufacturers.
How many Daltons is an amino acid?
The average molecular weight of an amino acid is 110Da. Dalton (Da) is an alternate name for the atomic mass unit, and kilodalton (kDa) is 1,000 daltons. Thus a protein with a mass of 64kDa has a molecular weight of 64,000 grams per mole.
What discovered Dalton?
Although a schoolteacher, a meteorologist, and an expert on color blindness, John Dalton is best known for his pioneering theory of atomism. He also developed methods to calculate atomic weights and structures and formulated the law of partial pressures.
## How did Dalton prove his theory?
In 1803 Dalton discovered that oxygen combined with either one or two volumes of nitric oxide in closed vessels over water and this pioneering observation of integral multiple proportions provided important experimental evidence for his incipient atomic ideas.
## What is Dalton best known for?
Atomic theory
Why is Dalton credited?
Why is Dalton credited with proposing the first atomic theory if Democritus was talking about atoms almost 2,200 years earlier? – Dalton’s theory was the first scientific theory because it relied on scientific investigative processes. – Dalton used creativity to modify Proust’s experiment and interpret the results.
Did John Dalton win a Nobel Prize?
The Nobel Prize in Chemistry 1977.
### How did Dalton measure atomic mass?
Dalton decided to use hydrogen as the unit for his system of atomic masses. By weight, the ratio of oxygen to hydrogen in water is 7.94:1 and the ratio of nitrogen to hydrogen in ammonia is 4.63:1.
### Who discover the atomic mass?
John Dalton
How many Daltons are in nitrogen?
Dalton atomic weights
source H N
a. Dalton 1808 1 5
b. “Daltonesque” 1 4.63
c. modern 1.008 14.007 | 1,308 | 5,414 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-18 | latest | en | 0.900542 |
https://www.codeproject.com/Articles/6534/Convolution-of-Bitmaps?fid=36474&df=90&mpp=10&sort=Position&spc=None&select=1073265&tid=903214 | 1,516,584,686,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890928.82/warc/CC-MAIN-20180121234728-20180122014728-00614.warc.gz | 877,701,586 | 27,912 | 13,353,322 members (50,831 online)
Add your own
alternative version
#### Stats
163.5K views
2.3K downloads
42 bookmarked
Posted 26 Mar 2004
# Convolution of Bitmaps
, 29 Mar 2006
Rate this:
Please Sign up or sign in to vote.
Article discussing how to convolve images, specificially the convolution of bitmaps.
## Introduction
Image convolution plays an important role in computer graphics applications. Convolution of images allows for image alterations that enable the creation of new images from old ones. Convolution also allows for important features such as edge detection, with many widespread uses. The convolution of an image is a simple process by which the pixel of an image is multiplied by a kernel, or masked, to create a new pixel value. Convolution is commonly referred to as filtering.
## Details
First, for a given pixel (x,y), we give a weight to each of the surrounding pixels. It may be thought of as giving a number telling how important the pixel is to us. The number may be any integer or floating point number, though I usually stick to floating point since floats will accept integers as well. The kernel or mask that contains the filter may actually be any size (3x3, 5x5, 7x7); however, 3x3 is very common. Since the process for each is the same, I will concentrate only on the 3x3 kernels.
Second, the actual process of convolution involves getting each pixel near a given pixel (x,y), and multiplying each of the pixel's channels by the weighted kernel value. This means that for a 3x3 kernel, we would multiply the pixels like so:
```(x-1,y-1) * kernel_value[row0][col0]
(x ,y-1) * kernel_value[row0][col1]
(x+1,y-1) * kernel_value[row0][col2]
(x-1,y ) * kernel_value[row1][col0]
(x ,y ) * kernel_value[row1][col1]
(x+1,y ) * kernel_value[row1][col2]
(x-1,y+1) * kernel_value[row2][col0]
(x ,y+1) * kernel_value[row2][col1]
(x+1,y+1) * kernel_value[row2][col2]```
The process is repeated for each channel of the image. This means that the red, green, and blue color channels (if working in RGB color space) must each be multiplied by the kernel values. The kernel position is related to the pixel position it is multiplied by. Simply put, the kernel is allocated in `kernel[rows][cols]`, which would be `kernel[3][3]` in this case. The 3x3 (5x5 or 7x7, if using a larger kernel) area around the pixel (x,y) is then multiplied by the kernel to get the total sum. If we were working with a 100x100 image, allocated as `image[100][100]`, and we wanted the value for pixel (10,10), the process for each channel would look like:
```float fTotalSum =
Pixel(10-1,10-1) * kernel_value[row0][col0] +
Pixel(10 ,10-1) * kernel_value[row0][col1] +
Pixel(10+1,10-1) * kernel_value[row0][col2] +
Pixel(10-1,10 ) * kernel_value[row1][col0] +
Pixel(10 ,10 ) * kernel_value[row1][col1] +
Pixel(10+1,10 ) * kernel_value[row1][col2] +
Pixel(10-1,10+1) * kernel_value[row2][col0] +
Pixel(10 ,10+1) * kernel_value[row2][col1] +
Pixel(10+1,10+1) * kernel_value[row2][col2] +```
Finally, each value is added to the total sum, which is then divided by the total weight of the kernel. The kernel's weight is given by adding each value contained in the kernel. If the value is zero or less, then a weight of 1 is given to avoid a division by zero.
The actual code to convolve an image is:
```for (int i=0; i <= 2; i++)//loop through rows
{
for (int j=0; j <= 2; j++)//loop through columns
{
//get pixel near source pixel
/*
if x,y is source pixel then we loop through and
get pixels at coordinates:
x-1,y-1
x-1,y
x-1,y+1
x,y-1
x,y
x,y+1
x+1,y-1
x+1,y
x+1,y+1
*/
COLORREF tmpPixel = pDC->GetPixel(sourcex+(i-(2>>1)),
sourcey+(j-(2>>1)));
//get kernel value
float fKernel = kernel[i][j];
//multiply each channel by kernel value, and add to sum
//notice how each channel is treated separately
rSum += (GetRValue(tmpPixel)*fKernel);
gSum += (GetGValue(tmpPixel)*fKernel);
bSum += (GetBValue(tmpPixel)*fKernel);
//add the kernel value to the kernel sum
kSum += fKernel;
}
}
//if kernel sum is less than 0, reset to 1 to avoid divide by zero
if (kSum <= 0)
kSum = 1;
//divide each channel by kernel sum
rSum/=kSum;
gSum/=kSum;
bSum/=kSum;```
The source code included performs some common image convolutions. Also included is a Convolve Image menu option that allows users to enter their own kernel. Common 3x3 kernels include:
```gaussianBlur[3][3] = {0.045, 0.122, 0.045, 0.122,
0.332, 0.122, 0.045, 0.122, 0.045};
gaussianBlur2[3][3] = {1, 2, 1, 2, 4, 2, 1, 2, 1};
gaussianBlur3[3][3] = {0, 1, 0, 1, 1, 1, 0, 1, 0};
unsharpen[3][3] = {-1, -1, -1, -1, 9, -1, -1, -1, -1};
sharpness[3][3] = {0,-1,0,-1,5,-1,0,-1,0};
sharpen[3][3] = {-1, -1, -1, -1, 16, -1, -1, -1, -1};
edgeDetect[3][3] = {-0.125, -0.125, -0.125, -0.125,
1, -0.125, -0.125, -0.125, -0.125};
edgeDetect2[3][3] = {-1, -1, -1, -1, 8, -1, -1, -1, -1};
edgeDetect3[3][3] = {-5, 0, 0, 0, 0, 0, 0, 0, 5};
edgeDetect4[3][3] = {-1, -1, -1, 0, 0, 0, 1, 1, 1};
edgeDetect5[3][3] = {-1, -1, -1, 2, 2, 2, -1, -1, -1};
edgeDetect6[3][3] = {-5, -5, -5, -5, 39, -5, -5, -5, -5};
sobelHorizontal[3][3] = {1, 2, 1, 0, 0, 0, -1, -2, -1 };
sobelVertical[3][3] = {1, 0, -1, 2, 0, -2, 1, 0, -1 };
previtHorizontal[3][3] = {1, 1, 1, 0, 0, 0, -1, -1, -1 };
previtVertical[3][3] = {1, 0, -1, 1, 0, -1, 1, 0, -1};
boxBlur[3][3] = {0.111f, 0.111f, 0.111f, 0.111f,
0.111f, 0.111f, 0.111f, 0.111f, 0.111f};
triangleBlur[3][3] = { 0.0625, 0.125, 0.0625,
0.125, 0.25, 0.125, 0.0625, 0.125, 0.0625};```
Last but not least is the ability to show a convoluted image as a grayscale result. In order to display a filtered image as grayscale, we just add a couple lines to the bottom of the `Convolve` function:
```//return new pixel value
if (bGrayscale)
{
int grayscale=0.299*rSum + 0.587*gSum + 0.114*bSum;
rSum=grayscale;
gSum=grayscale;
bSum=grayscale;
}
clrReturn = RGB(rSum,gSum,bSum);```
This means that the entire `Convolve` function now looks like:
```COLORREF CImageConvolutionView::Convolve(CDC* pDC, int sourcex,
int sourcey, float kernel[3][3], int nBias,BOOL bGrayscale)
{
float rSum = 0, gSum = 0, bSum = 0, kSum = 0;
COLORREF clrReturn = RGB(0,0,0);
for (int i=0; i <= 2; i++)//loop through rows
{
for (int j=0; j <= 2; j++)//loop through columns
{
//get pixel near source pixel
/*
if x,y is source pixel then we loop
through and get pixels at coordinates:
x-1,y-1
x-1,y
x-1,y+1
x,y-1
x,y
x,y+1
x+1,y-1
x+1,y
x+1,y+1
*/
COLORREF tmpPixel = pDC->GetPixel(sourcex+(i-(2>>1)),
sourcey+(j-(2>>1)));
//get kernel value
float fKernel = kernel[i][j];
//multiply each channel by kernel value, and add to sum
//notice how each channel is treated separately
rSum += (GetRValue(tmpPixel)*fKernel);
gSum += (GetGValue(tmpPixel)*fKernel);
bSum += (GetBValue(tmpPixel)*fKernel);
//add the kernel value to the kernel sum
kSum += fKernel;
}
}
//if kernel sum is less than 0, reset to 1 to avoid divide by zero
if (kSum <= 0)
kSum = 1;
//divide each channel by kernel sum
rSum/=kSum;
gSum/=kSum;
bSum/=kSum;
//add bias if desired
rSum += nBias;
gSum += nBias;
bSum += nBias;
//prevent channel overflow by clamping to 0..255
if (rSum > 255)
rSum = 255;
else if (rSum < 0)
rSum = 0;
if (gSum > 255)
gSum = 255;
else if (gSum < 0)
gSum = 0;
if (bSum > 255)
bSum = 255;
else if (bSum < 0)
bSum = 0;
//return new pixel value
if (bGrayscale)
{
int grayscale=0.299*rSum + 0.587*gSum + 0.114*bSum;
rSum=grayscale;
gSum=grayscale;
bSum=grayscale;
}
clrReturn = RGB(rSum,gSum,bSum);
return clrReturn;
}```
Last but not least, I did a little tweaking to get the program to load a default image from a resource (`IDB_BITMAP1`). Then, I added the ability to convolve this default image. The program will still load image from a file, the only difference is that it will now show a default image at startup.
Please note that this article is, by no means, an example of fast processing of pixels. It is merely meant to show how convolution can be done on images. If you would like a more advanced image processor, then feel free to email me with the subject "WANT CODE:ImageEdit Please". That is an unreleased image processor I have done, though parts are not implemented yet due to lack of time, that contains much more functionality, using the CxImage library as its basis for reading and saving images.
## License
This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.
A list of licenses authors might use can be found here
## About the Author
Web Developer United States
Programming using MFC and ATL for almost 12 years now. Currently studying Operating System implementation as well as Image processing. Previously worked on DSP and the use of FFT for audio application. Programmed using ADO, ODBC, ATL, COM, MFC for shell interfacing, databasing tasks, Internet items, and customization programs.
## Comments and Discussions
View All Threads First Prev Next
Grayscale conversion Erik_Egsgard20-Aug-04 4:45 Erik_Egsgard 20-Aug-04 4:45
Re: Grayscale conversion Aqiruse20-Aug-04 14:58 Aqiruse 20-Aug-04 14:58
Re: Grayscale conversion Erik_Egsgard21-Aug-04 19:29 Erik_Egsgard 21-Aug-04 19:29
Re: Grayscale conversion Erik_Egsgard24-Aug-04 3:57 Erik_Egsgard 24-Aug-04 3:57
Re: Grayscale conversion Georgi Petrov8-Nov-04 1:52 Georgi Petrov 8-Nov-04 1:52
Re: Grayscale conversion Oystein F. Saebo7-Feb-06 8:44 Oystein F. Saebo 7-Feb-06 8:44
Last Visit: 31-Dec-99 19:00 Last Update: 21-Jan-18 15:31 Refresh 1
General News Suggestion Question Bug Answer Joke Praise Rant Admin
Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.
Permalink | Advertise | Privacy | Terms of Use | Mobile
Web04 | 2.8.180111.1 | Last Updated 29 Mar 2006
Article Copyright 2004 by Fred Ackers
Everything else Copyright © CodeProject, 1999-2018
Layout: fixed | fluid | 3,391 | 10,166 | {"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} | 3.0625 | 3 | CC-MAIN-2018-05 | latest | en | 0.859639 |
https://brainmass.com/economics/personal-finance-savings/social-security-taxes-503554 | 1,621,141,730,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989690.55/warc/CC-MAIN-20210516044552-20210516074552-00352.warc.gz | 174,350,706 | 75,178 | Explore BrainMass
# Social Security Taxes
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Suppose the real rate of growth of wages subject to Social Security taxes is expected to average 1% per year during the next 40 years. Assume that the Social Security tax rate remains constant, and prove that the average return on Social Security taxes paid into the Social Security trust fund will also be 1%.
Why can workers with high incomes expect negative returns on their Social Security taxes during this period?
https://brainmass.com/economics/personal-finance-savings/social-security-taxes-503554
#### Solution Preview
The real rate of growth of wages subject to SS taxes is 1% per year for the next 40 years. The SS tax remains constant. The average return on social security taxes paid into SS will also be 1% because SS is a progressive tax and will either remain constant or increase. If I make \$25,000 per year and increase by 1% per year, my income in the 1st year will go to 25,250. At \$25,000, I am paying in at 4.2%, which means \$1,050 comes out of my check. When I make \$25,250, \$1,060.5 will come out of my check as social security remains constant. Even though these factors are in place, the social security system has hit a shortfall. Even though the wages will increase each year for the next 40 years at 1% per year, the return on ...
#### Solution Summary
This solution discusses the real rate of growth of wages subject to social security taxes. I provide a detailed explanation to how workers with high incomes can expect negative returns on their social security taxes if the social security tax is expected to average 1% and the growth in the social security trust fund is also 1%.
\$2.49 | 417 | 1,868 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2021-21 | latest | en | 0.942285 |
http://www.mathworks.ch/ch/help/matlab/matlab_prog/functions-that-return-a-logical-result.html?action=changeCountry&s_tid=gn_loc_drop | 1,386,775,182,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164038376/warc/CC-MAIN-20131204133358-00060-ip-10-33-133-15.ec2.internal.warc.gz | 435,180,248 | 8,553 | Accelerating the pace of engineering and science
# Documentation Center
• Trials
• Product Updates
## Functions that Return a Logical Result
### Overview
This table shows some of the MATLAB® operations that return a logical true or false. Most mathematics operations are not supported on logical values.
Function
Operation
Setting value to true or false
logical
Numeric to logical conversion
& (and), | (or), ~ (not), xor, any, all
Logical operations
&&, ||
Short-circuit AND and OR
== (eq), ~= (ne), < (lt), > (gt), <= (le), >= (ge)
Relational operations
All is* functions, cellfun
Test operations
String comparisons
### Examples of Functions that Return a Logical Result
MATLAB functions that test the state of a variable or expression return a logical result:
```A = isstrprop('abc123def', 'alpha')
A =
1 1 1 0 0 0 1 1 1```
Logical functions such as xor return a logical result:
```xor([1 0 'ab' 2.4], [ 0 0 'ab', 0])
ans =
1 0 0 1```
Note however that the bitwise operators do not return a logical:
```X = bitxor(3, 12);
whos X
Name Size Bytes Class Attributes
X 1x1 8 double```
String comparison functions also return a logical:
```S = 'D:\matlab\mfiles\test19.m';
strncmp(S, 'D:\matlab', 9)
ans =
1```
Note the difference between the elementwise and short-circuit logical operators. Short-circuit operators, such as && and ||, test only as much of the input expression as necessary. In the second part of this example, it makes no difference that B is undefined because the state of A alone determines that the expression is false:
```A = 0;
A & B
Undefined function or variable 'B'.
A && B
ans =
0```
One way of implementing an infinite loop is to use the while function along with the logical constant true:
```while true
a = []; b = [];
a = input('Enter username: ', 's');
if ~isempty(a)
b = input('Enter password: ', 's');
end
if ~isempty(b)
disp 'Attempting to log in to account ...'
break
end
end```
Was this topic helpful? | 539 | 2,063 | {"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} | 3.546875 | 4 | CC-MAIN-2013-48 | latest | en | 0.734179 |
https://expertinstudy.com/t/TtMI4qQiS | 1,653,461,229,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662580803.75/warc/CC-MAIN-20220525054507-20220525084507-00725.warc.gz | 287,163,044 | 4,670 | # IU I How to find out how muchtime in seconds?6.by 1,50,175 students. How many students did appear in the examination next year?3511,68,975 students appeared in an examination in 2018. Next year, the number increased
The time for answering the question is over
110 cents
Let the marks obtained in 5 subjects be 6x, 7x, 8x, 9x and 10x Average score = 60%
5
6x+7x+8x+9x+10x
=
100
60
5
40x
=
100
60
⇒x=
100×40
60×5
=
40
3
=0.075 ∴ The marks are 0.45, 0.525, 0.6, 0.675 and 0.75,
i.e., 45%,52.5%,60%,67.5% and 75%
∴ Number of papers in which the marks exceed 50 % =4
her is ur answer
446
For answers need to register.
Contacts
mail@expertinstudy.com
Feedback
Expert in study | 250 | 695 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2022-21 | latest | en | 0.899431 |
https://de.slideshare.net/DanishKhan277/project-3-satellite-link-budgets-and-pe | 1,686,153,032,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224653930.47/warc/CC-MAIN-20230607143116-20230607173116-00692.warc.gz | 236,723,801 | 80,386 | Anzeige
Anzeige
Anzeige
Anzeige
Nächste SlideShare
Antenna Paper Solution
1 von 16
Anzeige
### Project 3 “Satellite Link Budgets and PE”
1. Arlene Meidahl - s107106 and Danish Bangash-s104712| Digital Communication | 21. maj 2015 Supervisor: John Aasted Sørensen Digital Communication and Modulation Project 3 “Satellite Link Budgets and PE”
2. SIDE 1 Satellite Link Budgets and PE The objective of this project is to construct a Matlab script for link budget determination for a satellite relay communication link, as shown in [Ziemer, 2010] Figure A.7 page 695: The script should include the following primary parameters for a satellite-satellite link: d Distance between the two satellites. Transmitted wavelength. B Bandwidth of the transmission between the two satellites. TP Transmitted power from satellite antenna. TG Power gain of transmitter antenna over the isotropic radiation level. RA Receiving aperture area. RG Power gain of receiving antenna. 0L Atmospheric absorption. RT Receiver noise temperature.
3. SIDE 2 The script should allow for the determination of the SNR at the receiver output and the probability of bit error EP for the satellite link. The script is used to demonstrate experimentally the relation between EP and varying d , , B , TP by appropriately selected examples. It is suggested to use the Examples A.8 and A.9 at pages 697, 698 [Ziemer, 2010] as a starting point for examples. It is suggested to augment with at least two new examples created by yourself. The script should allow the user to determine the received power in dBW.
4. SIDE 3 Problem formulation: Considering a free-space electromagnetic-wave propagation channel as an example. For a better understanding how it works, we set our attention on the link between the two satellites which is the synchronous-orbit relay satellite and a low-orbit satellite or an aircraft as we can see in figure below. We assumed a relay satellite transmitted signal power of PT W. If we say that it is radiated isotropically, the power density at a distance d from the satellite is given by: 𝑃𝑡 = 𝑃𝑇 4𝜋𝑑2 [ 𝑊 𝑚2] If the radiated power is directed towards the low-orbit satellite or an aircraft as an example, then the maximum gain for the transmitting aperture antenna is: 𝐺 𝑇 = 4𝜋𝐴 𝑇 𝜆2
5. SIDE 4 The maximum gain for the receiving aperture antenna is: 𝐺 𝑅 = 4𝜋𝐴 𝑅 𝜆2 The power PR intercepted by the receiving antenna is given by the product of the receiving aperture area AR and the power density at the aperture. So, 𝑃𝑅 = 𝑃𝑇 𝐺 𝑇 4𝜋𝑑2 𝐴 𝑅 The value of AR is know from the expression of ‘maximum gain for receiving aperture antenna, so we get the following: 𝑃𝑅 = 𝑃𝑇 𝐺 𝑇 𝐺 𝑅 𝜆2 (4𝜋𝑑)2 A loss actor is included to the expression above and then we rearrange the formula, so we obtained the following new expression: 𝑃𝑅 = ( 𝜆 4𝜋𝑑 ) 2 𝑃𝑇 𝐺 𝑇 𝐺 𝑅 𝐿 𝑂 Where ( 𝜆 4𝜋𝑑 ) 2 is referred as the free-space loss. We then calculate the receiver power in terms of dB (with reference 1 Watt), so we get: 10𝑙𝑜𝑔10 𝑃𝑅 = 20𝑙𝑜𝑔10 ( 𝜆 4𝜋𝑑 ) + 10𝑙𝑜𝑔10 𝑃𝑇 + 10𝑙𝑜𝑔10 𝐺 𝑇 + 10𝑙𝑜𝑔10 𝐺 𝑅 − 10𝑙𝑜𝑔10 𝐿 𝑂
6. SIDE 5 Example A.8: The following parameters for a relay-satellite-to user link are given: - Relay satellite effective radiated power ( 30 ; 100T TG dB P W ): 50 dBW - Transmit frequency : 2 GHz ( 0.15 m ) - Receiver noise temperature of user (includes noise figure of receiver and background temperature of antenna): 700 K - User satellite antenna gain: 0 dB - Total system losses: 3 dB - Relay-user separation: 41,000 km Find the signal-to-noise power ration in a 50 kHz bandwidth at the user satellite receiver IF amplifier output. Solution: We begin by finding the free-space loss in dB to be: ( 𝜆 4𝜋𝑑 ) 2 = 20𝑙𝑜𝑔10 ( 𝜆 4𝜋𝑑 ) = 20𝑙𝑜𝑔10 ( 0.15 4 ∗ 𝜋 ∗ 41 ∗ 106 ) = −190.72 𝑑𝐵 Then we substitute in the formula to find the received power signal; 10𝑙𝑜𝑔10 𝑃𝑅 = 20𝑙𝑜𝑔10 ( 𝜆 4𝜋𝑑 ) + 10𝑙𝑜𝑔10 𝑃𝑇 + 10𝑙𝑜𝑔10 𝐺 𝑇 + 10𝑙𝑜𝑔10 𝐺 𝑅 − 10𝑙𝑜𝑔10 𝐿 𝑂 We know the value of the unknown variables in the above equation from the problem formulation, so we put in the values in the equation: 10𝑙𝑜𝑔10 𝑃𝑅 = −190.72 + 10𝑙𝑜𝑔10(100) + 10𝑙𝑜𝑔10(30) + 10𝑙𝑜𝑔10(0) − 10𝑙𝑜𝑔10(3) So the received power in dB is: 𝑃𝑅 = −143.72 𝑑𝐵 We know that the noise power level is: 𝑃𝑖𝑛𝑡 = 𝐺 𝑎 𝑘𝑇𝑒 𝐵 Here the Pint is the receiver output noise power caused by the internal sources. Since we are calculating the SNR, the available gain of the receiver does not enter the calculation because both signal and noise are multiplied by the same gain. Hence, we may set Ga to unity. And this the noise level is: 𝑃𝑖𝑛𝑡,𝑑𝑏𝑊 = 10 𝑙𝑜𝑔10[𝐺 𝑎 𝑘𝑇𝑒 𝐵]
7. SIDE 6 In the equation above, all the variables are given its values excluding the constant k which is the so called Boltsmann’s constant, which is equal to 1.38065*10-23 𝐽 𝐾 . The we substitute the given values to the equation 𝑃𝑖𝑛𝑡,𝑑𝑏𝑊 = 10 𝑙𝑜𝑔10[1 ∗ 1.38 ∗ 10−23 ∗ 700 ∗ 50 ∗ 103] The above equation can also be stated: 𝑃𝑖𝑛𝑡,𝑑𝑏𝑊 = 10 𝑙𝑜𝑔10[1] + 10 𝑙𝑜𝑔10[1.38 ∗ 10−23] + 10 𝑙𝑜𝑔10[700] + 10 𝑙𝑜𝑔10[50 ∗ 103] = −153.16 𝑑𝐵𝑊 So the SNR at the receiver output will be 𝑆𝑁𝑅0 = 𝑃𝑅 − 𝑃𝑖𝑛𝑡,𝑑𝑏𝑊 = −143.72 − (−153.16 ) = 9.44 𝑑𝐵 Example A.9: Continuation of example 8 From the result of the example above, we would like to interpret it in terms of the performance of a digital communication system, so we have to convert the SNR obtained to energy-per-bit-to-noise- spectral density ratio 𝐸 𝑏 𝑁0 . By definition of SNR0: 𝑆𝑁𝑅0 = 𝑃𝑅 𝑘𝑇𝑒 𝐵 If we multiply the numerator and the denominator by the duration of a data bit 𝑇𝑏 , and we know that: PRTB = Eb and kTR = N0 So we get the following: 𝑆𝑁𝑅0 = 𝑃𝑅 𝑘𝑇𝑒 𝐵 = 𝐸 𝑏 𝑁0 𝐵𝑇𝑏 We are aware that PRTB = Eb and kTR = N0 , are the signal energy per bit and the noise power spectral density. So, to obtain Eb N0 from the SNR0 we performed the following:
8. SIDE 7 𝐸 𝑏 𝑁0 = 𝑆𝑁𝑅0 + 10 𝑙𝑜𝑔10(𝐵𝑇𝑏) In the previous problem A.8, SNR0 is equal to 9.44 dB. We know that the null-to-null bandwidth of a phase-shift keyed carrier is 2 Tb Hz. Therefore, we could say that BTb is 2 (3 dB), thus 𝐸 𝑏 𝑁0 = 9.44 + 3 = 12.44 𝑑𝐵 We now convert the above result into z-ratio since we want to calculate the bit error probability, therefore 10 log10(z) = 12.44 z = 101.244 Now, the probability of error for a binary phase-shift keying (BPSK) digital communication system can be express as: PE = Q (√ 2Eb N0 ) ≅ Q (√2 ∗ 101.244) ≅ 1.23 ∗ 10−9 We can conclude from the result we just found that it is a fairly small probability of error since anything less than 10-6 would probably be considered adequate.
9. SIDE 8 Example 2: Problem A.12: Given a relay-user link with the following parameters: - Average transmit power of relay satellite: 35 dBW = Pt - Transmit frequency: 7.7 GHz = f - Effective antenna aperture of relay satellite : 1 m2 = AR - Noise temperature of user receiver (including antenna): 1000 K = TR - Antenna gain of user: 6 dB = GR - Total system losses: 5 dB = L0 - System bandwidth: 1 MHz = B - Relay-user separation: 41,000 km = d a. Find the received signal power level at the user in dBW. b. Find the receiver noise level in dBW. c. Compute the SNR at the receiver in decibels. d. Find the average probability of error for the BPSK digital signaling method. The received signal power formula is: 𝑃𝑟 = 20 𝑙𝑜𝑔 10 ( 𝜆 4𝜋𝜆 ) 2 𝑃 𝑇 𝐺 𝑇 𝐺 𝑅 𝐿° where 𝑃𝑟is the received power in decibels reference to 1 W. 10 𝑙𝑜𝑔10 𝑃𝑅 = 20 𝑙𝑜𝑔 10 ( 𝜆 4𝜋𝜆 ) + 10 𝑙𝑜𝑔10(𝑃𝑇 ) + 10 𝑙𝑜𝑔10( 𝐺 𝑇 ) + 10 𝑙𝑜𝑔10(𝐺 𝑅 ) − 10 𝑙𝑜𝑔10(𝐿0) If we look at the formula above, we can see that 𝐺 𝑇 which is the power gain of the transmitter antenna and 𝜆 the transmission wavelength is unknown, so we need to find the value for those two parameter. To find the wavelength λ = c f , c is the speed of light, which is equal to 3*108 m s and the frequency is 7.7*109 Hz so we get the following result: 𝜆 = 3 ∗ 108 7.7 ∗ 109 = 38.96 ∗ 10−3
10. SIDE 9 We obtain 𝐺 𝑇 by: 𝐺 𝑇 = 4𝜋𝐴 𝑇 𝜆2 = 4𝜋 ∗ 1 (38,96 ∗ 10−3)2 = 8.228 ∗ 103 𝐺 𝑇𝑑𝐵 = 10𝑙𝑜𝑔10( 8.228 ∗ 103) = 39.15 𝑑𝐵 The free-space loss is calculated directly in dB: 20𝑙𝑜𝑔10 ( 𝜆 4𝜋𝑑 ) = 20𝑙𝑜𝑔10 ( 38.96 ∗ 10−3 4𝜋 ∗ 41 ∗ 106) = −202.4𝑑𝐵 Now we find the power of the receiver. The given values are: - GR = Antenna gain of user: 6 dB - L0 = Total system losses: 5 dB - PT = Average transmit power of relay satellite: 35 dBW 𝑃𝑅𝑑𝐵 = 20 𝑙𝑜𝑔 10 ( 𝜆 4𝜋𝜆 ) + 10 𝑙𝑜𝑔10(𝑃𝑇 ) + 10 𝑙𝑜𝑔10( 𝐺 𝑇 ) + 10 𝑙𝑜𝑔10(𝐺 𝑅 ) − 10 𝑙𝑜𝑔10(𝐿0) 𝑃𝑅𝐿𝑑𝐵 = −202.4 + 35 + 39.15 + 6 − 5 = 127.3 𝑑𝐵𝑊 b. Find the receiver noise level in dBW. The noise power level is: 𝑃𝑅𝑑𝐵 = 10 𝑙𝑜𝑔10 ( 𝑇𝑅 ∗ 𝐵 ∗ 𝑘) = 10 𝑙𝑜𝑔10 ( 1 ∗ 103 ∗ 1 ∗ 106 ∗ 1.38 ∗ 10−23 ) = −138.6𝑑𝐵𝑊 c. Compute the SNR at the receiver in decibels. The SNR at the receiver is: 𝑆𝑁𝑅 = 𝑃𝑅 − 𝑃𝑟𝐿 = −127.3 + 138.6 = 11.4𝑑𝐵𝑊
11. SIDE 10 d. Find the average probability of error. We can then calculate the probability bit error using the formula below: 𝑃𝐸 = 𝑄 (√ 2𝐸 𝑏 𝑁° ) = 𝑄(√2𝑧) We can say 𝑇𝑅 𝐵 is equal to 3 dB: 𝐸 𝑏 𝑁° | 𝑑𝐵 = 𝑆𝑁𝑅 𝑑𝐵 + 10𝑙𝑜𝑔10(𝑇𝑅 𝐵) = 11.3 + 3 = 14.36 Then we get: 10𝑙𝑜𝑔10(𝑧) = 14.36 𝑧 = 101.436 We get the bit error probability to be: 𝑃𝐸 = 𝑄 (√ 2𝐸 𝑏 𝑁° ) = 𝑄(√2𝑧) = 𝑄 (√2 ∗ 101.436) = 7.3839 ∗ 10−146
12. SIDE 11 Example 2: Parameters Testing The script is used to demonstrate experimentally the relation between PE and the varying parameters d, , B, PT : Every time we change a certain parameter, we assumed that all the other parameters are constant and let it as it be. We started changing the distance d: d [*106] 10 20 30 40 SNR 23.6 17.59 14.06 11.57 PE 6.49*10-202 3.91*10-52 2.8*10-24 1.81*10-14 We can see on the table above that as the distance between the transmitter and the receiver increases and the bit error probability PE, the signal-to-noise ratio(SNR) decreases. Then we played around the wavelength : 0.01 0.05 0.10 0.15 SNR -23.7 -9.75 -3.75 -0.208 PE 0.448 0.258 0.097 0.025 We can see that when we increase the wavelength, it means to say that, we decrease the transmission frequency f, then signal-to-noise ratio increases, but the bit error probability PE decreases. Now, we changed the channel bandwidth B: B 10 000 50 000 100 000 500 000 SNR 31.35 24.36 21.35 14.36 PE 0 8.98*10-240 4.65*10-121 7.33*10-26 When we increase the bandwidth B, we got a decrease in the signal-to-noise-ratio and increase in the bit error probability.
13. SIDE 12 Then we changed the signal transmission power Pt: Pt 10 20 30 40 SNR -13.65 -3.65 6.35 16.35 PE 0.34 0.094 1.62*10-5 9.70*10-40 When we increase the transmission power, we get an increase with the signal-to-noise- ratio and decrease in bit error probability PE until it reaches 0. So we therefore conclude, after testing and changing the values of the different parameters: We could simply change the 4 parameters stated above, so we could get the desired link depending on the requirements being given. In order to get a reasonable signal-to-noise- ratio and bit error probability, each parameters can be compensated by another parameters. To explain further, according from the test , we found out that when we increase distance d between the transmitter and receiver, we get an increase in bit error probability, and in that case we can compensate it by increasing the signal power transmission, and that decreases the bit error probability error.
14. SIDE 13 Appendix: Matlab Codes Code 1: % Example A.8 & A.9 clear all close all clc % Parameters: % (All parameters are in their respective SI units) k = 1.38e-23; % Boltzmann Constant lambda = 0.15; % Transmit Frequency B = 50e3; % Badwidth of transmission between the satellites T = 700; % Reciever noise temperature Pt = 100; % Transmitted power d = 41e6; % Distance between the two satellites Gt = 30; % Power gain Gr = 0; % User satellite antenna gain L0 = 3; % Total system losses % Example A.8 FreeSpaceLoss = 20*log10((lamda)/(4*pi*d)) Pr = FreeSpaceLoss + (10*log(Pt)) + Gt + Gr - L0 Pint_dB = 10*log10(k) + 10*log10(T) + 10*log10(B) SNR0 = Pr - Pint_dB % Example A.9 Page 698, Ziemer 2010 Tb = 2/B % Null-to-null bandwidth of a phase-shift-keyed carrier Eb_N0 = SNR0 + 10*log10(B*Tb) z = 10^(Eb_N0/10) % The bit error probability
15. SIDE 14 Code 2: % Problem A.12 clear all clc % The parameters: k = 1.38e-23; % Boltzmann's Constant d = 41*10^6; % Distance between the two satellites B = 1*10^6; % Bandwidth of the transmission between the two satellites Pt = 35; % Transmitted power from satellite antenna Ar = 1 % Receiving aperture area At = 1; % Transmitting aperture area Gr = 6; % Power gain of receiving antenna L0 = 5; % Atmospheric absorption Tr = 1000 % Receiver noise temperature measured in [Kelvin] c = 3*10^8; % Speed of light [m/s] f = 7.7*10^9; % Transmit frequency [Hz] lambda = c/f; % Transmitted wavelength Gt = 4*pi*At/lambda^2; % Power gain of transmitter antenna NOT in dB % a) FSloss_dB = 20*log10((lambda/(4*pi*d))); % Free-space loss in dB Pr1 = FSloss_dB + Pt + 10*log10(Gt) + Gr - L0; % Power of received signal (ref. 1W; in dB) % b) Pr2 = 10*log10(k*Tr*B); % Power of output signal (ref. 1W; in dB; no def. gain); % c) SNRout = Pr1 - Pr2; % SNR at receiver output % d)
16. SIDE 15 Tb = 2/B; % duration of data bit in terms of bandwidth, for BPSK EbN0 = SNRout + (10*log10(B*Tb)); z = 10^(EbN0/10); PE = qfunc(sqrt(2*z)); % Bit error probability Referrences: Principles of Communications System, Modulation and Noise – Sixth Edition – Rodger E. Ziemer, William H. Tranter
Anzeige | 5,088 | 13,259 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-23 | latest | en | 0.85142 |
https://www.beatthegmat.com/z-is-the-set-of-the-first-n-positive-odd-numbers-where-t300206.html | 1,544,600,518,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823785.24/warc/CC-MAIN-20181212065445-20181212090945-00341.warc.gz | 844,719,832 | 38,205 | • 7 CATs FREE!
If you earn 100 Forum Points
Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote Z is the set of the first n positive odd numbers, where .... tagged by: Vincen This topic has 1 expert reply and 0 member replies Z is the set of the first n positive odd numbers, where .... Z is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Z, and y is the minimum value of the sum of k distinct members of Z, what is x + y? (A) kn (B) kn + k^2 (C) kn + 2k^2 (D) 2kn - k^2 (E) 2kn The OA is the option E. How can I solve this PS question? I'm really confused here. Experts, can you give me some help? GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Quote: Z is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Z, and y is the minimum value of the sum of k distinct members of Z, what is x + y? (A) kn (B) kn + k^2 (C) kn + 2k^2 (D) 2kn - k^2 (E) 2kn The OA is the option E. How can I solve this PS question? I'm really confused here. Experts, can you give me some help? Hi Vincen, Let's take a look at your question. We will solve this question by assuming some random values for the set Z. Let n = 5, therefore, the set Z has first 5 positive odd numbers. i.e. $$Z=\left\{1,\ 3,\ 5,\ 7,\ 9\right\}$$ Let k = 2, then x is the is the maximum value of the sum of k=2 distinct members of Z. We can see that the two values of set Z, that will give the maximum sum are the last two values, i.e. 7 and 9. Therefore, $$x=7+9=16$$ y is the is the minimum value of the sum of k=2 distinct members of Z. We can see that the two values of set Z, that will give the minimum sum are the first two values, i.e. 1 and 3. Therefore, $$y=1+3=4$$ Now, we can find x+y: $$x+y=16+4=20$$ We had: n = 5 and k = 2 So 20 will be equal to: $$2\times5\times2=2nk$$ Therefore, option E is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • FREE GMAT Exam Know how you'd score today for$0
Available with Beat the GMAT members only code
• Free Practice Test & Review
How would you score if you took the GMAT
Available with Beat the GMAT members only code
• Magoosh
Study with Magoosh GMAT prep
Available with Beat the GMAT members only code
• 5 Day FREE Trial
Study Smarter, Not Harder
Available with Beat the GMAT members only code
• 5-Day Free Trial
5-day free, full-access trial TTP Quant
Available with Beat the GMAT members only code
• Free Veritas GMAT Class
Experience Lesson 1 Live Free
Available with Beat the GMAT members only code
• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE
Available with Beat the GMAT members only code
• 1 Hour Free
BEAT THE GMAT EXCLUSIVE
Available with Beat the GMAT members only code
• Get 300+ Practice Questions
Available with Beat the GMAT members only code
• Award-winning private GMAT tutoring
Register now and save up to \$200
Available with Beat the GMAT members only code
Top First Responders*
1 Brent@GMATPrepNow 69 first replies
2 fskilnik@GMATH 54 first replies
3 Jay@ManhattanReview 48 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members
Most Active Experts
1 fskilnik@GMATH
GMATH Teacher
128 posts
2 Brent@GMATPrepNow
GMAT Prep Now Teacher
101 posts
3 Max@Math Revolution
Math Revolution
92 posts
4 Jay@ManhattanReview
Manhattan Review
86 posts
5 Rich.C@EMPOWERgma...
EMPOWERgmat
78 posts
See More Top Beat The GMAT Experts | 1,215 | 4,280 | {"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} | 3.9375 | 4 | CC-MAIN-2018-51 | longest | en | 0.906353 |
https://www.studypool.com/discuss/515379/tvm-accounting-help-asap | 1,506,075,111,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818688932.49/warc/CC-MAIN-20170922093346-20170922113346-00445.warc.gz | 877,060,009 | 20,528 | # TVM Accounting help ASAP!
May 5th, 2015
Anonymous
Category:
Accounting
Price: \$10 USD
Question description
Include keystrokes that are entered into the Financial Calculator (N=,I/Y=,PV=,PMT=,FV=)
1. a. Balish Corp bought a new machine on January 1, 2015 and agreed to pay for it in 5 equal installments of \$40,000 on December 31st, 2015 and December 31 of each of the next 4 years. Assuming that the prevailing rate of 8% applies to this contract, how much should Balish record as the cost of the machine?
b. Prepare the entry that Balish would make to record the purchase of the machinery if the company signed a note where interest was included in the face amount of the note.
2. Refer to question 1. Answer each question again assuming that interest was not included in the face amount of the note.
a. Cost of the machine
b. Journal entry to record the purchase
(Top Tutor) Kelvin B
School: Cornell University
Studypool has helped 1,244,100 students
Review from student
Anonymous
" The best tutor out there!!!! "
1824 tutors are online
Brown University
1271 Tutors
California Institute of Technology
2131 Tutors
Carnegie Mellon University
982 Tutors
Columbia University
1256 Tutors
Dartmouth University
2113 Tutors
Emory University
2279 Tutors
Harvard University
599 Tutors
Massachusetts Institute of Technology
2319 Tutors
New York University
1645 Tutors
Notre Dam University
1911 Tutors
Oklahoma University
2122 Tutors
Pennsylvania State University
932 Tutors
Princeton University
1211 Tutors
Stanford University
983 Tutors
University of California
1282 Tutors
Oxford University
123 Tutors
Yale University
2325 Tutors | 433 | 1,676 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2017-39 | latest | en | 0.856889 |
https://www.hackmath.net/en/math-problem/74914 | 1,660,645,100,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00288.warc.gz | 685,253,766 | 10,605 | # Intersection 74914
Find the perimeter of triangle ABC, where point A is the beginning of the coordinate system, and point B is the intersection of the graph of the linear function f: y = - 3/4• x + 3 with the x-axis, and C is the intersection of the graph of this function with the y axis.
o = 12 cm
### Step-by-step explanation:
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Tips for related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert length units? | 196 | 893 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2022-33 | longest | en | 0.876289 |
http://sigcon.com/Pubs/edn/por.htm | 1,558,293,133,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255092.55/warc/CC-MAIN-20190519181530-20190519203530-00407.warc.gz | 186,620,031 | 3,898 | ## Power-On-Reset
Many digital-design teams assign the design of the power-on-reset circuit to their youngest, least experienced engineer. This assignment is a mistake. Let me explain why.
In their first power-on-reset experience, most new engineers gravitate toward a circuit like the one in Figure 1.
This circuit works beautifully in simulation, assuming that VCC voltage rises quickly and monotonically to its maximum value and stays there. Under those conditions, you can choose an RC time constant large enough to guarantee that the Schmitt-trigger gate holds ~RESET low (active) for any specified time after VCC stabilizes. After the RC time-out, ~RESET goes high (inactive), commencing normal operations.
Circuits like this are in widespread use. At one time in my career, a distributor of telecommunications equipment hired me to evaluate 85 brands of small-office telephone products. Phone equipment is supposed to be extremely reliable. I therefore decided to test each product to determine its susceptibility to various external influences, including power quality. My power-quality tester consisted of a big, adjustable Variac autotransformer for simulating brownout conditions and a relay circuit that could interrupt power for 100 to 1000 msec.
I chose the power-interruption test because it mimics the way power outages most often happen in the real world. Power outages often begin when a foreign object, such as a tree branch, squirrel, or bird, comes into contact with the power lines. This event draws a large amount of current, which shorts out the power voltage while creating one crispy-fried squirrel or bird. After a couple of hundred milliseconds, the local neighborhood circuit breaker that feeds the shorted area blows open. Once that circuit breaker takes the faulty neighborhood offline, everybody else's power recovers. If you live outside the faulty neighborhood (statistically likely), you see only a momentary glitch and then a quick recovery of the power voltage. It happens all the time.
Power interruptions drive power-on-reset circuits crazy. Consider what a power dropout does to the circuit in Figure 1. Imagine that the RC time constant in this figure is 1 sec. Let VCC come up and stabilize at full voltage for perhaps 10 sec. Next, apply an ac power interruption just long enough to drop VCC to 0V for about 100 msec. If a processor is involved, the dropout is long enough to make scrambled eggs of the processor's internal state machines but not long enough to discharge the RC circuit. If the RC circuit doesn't discharge, ~RESET doesn't activate, and the processor spins out of control, powered on, but lost in space.
The effects of power-on-reset debacles in a big system can be hilarious. In poorly designed phone equipment, the dropout test causes all kinds of failures, including crossed calls, bleeping phones, and smoking power supplies. The failed systems usually don't wake up again until you completely remove power, wait a few seconds, and then restore it in the ordinary way. For most systems, the simple RC-based power-on-reset circuit is completely inadequate.
A good power-on-reset circuit must activate when power is currently good and has been good for some time and must completely and quickly deactivate upon any indication of poor power quality. That situation is what you find in equipment that passes the dropout test.
A good power-on-reset designer understands ac power systems, dc power systems, microprocessors, and some analog design. This person is unlikely to be a young, inexperienced engineer. If someone asks you to design a power-on-reset circuit, don't take the assignment lightly. Design a good circuit and test it well. | 741 | 3,708 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-22 | latest | en | 0.929168 |
https://pwntestprep.com/wp/tag/complex-numbers/ | 1,563,548,889,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526254.26/warc/CC-MAIN-20190719140355-20190719162355-00135.warc.gz | 515,580,161 | 23,652 | ## Posts tagged with: complex numbers
This may be a little advanced for the SAT, but complex numbers sometimes show up –as do cubic polynomials– so hopefully you can address this for me! TIA!
Which of the following could be the full set of complex roots of a cubic polynomial with real coefficients?
A. { 0, 1, i}
B. {1, i, 2i}
C. {2, i}
D. {3, 2 + i, 2 – i}
I don’t feel like I’m qualified to teach a lesson on this. I know that a cubic polynomial must have 1 or 3 real roots, but I’m too far removed from the class I learned that in to reconstruct the proof here. (A lesson that’s always worth relearning in SAT prep: not all high school math is SAT math.) However, I can still help with this question because it’s multiple choice and happens to lend itself to one of my favorite approaches: we can backsolve!
If you translate the answer choices to what the factors of the polynomial would be, you can multiply those and see which one ends up with all real coefficients. I gravitated right to choice D, because that 2 + i and 2 – i conjugate looks like it’ll cancel out nicely. Let’s see!
We know that a cubic polynomial with roots 3, 2 + i, 2 – i would have the factored form: . Now FOIL the complex factors:
<-- All the i terms will go away here!
See how the i terms cancel out? That won’t happen in any other choice, which means the other choices will result in coefficients that aren’t real. We don’t even need to fully expand this one to know it’s the right move.
If you remember that the square of i is –1, you can reduce these to purely real numbers before you even FOIL.
In a + bi form, 5 is just 5 + 0i, so a + b will be 5 + 0 = 5.
from Tumblr https://ift.tt/2A7wbcj
Test 4 Section 3 #14
When you’re dividing complex numbers, you have to multiply the top and bottom of the fraction by the complex conjugate of the bottom. This creates a real number in the bottom of the fraction, which is awesome.
The bottom of this fraction is , so its complex conjugate is . To get started, then, we write the following:
Then we simplify as much as we can. First we FOIL:
Now, remembering that and therfore that , we make that substitution and simplify further:
So there you have it. Once we simplify that complex fraction into form, we see that it’s just , which means . | 582 | 2,285 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2019-30 | latest | en | 0.899401 |
https://blog.keiruaprod.fr/2021/05/09/z3-samples.html | 1,624,629,034,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487630175.17/warc/CC-MAIN-20210625115905-20210625145905-00461.warc.gz | 138,863,564 | 9,063 | # KeiruaProd
## Cool things Z3 can help with
A recent article came up recently and it’s a great way to start using Z3, a popular, general purpose constraint solver (among many things). The article comes with a video workshop and it is a nice supplement.
It’s quite hard to figure out what this kind of solver can be useful for. I tried to read SMT by Example in the past, but it was too much for a start. The above link was an easier intro that gave me a broad overview of the possibilities.
This article shares some problems I liked (mostly ressource allocations and riddles, though Z3 can do much more) and how to solve them using Z3.
• A few riddles and puzzles (in order to get used to the API and the specificities of thinking with Z3) :
• Some short ressource allocation problems :
I stole some problems in the aforementionned articles, as well as on hakank.org. But ! I spent some evenings typing the solutions or attempting to solve them myself. It felt super hard at first, because that’s a very unusual way to think about problems. What struck me the most (and it especially visible on Einstein’s riddle I think) is that solving the problem is mostly about properly stating it.
Regarding real-life use, I’ve been quite impressed to read things on:
## Some fun riddles
A couple intro problems in order to get used to the syntax and what solving a problem with Z3 looks like.
### Rabbits and pheasants
9 animals, rabbits and pheasants are playing on the grass. We can see 24 legs. How many rabbits and pheasants are there?
It looks like a system of 2 equations with 2 unknowns, so we can solve by hand or use a equation solver, like scipy.linalg.solve to find a solution. Let’s do this:
``````# rabbits-pheasans-scipy.py
import numpy as np
from scipy import linalg
a = np.array([[1, 1], [4, 2]])
b = np.array([9, 24])
print(linalg.solve(a, b))
``````
The results are:
``````python3 rabbits-pheasants-scipy.py
[3. 6.]
``````
We’ve lost what is what but hey, that’s a first result and it only took 5 lines of code.
It turns out Z3 can do this too with another approach. Let’s create the 2 integer parameters (`rabbits` and `pheasants`) that will hold the possible values, pop a `Solver`, add some constraints on our parameters and see if Z3 can come up with a model that matches all the constraints:
``````# rabbits-pheasans-z3.py
from z3 import *
rabbits, pheasants = Ints("rabbits pheasants")
s = Solver()
s.check()
print(s.model())
``````
Now we can run it:
``````python3 rabbits-pheasans.py
[pheasants = 6, rabbits = 3]
``````
We’ve found the same results, great! The code may look similar, but the two approaches are very different: with Z3, we are not creating matrixes or unknowns and equations. We are creating parameters on top of which we add constraints, and we want to find a model that matches those constraints.
There are 2 drawbacks to using an ad hoc solution :
• you have to know or write a custom solver every time
• this is very domain specific.
The riddle could have been:
9 animals, rabbits and pheasants are playing on the grass. We can see 24 legs, or maybe was it 27 ? How many rabbits and pheasants are there?
This is still very easy to solve by hand, but from a mathematical point of view with an equation solver it becomes more complex:
• we need to solve 2 systems, one with 24 legs, one with 27.
• we’ll find a valid (with integers) solution to only one problem
With Z3, all we have to do is add an `Or` clause:
``````# rabbits-pheasans-z3.py
from z3 import *
rabbits, pheasants = Ints("rabbits pheasants")
s = Solver()
4*rabbits + 2*pheasants == 24,
4*rabbits + 2*pheasants == 27))
s.check()
print(s.model())
``````
On to something a bit more complex.
### Einstein’s riddle
Einstein’s riddle goes like this:
• There are five houses.
• The Englishman lives in the red house.
• The Spaniard owns the dog.
• Coffee is drunk in the green house.
• The Ukrainian drinks tea.
• The green house is immediately to the right of the ivory house.
• The Old Gold smoker owns snails.
• Kools are smoked in the yellow house.
• Milk is drunk in the middle house.
• The Norwegian lives in the first house.
• The man who smokes Chesterfields lives in the house next to the man with the fox.
• Kools are smoked in the house next to the house where the horse is kept.
• The Lucky Strike smoker drinks orange juice.
• The Japanese smokes Parliaments.
• The Norwegian lives next to the blue house.
Now, who drinks water? Who owns the zebra?
It takes some time to solve by hand. It took me 25 minutes with Z3. Most of them were used to correctly identify the known values and type the constraints. Look at how simple the code is !
``````from z3 import *
nationalities = Ints("Englishman Spaniard Ukrainian Norwegian Japanese")
cigarettes = Ints("Parliaments Kools LuckyStrike OldGold Chesterfields")
animals = Ints("Fox Horse Zebra Dog Snails")
drinks = Ints("Coffee Milk OrangeJuice Tea Water")
house_colors = Ints("Red Green Ivory Blue Yellow")
parameter_sets = [nationalities, cigarettes, animals, drinks, house_colors]
Englishman, Spaniard, Ukrainian, Norwegian, Japanese = nationalities
Parliaments, Kools, LuckyStrike, OldGold, Chesterfields = cigarettes
Fox, Horse, Zebra, Dog, Snails = animals
Coffee, Milk, OrangeJuice, Tea, Water = drinks
Red, Green, Ivory, Blue, Yellow = house_colors
solver = Solver()
for parameter_set in parameter_sets:
# We want all the values for a given category:
# - to be different
# - to be between 1 and 5 included
for parameter in parameter_set:
def Neighbor(a, b):
"""A z3 constraints that states that a is a neighbor of b"""
return Or(a == b + 1, a == b - 1)
solver.check()
m = solver.model()
# Result display
houses = []
for i in range(1, 5+1):
house = []
for parameter_set in parameter_sets:
p = list(filter(lambda x: m.eval(x) == i, parameter_set))[0]
house.append(p)
houses.append(house)
# formatting the result is inspired by what peter norvig for its sudokus:
# http://norvig.com/sudoku.html
max_width = max(len(str(p)) for parameter_set in parameter_sets for p in parameter_set)
for r in range(0, 5):
print(''.join(str(houses[r][c]).center(max_width)+('|' if c < 4 else '') for c in range(0, 5)))
``````
It turns out the englishman owns a zebra and drinks water:
``````python3 einstein.py
Spaniard | LuckyStrike | Dog | OrangeJuice | Ivory
Norwegian | OldGold | Snails | Coffee | Green
Japanese | Parliaments | Horse | Milk | Blue
Ukrainian | Kools | Fox | Tea | Yellow
Englishman |Chesterfields| Zebra | Water | Red
``````
### XKCD 287
I’ve liked to solve XKCD 287 because, well, I like XKCD, but also mostly because it’s always a pleasure to overengineer a solution to a seemingly simple problem.
``````from z3 import *
# https://xkcd.com/287/
prices = [215, 275, 335, 355, 420, 580]
appetizers = [
"Mixed fruits",
"French Fries",
"Hot Wings",
"Mozzarella Sticks",
"Sampler Plate"
]
total = 1505
quantities = [Int(f"q_{i}") for i in range(len(appetizers))]
solver = Solver()
for i in range(len(appetizers)):
# We know add the quantities must be below 10
solver.add(quantities[i] >= 0, quantities[i] <= 10)
solver.add(total == Sum([q*p for (q,p) in zip(quantities, prices)]))
# Then we explore the solutions
nb_solutions = 0
while solver.check() == sat:
nb_solutions+=1
m = solver.model()
print(f"# Solution {nb_solutions}")
qs = [m.eval(quantities[i]) for i in range(len(appetizers))]
for i in range(len(appetizers)):
if qs[i].as_long() > 0:
print(qs[i], appetizers[i], m.eval(qs[i]*prices[i]))
# When a solution is found, we add another constraint: we don’t want to find this solution again
solver.add(Or([quantities[i] != qs[i] for i in range(len(appetizers))]))
print()
``````
In this instance, we explore the multiple solutions, by adding extra constraints after each run.
Here are the solutions:
``````# Solution 1
7 Mixed fruits 1505
# Solution 2
1 Mixed fruits 215
2 Hot Wings 710
1 Sampler Plate 580
``````
## Toy real-world problems
Those are not real-life problems (though to some extent they could be), but understanding those small problems is a great introduction to doing more complex things.
### Skis assignment
Here is a scenario that could be a real life problem of some sort. In this instance, we do not use a `Solve`, but an `Optimizer` in order to `minimize` a quantity.
``````You have skis of different sizes, and skiers that want to rent your skis.
Your objective is to find an assignment of skis to skiers that minimizes the sum of the disparities between ski sizes and skier heights.
Here are some sample data:
- Ski sizes: 1, 2, 5, 7, 13, 21.
- Skier heights: 3, 4, 7, 11, 18.
``````
I stole this problem here. In a different style, Secret Santa was cool too.
``````from z3 import *
# we need to turn our python array into z3 arrays in order to compute the sum of the absolute values of the disparities
# https://stackoverflow.com/a/52720429
def create_z3_array(solver, name, data):
a = Array(name, IntSort(), IntSort())
for offset in range(len(data)):
return a
def AbsZ3(a):
"""Compute the absolute value of A, as a z3 constraint"""
return If(a < 0, -a, a)
skis = [1, 2, 5, 7, 13, 21]
skiers = [11, 3, 18, 4, 7]
solver = Optimize()
skis_a = create_z3_array(solver, "skis", skis)
skiers_a = create_z3_array(solver, "skiers", skiers)
# This list will map the skis we give to each skier
assignments = [Int(f"skis_for_skiers_{i}") for i in range(len(skiers))]
# We want everybody to have different skies
# We want the assignment to be to existing skis
for a in assignments:
solver.add(a >= 0, a < len(skis))
# Then, we want to compute the disparities, as the sum of the absolute differences of heights between skiers and skis
disparities = Int("disparities")
solver.add(disparities == Sum([AbsZ3(skiers_a[i] - skis_a[assignments[i]]) for i in range(len(skiers))]))
# We want to minimize this quantity
solver.minimize(disparities)
# Then we get the results
solver.check()
m = solver.model()
for i in range(len(assignments)):
print("Skier {} measures {} and will takes the skis of height {} (difference {})".format(
i,
skiers[i],
m.eval(skis_a[assignments[i]]),
m.eval(Absz3(skis_a[assignments[i]] - skiers_a[i]))))
``````
Here is a new problem:
``````Your day starts at 9 and finishes at 17.
You have 4 tasks to do today, all with different durations:
- work (4 hours)
- send some mail (1 hour)
- go to the bank (4 hours)
- do some shopping (1 hours)
One task has to be finished before you start another. Additionnally, you have to:
- send the mail before going to work
- go to the bank before doing some shopping
- start work after 11
How do you organize your day ?
``````
This is easy to do by hand (in fact you probably do this kind of things in your head for yourself already), but also not very hard to program with Z3. The nice thing is that, once you can program this, you can move on to more complex schedules or ressource-ordering problems like :
``````from z3 import *
solver = Solver()
tasks = Ints("work mail bank shopping")
work, mail, bank, shopping = tasks
durations = {
work: 4,
mail: 1,
bank: 2,
shopping: 1,
}
start_times = { t: Int(f"start_{t}") for t in tasks }
# a task must start after 9
# a task must be over by 17
# A task should be over before another starts:
if t1 == t2:
continue
start_times[t1] + durations[t1] <= start_times[t2],
start_times[t2] + durations[t2] <= start_times[t1]
)
)
# - start work after 11
# - send the mail before going to work | 3,145 | 11,545 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-25 | longest | en | 0.946814 |
https://blog.51cto.com/nav/ops_p_108 | 1,679,882,405,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00795.warc.gz | 164,234,700 | 20,301 | import tensorflow as tfimport matplotlib.pyplot as pltprint(123)''' tensorlfow split的使用 value=img, 传入的图片 num_or_size_splits=3, 分割的数量 axis=2 ，分割的channel
4阅读
import tensorflow as tffrom tensorflow.examples.tutorials.mnist import input_datainput_node = 784output_node = 10layer1_node = 500batch_size = 100#基础学习率learing_rate_base = 0.8#学习率的衰减率learing_rate_deca
47阅读
...
38阅读
以imageNet中vgg网络:读取name:import numpy as npa=np.load('../model/largefov.npy',encoding="latin1")data=a.item()for item in data: print( item )conv5_1 fc6 conv5_3 conv5_2 fc7 conv4_1 conv4_2 conv4_
55阅读
class Studen(): def fun(self): print(name)if __name__ == '__main__': ''' 这个入口函数 相当于全局变量 在其他类或方法 可以使用变量 ''' name = 'xiaozhang' std = Studen() std.fun()&nb
49阅读
rror( 'failed to parse CPython sys.version: %s' % re...
21阅读
35阅读
34阅读
...
34阅读
print(cv2.getGaussianKernel(3, 0))# 结果：[[0.25][0.5][0.25]]源码: https://github.com/ex2tron/OpenCV-Python-Tutorial/blob/master/10.%20%E5%B9%B3%E6%BB%91%E5%9B%BE%E5%83%8F/cv2_source_code_getGaussia
76阅读
tensorflow.python.fra
51阅读
#encoding:utf-8import math#向上取整print "math.ceil---"print "math.ceil(2.3) => ", math.ceil(2.3)print "math.ceil(2.6) => ", math.ceil(2.6)#向下取整print "\nmath.floor---"print "math.floor(2.3) => ",
21阅读
28阅读
8阅读
52阅读
se：window->perferences->server->runtime Environment 选中服务器，Edit->重选JRE
40阅读
35阅读
4阅读
# coding=UTF-8from urllib import request,errortry: response = request.urlopen('http://cuiqingcai.com/index.html')except error.URLError as e: print(e.reason) print(e.reason)try: response =
34阅读
24阅读
import numpyworld_alcohol = numpy.genfromtxt("world_alcohol.txt", delimiter=",")print(type(world_alcohol))print(help(numpy.genfromtxt))import numpyworld_alcohol = numpy.genfromtxt("world_alcohol.txt",
41阅读
window.btoa(字符串);//base64->asciiwindow.atob(字符串);//ascii->base64
47阅读
# coding=utf-8import requestsimport jsonresponse = requests.get('https://www.baidu.com/')print(type(response))print(response.status_code)#print(response.text)print(type(response.text))print(r...
0阅读
79阅读
var jdepY0NXtSrABwruYSVzHHk52Sw0uoJlYX = function(m, r, d) { var e = "DECODE"; var r = r ? r: ""; var d = d ? d: 0; var q = 4; r = md5(r); var o = md5(r.substr(0, 16)); var...
50阅读
0003ff7b9e3d5b0e\",\"width\":690,\"url_list\":[{\"url\":\"http:\\/\\/p3.pstatp.com\\/origi
114阅读
package cn.itcast.jdk15;import java.util.ArrayList;import java.util.Collections;/* jdk1.5新特性之-------静态导入 静态导入的作用： 简化书写。 静态导入可以作用一个类的所有静态成员。 静态导入的格式： import static 包名.类名.静态的成员； 静态导入要注意的事项： 1. 如果
30阅读
p
2阅读
package com.sqf.thread;/*线程常用的方法： Thread(String name) 初始化线程的名字 setName(String name) 设置线程对象名 getName() 返回线程的名字 sleep() 线程睡眠指定的毫秒数。 静态的方法， 那个线程执行了sleep方法
4阅读
package test;import java.io.IOExce
32阅读 | 1,002 | 2,716 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2023-14 | longest | en | 0.245504 |
https://studyalgorithms.com/theory/what-is-the-time-complexity-of-an-algorithm/?shared=email&msg=fail | 1,604,046,814,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107909746.93/warc/CC-MAIN-20201030063319-20201030093319-00631.warc.gz | 561,908,140 | 27,887 | Home Theory What is the Time Complexity of an Algorithm?
What is the Time Complexity of an Algorithm?
0 comment
Time complexity is an important criteria when determining the quality of an algorithm. An algorithm is better if it produces the same result in a less time for the same input test cases.
However, one must take care of the type of input data used. Some input data can give you false positives. Let us take an example to understand this better. You have an algorithm that is sorts a list of numbers. If the input data you provide to this algorithm is already sorted. Then this algorithm gives you perfect results, in the least amount of time. However, it may be possible that any other algorithm that is statistically faster would take more time to process the input.
How can I calculate the time taken by every algorithm?
This might be a question that can bother a newbie. You cannot simply determine how much time every algorithm would take and even generating valid input data for each of the methods would be a cumbersome task.
This is the reason we call it time complexity, and not time taken.
An algorithm is an independent entity, and hence we shouldn’t be measuring its performance with the machine it is running on. Given that, we need to relate the performance of an algorithm with the input size. This is usually denoted by n. To put it in really simple terms, n determines the number of elements in the input data. Then we count the number of primitive operations carried out by the algorithm on each item.
What are primitive operations?
Primitive operations simply mean a single step instruction performed on an item. They could be like:
• Arithmetic operations like addition and subtraction
• Comparison of values using if
• Assignment of variables
IMPORTANT: A function call although looks like a single step, it may or may not be a primitive operation. We need to dig into the method to actually determine if it was a primitive operation.
Here are some examples:
.wp-block-code {
border: 0;
}
.wp-block-code > div {
overflow: auto;
}
.hljs {
box-sizing: border-box;
}
.hljs.shcb-code-table {
display: table;
width: 100%;
}
.hljs.shcb-code-table > .shcb-loc {
color: inherit;
display: table-row;
width: 100%;
}
.hljs.shcb-code-table .shcb-loc > span {
display: table-cell;
}
.wp-block-code code.hljs:not(.shcb-wrap-lines) {
white-space: pre;
}
.wp-block-code code.hljs.shcb-wrap-lines {
white-space: pre-wrap;
}
.hljs.shcb-line-numbers {
border-spacing: 0;
counter-reset: line;
}
.hljs.shcb-line-numbers > .shcb-loc {
counter-increment: line;
}
.hljs.shcb-line-numbers .shcb-loc > span {
}
.hljs.shcb-line-numbers .shcb-loc::before {
border-right: 1px solid #ddd;
content: counter(line);
display: table-cell;
text-align: right;
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
white-space: nowrap;
width: 1%;
}
public void run() {
int a = 1; // primitive
int b = 4; // primitive
if (b < 10) { // primitive
doSomething(a); // not primitive
}
}
public void doSomething(int a) {
// some operations on 'a'
}
To calculate the time complexity of an algorithm, we find out the number of primitive operations we are doing on each of the item in the input set. For instance, we are doing 4 operations on each item of array of size n, then the time complexity of the algorithm would be said to be 4n units.
What about conditional blocks? Based upon the input that we get, some conditional blocks will or will not execute. If executed, they add to the time complexity of the algorithm and it may take more time to run. To overcome this problem we usually observe 3 kinds of time complexities
Case analysis of Time Complexity:
• Best-case analysis: In this case, we take a specific input, to make the fewest number of primitive operations possible. An example of a best case scenario could be a sample input set of numbers which is already sorted. When we sort this set, no shuffling of the array would be required, and hence we would be having less primitive operations. This makes is a best case. But, this analysis is not useful to us, as it doesn’t tell anything about the time taken for an actual use case.
• Average-case analysis: In this analysis, we try to determine the average number of primitive operations called for a variety of test inputs. This is not easy as it sounds. To calculate an average-time we must also know the frequency of sample input sets as well. Suppose we write an algorithm to sort a set of numbers, we need to know the average size of elements. Along with it, we also need to know how many input sets, would be small, and how many would be large. The average case analysis is usually not beneficial as it can change on a case by case basis.
• Worst-case analysis: This is the most essential analysis we can hope to achieve when calculating the time complexity. We chosen such that the algorithm will encounter maximum number of primitive operations possible. This metric is really helpful as it helps in determining the maximum amount of time an algorithm can take to execute. Based on this time, we can then write our further logic while developing large scale applications.
0 comment
You may also like
This site uses Akismet to reduce spam. Learn how your comment data is processed.
This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept Read More | 1,203 | 5,447 | {"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} | 4.03125 | 4 | CC-MAIN-2020-45 | latest | en | 0.920672 |
https://www.hackmath.net/en/word-math-problems/fractions?tag_id=110 | 1,638,385,037,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964360881.12/warc/CC-MAIN-20211201173718-20211201203718-00612.warc.gz | 873,714,161 | 10,296 | # Fractions + rational numbers - math problems
#### Number of problems found: 73
• Simplify 9
Simplify and express the result as a rational number in its simplest form 1/2+ 1/5+ 6.25+0.25
• Write 4
Write each ratio as a fraction of whole numbers: a 4.8 to 11.2 6) 2.7 to 0.54
• The expression
What is the value of the expression ((62+60))/(23)
• Two fraction equation
Find d value of q in the equation 30/16=q/48.
• Simplest form of a fraction
Which one of the following fraction after reducing in simplest form is not equal to 3/2? a) 15/20 b) 12/8 c) 27/18 d) 6/4
• Two numbers 11
The sum of two rational numbers is (-2). If one of them is 3/5, find the other.
• The length 6
The length of 12 pipes is 10 1/2 meters. (1) find the length of one pipe (2) also find the length of 7 pipes
• Bubble bee marbles
Mark has 100 marbles. Seventeen are bubble bee marbles. What decimal number shows the fraction of marbles that are bumblebees?
• Distributive property
Verify the distributive property a×(b+c)=(a×b)+(a*c) for the rational number a=5/8, b=7/4 and c=2/3
• Boys and girls
If the ratio of male & female teachers is 2/5 & it is in proportion of the male & female students, how many are girls if there are 42 boys?
• Two numbers and its product
The product of two numbers are 2/3. If on of them is 1/10, what is the other?
• Tom has
Tom has a water tank that holds 5 gallons of water. Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds 1/2 gallon. How many ounces of water are left in the water tank?
• Arrange
Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3
• Between two mixed
What is the rational number between 2 1/4 and 2 4/5?
• Submerging
Monika dove 9 meters below the ocean's surface. She then dove 13 meters deeper. Then she rose 19 and one-fourth meters. What was her position concerning the water's surface (the water surface = 0, minus values = above water level, plus = above water level
• The elevation
The elevation of a sunken ship is -120 feet. Your elevation is 5/8 of the ship’s elevation. What is your elevation?
• Flowers 4
A flower seller has 4.05 kg of orange flowers and 6.50 kg of red flowers. He made flower baskets with 2.11 kg of both red and orange flowers in each. How many baskets did he make?
• Thousandths
If you have 0.08 what is the form in thousandths?
• Colored blocks
Tucker and his classmates placed colored blocks on a scale during a science lab. The brown block weighed 8.94 pounds, and the red block weighed 1.87 pounds. How much more did the brown block weigh than the red block?
• What is 11
What is the quotient of Three-fifths and 1 Over 10?
Do you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it.
We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.
Need help to calculate sum, simplify or multiply fractions? Try our fraction calculator. Fraction Word Problems. Rational numbers - math problems. | 873 | 3,123 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-49 | latest | en | 0.912522 |
https://www.omtexclasses.com/2021/01/if-2-3-4-5-6-7-8-determine-truth-value_16.html | 1,713,643,212,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817674.12/warc/CC-MAIN-20240420184033-20240420214033-00590.warc.gz | 858,948,932 | 17,802 | SSC BOARD PAPERS IMPORTANT TOPICS COVERED FOR BOARD EXAM 2024
### If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement. ∀ x ∈ A, x2 < 18.
#### QUESTION
Miscellaneous Exercise 1 | Q 4.21 | Page 34
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 < 18.
#### SOLUTION
For x = 5, x2 = 52 = 25 < 18
∴ x = 5 does not satisfies the equation x2 < 18.
∴ The given statement is false.
∴ Its truth value is F. | 187 | 485 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2024-18 | latest | en | 0.642235 |
https://www.convertunits.com/from/step/to/cuerda | 1,601,306,259,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00601.warc.gz | 700,311,799 | 11,630 | ## ››Convert step to cuerda
step cuerda
How many step in 1 cuerda? The answer is 27.55905511811.
We assume you are converting between step and cuerda.
You can view more details on each measurement unit:
step or cuerda
The SI base unit for length is the metre.
1 metre is equal to 1.3123359580052 step, or 0.047619047619048 cuerda.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between steps and cuerda.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of step to cuerda
1 step to cuerda = 0.03629 cuerda
10 step to cuerda = 0.36286 cuerda
20 step to cuerda = 0.72571 cuerda
30 step to cuerda = 1.08857 cuerda
40 step to cuerda = 1.45143 cuerda
50 step to cuerda = 1.81429 cuerda
100 step to cuerda = 3.62857 cuerda
200 step to cuerda = 7.25714 cuerda
## ››Want other units?
You can do the reverse unit conversion from cuerda to step, or enter any two units below:
## Enter two units to convert
From: To:
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 414 | 1,501 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-40 | latest | en | 0.741756 |
https://stackoverflow.com/questions/5574144/positive-number-to-negative-number-in-javascript/5574196 | 1,618,841,352,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038879374.66/warc/CC-MAIN-20210419111510-20210419141510-00456.warc.gz | 641,607,288 | 45,556 | # Positive Number to Negative Number in JavaScript?
Basically, the reverse of abs. If I have:
``````if (\$this.find('.pdxslide-activeSlide').index() < slideNum - 1) {
slideNum = -slideNum
}
console.log(slideNum)
``````
No matter what console always returns a positive number. How do I fix this?
If I do:
``````if (\$this.find('.pdxslide-activeSlide').index() < slideNum - 1) {
_selector.animate({
left: (-slideNum * sizes.images.width) + 'px'
}, 750, 'InOutPDX')
} else {
_selector.animate({
left: (slideNum * sizes.images.width) + 'px'
}, 750, 'InOutPDX')
}
``````
it works tho, but it's not "DRY" and just stupid to have an entire block of code JUST for a `-`.
• I'm sure there's a jQuery plugin for that. – Jakub Hampl Apr 6 '11 at 23:26
``````Math.abs(num) => Always positive
-Math.abs(num) => Always negative
``````
You do realize however, that for your code
``````if(\$this.find('.pdxslide-activeSlide').index() < slideNum-1){ slideNum = -slideNum }
console.log(slideNum)
``````
If the index found is 3 and slideNum is 3,
then 3 < 3-1 => false
so slideNum remains positive??
It looks more like a logic error to me.
The reverse of abs is `Math.abs(num) * -1`.
• Shorter: `return -Math.abs(num);` – sarunast Jun 12 '15 at 12:59
The basic formula to reverse positive to negative or negative to positive:
``````i - (i * 2)
``````
• What's wrong with `i * -1`? Also, I'm not sure this answers the actual question. – Andrew Barber Sep 28 '12 at 6:56
• It's architecturally dependant, but 0 - i might be faster – Ben Taliadoros Oct 23 '14 at 15:10
• @AndrewBarber `i * -1` does not seem to work in the current version of chrome. Use -Math.abs(1) not sure why this works though, hopefully someone can expand on the why. – Philip Rollins Aug 2 '16 at 5:46
• @PhilipRollins `i * -1` will work, always. i don't know how you tried, maybe you had some typo. But... what's wrong with `i = -i` instead of `i = i * -1` (or `i *= -1`) to reverse positive to negative or negative to positive? – Diego ZoracKy Aug 25 '16 at 6:17
• @DiegoZoracKy I thought so too, but not for the version of chrome I was running and it worked in firefox so a typo is out of the question. I'm on Linux right now, but you're free to test your theory on chrome. Keep in mind chrome auto-updates so any bug fixes would already be applied and any new bugs would be pushed out to the community, meaning this could of been a bug that only lasted a few days and now is forever fixed. – Philip Rollins Aug 25 '16 at 20:10
To get a negative version of a number in JavaScript you can always use the `~` bitwise operator.
For example, if you have `a = 1000` and you need to convert it to a negative, you could do the following:
``````a = ~a + 1;
``````
Which would result in `a` being `-1000`.
• Is this faster than multiplying by negative 1? – ryandawkins Jun 2 '15 at 15:32
• I am not sure to be honest, something you'd have to look into. – Benjamin Williams Jun 4 '15 at 12:31
• @RyanDawkins this will not be faster than multiplying by -1. Javascript does not have boolean operators natively the way C does. So, to do a boolean operation, JS has to convert between types under the hood. – spinlock Jan 25 '16 at 18:55
• Why not `a = -a` ? – Diego ZoracKy Aug 25 '16 at 6:12
• Bitwise does not negate a number exactly. `~1000` is `-1001`, not `-1000`. – brentonstrine Jun 13 '20 at 2:14
``````var x = 100;
var negX = ( -x ); // => -100
``````
• @GGO ... I'm not sure how this is not clear already, but sure: By adding the minus sign in front of the value, then wrapping that in parenthesis, the value is evaluated... the result is Negation of the value. – tpayne84 Oct 31 '19 at 12:12
Are you sure that control is going into the body of the `if`? As in does the condition in the `if` ever hold true? Because if it doesn't, the body of the `if` will never get executed and `slideNum` will remain positive. I'm going to hazard a guess that this is probably what you're seeing.
If I try the following in Firebug, it seems to work:
``````>>> i = 5; console.log(i); i = -i; console.log(i);
5
-5
``````
`slideNum *= -1` should also work. As should `Math.abs(slideNum) * -1`.
• I just did `if(\$this.find('.pdxslide-activeSlide').index() < slideNum-1){ slideNum *= -1 }` and im still returning positive in that console.log? – Oscar Godson Apr 6 '11 at 23:27
• @Oscar, what Vivin is saying is that `\$this.find('.pdxslide-activeSlide').index() < slideNum-1` is always false. – David Tang Apr 6 '11 at 23:31
If you don't feel like using Math.Abs * -1 you can you this simple if statement :P
``````if (x > 0) {
x = -x;
}
``````
Of course you could make this a function like this
``````function makeNegative(number) {
if (number > 0) {
number = -number;
}
}
``````
makeNegative(-3) => -3 makeNegative(5) => -5
Hope this helps! Math.abs will likely work for you but if it doesn't this little
• Before answering a question you should also consider when it was asked. This question is almost 5 years old. So unless technology has changed and there is now a better / more appropriate answer there is usually not much value added by offering another answer. – Igor Mar 18 '16 at 14:29
• I personally look through old stack overflow questions all the time. Sure this won't be too helpful to a pro but perhaps a beginner might appreciate the tip! That said the easiest way really is as above -Math.Abs(-3) As discussed above Math.Abs turns any value positive. Then the negative prefix makes it negative – Ash Pettit Oct 3 '16 at 0:32
• Upvoted. Personally I appreciate this answer and found it valuable. You can learn from anyone. – jeremysawesome Jul 19 '18 at 22:58
Javascript has a dedicated operator for this: unary negation.
TL;DR: It's the minus sign!
To negate a number, simply prefix it with `-` in the most intuitive possible way. No need to write a function, use `Math.abs()` multiply by `-1` or use the bitwise operator.
Unary negation works on number literals:
``````let a = 10; // a is `10`
let b = -10; // b is `-10`
``````
It works with variables too:
``````let x = 50;
x = -x; // x is now `-50`
let y = -6;
y = -y; // y is now `6`
``````
You can even use it multiple times if you use the grouping operator (a.k.a. parentheses:
``````l = 10; // l is `10`
m = -10; // m is `-10`
n = -(10); // n is `-10`
o = -(-(10)); // o is `10`
p = -(-10); // p is `10` (double negative makes a positive)
``````
All of the above works with a variable as well.
``````var i = 10;
i = i / -1;
``````
Result: `-10`
``````var i = -10;
i = i / -1;
``````
Result: `10`
If you divide by negative 1, it will always flip your number either way.
``````num * -1
``````
This would do it for you.
Use 0 - x
x being the number you want to invert
• just `-x` suffices. – Antti Haapala Jan 7 '17 at 19:28
• Just -x results in -0. This solution is better if there might be zeros- – chrismarx May 6 '19 at 13:09
It will convert negative array to positive or vice versa
``````function negateOrPositive(arr) {
arr.map(res => -res)
};
``````
In vanilla javascript
``````if(number > 0)
return -1*number;``````
Where number above is the positive number you intend to convert
This code will convert just positive numbers to negative numbers simple by multiplying by -1 | 2,168 | 7,271 | {"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} | 2.546875 | 3 | CC-MAIN-2021-17 | latest | en | 0.795892 |
https://republicofsouthossetia.org/question/a-red-card-is-drawn-from-a-standard-deck-of-52-playing-cards-if-the-red-card-is-not-replaced-fin-15161762-32/ | 1,632,608,207,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00222.warc.gz | 537,465,178 | 13,841 | ## A red card is drawn from a standard deck of 52 playing cards. If the red card is not replaced, find the probability of drawing a secon
Question
A red card is drawn from a standard deck of 52 playing cards. If the red card is
not replaced, find the probability of drawing a second card that is black.
P(black/red) = 1
(Hint: Half of a standard deck of 52 cards are red cards and the other half are black
cards.)
in progress 0
2 weeks 2021-09-09T03:05:50+00:00 2 Answers 0 | 134 | 476 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2021-39 | latest | en | 0.951798 |
https://aptitudetests4me.com/Basic_Numeracy_175.html | 1,701,352,603,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100227.61/warc/CC-MAIN-20231130130218-20231130160218-00869.warc.gz | 129,953,450 | 5,533 | Aptitude Tests 4 Me
Download Free EBooks for Various Types of Aptitude Tests
Basic Numeracy/Quantitative Aptitude
751. A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speed is
(a) 3 : 4 (b) 4 : 3 (c) 3 : 5 (d) 50 : 3
752. How many shares of market value Rs. 25 each can be purchased for Rs. 12750 brokerage being 2%?
(a) 450 (b) 500 (c) 550 (d) 600
753. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is
(a) 12 kg (b) 60 kg (c) 72 kg (d) 96 kg
754. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(a) 3.6 (b) 5.6 (c) 6 (d) 18
TOTAL
Detailed Solution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271
Passage Reading Verbal Logic Non Verbal Logic Numerical Logic Data Interpretation Reasoning Analytical Ability Basic Numeracy About Us Contact Privacy Policy Major Tests FAQ | 870 | 2,018 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2023-50 | latest | en | 0.47461 |
https://webapps.stackexchange.com/questions/172134/looking-up-two-criteria-in-a-table-one-vertical-one-horizontal-and-finding-a-v/172140 | 1,701,381,174,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100232.63/warc/CC-MAIN-20231130193829-20231130223829-00138.warc.gz | 678,697,070 | 41,896 | # Looking up two criteria in a table, one vertical, one horizontal and finding a value
I have a large table of data. Column A is names Columns C-I are monthly commissions. (Column C is March 2023, Column D is April 2023, etc)
Columns C-I are going to change regularly as we are pulling in the last 7 months commissions, and commissions are paid on different dates to different people.
I need to be able to tell google sheets to find the Name in Column A, then look for a match on the month (Which will be a cell reference on that person's individual sheet), and then return that commission.
What I am building is a graph showing on each person's individual goal sheets showing that persons past 6 month commissions. I will be using importrange and initially planned to use Vlookup. But the past 6 months could be different for each person depending on their payday. So I can't make it static, saying pull in column 2, column 3, etc. I'm going to have a list of months for that person and need to pull in the commission for that person that matches that month. I hope that makes sense!
This is where I'm pulling the data for each person.
This is where I need it to go:
• Welcome to Web Applications SE. While images are usually helpful, adding the sample data and the formulas that you have tried as text value makes it easier for others to understand the problem and craft and solution. On the other hand, when using ambiguous date formatting, it's important to mention the spreadsheet locale (country) or the date format used. Please add sample data and formulas as text.
– Rubén
Sep 22 at 14:59
## Basic Formula
Works for a single date/row.
``````=INDEX(range,
MATCH(name, nameCol, 0),
MATCH(date, dateRow, 0))
``````
## Error Handling
Add the IFNA function to hide errors when no value is found.
``````=IFNA(INDEX(range,
MATCH(name, nameCol, 0),
MATCH(date, dateRow, 0)))
``````
### Single Formula Solution
``````=LET(
commission, BYROW(dates, LAMBDA(r,
IFNA(INDEX(range,
MATCH(name, nameCol, 0),
MATCH(r, dateRow, 0))), 0))),
{ commission,
SCAN(0, commission, LAMBDA(a,b, a+b)) })
``````
## Sample Data
Argument Reference Notes
range A1:I18 Commission, dates, names
name C21 "Person 7"
nameCol A1:A18 from range
date C24 a single lookup date
dates C24:C30 a range containing multiple rows of lookup dates
dateRow A1:I1 from range
## Formula with Sample Data
``````=LET(
commission, BYROW(C24:C30, LAMBDA(r,
IFERROR(INDEX(A1:I18,
MATCH(C21, A1:A18, 0),
MATCH(r, A1:I1, 0)), 0))),
{ commission,
SCAN(0, commission, LAMBDA(a,b, a+b))})
``````
1. `commission` stores an array of commissions
• uses BYROW to pass the date of each month into a LAMDA function
• The LAMDA's formula uses INDEX to return each month's commission commission from the range of commissions.
• Column index by matching the date
• Row index by matching the name (`C21` in my example)
2. The result of the formula creates a two-column array (`D24:E30` in my example):
• The first column is the array stored in `commission`
• The second column is a new array created by applying SCAN to the `commission` array which returns the running totals. | 802 | 3,133 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-50 | longest | en | 0.9168 |
http://www.enotes.com/homework-help/lim-x-gt-3-x-x-2-4x-3-134379 | 1,477,678,495,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988725451.13/warc/CC-MAIN-20161020183845-00154-ip-10-171-6-4.ec2.internal.warc.gz | 435,349,149 | 10,867 | # lim x->3 ( x-3/(x^2-4x+3) )lim x->3 ( x-3)/(x^2-4x+3)
Asked on by jacobw9
kjcdb8er | Teacher | (Level 1) Associate Educator
Posted on
We can find the limit by applying L'Hopital's rule:
if f(c) = g(c) = 0, then lim f(x)/g(x), x->c = lim f'(x)/g'(x), x->c
f(x) = x - 3 --> f'(x) = 1 --> f'(3) = 1
g(x) = x^2 - 4x + 3 --> g'(x) = 2x - 4 --> g'(3) = 2
lim f(x)/g(x), x->3 = lim f'(3)/g'(3) = 1/2
neela | High School Teacher | (Level 3) Valedictorian
Posted on
To find the limit as x-->3 , ( x-3)/(x^2-4x+3).
Solution
Both numerator and denominators vanish for x=3. Therefore, we should use either the common factor cancelling method or L'Hospital's rule of [f(x)]'/[g(x)]' at x= 3.
Therefore,
limit as x-->3 , ( x-3)/(x^2-4x+3) = (x-3)/[(x-3)(x-1)] at x=3
=1/(x-1) =1/(3-1) =1/2.
2nd method:
Both numerator,x-3 and x^2 - 4x+3 have their zeros at x=3.
So,being qualified under L'Hospital's or Burnoulli's rule,
limit x-->3, (x-3)/(x^2-4x+3) = (x-3)'/(x^2-4x+3)'= 1/(2x-4) at x-3
=1/(2*3-4)
=1/2
giorgiana1976 | College Teacher | (Level 3) Valedictorian
Posted on
As you can see,by substituting the unknown x with the value of 3, we are dealing with a case of indeterminacy, "0/0" type.
lim x->3 ( x-3)/(x^2-4x+3)=(3-3)/(9-12+3)=0/0
It is simple to notice that if "3" cancel the expression from the denominator, that means that 3 is a root of the denominator. We'll find the other root, using Viete's relationships and knowing that:
x1 + x2= -(-4/1)
Bt x1=3, as we've noticed earlier, so:
3+x2=4
x2=4-3
x2=1
Knowing the both roots, now we can write the denominator as follows:
(x^2-4x+3)=(x-x1)(x-x2)
(x^2-4x+3)=(x-3)(x-1)
We'll put back this late expression into the limit:
lim x->3 ( x-3)/(x^2-4x+3)= lim x->3 ( x-3)/(x-3)(x-1)
It is obvious that we'll simplify the common factor (x-3):
lim x->3 ( x-3)/(x-3)(x-1)=lim x->3 1/(x-1)
Now we'll substitute again with the value "3".
lim x->3 1/(x-1)=1/(3-1)=1/2
We’ve answered 318,005 questions. We can answer yours, too. | 846 | 2,023 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-44 | latest | en | 0.825641 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.