url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3
values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93
values | snapshot_type stringclasses 2
values | language stringclasses 1
value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://www.physicsforums.com/threads/calculating-precipitate-mass-how-much-can-form-in-a-chemical-reaction.534386/ | 1,723,008,895,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640682181.33/warc/CC-MAIN-20240807045851-20240807075851-00713.warc.gz | 726,798,420 | 17,730 | # Calculating Precipitate Mass: How Much Can Form in a Chemical Reaction?
• melxo
In summary, the question involves determining the maximum amount of precipitate that can form in a reaction between 24.8 g of BA(No3)2 and 25 mL of 0.329 M Na2So4. To solve this, you must first calculate the moles of each reactant and determine the limiting reactant. Then, using the reaction equation and the ratio of reactants to products, you can solve for the maximum amount of precipitate formed."
melxo
I have a question in my Chemistry homework that has to do with precipitates. Theres nothing in my notes what so ever and I ont remember my prof going over any of this. Any help would be appreciated, thanks!
Question:
24.8 g of BA(No3)2 were dissolved in enough water to make 150mL of solution. To this, 25 mL of 0.329 M Na2So4 was added and a precipitate formed.
What is the maximum amount of precipitate, in grams, that can form in this reaction?
so far I have...
moles Ba(NO3)2=24.8 g (1 mole/261.32g)=.0949
moles NA2(SO4)= .025L(.329M)=.008225 mol which is the limiting reactant
now what do i do?! and please don't just give me the answer!
What is the precipitate formed?
What is the ratio of reactants to products? (e.g. if A + 2B --> B2A, then B : B2A is 2 : 1)
Knowing this you can solve.
And post this type of the questions in the homework subforum. I am moving the thread.
## What is precipitate mass?
Precipitate mass refers to the amount or weight of solid material that forms when a chemical reaction occurs between two or more substances in a solution.
## How is precipitate mass measured?
Precipitate mass can be measured using a balance or scale that is sensitive enough to detect small changes in weight. The precipitate is typically filtered out of the solution and then dried before being weighed.
## What factors can affect precipitate mass?
The amount and concentration of the reactants, temperature, and the presence of other substances in the solution can all affect the amount of precipitate that forms and its mass.
## Why is measuring precipitate mass important in scientific experiments?
Precipitate mass is an important factor to measure in chemical reactions because it can provide information about the rate and extent of the reaction, as well as the identity and properties of the products formed.
## How can precipitate mass be used in industrial processes?
Precipitate mass is often used in industrial processes to monitor and control chemical reactions, such as in wastewater treatment or the production of pharmaceuticals. By accurately measuring the precipitate mass, companies can ensure the efficiency and quality of their products and processes.
• Biology and Chemistry Homework Help
Replies
14
Views
9K
• Chemistry
Replies
6
Views
2K
• Biology and Chemistry Homework Help
Replies
1
Views
2K
• Biology and Chemistry Homework Help
Replies
6
Views
4K
• Biology and Chemistry Homework Help
Replies
5
Views
2K
• Biology and Chemistry Homework Help
Replies
4
Views
2K
• Biology and Chemistry Homework Help
Replies
1
Views
3K
• Biology and Chemistry Homework Help
Replies
1
Views
1K
• Biology and Chemistry Homework Help
Replies
7
Views
2K
• Biology and Chemistry Homework Help
Replies
7
Views
2K | 783 | 3,239 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-33 | latest | en | 0.937345 |
http://www.1-script.com/forums/php/traversing-friends-graph-how-does-friendster-do-it-19479-.htm | 1,477,594,297,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721387.11/warc/CC-MAIN-20161020183841-00312-ip-10-171-6-4.ec2.internal.warc.gz | 287,195,637 | 16,994 | # Traversing Friends Graph - How does Friendster do it?
#### Do you have a question? Post it now! No Registration Necessary. Now with pictures!
• Subject
• Author
• Posted on
I'm not sure if this forum is the correct place to post this, but I
couldn't think of any other group. I would really appreciate any help
you could give me.
FINAL GOAL OF MY APPLICATION:
Building a friendster clone for a very large organization (10,000
people). I am using Php/Mysql.
SETUP OF SYSTEM:
(it may help if you are familiar with how friendster works)
Mathematically what I have is a graph, with around 10,000 nodes (each
node representing one person). Each of these nodes have an avg of appx
40 edges coming out from them going to other nodes in the graph.
I have implemented this graph in my database using two tables. One, I
have a Person table which assigns each person a ID. Then I have a table
called "Edge" that defines the edges. It has two cells in every row of
the table (each cell holds the ID of one of the two ends of an edge).
WHAT I WANT TO DO:
Starting at any node, I want to be able to (as quickly as possible)
calculate which nodes are up to 3 degrees of separation away from it.
This would be needed because I want to allow someone to search for
people within 3 degrees of distance away from themselves.
WHAT I HAVE TRIED:
I wrote a recursive function that starts at a certain node and just
traverses all the nodes that are a given distance away. I have done
optimizations to this function like keeping track of which nodes have
already been visited, and not revisiting them. On the site, I was
planning on running this function the first time someone does a search,
and then storing the results in the session so I wouldn't have to run
it again.
The problem is with a test database where each person has about 40
edges going from them to random nodes, it takes about 60 seconds to
calculate the 3rd degree friends. It is taking about 800 sql select
queries. 60 seconds however is WAY too slow...
Can someone explain to me, or take a stab at how friendster (or any
website like it, orkut, linkedin, hi5 etc) does it (their database is
far greater than mine). Friendster not only keeps track of WHO is up to
3 degrees away from you, but they also tell you ALL the paths between
you and any other person within those 3 degrees.
If you can come up with some smart way that I could solve my problem
(like maybe store everyone's 2nd degree friends before hand, or
something). I'm really stuck...any help would be GREATLY appreciated.
Thanks,
Timin
## Re: Traversing Friends Graph - How does Friendster do it?
Timin Uram wrote:
OK, here is an idea... Imagine a database table:
CREATE TABLE `knows` (
`who` int,
`whom` int,
KEY `who` (`who`),
KEY `whom` (`whom`)
) COMMENT='The Who Knows Whom Table'
So if the person whose data stored in another table under
ID number 1578 knows the person whose data stored in that
same table under ID number 8690, there would be two records
in the table `knows`:
===========
who whom
===========
1578 8690
8690 1578
===========
Now we need to figure out, say, who knows ID 6231 firsthand:
SELECT who FROM knows WHERE whom=6231;
Then, we can figure out the first degree of separation (i.e.,
who knows someone who knows 6231):
SELECT
k1.who AS who,
k2.who AS through,
k2.whom AS whom
FROM knows AS k1 LEFT JOIN knows AS k2 ON k1.whom=k2.who
WHERE k2.whom=6231;
Hopefully, this will return something like:
=========================
who through whom
=========================
4572 9421 6231
=========================
meaning, 4572 knows 6231 through 9421.
Now comes the second degree of separation:
SELECT
k1.who AS who,
k2.who AS through1,
k3.who AS through2,
k3.whom AS whom
FROM (knows AS k1 LEFT JOIN knows AS k2 ON k1.whom=k2.who)
LEFT JOIN knows AS k3 ON k2.whom=k3.who
WHERE k3.whom=6231;
And, finally, voila: the third degree:
SELECT
k1.who AS who,
k2.who AS through1,
k3.who AS through2,
k4.who AS through3,
k4.whom AS whom
FROM ((knows AS k1 LEFT JOIN knows AS k2 ON k1.whom=k2.who)
LEFT JOIN knows AS k3 ON k2.whom=k3.who)
LEFT JOIN knows AS k4 ON k3.whom=k4.who
WHERE k4.whom=6231;
Actually, you can write a function that would generate a query
automatically given the number of degrees of separation...
Cheers,
NC
## Re: Traversing Friends Graph - How does Friendster do it?
Hi NC, Thanks for your response. Thanks for your suggestion, and it
definitely cut down on the time, however, because of multiple joins,
the query still ends up taking about 20 seconds. It also doesn't take
loops into account (but that's ok because we're not infinitely
looping).
Are there any other optimizations possible...or something else, like
caching some information somehow? It seems like these friendster sites
do this pretty fast...is there something else possible?
Timin
NC wrote:
it.
## Re: Traversing Friends Graph - How does Friendster do it?
Timin Uram wrote:
???
A similar query I tested on a shared hosting with a table
of about 7500 records consistently completes in under one
second. Are you sure you have proper indexes in place?
Cheers,
NC
## Re: Traversing Friends Graph - How does Friendster do it?
NC wrote:
I have a table of about 100,000 edges (200,000 rows), and it is taking
about 20 seconds. I've tried it on two different servers (a local one,
and one on a shared host).
Another thing is that in a friendster type network, there is a
clustering effect where say 40 friends have most of each other in each
other's lists. This leads to a lot of loops (paths such as 8->7->8->9
for a path from 8 to 9). So maybe it's faster when there are completely
random connections...(but I wouldn't thinks so).
I also have an index on both of the primary keys (who and whom)
Is there anything else possible? Or do you there there is something
wrong with my setup?
## Re: Traversing Friends Graph - How does Friendster do it?
You can modify the queries to avoid loops, or at least minimize
them. Whether or not the added conditions take more time to check
than they do cut down the number of combinations, I don't know.
You will still get many combinations where there are multiple paths
between two people that don't involve loops.
Assuming you are doing a join of 4 instances of the "who knows whom"
table (k1, k2, k3, and k4), for a 3-degrees-of-separation query.
Assuming for the moment that nobody "knows" himself in the table
(and this is somehow enforced), you might want to put in the
conditions:
k1.who != k3.who
k1.who != k4.who and k2.who != k4.who
which prevents the same person showing up in the chain more than once.
Gordon L. Burditt
## Re: Traversing Friends Graph - How does Friendster do it?
Timin Uram wrote:
OK, let's try this:
1. Change your indexing. Right now, you have a primary
index based on both columns. Replace it with two non-
unique indexes, one for each column.
2. Rewrite the query like this:
SELECT
k1.who AS who,
k2.who AS through1,
k3.who AS through2,
k4.who AS through3,
k4.whom AS whom
FROM ((knows AS k1 LEFT JOIN knows AS k2 ON k1.whom=k2.who)
LEFT JOIN knows AS k3 ON k2.whom=k3.who)
LEFT JOIN knows AS k4 ON k3.whom=k4.who
WHERE k1.who = 6231
AND k3.who <> 6231
AND k4.who <> 6231
AND k4.whom <> 6231
My first post to this topic said "WHERE k4.whom=6231", which
created a lot of completely unnecessary overhead (my apologies
for not thinking about it sooner). This way, it runs MUCH
faster... Also, looping is taken care of by adding extra
WHERE clauses.
Cheers,
NC
## Re: Traversing Friends Graph - How does Friendster do it?
Timin Uram wrote:
Of course there is always something possible. You can get
better hardware (lots of it) and/or hire Jeremy Zawodny to
advise you on performance tuning and replication (the latter,
by the way, is exactly what Friendster did).
Cheers,
NC
## [OT] Re: Traversing Friends Graph - How does Friendster do it?
<snip>
Surprise. I'm reading J.Z's blog for sometime and might have missed
this news. Couldn't even find that in Google. Just curious, where did
you find this news?
--
<?php echo 'Just another PHP saint'; ?>
Email: rrjanbiah-at-Y!com Blog: http://rajeshanbiah.blogspot.com /
## Re: Traversing Friends Graph - How does Friendster do it?
R. Rajesh Jeba Anbiah wrote:
NC> hire Jeremy Zawodny to advise you on performance tuning and
NC> replication (the latter, by the way, is exactly what Friendster
NC> did).
It's not on the blog, it's in the "MySQL Stuff" section:
Consulting
I occasionally (as time permits) help out companies with their
MySQL needs. I specialize in performance tuning and replication
but can handle nearly all aspects of MySQL on Linux/Unix systems.
Here are some of my current and past clients.
Quest Software - Foglight group
Plaxo
CafeDVD
Friendster
Feedster LLC
Technorati
Spam Arrest LLC
Cloudmark
Rackspace
LiveJournal
Eight Days Inc.
Contact me for rates and availability.
http://jeremy.zawodny.com/mysql /
Cheers,
NC
## [OT]Re: Traversing Friends Graph - How does Friendster do it?
NC wrote:
did
<snip>
Thanks. Interesting, I missed it really. Now I wonder, why Yahoo
didn't fire him yet;)
--
<?php echo 'Just another PHP saint'; ?>
Email: rrjanbiah-at-Y!com Blog: http://rajeshanbiah.blogspot.com /
## Re: Traversing Friends Graph - How does Friendster do it?
wrote:
Here is what I tried.
Tables
----------
persons
pid serial // int4 with autoincrement
name varchar(32)
lid serial // int4 with autoincrement (not
required but I like to have uniq id
in all tables
parent int4
child int4
Then I filled the persons table with 10000 random names and then
I can then select all linked persons to used id 1201 with:
SELECT DISTINCT
pid
FROM
WHERE
(parentid IN (
WHERE (pid=childid AND parentid IN (
WHERE (pid=childid AND parentid=1201
))
)) AND pid=childid);
This takes about 1-2 secs on my PostgreSQL server and could be even
faster with indexes in links table.
- Allan Savolainen
## Re: Traversing Friends Graph - How does Friendster do it?
Hey, one thing is that my host has mysql version 4.0 which doesn't
support subqueries, but I can get around that by just doing each of
those queries separately, and then inserting those results in the ()
separated by commas individually.
However, I did try the query on my local server with mysql 4.1, and it
still took about 18 seconds. Here is an image of my table's setup from
Is something wrong with my setup or indexes?
## Re: Traversing Friends Graph - How does Friendster do it?
Timin Uram wrote:
Yes. Instead of creating two separate indexes for `who`
and `whom`, you created a single index for both fields.
This makes it difficult to join the table to itself on
copy1.who = copy2.whom.
Cheers,
NC
## Re: Traversing Friends Graph - How does Friendster do it?
hey timin,
i read your post. ya i've also been surfing the friendster and hi5. but
right now i'm writing to you to ask that do you have any idea that how
theirs Invitation works. You might be familiar about their invitation
program. Just give your msn/yahoo id and pasword, they just grabs all
the contacts of that id and sends an invitaion.
do you know how it works???
hope listen from you soon.
Sachin
## Re: Traversing Friends Graph - How does Friendster do it?
Hey Sachin, I don't know the exact answer for your query, but I can
guess that they are doing the same thing that 3rd party chatting
programs like trillian and gaim do.
Gaim is open source, so you could possibly look at the code for doing
that there. Friendster or hi5 must have this code running in the
backend.
Also note that gaim and trillian are not authorized to do what they do,
but for now, i think the chatting networks (msn, yahoo, aol) have just
given up trying to fight and are allowing third party chatting programs
on their network. | 3,136 | 11,841 | {"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} | 2.890625 | 3 | CC-MAIN-2016-44 | latest | en | 0.967863 |
https://en.m.wikipedia.org/wiki/Geometric_distribution | 1,670,323,766,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711077.50/warc/CC-MAIN-20221206092907-20221206122907-00489.warc.gz | 267,245,120 | 33,593 | # Geometric distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions:
• The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set ${\displaystyle \{1,2,3,\ldots \}}$;
• The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set ${\displaystyle \{0,1,2,\ldots \}}$.
Parameters Support Probability mass function Cumulative distribution function ${\displaystyle 0 success probability (real) ${\displaystyle 0 success probability (real) k trials where ${\displaystyle k\in \{1,2,3,\dots \}}$ k failures where ${\displaystyle k\in \{0,1,2,3,\dots \}}$ ${\displaystyle (1-p)^{k-1}p}$ ${\displaystyle (1-p)^{k}p}$ ${\displaystyle 1-(1-p)^{\lfloor k\rfloor }}$ if ${\displaystyle k\geq 1}$,${\displaystyle 0}$ if ${\displaystyle k<1}$ ${\displaystyle 1-(1-p)^{\lfloor k\rfloor +1}}$ if ${\displaystyle k\geq 0}$,${\displaystyle 0}$ if ${\displaystyle k<0}$ ${\displaystyle {\frac {1}{p}}}$ ${\displaystyle {\frac {1-p}{p}}}$ ${\displaystyle \left\lceil {\frac {-1}{\log _{2}(1-p)}}\right\rceil }$ (not unique if ${\displaystyle -1/\log _{2}(1-p)}$ is an integer) ${\displaystyle \left\lceil {\frac {-1}{\log _{2}(1-p)}}\right\rceil -1}$ (not unique if ${\displaystyle -1/\log _{2}(1-p)}$ is an integer) ${\displaystyle 1}$ ${\displaystyle 0}$ ${\displaystyle {\frac {1-p}{p^{2}}}}$ ${\displaystyle {\frac {1-p}{p^{2}}}}$ ${\displaystyle {\frac {2-p}{\sqrt {1-p}}}}$ ${\displaystyle {\frac {2-p}{\sqrt {1-p}}}}$ ${\displaystyle 6+{\frac {p^{2}}{1-p}}}$ ${\displaystyle 6+{\frac {p^{2}}{1-p}}}$ ${\displaystyle {\tfrac {-(1-p)\log _{2}(1-p)-p\log _{2}p}{p}}}$ ${\displaystyle {\tfrac {-(1-p)\log _{2}(1-p)-p\log _{2}p}{p}}}$ ${\displaystyle {\frac {pe^{t}}{1-(1-p)e^{t}}},}$for ${\displaystyle t<-\ln(1-p)}$ ${\displaystyle {\frac {p}{1-(1-p)e^{t}}},}$for ${\displaystyle t<-\ln(1-p)}$ ${\displaystyle {\frac {pe^{it}}{1-(1-p)e^{it}}}}$ ${\displaystyle {\frac {p}{1-(1-p)e^{it}}}}$
Which of these is called the geometric distribution is a matter of convention and convenience.
These two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of the number X); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.
The geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p. If the probability of success on each trial is p, then the probability that the kth trial (out of finite trials) is the first success is
${\displaystyle \Pr(X=k)=(1-p)^{k-1}p}$
for k = 1, 2, 3, 4, ....
The above form of the geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success:
${\displaystyle \Pr(Y=k)=\Pr(X=k+1)=(1-p)^{k}p}$
for k = 0, 1, 2, 3, ....
In either case, the sequence of probabilities is a geometric sequence.
For example, suppose an ordinary die is thrown repeatedly until the first time a "1" appears. The probability distribution of the number of times it is thrown is supported on the infinite set { 1, 2, 3, ... } and is a geometric distribution with p = 1/6.
The geometric distribution is denoted by Geo(p) where 0 < p ≤ 1. [1]
## Definitions
Consider a sequence of trials, where each trial has only two possible outcomes (designated failure and success). The probability of success is assumed to be the same for each trial. In such a sequence of trials, the geometric distribution is useful to model the number of failures before the first success since the experiment can have an indefinite number of trials until success, unlike the binomial distribution which has a set number of trials. The distribution gives the probability that there are zero failures before the first success, one failure before the first success, two failures before the first success, and so on.
### Assumptions: When is the geometric distribution an appropriate model?
The geometric distribution is an appropriate model if the following assumptions are true.
• The phenomenon being modeled is a sequence of independent trials.
• There are only two possible outcomes for each trial, often designated success or failure.
• The probability of success, p, is the same for every trial.
If these conditions are true, then the geometric random variable Y is the count of the number of failures before the first success. The possible number of failures before the first success is 0, 1, 2, 3, and so on. In the graphs above, this formulation is shown on the right.
An alternative formulation is that the geometric random variable X is the total number of trials up to and including the first success, and the number of failures is X − 1. In the graphs above, this formulation is shown on the left.
### Probability outcomes examples
The general formula to calculate the probability of k failures before the first success, where the probability of success is p and the probability of failure is q = 1 − p, is
${\displaystyle \Pr(Y=k)=q^{k}\,p.}$
for k = 0, 1, 2, 3, ....
E1) A doctor is seeking an antidepressant for a newly diagnosed patient. Suppose that, of the available anti-depressant drugs, the probability that any particular drug will be effective for a particular patient is p = 0.6. What is the probability that the first drug found to be effective for this patient is the first drug tried, the second drug tried, and so on? What is the expected number of drugs that will be tried to find one that is effective?
The probability that the first drug works. There are zero failures before the first success. Y = 0 failures. The probability Pr(zero failures before first success) is simply the probability that the first drug works.
${\displaystyle \Pr(Y=0)=q^{0}\,p\ =0.4^{0}\times 0.6=1\times 0.6=0.6.}$
The probability that the first drug fails, but the second drug works. There is one failure before the first success. Y = 1 failure. The probability for this sequence of events is Pr(first drug fails) ${\displaystyle \times }$ p(second drug succeeds), which is given by
${\displaystyle \Pr(Y=1)=q^{1}\,p\ =0.4^{1}\times 0.6=0.4\times 0.6=0.24.}$
The probability that the first drug fails, the second drug fails, but the third drug works. There are two failures before the first success. Y = 2 failures. The probability for this sequence of events is Pr(first drug fails) ${\displaystyle \times }$ p(second drug fails) ${\displaystyle \times }$ Pr(third drug is success)
${\displaystyle \Pr(Y=2)=q^{2}\,p,=0.4^{2}\times 0.6=0.096.}$
E2) A newlywed couple plans to have children and will continue until the first girl. What is the probability that there are zero boys before the first girl, one boy before the first girl, two boys before the first girl, and so on?
The probability of having a girl (success) is p= 0.5 and the probability of having a boy (failure) is q = 1 − p = 0.5.
The probability of no boys before the first girl is
${\displaystyle \Pr(Y=0)=q^{0}\,p\ =0.5^{0}\times 0.5=1\times 0.5=0.5.}$
The probability of one boy before the first girl is
${\displaystyle \Pr(Y=1)=q^{1}\,p\ =0.5^{1}\times 0.5=0.5\times 0.5=0.25.}$
The probability of two boys before the first girl is
${\displaystyle \Pr(Y=2)=q^{2}\,p\ =0.5^{2}\times 0.5=0.125.}$
and so on.
## Properties
### Moments and cumulants
The expected value for the number of independent trials to get the first success, and the variance of a geometrically distributed random variable X is:
${\displaystyle \operatorname {E} (X)={\frac {1}{p}},\qquad \operatorname {var} (X)={\frac {1-p}{p^{2}}}.}$
Similarly, the expected value and variance of the geometrically distributed random variable Y = X - 1 (See definition of distribution ${\displaystyle \Pr(Y=k)}$ ) is:
${\displaystyle \operatorname {E} (Y)=\operatorname {E} (X-1)=\operatorname {E} (X)-1={\frac {1-p}{p}},\qquad \operatorname {var} (Y)={\frac {1-p}{p^{2}}}.}$
### Proof
That the expected value is (1 − p)/p can be shown in the following way. Let Y be as above. Then
{\displaystyle {\begin{aligned}\mathrm {E} (Y)&{}=\sum _{k=0}^{\infty }(1-p)^{k}p\cdot k\\&{}=p\sum _{k=0}^{\infty }(1-p)^{k}k\\&{}=p(1-p)\sum _{k=0}^{\infty }(1-p)^{k-1}\cdot k\\&{}=p(1-p)\left[{\frac {d}{dp}}\left(-\sum _{k=0}^{\infty }(1-p)^{k}\right)\right]\\&{}=p(1-p){\frac {d}{dp}}\left(-{\frac {1}{p}}\right)={\frac {1-p}{p}}.\end{aligned}}}
The interchange of summation and differentiation is justified by the fact that convergent power series converge uniformly on compact subsets of the set of points where they converge.
Let μ = (1 − p)/p be the expected value of Y. Then the cumulants ${\displaystyle \kappa _{n}}$ of the probability distribution of Y satisfy the recursion
${\displaystyle \kappa _{n+1}=\mu (\mu +1){\frac {d\kappa _{n}}{d\mu }}.}$
#### Expected value examples
E3) A patient is waiting for a suitable matching kidney donor for a transplant. If the probability that a randomly selected donor is a suitable match is p = 0.1, what is the expected number of donors who will be tested before a matching donor is found?
With p = 0.1, the mean number of failures before the first success is E(Y) = (1 − p)/p =(1 − 0.1)/0.1 = 9.
For the alternative formulation, where X is the number of trials up to and including the first success, the expected value is E(X) = 1/p = 1/0.1 = 10.
For example 1 above, with p = 0.6, the mean number of failures before the first success is E(Y) = (1 − p)/p = (1 − 0.6)/0.6 = 0.67.
#### Higher-order moments
The moments for the number of failures before the first success are given by
{\displaystyle {\begin{aligned}\mathrm {E} (Y^{n})&{}=\sum _{k=0}^{\infty }(1-p)^{k}p\cdot k^{n}\\&{}=p\operatorname {Li} _{-n}(1-p)\end{aligned}}}
where ${\displaystyle \operatorname {Li} _{-n}(1-p)}$ is the polylogarithm function.
### General properties
{\displaystyle {\begin{aligned}G_{X}(s)&={\frac {s\,p}{1-s\,(1-p)}},\\[10pt]G_{Y}(s)&={\frac {p}{1-s\,(1-p)}},\quad |s|<(1-p)^{-1}.\end{aligned}}}
• Like its continuous analogue (the exponential distribution), the geometric distribution is memoryless. That means that if you intend to repeat an experiment until the first success, then, given that the first success has not yet occurred, the conditional probability distribution of the number of additional trials does not depend on how many failures have been observed. The die one throws or the coin one tosses does not have a "memory" of these failures. The geometric distribution (that counts the trials rather than the failures) is the only memoryless discrete distribution.
${\displaystyle \Pr\{X>m+n|X>n\}=\Pr\{X>m\}}$ [2]
• Among all discrete probability distributions supported on {1, 2, 3, ... } with given expected value μ, the geometric distribution X with parameter p = 1/μ is the one with the largest entropy.[3]
• The geometric distribution of the number Y of failures before the first success is infinitely divisible, i.e., for any positive integer n, there exist independent identically distributed random variables Y1, ..., Yn whose sum has the same distribution that Y has. These will not be geometrically distributed unless n = 1; they follow a negative binomial distribution.
• The decimal digits of the geometrically distributed random variable Y are a sequence of independent (and not identically distributed) random variables.[citation needed] For example, the hundreds digit D has this probability distribution:
${\displaystyle \Pr(D=d)={q^{100d} \over 1+q^{100}+q^{200}+\cdots +q^{900}},}$
where q = 1 − p, and similarly for the other digits, and, more generally, similarly for numeral systems with other bases than 10. When the base is 2, this shows that a geometrically distributed random variable can be written as a sum of independent random variables whose probability distributions are indecomposable.
## Related distributions
• The geometric distribution Y is a special case of the negative binomial distribution, with r = 1. More generally, if Y1, ..., Yr are independent geometrically distributed variables with parameter p, then the sum
${\displaystyle Z=\sum _{m=1}^{r}Y_{m}}$
follows a negative binomial distribution with parameters r and p.[5]
• The geometric distribution is a special case of discrete compound Poisson distribution.
• If Y1, ..., Yr are independent geometrically distributed variables (with possibly different success parameters pm), then their minimum
${\displaystyle W=\min _{m\in 1,\ldots ,r}Y_{m}\,}$
is also geometrically distributed, with parameter ${\displaystyle p=1-\prod _{m}(1-p_{m}).}$ [6]
• Suppose 0 < r < 1, and for k = 1, 2, 3, ... the random variable Xk has a Poisson distribution with expected value r k/k. Then
${\displaystyle \sum _{k=1}^{\infty }k\,X_{k}}$
has a geometric distribution taking values in the set {0, 1, 2, ...}, with expected value r/(1 − r).[citation needed]
• The exponential distribution is the continuous analogue of the geometric distribution. If X is an exponentially distributed random variable with parameter λ, then
${\displaystyle Y=\lfloor X\rfloor ,}$
where ${\displaystyle \lfloor \quad \rfloor }$ is the floor (or greatest integer) function, is a geometrically distributed random variable with parameter p = 1 − eλ (thus λ = −ln(1 − p)[7]) and taking values in the set {0, 1, 2, ...}. This can be used to generate geometrically distributed pseudorandom numbers by first generating exponentially distributed pseudorandom numbers from a uniform pseudorandom number generator: then ${\displaystyle \lfloor \ln(U)/\ln(1-p)\rfloor }$ is geometrically distributed with parameter ${\displaystyle p}$ , if ${\displaystyle U}$ is uniformly distributed in [0,1].
• If p = 1/n and X is geometrically distributed with parameter p, then the distribution of X/n approaches an exponential distribution with expected value 1 as n → ∞, since
{\displaystyle {\begin{aligned}\Pr(X/n>a)=\Pr(X>na)&=(1-p)^{na}=\left(1-{\frac {1}{n}}\right)^{na}=\left[\left(1-{\frac {1}{n}}\right)^{n}\right]^{a}\\&\to [e^{-1}]^{a}=e^{-a}{\text{ as }}n\to \infty .\end{aligned}}}
More generally, if p = λ/n, where λ is a parameter, then as n→ ∞ the distribution of X/n approaches an exponential distribution with rate λ:
${\displaystyle \Pr(X>nx)=\lim _{n\to \infty }(1-\lambda /n)^{nx}=e^{-\lambda x}}$
therefore the distribution function of X/n converges to ${\displaystyle 1-e^{-\lambda x}}$ , which is that of an exponential random variable.
## Statistical inference
### Parameter estimation
For both variants of the geometric distribution, the parameter p can be estimated by equating the expected value with the sample mean. This is the method of moments, which in this case happens to yield maximum likelihood estimates of p.[8][9]
Specifically, for the first variant let k = k1, ..., kn be a sample where ki ≥ 1 for i = 1, ..., n. Then p can be estimated as
${\displaystyle {\widehat {p}}=\left({\frac {1}{n}}\sum _{i=1}^{n}k_{i}\right)^{-1}={\frac {n}{\sum _{i=1}^{n}k_{i}}}.\!}$
In Bayesian inference, the Beta distribution is the conjugate prior distribution for the parameter p. If this parameter is given a Beta(αβ) prior, then the posterior distribution is
${\displaystyle p\sim \mathrm {Beta} \left(\alpha +n,\ \beta +\sum _{i=1}^{n}(k_{i}-1)\right).\!}$
The posterior mean E[p] approaches the maximum likelihood estimate ${\displaystyle {\widehat {p}}}$ as α and β approach zero.
In the alternative case, let k1, ..., kn be a sample where ki ≥ 0 for i = 1, ..., n. Then p can be estimated as
${\displaystyle {\widehat {p}}=\left(1+{\frac {1}{n}}\sum _{i=1}^{n}k_{i}\right)^{-1}={\frac {n}{\sum _{i=1}^{n}k_{i}+n}}.\!}$
The posterior distribution of p given a Beta(αβ) prior is[10][11]
${\displaystyle p\sim \mathrm {Beta} \left(\alpha +n,\ \beta +\sum _{i=1}^{n}k_{i}\right).\!}$
Again the posterior mean E[p] approaches the maximum likelihood estimate ${\displaystyle {\widehat {p}}}$ as α and β approach zero.
For either estimate of ${\displaystyle {\widehat {p}}}$ using Maximum Likelihood, the bias is equal to
${\displaystyle b\equiv \operatorname {E} {\bigg [}\;({\hat {p}}_{\mathrm {mle} }-p)\;{\bigg ]}={\frac {p\,(1-p)}{n}}}$
which yields the bias-corrected maximum likelihood estimator
${\displaystyle {\hat {p\,}}_{\text{mle}}^{*}={\hat {p\,}}_{\text{mle}}-{\hat {b\,}}}$
## Computational methods
### Geometric distribution using R
The R function dgeom(k, prob) calculates the probability that there are k failures before the first success, where the argument "prob" is the probability of success on each trial.
For example,
dgeom(0,0.6) = 0.6
dgeom(1,0.6) = 0.24
R uses the convention that k is the number of failures, so that the number of trials up to and including the first success is k + 1.
The following R code creates a graph of the geometric distribution from Y = 0 to 10, with p = 0.6.
Y=0:10
plot(Y, dgeom(Y,0.6), type="h", ylim=c(0,1), main="Geometric distribution for p=0.6", ylab="Pr(Y=Y)", xlab="Y=Number of failures before first success")
### Geometric distribution using Excel
The geometric distribution, for the number of failures before the first success, is a special case of the negative binomial distribution, for the number of failures before s successes.
The Excel function NEGBINOMDIST(number_f, number_s, probability_s) calculates the probability of k = number_f failures before s = number_s successes where p = probability_s is the probability of success on each trial. For the geometric distribution, let number_s = 1 success.
For example,
=NEGBINOMDIST(0, 1, 0.6) = 0.6
=NEGBINOMDIST(1, 1, 0.6) = 0.24
Like R, Excel uses the convention that k is the number of failures, so that the number of trials up to and including the first success is k + 1.
## References
1. ^ a b A modern introduction to probability and statistics : understanding why and how. Dekking, Michel, 1946-. London: Springer. 2005. pp. 48–50, 61–62, 152. ISBN 9781852338961. OCLC 262680588.{{cite book}}: CS1 maint: others (link)
2. ^ Guntuboyina, Aditya. "Fall 2018 Statistics 201A (Introduction to Probability at an advanced level) - All Lecture Notes" (PDF). Archived (PDF) from the original on 2019-11-06.
3. ^ Park, Sung Y.; Bera, Anil K. (June 2009). "Maximum entropy autoregressive conditional heteroskedasticity model". Journal of Econometrics. 150 (2): 219–230. doi:10.1016/j.jeconom.2008.12.014.
4. ^ Gallager, R.; van Voorhis, D. (March 1975). "Optimal source codes for geometrically distributed integer alphabets (Corresp.)". IEEE Transactions on Information Theory. 21 (2): 228–230. doi:10.1109/TIT.1975.1055357. ISSN 0018-9448.
5. ^ Pitman, Jim. Probability (1993 edition). Springer Publishers. pp 372.
6. ^ Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David (1 June 1995). "On the minimum of independent geometrically distributed random variables". Statistics & Probability Letters. 23 (4): 313–326. doi:10.1016/0167-7152(94)00130-Z. S2CID 1505801.
7. ^ "Wolfram-Alpha: Computational Knowledge Engine". www.wolframalpha.com.
8. ^ casella, george; berger, roger l (2002). statistical inference (2nd ed.). pp. 312–315. ISBN 0-534-24312-6.
9. ^ "MLE Examples: Exponential and Geometric Distributions Old Kiwi - Rhea". www.projectrhea.org. Retrieved 2019-11-17.
10. ^ "3. Conjugate families of distributions" (PDF). Archived (PDF) from the original on 2010-04-08.
11. ^ "Conjugate prior", Wikipedia, 2019-10-03, retrieved 2019-11-17 | 5,746 | 19,686 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 82, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2022-49 | latest | en | 0.575655 |
https://rowcoding.com/how-to-perform-an-integer-division-and-separately-get-the-remainder-in-javascript/ | 1,680,052,541,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948900.50/warc/CC-MAIN-20230328232645-20230329022645-00242.warc.gz | 551,015,405 | 11,580 | # How to perform an integer division, and separately get the remainder, in JavaScript?
For some number `y` and some divisor `x` compute the quotient (`quotient`)[1] and remainder (`remainder`) as:
``````const quotient = Math.floor(y/x);
const remainder = y % x;
``````
Example:
``````const quotient = Math.floor(13/3); // => 4 => the times 3 fits into 13
const remainder = 13 % 3; // => 1
``````
[1] The integer number resulting from the division of one number by another | 132 | 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} | 2.96875 | 3 | CC-MAIN-2023-14 | latest | en | 0.775498 |
https://www.coursehero.com/file/6649562/SC07MatlabWorkshop12nov2007/ | 1,513,034,771,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948514113.3/warc/CC-MAIN-20171211222541-20171212002541-00759.warc.gz | 730,772,804 | 433,305 | SC07MatlabWorkshop12nov2007
# SC07MatlabWorkshop12nov2007 - Parallel Sparse Operations in...
This preview shows pages 1–12. Sign up to view the full content.
1 Parallel Sparse Operations in Matlab: Exploring Large Graphs John R. Gilbert University of California at Santa Barbara Aydin Buluc (UCSB) Brad McRae (NCEAS) Steve Reinhardt (Interactive Supercomputing) with thanks to Alan Edelman (MIT & ISC) and Jeremy Kepner (MIT-LL) Support: DOE, NSF, DARPA, SGI, ISC
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2 3D Spectral Coordinates
3 2D Histogram: RMAT Graph
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
4 Strongly Connected Components
5 Social Network Analysis in Matlab: 1993 Co-author graph from 1993 Householder symposium
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
6 Combinatorial Scientific Computing Emerging large scale, high-performance applications: Web search and information retrieval Knowledge discovery Computational biology Dynamical systems Machine learning Bioinformatics Sparse matrix methods Geometric modeling . . . How will combinatorial methods be used by nonexperts?
7 Outline Infrastructure: Array-based sparse graph computation An application: Computational ecology Some nuts and bolts: Sparse matrix multiplication
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
8 Matlab*P A = rand(4000 *p , 4000 *p ); x = randn(4000 *p , 1); y = zeros(size(x)); while norm(x-y) / norm(x) > 1e-11 y = x; x = A*x; x = x / norm(x); end;
9 MATLAB ® Star-P Architecture Ordinary Matlab variables Star-P client manager server manager package manager processor #0 processor #n-1 processor #1 processor #2 processor #3 . . . ScaLAPACK FFTW FPGA interface matrix manager Distributed matrices sort dense/sparse UPC user code MPI user code
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
10 P 0 P 1 P 2 P n 59 41 53 26 31 2 3 1 3 1 Each processor stores local vertices & edges in a compressed row structure. Has been scaled to >10 8 vertices, >10 9 edges in interactive session. Distributed Sparse Array Structure 1 2 3 26 53 41 31 59
11 Sparse Array and Matrix Operations dsparse layout, same semantics as ordinary full & sparse Matrix arithmetic: + , max , sum , etc. matrix * matrix
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.
{[ snackBarMessage ]}
### Page1 / 35
SC07MatlabWorkshop12nov2007 - Parallel Sparse Operations in...
This preview shows document pages 1 - 12. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 693 | 2,909 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-51 | latest | en | 0.753298 |
http://www.okstate.edu/sas/v8/sashtml/qc/chap33/sect6.htm | 1,508,699,705,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825436.78/warc/CC-MAIN-20171022184824-20171022204824-00636.warc.gz | 534,623,605 | 3,449 | Chapter Contents Previous Next
CCHART Statement
## Creating c Charts from Nonconformities per Unit
See SHWCCHR1 in the SAS/QC Sample Library
In the previous example, the input data set provided the number of nonconformities per subgroup sample. However, in some applications, as illustrated here, the data may be provided as the number of nonconformities per inspection unit for each subgroup.
A clothing manufacturer ships shirts in boxes of ten. Prior to shipment, each shirt is inspected for flaws. Since the manufacturer is interested in the average number of flaws per shirt, the number of flaws found in each box is divided by ten and then recorded. The following statements create a SAS data set named SHIRTS, which contains the average number of flaws per shirt for 25 boxes:
``` data shirts;
input box avgdefu @@;
avgdefn=10;
datalines;
1 0.4 2 0.7 3 0.5 4 1.0 5 0.3
6 0.2 7 0.0 8 0.4 9 0.4 10 0.6
11 0.2 12 0.7 13 0.3 14 0.1 15 0.3
16 0.6 17 0.6 18 0.3 19 0.7 20 0.3
21 0.0 22 0.1 23 0.5 24 0.6 25 0.4
;
```
A listing of SHIRTS is shown in Figure 33.6.
Average Number of Shirt Flaws
box avgdefu avgdefn 1 0.4 10 2 0.7 10 3 0.5 10 4 1.0 10 5 0.3 10 6 0.2 10 7 0.0 10 8 0.4 10 9 0.4 10 10 0.6 10 11 0.2 10 12 0.7 10 13 0.3 10 14 0.1 10 15 0.3 10 16 0.6 10 17 0.6 10 18 0.3 10 19 0.7 10 20 0.3 10 21 0.0 10 22 0.1 10 23 0.5 10 24 0.6 10 25 0.4 10
Figure 33.6: The Data Set SHIRTS
The data set SHIRTS contains three variables: the box number (BOX), the average number of flaws per shirt (AVGDEFU), and the number of shirts per box (AVGDEFN). Here, a subgroup is a box of shirts, and an inspection unit is an individual shirt. Note that each subgroup consists of ten inspection units.
To create a c chart plotting the total number of flaws per box (instead of per shirt), you can specify SHIRTS as a HISTORY= data set.
``` title 'Total Flaws per Box of Shirts';
symbol v=dot c=red;
proc shewhart history=shirts;
cchart avgdef*box / cframe = steel
cconect = red
cinfill = ligr
coutfill = yellow ;
run;
```
Note that AVGDEF is not the name of a SAS variable in the data set but is instead the common prefix for the SAS variable names AVGDEFU and AVGDEFN. The suffix characters U and N indicate number of nonconformities per unit and sample size, respectively. This naming convention enables you to specify two variables in the HISTORY= data set with a single name referred to as the process. The name BOX specified after the asterisk is the name of the subgroup-variable. The c chart is shown in Figure 33.7.
Figure 33.7: A c Chart for Boxes of Shirts
In general, a HISTORY= input data set used with the CCHART statement must contain the following variables:
• subgroup variable
• subgroup number of nonconformities per unit variable
• subgroup sample size variable
Furthermore, the names of the nonconformities per unit and sample size variables must begin with the process name specified in the CCHART statement and end with the special suffix characters U and N, respectively. If the names do not follow this convention, you can use the RENAME option to rename the variables for the duration of the SHEWHART procedure step. Suppose that, instead of the variables AVGDEFU and AVGDEFN, the data set SHIRTS contained the variables SHIRTDEF and SIZES. The following statements would temporarily rename SHIRTDEF and SIZES to AVGDEFU and AVGDEFN:
``` proc shewhart
history=shirts (rename=(shirtdef = avgdefu
sizes = avgdefn ));
cchart avgdef*box;
run;
``` | 1,127 | 3,556 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2017-43 | latest | en | 0.759826 |
https://beyond-universe.fandom.com/wiki/Cypricuneifillion | 1,590,999,425,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347415315.43/warc/CC-MAIN-20200601071242-20200601101242-00361.warc.gz | 268,599,107 | 83,791 | ## FANDOM
4,542 Pages
The cypricuneifillion (formerly seventyillion) is equal to 103x103x103x103x103x10210+3.[1] The term was coined by UniversePoker777.
## Expressions in other notations Edit
Notation Expression
Up-arrow notation $$10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow 210)))))))+3)$$
Chained arrow notation $$10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \rightarrow 210))))))+3)$$
BEAF $$\{10,\{3\times \{10,3 \times \{10,3 \times \{10,3 \times \{10,3 \times \{10,210\}\}\}\}\}+3\}\}$$
Munafo's ASCII-lexicographic ordering p3_c3000_477121254720
1. [1] | 267 | 737 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2020-24 | latest | en | 0.597364 |
http://serigalapoker.com/what-is-a-lottery/ | 1,716,121,454,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057786.92/warc/CC-MAIN-20240519101339-20240519131339-00472.warc.gz | 23,315,805 | 8,545 | # What is a Lottery?
The practice of dividing property by lot dates back to ancient times. Moses is instructed in the Old Testament to take a census of the people of Israel and to divide their land by lot. The Roman emperors used lotteries to distribute property and slaves. They made lotteries a common part of dinner entertainment. Apophoreta, which means “that which you carry home,” was a popular game of chance. The ancient Romans also used lottery games to distribute gifts.
## Lottery is a game where players select a group of numbers from a large set
A lottery is a type of game in which players choose a group of numbers from a large list in order to win a prize. The prize is usually split between the winners. There are various types of lotteries, including the traditional five-digit game, the pick-five game, and the daily numbers games. The five-digit game requires players to choose five numbers from a set of ten. The winning numbers of a daily lottery are often fixed regardless of how many tickets are sold. In some jurisdictions, such as New Jersey, lottery prizes are awarded daily, while those of five-digit games are not guaranteed.
Players choose a group of numbers from a large field, such as the Powerball game. Each lottery has different prize levels, with the jackpot prize being the highest. If a player matches all six numbers, he or she wins a jackpot prize. However, if a player matches three, four, or five numbers, he or she can win a prize as well. Typically, the jackpot prize is the highest prize and can be quite substantial.
## Lotto is a game where players select a group of numbers from a large set and are awarded prizes based on how many match a second set chosen by a random drawing
A lotto game is a lottery game in which players choose a group of numbers from a list of numbers, or “strips,” and are then awarded prizes based on how many match corresponding numbers in another set chosen by a random drawing. The prize payouts depend on how many tickets are sold, and a large jackpot prize can increase over time if not won. Every American state offers Mega Millions, a \$2 multi-jurisdictional lotto game that can be very lucrative and generate massive jackpots.
In order to win a lottery prize, players must choose six numbers from a pool of 50. It is important to remember that the probability of picking a single correct number will depend on how many balls are drawn. There are no sets that will match all the numbers. If you select the wrong numbers, you could end up in jail. But there are some ways to increase your chances of winning a lotto game. | 549 | 2,608 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-22 | latest | en | 0.978017 |
http://blog.alex-turok.com/2012/01/ | 1,566,200,140,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027314696.33/warc/CC-MAIN-20190819073232-20190819095232-00097.warc.gz | 28,740,422 | 15,522 | ## воскресенье, 22 января 2012 г.
### Simple Models
Recently I've started exploring Microsoft XNA platform. In an attempt to get familiar with numerous powerfull tools it offers I've decided to use it to accomplish some relatively simple but interesting task that will make use of graphics but won't prompt me to focus on sophisticated graphics stuff. Due to some strange reasons I've choosen to start with developing Rubik's Cube puzzle game. The idea for application here is quite simple - the only thing my game must offer to a user is an opportunity to solve the well-known puzzle on a computer screen.
As for development,the task accomplishment, roughly speaking, requires two smaller problems being solved: firstly I should design a Rubik's Cube representation for storing and modifying tha state of the toy in line with player's actions and secondly I need to introduce routines for showing the Cube in an appropriate state on the screen. I haven't started writing graphics-related code yet, but I feel I'm almost finished with the first stage - that means I have developed a couple of classes representing the puzzle which provide convenient ways for performing any required in-game operation on the toy (e.g. rotating one of the cube's faces).
These recent efforts to develop a simple and convenient model of a real world object encouraged me to think over Leonard Susskind's words across which I had come some time ago. Speaking about the legendary physicist - Richard Feynman - Susskind had said:
"He [Feynman] truly believed that if you couldn't explain something simply, you didn't understand it."
My intuition supported this idea long before I've heard these words, although I have never thought about it deeply. However this time the attempts to design a representation of a real world thing combined with revisiting Susskind's speech made me contemplate the thought.
The above quote suggests that to understand something one needs to have a simple model of the thing in mind - only possessing such a model one can explain something - that is share the model - and the explanation will be simple only in case the model is. In fact having a complete model of some object or process means understanding it - and vice-versa - so the only way to understand something is to study or design a model of the thing. A task of designing a model is usually a hard one and requires a lot of work to be done. Such a design process involves overcoming numerous problems which actually help the developer to form a better understanding of the entire object or process being described. Obviously it is difficult to design either a simple model of an object or a sophisticated one, but surprisingly the former are usually much harder to discover and develop. That means one often needs to do much more work, to face much more problems to achieve a goal of designing a simple but workable model - that is precisely one of the reasons why simpler models correspond to a better understanding.
However we actually don't design all the models we use ourselves - we tend to take ready ones and use these for our purposes. In this case one can't directly benefit from the difficulties connected with developing a simple model, though one benefits from the model's simplicity itself and really understands the things better than in case he would use a large and sophisticated one. That's because our mind's power is finite, hence it may be quite difficult for our brain to handle a sophisticated thing - roughly speaking it may fail to 'cache' a complex model completely with all of it's numerous although important details. I suppose we tend to unconsciously simplify the model if one is too sophisticated for us to handle, but in case our mind is not familiar with the model such a simplification may result in losing some important details which are just cut away and eventually this will lead to mistakes.
In this way simple models really produce better understanding through representing corresponding objects in a complete and convenient (particularly for our mind) manner. Moreover such models have another advantage over the complex ones: if your model is simple it is easy to share it because it can be explained simply.
## четверг, 12 января 2012 г.
### Right Choice
There are dozens of doors before me - open and tempting.
Is there any one, that won't bring me to Hell, I wonder?
## среда, 4 января 2012 г.
### Righteous Insomnia
Note: I do not connect the word "(un)righteous" and any of it's derivatives with religion - either with any specific one or with religion in general. A kind of explanation of my understanding of righteousness and unrighteousness may be extracted from the lines below.
About a half a year ago I've somehow concluded that insomnia is caused by living an unrighteous life. The reasoning behind this conclusion is pretty simple and obvious: insomnia is usually closely related to unstoppable thinking about problems and choices one encounters and with the attempts to find proper solutions to these problems and to make a good choice. At the same time inability to solve a problem or to make a choice is frequently caused by a lack of inner principles or by failing to follow these. This way we come to unrighteousness because being unrighteous means exactly to be unable to follow one's moral principles or to lack these principles.
The simplicity of such an explanation to insomnia attracted me. Moreover there is another reason why I haven't explored the problem deeper - everytime I struggled with insomnia myself it had been precisely because of my own lack of righteousness and for an unrighteous one it was much more difficult to see one more possible reason for insomnia. If you think this out you may notice that such an explanation to the problem of insomnia isn't complete - that is it fails to predict insomnia in some cases because righteous people are exposed to the problem too. Moreover it is easy to discover that if one has very strong moral principles, is confident about these and doesn't fail to live accordingly, then such a person has even greater chances to encounter insomnia one night. In other words, the more righteous one is - the more is he or she exposed to insomnia.
The explanation here turns out to be fairly simple too: righteous people are usually surrounded by unrighteous ones and the fact is that the former tend to care about the latter. So even if you're extremely righteous, your relatives and friends sometimes do act in an unrighteous manner and if your principles are strong you may at least get upset if someone you admire acts in a manner you consider wrong. This way when a close friend of yours behaves unrighteously you feel sorry and sometimes even guilty for that. Whenever feelings of this kind prevent somebody from sleeping I would call it a righteous insomnia. | 1,346 | 6,860 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2019-35 | latest | en | 0.956273 |
http://www.calcudoku.org/forum/viewtopic.php?f=19&t=326&start=30&view=print | 1,513,162,524,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948522999.27/warc/CC-MAIN-20171213104259-20171213124259-00169.warc.gz | 335,338,867 | 2,581 | Calcudoku puzzle forumhttp://www.calcudoku.org/forum/ Difficult Killer Sudoku for 16 Sept 2012http://www.calcudoku.org/forum/viewtopic.php?f=19&t=326 Page 4 of 4
Author: clm [ Wed Sep 26, 2012 8:18 am ] Post subject: Re: Difficult Killer Sudoku for 16 Sept 2012 pharosian wrote:clm wrote: Let's see: f1 = 7 is inmediate (column e); g7 + i7 = 15 (nonet 3) >>> [6,9] ...I think you meant to say g3 + i3 = 15...But other than that, you lay out a solid case for why this puzzle wasn't as difficult as advertised. I missed a couple of the clues that seem so obvious once you point them out, but I did find several of them on my own. I'll be curious to hear what Patrick figures out with regard to the solver strategy. Yes, yes, of course, I am sorry, this happens to me for doing the coordinates "in mind", I am reediting the post, thank you.
Author: pnm [ Wed Sep 26, 2012 7:31 pm ] Post subject: Re: Difficult Killer Sudoku for 16 Sept 2012 pnm wrote:Hm, this may mean that I'm still missing an important solving strategy in my solver(I thought I had them all now )It turns out it's more a matter of interpreting the results of the solver,you're right, this puzzle is fairly straight-forward.Thanks for the description of the solution,Patrick
Page 4 of 4 All times are UTC + 1 hour [ DST ] Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Grouphttp://www.phpbb.com/ | 394 | 1,369 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2017-51 | latest | en | 0.93834 |
http://mathoverflow.net/feeds/question/48913 | 1,369,000,381,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368698090094/warc/CC-MAIN-20130516095450-00049-ip-10-60-113-184.ec2.internal.warc.gz | 169,766,297 | 3,178 | uneven spaced time series - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T21:53:03Z http://mathoverflow.net/feeds/question/48913 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48913/uneven-spaced-time-series uneven spaced time series Tim van Beek 2010-12-10T12:20:20Z 2010-12-30T01:17:24Z <p>Let $(t_k), k \in \mathbb{N}$, be an increasing sequence of real numbers ($t_{k-1} < t_k$) and $(X_{t_k}$) be a sequence of real numbers indexed by $(t_k)$. Such a sequence is sometimes called a time series.</p> <p>The idea is that this series represents a sequence of measurements of some sort, like, for example, the average temperature of some location at time $t_k$.</p> <p>The analysis of time series is an established area of statistics. In concrete applications, for example in climate science, there are two common problems when applying statistical algorithms to time series:</p> <ol> <li><p>The time series are finite, which produces artefacts in statistical algorithms that are designed for infinite time series. This problem is well known and there exist several approches to handle it.</p></li> <li><p>The times series are uneven spaced, that is $t_k - t_{k-1}$ is not independent of $k$.</p></li> </ol> <p>I don't know of any textbook, algorithm or paper that explicitly addresses the latter problem. My question is therefore: Is this not a problem, is the solution trivial or, if not, are there any treatments?</p> <p>Of course it is possible to interpolate missing values to generate a time series with an even time spacing $\min_k (t_k - t_{k-1})$, but it seems to me that this is not a solution, because algorithms like the fast fourier transform, nonlinear regression analysis or wavelet transforms would produce artefacts that depend on the kind of interpolation (linear, qubic splines, whatever). And therefore an explicit explanation of why the kind of interpolation one uses does not produce any artefacts in the analysis of the time series seems to be warranted to me, but I have never seen one in the literature.</p> http://mathoverflow.net/questions/48913/uneven-spaced-time-series/48923#48923 Answer by sleepless in beantown for uneven spaced time series sleepless in beantown 2010-12-10T13:56:50Z 2010-12-10T13:56:50Z <p>Fourier transforms depend upon the fact that the modeled signal are going to be infinite in time-span and time-extent. While it is possible to get a very good example of a time-limited signal by using a finite set of Fourier coefficients, the finite-fourier-coefficient-approximation always ends up with "ringing artefacts" at any high-frequency edges beyond the bandwidth-limited approximation. These artifacts arise from the fact that Fourier decomposition using the "infinite-time-extent" sine-wave as its base-component.</p> <p>This type of problem in representing "limited-time-span" signals is what led to the concepts of "wavelets" and wavelet-transforms, using such limited-time-span base components such as the Haar wavelet. This is a slightly different problem from having non-equally-spaced-in-time samples extracted from a time series, but even then in these cases, there is the assumption that the underlying time series is continuous over time or is composed of the superposition of multiple discrete events occuring as Bernoulli or Poisson processes over time with some convolution of the discrete events by a smoothing factor (volcano eruption or geyser spouting, with the effluent "smoothed out" by prevailing winds or water currents).</p> http://mathoverflow.net/questions/48913/uneven-spaced-time-series/48948#48948 Answer by Pascal Orosco for uneven spaced time series Pascal Orosco 2010-12-10T17:28:05Z 2010-12-10T17:28:05Z <p>... This is a problem, there is no trivial solution, just because you cannot and must not solve both problems (the interpolation problem and your problem of interest) separately: you must solve them jointly.</p> <p>However, if adapting the algorithm of interest to uneven spaced times or solving both problem jointly is too difficult, you may consider resorting to "Poincaré-Jaynes-Bretthorst" interpolation that can be easily adapted to handle uneven spaced times. Please see my question </p> <p><a href="http://mathoverflow.net/questions/48913/uneven-spaced-time-series" rel="nofollow">http://mathoverflow.net/questions/48913/uneven-spaced-time-series</a></p> <p>for references.</p> <p>"Poincaré-Jaynes-Bretthorst" interpolation is in some extent exact: it is necessary (according to Poincaré) and also sufficient, provided that you equip yourself with Jaynes' Principle of Maximum Entropy. Essentially, you "just" need to choose the order of the derivative to constrain (that makes no big difference in some cases.)</p> http://mathoverflow.net/questions/48913/uneven-spaced-time-series/50692#50692 Answer by Andreas Eckner for uneven spaced time series Andreas Eckner 2010-12-30T01:09:52Z 2010-12-30T01:17:24Z <p>Unfortunately the problem is not trivial. Right now, there is virtually no theory for analyzing unevenly-spaced time series in their unaltered form. I have been working extensively on the problem over the past year and have typed up some notes that might be helpful (they can be found at <a href="http://www.eckner.com/research.html" rel="nofollow">http://www.eckner.com/research.html</a>)</p> | 1,321 | 5,364 | {"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} | 3.34375 | 3 | CC-MAIN-2013-20 | latest | en | 0.856844 |
https://www.freezingblue.com/flashcards/print_preview.cgi?cardsetID=2120 | 1,600,570,149,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400193087.0/warc/CC-MAIN-20200920000137-20200920030137-00308.warc.gz | 868,944,185 | 9,638 | # Intro to Logic
The flashcards below were created by user tiffanyscards on FreezingBlue Flashcards.
1. Rules of Inference (definition)
Rules that permit valid inferences from statements assumed as premises. There are 23 total: 9 elementary argument forms, 10 replacement rules, and 4 instantiation/generalization rules.
2. Difference between elementary argument forms and replacement rules
• The first 9 elementary rules can be applied only to whole lines of a proof. For example, A can be inferred from A • B only if A • B constitutes a whole line.
• Any of the last 10 replacement rules can be applied either to whole lines or to parts of lines.
3. Difference between a valid and invalid argument
• An argument is valid if and only if it has no substitution instances with true premises and a false conclusion.
• An argument is invalid if it has at least one substitution instance with true premises and a false conclusion.
4. When are two statements materially equivalent?
Two statements are materially equivalent (≡) if they have the same truth value. This means that either they are both true or both false…and that they materially imply each other.
5. Replacement (definition)
• The exchange of a component of one statement only by a statement that is known (by one of the 10 replacement rules) to be logically equivalent to that component. Unlike substitution instances, it isn’t necessary to replace every occurrence of the component being replaced.
• Ex: A ⊃ B can be replaced by ~B ⊃ ~A
6. Substitution instance (definition)
• A substitution of statements for statement variables, which can be done as long as it is substituted for every occurrence of that statement variable.
• Ex: A ⊃ B is a substitution instance of p ⊃ q
7. Natural deduction (definition)
A method of proving the validity of a deductive argument by using the rules of inference. It’s a complete system, in that it is compact and readily mastered, and with it, one can construct a formal proof of validity for any valid truth functional argument.
8. Formal proof of validity (definition)
A sequence of statements, each of which is either a premise of that argument or follows from preceding statements of the sequence by an elementary valid argument, such that the last statement in the sequence is the conclusion of the argument whose validity is being proved.
9. Rule of replacement (definition)
A rule that permits us to infer from any statement the result of replacing any component of that statement by any other statement that is logically equivalent to the component replaced.
10. 4 Quantification Rules
• ~(x)Mx ⇔ (∃x)~Mx
• The statement “Not everything is mortal” is logically equivalent to the statement “There is at least one thing that is not mortal.”
• (x)Mx ⇔ ~(∃x)~Mx
• The statement “Everything is mortal” is logically equivalent to the statement “There is not at least one thing that is not mortal.”
• ~(x)~Mx ⇔ (∃x)Mx
• The statement “Nothing is not mortal” is logically equivalent to the statement “Something is mortal.”
• (x)~Mx ⇔ ~(∃x)Mx
• The statement “Everything is not mortal” is logically equivalent to the statement “There is not at least one thing that is mortal.”
11. Express the following quantification rule in predicate logic: The statement “Not everything is mortal” is logically equivalent to the statement “There is at least one thing that is not mortal.”
~(x)Mx ⇔ (∃x)~Mx
12. Express the following quantification rule in predicate logic: The statement “Everything is mortal” is logically equivalent to the statement “There is not at least one thing that is not mortal.”
(x)Mx ⇔ ~(∃x)~Mx
13. Express the following quantification rule in predicate logic: The statement “Nothing is not mortal” is logically equivalent to the statement “Something is mortal.”
~(x)~Mx ⇔ (∃x)Mx
14. Express the following quantification rule in predicate logic: The statement “Everything is not mortal is logically equivalent to the statement “There is not at least one thing that is mortal.”
(x)~Mx ⇔ ~(∃x)Mx
15. Express the following quantification rule in English: ~(x)Mx ⇔ (∃x)~Mx
The statement “Not everything is mortal” is logically equivalent to the statement “There is at least one thing that is not mortal.”
16. Express the following quantification rule in English: (x)Mx ⇔ ~(∃x)~Mx
The statement “Everything is mortal” is logically equivalent to the statement “There is not at least one thing that is not mortal.”
17. Express the following quantification rule in English: ~(x)~Mx ⇔ (∃x)Mx
The statement “Nothing is not mortal” is logically equivalent to the statement “Something is mortal.”
18. Express the following quantification rule in English: (x)~Mx ⇔ ~(∃x)Mx
The statement “Everything is not mortal is logically equivalent to the statement “There is not at least one thing that is mortal.”
19. Association (Replacement Rule)
• [p v (q v r)] ⇔ [(p v q) v r]
• [p • (q • r)] ⇔ [(p • q) • r]
• In a conjunction or disjunction of three true statements, it does not matter if you group the first two or the last two.
20. Double Negation (Replacement Rule)
• p ⇔ ~~p
• Any statement is logically equivalent to the negation of the negation of that statement.
21. Commutation (Replacement Rule)
• (p v q) ⇔ (q v p)
• (p • q) ⇔ (q • p)
• The order of the elements of a conjunction or disjunction does not matter.
22. Material Implication (Replacement Rule)
• (p ⊃ q) ⇔ (~p v q)
• Either the antecedent (p) is false or the consequent (q) is true.
23. Transposition (Replacement Rule)
• (p ⊃ q) ⇔ (~q ⊃ ~p)
• Any conditional statement is logically equivalent to the conditional statement asserting that the negation of its consequent implies the negation of its antecedent.
24. Tautology (Replacement Rule)
• p ⇔ (p v p)
• p ⇔ (p • p)
• Any statement is logically equivalent to the conjunction or disjunction of itself.
25. Exportation (Replacement Rule)
• [(p • q) ⊃ r] ⇔ [p ⊃ (q ⊃ r)]
• If two propositions conjoined imply a third, that is logically equivalent to asserting that if the first one is true, then the truth of the second must imply the truth of the third.
26. Material Equivalence (Replacement Rule)
• (p ⇔ q) [(p ⊃ q) • (q ⊃ p)]
• (p ⇔ q) [(p • q) v (~q • ~p)]
• The assertion that two statements are materially equivalent is logically equivalent to asserting that they are both true or both false…and that they materially imply each other.
27. De Morgan’s Theorems (Replacement Rule)
• ~(p • q) ⇔ (~p v ~q)
• ~(p v q) ⇔ (~p • ~q)
• The negation of a conjunction is logically equivalent to the disjunction of the negations of the conjuncts. The negation of a disjunction is logically equivalent to the conjunction of the negations of the disjuncts.
28. Distribution (Replacement Rule)
• [p • (q v r)] ⇔ [(p • q) v (p • r)]
• [p v (q • r)] ⇔ [(p v q) • (p v r)]
• The conjunction of one statement with the disjunction of two other statements is logically equivalent to either the conjunction of the first with the second or the conjunction of the first with the third. The disjunction of one statement with the conjunction of two others is logically equivalent to the conjunction of the disjunction of the first with the second and the disjunction of the first with the third.
• p
• ∴ p v q
30. Constructive Dilemma
• (p ⊃ q) • (r ⊃ s)
• p v r
• ∴ q v s
31. Conjunction
• p
• q
• ∴ p • q
32. Disjunction Syllogism
• p v q
• ~p
• ∴ q
33. Modus Ponens
• p ⊃ q
• p
• ∴ q
34. Simplification
• p • q
• ∴ p
35. Hypothetical Syllogism
• p ⊃ q
• q ⊃ r
• ∴ p ⊃ r
36. Modus Tollens
• p ⊃ q
• ~q
• ∴~p
37. Absorption
• p ⊃ q
• p ⊃ (p • q)
38. The fallacy of affirming the consequent
• p ⊃ q
• q
• ∴ p
39. The fallacy of denying the antecedent
• p ⊃ q
• ~p
• ∴ ~q
40. Tautology (definition of tautological statement form)
• A statement form with only true substitution instances.
• Ex: p v ~p
• Ex: (p ⊃ q) ⊃ [p ⊃ (p ⊃ q)]
• Ex: A truth table in which the conclusion column has only T values.
• A statement form with only false substitution instances.
• Ex: p • ~p
• Ex: A truth table in which the conclusion column has only F values.
42. Contingent (definition of contingent statement form)
• A statement form with some true and some false substitution instances.
• Ex: p • q
• Ex: A truth table in which the conclusion column has both T and F values.
43. Tautology (definition of tautological statement)
• A statement whose specific form is a tautology.
• Ex: (A ⊃ B) ⊃ [A ⊃ (A ⊃ B)]
44. 3 Meanings of Tautology
• A statement form with only true substitution instances: (p ⊃ q) ⊃ [p ⊃ (p ⊃ q)]
• A statement whose specific form is a tautology: (A ⊃ B) ⊃ [A ⊃ (A ⊃ B)]
• The particular logical equivalence: p ⇔ (p v p) p ⇔ (p • p)
45. The predicate logic form of “The common cold is never fatal.”
• Cx: x is the common cold.
• Fx: x is fatal.
• (x) (Cx ⊃ ~Fx)
46. The predicate logic form of “There is not a single witch or wizard who went bad who wasn’t in Slitherin.”
• Bx: x is a witch or wizard who went bad.
• Sx: x is a witch or wizard who was in Slitherin.
• (x) (Bx ⊃ Sx)
47. The predicate logic form of “Some humans are not mortal.”
• Hx: x is a human.
• Mx: x is mortal.
• (∃x) (Hx • ~Mx)
48. The predicate logic form of “Some humans are mortal.”
• Hx: x is a human.
• Mx: x is mortal.
• (∃x) (Hx • Mx)
49. The predicate logic form of “No humans are mortal.”
• Hx: x is a human.
• Mx: x is mortal.
• (x) (Hx ⊃ ~Mx)
50. The predicate logic form of “All humans are mortal.”
• Hx: x is a human.
• Mx: x is mortal.
• (x) (Hx ⊃ ~Mx)
51. Three laws of thought
• The principle of identity: p ⊃ p is always true (a tautology)
• The principle of contradiction: p • ~p is always false
• The principle of the excluded middle: p v ~p is always true (a tautology)
52. The principle of identity
• p ⊃ p
• always true (a tautology)
• p • ~p
• always false
54. The principle of the excluded middle
• p v ~p
• always true (a tautology)
55. Proposition (aka Statement)
A sentence with a truth value (true or false).
56. Sound argument
A deductive argument that is valid and has true premises.
57. Inference
A process by which one proposition is arrived at and affirmed on the basis of some other proposition or propositions.
58. Valid argument
In this type of argument, if the premises are true, then the conclusion must be true.
59. Enthymeme
An argument based on an unstated proposition.
60. Euphemisms
Gentle words that are used to refer to harsh realities.
61. Two things that disagreements can be about.
• Attitudes
62. Validity
A formal characteristic of arguments that refers to the relation between propositions (premises and conclusion).
63. Logic
The study of the methods and principles used to distinguish correct from incorrect reasoning.
64. Explanation
A group of statements from which some event (or thing) to be explained can logically be inferred and whose acceptance removes or diminishes the problematic character of that event (or thing).
65. Argument
Any group of propositions (premises and conclusion) of which one (conclusion) follows from the others.
66. Structure of definitions: Extension
Also called denotation, and it includes the objects to which a term may be correctly applied.
67. Structure of definitions: Intension
Also called connotation, and it includes the set of attributes shared by all and only those objects to which a general term refers.
68. Five rules for good definitions
• Should state essential attributes
• Must not be circular
• Must not be too broad or narrow
• Should not rely on ambiguous, obscure, or figurative language
• When possible, should not be negative
69. Three kinds of intensional definitions
• Synonymous
• Operational
• Definitions by genus and difference
70. A synonymous definition
A definition involving two words with the same meaning.
71. An operational definition
A definition in which the meaning is tied to a clearly describable set of actions or operations.
72. A definition by genus and difference
A definition involving a division into subclasses (genus) and the attribute (difference) that differentiates members of the classes.
73. Three different senses of intension
• Subjective
• Objective
• Conventional
74. Subjective intension of a word
A type of intension in which the set of all attributes the speaker believes to be possessed by objects denoted by that word.
75. Objective intension of a word
A type of intension in which the total set of characteristics shared by all objects in the word’s extension.
76. Conventional intension of a word
A type of intension of stable meaning by implicit agreement to use the same criterion for deciding whether an object is part of the term’s extension.
77. Four forms of language
• Declarative: A statement. (“Logic is easy.”)
• Exclamatory: An exclamation. (“You’ve got to be kidding!”)
• Imperative: A command. (“Trust me.”)
• Interrogative: A question. (“Why should I?”)
78. Five major functions (uses) of language
• Informative
• Expressive
• Directive
• Ceremonial
• Performative
79. What is the purpose of the informative function of language?
• To report facts.
• Example: “It is raining.”
80. What is the purpose of the expressive function of language?
• To express attitudes or beliefs.
• Example: “That’s great!”
81. What is the purpose of the directive function of language?
• To guide, command, or direct the behavior of others.
• Example: “Turn left at the next light.”
82. What is the purpose of the ceremonial function of language?
• To fulfill social obligations.
• Example: “How do you do?”
83. What is the purpose of the performative function of language?
• To perform the action that it describes.
• Example: “I now pronounce you man and wife.”
• Example: “I accept your offer.”
• Example: “I apologize.”
• Example: “I congratulate you on your engagement.”
• Example: “I promise you that I will be there.”
84. Five kinds of definitions
• Stipulative
• Lexical
• Precising
• Theoretical
• Persuasive
85. Stipulative definition
A definition that is deliberately assigned.
86. Lexical definition
A definition that reports an already established meaning.
87. Precising definition
A definition that eliminates ambiguity or vagueness.
88. Theoretical definition
A definition that encapsulates a larger understanding.
89. Persuasive definition
A definition used to resolve a dispute by influencing attitudes or stirring emotions.
90. Rhetorical question
Suggests or assumes an answer that is made to serve as the premise of an argument.
91. Vague term
A term for which there are borderline cases to which the term might or might not apply.
92. Deductive argument
A type of argument in which the conclusion is necessarily true if the premises are true.
93. Ambiguous term
A type of term for which there is more than one distinct meaning.
94. Two terms for definitions and their uses
• Definiendum
• Definiens
95. Definiendum
The part of a definition that contains the symbol being defined.
96. Definiens
The part of a definition that contains the symbol (or group of symbols) used to explain the meaning of the symbol being defined.
97. Inductive argument
A type of argument in which the conclusion is probably true if the premises are true.
98. Three types of disputes
• Genuine – about beliefs or attitudes
• Merely verbal – arising from the unrecognized use of ambiguous terms
• Apparently verbal but really genuine – in which a real difference remains even after apparent ambiguity has been eliminated
99. Conclusion
A proposition to which other propositions in the argument are claimed to give support.
100. Premise
A proposition that provides support for a conclusion.
101. Denotative definition structure
A type of definition structure that employs techniques that identify the extension of the term being defined.
102. Two types of denotative definition structures
• Ostensive
• Quasi-ostensive
103. Ostensive definition structure
A definition structure that points at or demonstrates what it defines.
104. Quasi-ostensive definition structure
A definition structure that includes a descriptive phrase about what it defines.
105. Six conclusion indicators (card 1 of three)
• for this reason
• which points to the conclusion that
• which allows us to infer that
• we may infer that
• therefore
• hence
106. Seven conclusion indicators (card 2 of three)
• thus
• for these reasons
• it follows that
• I conclude that
• which shows that
• so
• which entails that
107. Eight conclusion indicators (card 3 of three)
• so
• accordingly
• in consequence
• consequently
• which means that
• proves that
• as a result
• which implies that
108. Seven premise indicators (card 1 of two)
• since
• because
• in view of the fact that
• for
• as
• follows from
• as shown by
109. Seven premise indicators (card 2 of two)
• inasmuch as
• as indicated by
• the reason is that
• for the reason that
• may be inferred from
• may be derived from
• may be deduced from
110. Implies / entails
A relationship between statements (premises and conclusions).
111. Truth and falsity
Formal characteristics of individual propositions.
112. Translate the following into sentential logic: “Smith is either the owner or the manager.”
O v M
113. Translate the following into sentential logic: “You will do poorly on the exam unless you study.”
P v S
114. Translate the following into sentential logic: “If you don’t study, you will do poorly on the exam.”
~S ⊃ P
115. Translate the following into sentential logic: “Either Fillmore or Harding was the greatest U.S. president.”
F v H
116. Translate the following into sentential logic: “Neither Fillmore nor Harding was the greatest U.S. president.”
• ~(F v H)
• or it can be expressed as (~F • ~H)
117. Translate the following into sentential logic: “Jamal and Derek will not both be elected.”
• ~(J • D)
• or it can be expressed as (~J • ~D)
118. Translate the following into sentential logic: “I will study hard and pass the exam or I will fail the exam.”
(S • P) v F
119. Translate the following into sentential logic: “I will study hard and I will either pass the exam or fail it.”
S • (P v F)
Author: tiffanyscards ID: 2120 Card Set: Intro to Logic Updated: 2009-12-13T02:38:51Z Folders: Description: Study cards for PHILO 103. Show Answers: | 4,620 | 18,106 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-40 | latest | en | 0.888957 |
https://doc.opensuse.org/projects/libzypp/HEAD/Algorithm_8h_source.html | 1,713,496,847,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817253.5/warc/CC-MAIN-20240419013002-20240419043002-00175.warc.gz | 187,149,635 | 3,758 | libzypp 17.31.23
Algorithm.h
Go to the documentation of this file.
1/*---------------------------------------------------------------------\
2| ____ _ __ __ ___ |
3| |__ / \ / / . \ . \ |
4| / / \ V /| _/ _/ |
5| / /__ | | | | | | |
6| /_____||_| |_| |_| |
7| |
8\---------------------------------------------------------------------*/
12#ifndef ZYPP_BASE_ALGORITHM_H
13#define ZYPP_BASE_ALGORITHM_H
14
15#include <algorithm>
16
18namespace zypp
19{
20
29 template <class TIterator, class TFilter, class TFunction>
30 inline int invokeOnEach( TIterator begin_r, TIterator end_r,
31 TFilter filter_r,
32 TFunction fnc_r )
33 {
34 int cnt = 0;
35 for ( TIterator it = begin_r; it != end_r; ++it )
36 {
37 if ( filter_r( *it ) )
38 {
39 ++cnt;
40 if ( ! fnc_r( *it ) )
41 return -cnt;
42 }
43 }
44 return cnt;
45 }
46
55 template <class TIterator, class TFunction>
56 inline int invokeOnEach( TIterator begin_r, TIterator end_r,
57 TFunction fnc_r )
58 {
59 int cnt = 0;
60 for ( TIterator it = begin_r; it != end_r; ++it )
61 {
62 ++cnt;
63 if ( ! fnc_r( *it ) )
64 return -cnt;
65 }
66 return cnt;
67 }
68
69 template <class Container, class Elem>
70 bool contains ( const Container &c, const Elem &elem )
71 {
72 return ( std::find( c.begin(), c.end(), elem ) != c.end() );
73 }
74
75 template <class Container, class Fnc >
76 bool any_of ( const Container &c, Fnc &&cb )
77 {
78 return std::any_of( c.begin(), c.end(), std::forward<Fnc>(cb) );
79 }
80
82} // namespace zypp
84#endif // ZYPP_BASE_ALGORITHM_H
Easy-to use interface to the ZYPP dependency resolver.
Definition: CodePitfalls.doc:2
bool any_of(const Container &c, Fnc &&cb)
Definition: Algorithm.h:76
bool contains(const Container &c, const Elem &elem)
Definition: Algorithm.h:70
int invokeOnEach(TIterator begin_r, TIterator end_r, TFilter filter_r, TFunction fnc_r)
Iterate through [begin_r,end_r) and invoke fnc_r on each item that passes filter_r.
Definition: Algorithm.h:30 | 577 | 1,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2024-18 | latest | en | 0.270532 |
https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html | 1,708,992,336,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474669.36/warc/CC-MAIN-20240226225941-20240227015941-00174.warc.gz | 417,386,063 | 41,228 | Get Instant Help From 5000+ Experts For
Writing: Get your essay and assignment written from scratch by PhD expert
Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost
Variables
The height and the arm span of an individual are thought to be statistically correlated. The height of individual measures is believed to be directly proportional to the arm span of such an individual. Scientists and other researchers have concluded that the height of a particular student is directly proportional to their arm span. The arm span can be used to predict the height of an individual. How tall an individual depends on their arm span. The statistical test has drawn much attention, and I decided to carry out an experiment t to verify the truth of the above guess. Initially, it was my understanding that the height of an individual is itself an independent variable. An individual is born and his or her height depends on hereditary and genetic factors (Matsumoto et al., 2021). The height of an individual relied on the height s of the initial family members. However, following the fact, the scientists state that an individual's arm span can be used to determine their respective height. The experiment below tries to answer the question that an individual's arm span and height are statistically correlated. One can be used to predict the other r and vice versa.
Height is the dependent variable. The height is the variable that will receive the changes made to the arm span. We shall measure the different arm span and predict the height of that particular individual. Assume a scenario whereby at the school gate of entering an institution, scientists would like to determine if they measure the arm span of the students as they enter the university gate whether at the end of the day they shall come up with the appropriate measures of a given students height.
The arm span will be used as the independent variable in the experiment. We shall measure the different arm spans of the student at the university gate main entrance and later on use the measurement collected To predict the height of the particular student.
Gender will be the controlled variable. We can decide to ignore at all]l costs the Gender of a particular student and carry out the experiment assuming that the height and the arm span of the student are correlated despite the fact the height was obtained from a male or a female; e student. At all costs, we pick the height and the arm span without considering the Gender. We shall have the two variables correlated.
The null hypothesis: H0:e=0 (Meaning that the height and the arm span are not correlated. There is no particular relationship between the height and the arm span of an individual.
The alternative hypothesis: H0:e≠0 (meaning the correlation coefficient between the height and the arm span of an individual is not equal to 0. The correlation coefficient between the dependent and the independent variable is not 0). If we increase an individual's arm span, we shall expect an increase in the height of that particular individual.
µ1 represents the Average Height of the male students
## Hypothesis
µ2 represents the c=average arm span of the female students
Null hypothesis: µ1= µ2 (The average height of the male students is equal to the average height of the female students
The alternative hypothesis: µ1 > µ2 (The average height of the male students is greater than the average height of the female students. If we measure the arm span, and use it to predict the height of a given student, then if it results out that we obtain a considerable measure for the height, that particular student shall be a male student.
The experiment took place at one of the universe's laboratories. We set our experiment at an edge near the university's main gate. We had the tent stationed at the particular border. All the measurement tools were already staged at the venue several days before the actual experiment was done. The target population was the students at the university. The group of the students who agreed for their credentials to be taken was composed of the population of the students.
The photos were taken during the experiment
Picture 1
Picture 2
Picture 3
Procedures
The procedure for the above experiment was as follows:
The first step involved staging a place where we shall obtain the different measures of the student's arm span. We set as tend close to the universities' main gate, whereby as the students are done with their classes on that particular day, we would measure their respective arm span. We decided to experiment immediately after the course at the students early in the morning are always rushing to their classes. Most of them might not be willing to provide their credentials. Therefore doing it in the afternoon session would be the most suitable time. To make sure that we came up with a good number of observations, we decided to give incentives to the student who agreed for us to measure their arm span (Stagi et al., 2021). We decided that soda and a small piece of cake would be a better reward for the students who took part in the experiment. This is done to ensure that we come up with such a voluminous number of observations to mention the claims stated above at the end of the day.
The second step involved selecting a team to create public awareness of the same matter. We decided to create posters and spread them around all the university relaxing sites and the university's website with permission from the dean of the students. Then we set aside an entertainment team to entertain the student as the process continues. This is made to ensure that our guests have the best time they need possible.
The tent was divided into three stages. The first stage involved recording the Gender of the student. As the student enters the tent, the first question involves having them state their Gender. They proceed to stage two. In the second stage, the student's arm span is measured. The student Is required to stretch their two hands then a tape measure was used to measure the arm span of that particular student. The team in charge of taking the measurements will be forced to be as keen as possible to ensure that the correct measurements are taken for the male students who might have a broader chest capacity and the female students whose ability may trigger the measures.
## Experiment Setup
Immediately after this stage, the students proceed to stage three, where their respective height is recorded. The student must stand in an upright position to ensure that the precise measurement is taken. Additionally, the team responsible for measuring the height is well set and fits the unit to make sure that it is possible to measure the students who might be abnormally tall. In some rare cases, some individuals are so tall compared to the rest of the students.
Once the correct measurements had been taken, we had another that assisted us with data collection. We gathered all the Data data we obtained from the tents and composed it into an extensive composite data. To make precise calculations and tabulation and the keying of the data collected, we use the following statistical packages.
1. We used excel to enter what was collected from the field. Excel has good data entry options since it can place the data into respective rows and columns. In excel, we divided the data into four columns. In the first column, we recorded the student's name, and in the second column, we recorded the Gender of that particular student. In the following two columns, we had students' arm span recorded and height recorded, respectively, and we saved the document in a comma-delimited file.
2. R Programming Language. Since I am proficient with R statistical package, I decided to carry out my data analysis using an R programming language. I imported the data to R statistical package, then began my computations.
The process of data was relatively smooth. After importing the data To R statistical package, we had to carry out a few steps to make sure that our data was ideal. We at first had to clean the data. We had to make sure that the data was free of any missing variables and that there were no instances of having data keyed in wrongly. R statistical packages come with such tools for checking for any lost data. Afterward, we had to create a scatter diagram that helps to show the relationship between the two variables of interest: the dependent variable, height, and the independent variable, arm span. After creating a scatter plot for visualizing the relationship, we created a correlation matrix that shows the relationship between all the numeric variables used in the experiment. We further calculate the correlation coefficient between the two variables of interest (Träuble et al., 2021). Afterward, to verify that the average height of the male students is more enormous than that of female students, we calculated the summary statistics of our data. We then requested R to carry out hypothesis testing and check out whether the average height of the males is larger than the average height of the females. Before this, we were forced to group the data for the male students separately from the data of the female students.
Fig 1
The Graph above shows the Graphed Relationship between the students' Arm span on the x-axis and the Height of the particular student on the y axis. From the Graph, it is clear that a student's height and their arm span are related correlated. Two happen to have a remarkably intact linear Relationship with each other. The alignment of the plotted line shows this.
Fig 2
All the plotted points align close to the line of best fit marked by a blue line between the points. The points align very closely with the blue line, which is the line of best fit, then we deduce that students' height and the student arm span are closely related. Also, it is evident that as the arm span increases, the height of the student increases and vice versa. Therefore the height and the arm span of a student picked at random have a linear relationship (Saville et al., 2021).
## Procedures
The correlation of the Height and Arm span of the males.
Fig 3
The Graph below also reveals that male students' height and arm span have a linear relationship. One of the variables can be used to predict the other variable.
The correlation coefficient between the two variables amongst the males’ data was also significant and positive. Hence, the height and arm span of male students picked at random exhibit a linear relationship.
The correlation of the Height and Arm span of the females.
Fig 4
A linear relationship exists as well in the female data—the height of any female student exhibit a linear relation with the arm span of the student.
When two statistical objects portray a linear relationship, it is always possible to predict the outcome of the other variable given one of the variables. The Result of fitting a linear Regression Line between the two plotted points was as follows:
The slope and the intercept value are; 4.2797 and 0.9244, respectively. The regression line forecasting the height of a student given his arm span is
The height= 4.27972 + 0.92436(The arm Span )
We can use this equation each time we would like to determine the height of a given student given the measurements of their arm span.
The R – squared coefficient used to evaluate model fitness is 92.49. Therefore, the model is fit for prediction.
The correlation matrix above involves only two variables: the dependent variable is height, and the independent variable is Arm span. Therefore the correlation matrix, which 0only takes numerical variables, may not be as comprehensive as it might be thought. The correlation coefficient is positive(Fuchs et al., 2021 ). Which implies that two variables have a strong positive linear association with each other? Moreover, the correlation coefficient one is when a variable is compared against itself, but the coefficient is 0.9871703 when compared to aging, the opposite variable. This clearly shows that the height and arm span, as the scientists and researchers suggest, have an influential linear association. A single change in the independent variable will lead to an increase in a dependent variable. This further indicates that the longer the student, the longer the arm span and vice versa.
The output above summaries on the descriptive statistics. The student who had a minimum height had a height of 40.50 units, while the student who had the maximum height had a height of 76.50 units, and the students were Scott and Hellen Respectively. The mean height of all the students who took part in the experiment was 59.49 (Berriel et al., 2021). The student who recorded the minimum arm span recode a span of 37.50 units, while the student who recorded the highest arm span had an arm span of 76.50, and the student was Hellen and Scott. This further shows that the student who recorded the highest arm span also had the highest, which shows that arm span and height share a very close linear association.
Males students data
The male student's mean Height and arm span are 62.57 and 62.86, respectively. The shortest male student was Jeremy and mark, and the two had a size of 50.0 units but had the shortest arm span of 48.75.
Female students Data
The mean Height of the female student was 54.10, and the mean arm span was 54.09. The tallest female student was Irene, with a height of 63.0 units, while the shortest student was Hellen, with a size of 43.50 units. Charity had the longest arm span, and Hellen still had the shortest arm span.
Conclusion
The results of hypothesis testing depicted that, indeed, the mean of x variable, which is the mean of the male student's height, is greater than the mean height of the female students. The critical region had been set at Reject H0: µ1 =µ2 if the calculated t value is greater than the tabulated t value of ttab = 2.068658.
With the calculated t value, tcalc=2.1415, we reject the H0: µ1 =µ2 and conclude that the mean height of the male students is greater than the mean height of the female students.
Faulty gadgets- we had some of the devices used in the experiment failing us at the last moment, and this forced us to use them defective, which could have triggered errors.
The unwillingness of the students to take part in the experiment- most of the students preferred to have their information kept private. Some of them did not want their height and weight measured. Also, some of the students were in much hurry; therefore, we did not have much time to take their measurements precisely.
The measuring skill of science
I measured several students and therefore made use of the measuring skill outlined by science.
There was no need to ask a student which gender group they belonged to during the experiment. I could use my science observing skills to tell which Gender a given student belongs to. However, in rare observations, some of the students seemed to belong to both genders, which involved keen observation in ensuring that the correct Gender was indeed the one recorded for each student.
After doing several measurements, I was able to predict a student's heigh after measuring their arm span. Most of the students had a height equal s to their arm span. Therefore it was pretty easy for me to predict the height of such students after measuring their arm span, although some of the students had their arm span differing so much from their height.
The experiment above has helped me understand that a particular individual's height and arm span are directly correlated. The arm span can predict how tall or short an individual is if one knows their arm span. Moreover, I have also noted that the scientific claims made by researchers and scientists are really of great help in teaching the new generation how science plays a significant role in todays and upcoming lifestyles. Experimenting in science helps us reject or reinforce the claims made by the researcher or other scientists.
List of References
Berriel, G. P., Schons, P., Costa, R. R., Oses, V. H. S., Fischer, G., Pantoja, P. D., ... & Peyré-Tartaruga, L. A. (2021). Correlations between jump performance in block and attack and the performance in official games, squat jumps, and countermovement jumps of professional volleyball players. The Journal of Strength & Conditioning Research, 35, S64-S69.
Träuble, F., Creager, E., Kilbertus, N., Locatello, F., Dittadi, A., Goyal, A., ... & Bauer, S. (2021, July). On disentangled representations learned from correlated data. In International Conference on Machine Learning (pp. 10401-10412). PMLR.Matsumoto, H., Marciano, G., Redding, G., Ha, J., Luhmann, S., Garg, S., ... & White, K. (2021). Association between health-related quality of life outcomes and pulmonary function testing. Spine deformity, 9(1), 99-104.
Stagi, S., Ibáñez-Zamacona, M. E., Jelenkovic, A., Marini, E., & Rebato, E. (2021). Association between self-perceived body image and body composition between the sexes and different age classes. Nutrition, 82, 111030.
Fuchs, P. X., Mitteregger, J., Hoelbling, D., Menzel, H. J. K., Bell, J. W., von Duvillard, S. P., & Wagner, H. (2021). Relationship between broad jump types and spike jump performance in elite female and male volleyball players. Applied Sciences, 11(3), 1105.
Saville, N. M., Cortina-Borja, M., De Stavola, B. L., Pomeroy, E., Marphatia, A., Reid, A., ... & Wells, J. C. (2021). Comprehensive analysis of the association of seasonal variability with maternal and neonatal nutrition in lowland Nepal. Public Health Nutrition, 1-16.
Cite This Work
My Assignment Help. (2022). Statistical Correlation Between Height And Arm Span Essay.. Retrieved from https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html.
"Statistical Correlation Between Height And Arm Span Essay.." My Assignment Help, 2022, https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html.
My Assignment Help (2022) Statistical Correlation Between Height And Arm Span Essay. [Online]. Available from: https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html
[Accessed 27 February 2024].
My Assignment Help. 'Statistical Correlation Between Height And Arm Span Essay.' (My Assignment Help, 2022) <https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html> accessed 27 February 2024.
My Assignment Help. Statistical Correlation Between Height And Arm Span Essay. [Internet]. My Assignment Help. 2022 [cited 27 February 2024]. Available from: https://myassignmenthelp.com/free-samples/edse101-selected-school-science-topics/height-versus-arm-span-file-A1E4800.html.
Get instant help from 5000+ experts for
Writing: Get your essay and assignment written from scratch by PhD expert
Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost | 4,071 | 19,166 | {"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} | 3.796875 | 4 | CC-MAIN-2024-10 | longest | en | 0.939492 |
https://www.onlinemath4all.com/how-to-find-the-order-of-product-of-two-matrices.html | 1,582,221,323,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145260.40/warc/CC-MAIN-20200220162309-20200220192309-00357.warc.gz | 799,645,832 | 13,935 | # HOW TO FIND THE ORDER OF PRODUCT OF TWO MATRICES
How to Find the Order of Product of Two Matrices ?
Here we are going to see how to find the order of product of two matrices.
## How to Find the Order of Product of Two Matrices ?
To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
Consider the multiplications of 3×3 and 3×2 matrices.
(Order of left hand matrix) x (order of right hand matrix) -> (order of product matrix).
(3 × 3 ) x (3 × 2 ) -> (3 × 2 )
The product AB can be found if the number of columns of matrix A is equal to the number of rows of matrix B. If the order of matrix A is m x n and B is n x p then the order of AB is m x p .
Question 1 :
Find the order of the product matrix AB if
Solution :
(i) Order of A is 3 x 3, order of B is 3 x 3.
The order of the matrix AB is 3 x 3.
(ii) Order of A is 4 x 3, order of B is 3 x 2.
The order of the matrix AB is 4 x 2.
(iii) Order of A is 4 x 2, order of B is 2 x 2.
The order of the matrix AB is 4 x 2.
(iv) Order of A is 4 x 5, order of B is 5 x 1.
The order of the matrix AB is 4 x 1.
(v) Order of A is 1 x 1, order of B is 1 x 3.
The order of the matrix AB is 1 x 3.
Question 2 :
If A is of order p x q and B is of order q x r what is the order of AB and BA?
Solution :
(p x q) (q x r) = p x r
The order of matrix AB is p x r.
(q x r) (p x q) = p x r
The product of matrices B and A is not possible.
Hence it is not defined.
Question 3 :
A has ‘a’ rows and ‘a + 3 ’ columns. B has ‘b’ rows and ‘17–b’ columns, and if both products AB and BA exist, find a, b?
Solution :
Number of rows of A = a
Number of columns of A = a + 3
Number of rows of B = b
Number of columns of A = 17 - b
Since the product of matrices A and B is possible,
[a x (a + 3)] [b x (17 - b)]
a + 3 = b
a - b = -3 -----(1)
Since the product of matrices B and A is possible,
[b x (17 - b)] [a x (a + 3)]
17 - b = a
a + b = 17 ----(2)
(1) + (2)
2a = 14
a = 7
By applying the value of a in (1), we get
7 - b = -3
-b = -3 - 7
-b = -10
b = 10
After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Order of Product of Two Matrices".
Apart from the stuff given in this section "How to Find the Order of Product of Two Matrices"if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Algebra word problems
Word problems on trains
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on unit price
Word problems on unit rate
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Double facts word problems
Trigonometry word problems
Percentage word problems
Profit and loss word problems
Markup and markdown word problems
Decimal word problems
Word problems on fractions
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Word problems on ages
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Profit and loss shortcuts
Percentage shortcuts
Times table shortcuts
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6 | 1,268 | 4,728 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-10 | latest | en | 0.857228 |
https://www.smore.com/bw41 | 1,547,970,518,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583700734.43/warc/CC-MAIN-20190120062400-20190120084400-00461.warc.gz | 926,741,849 | 14,227 | Ms Watkins' PreCalculus Update
Progress Reports and Remediation Plans This Week!!
Greetings Parents,
We are already on Week 5 of school, time is flying! Progress reports will be issued on Tuesday to all students and on Wednesday, Remediation Plans will be issued to all students who have a 75 or lower in my class. Please review, sign, and have your student return it to me. I will then issue them a copy of their own to keep.
In class we will be completing our first unit on Data Analysis and be going into Sequences and Series. Sequences and Series requires that students look for patterns and create equations or rules to generate those patterns. Your student should spend time studying functions as this will be crucial to success in this unit.
Grades to be input this week:
Central Limit Theorem Quiz – Students were given a quiz on CLT; these question were some of the exact same questions reviewed in class. If your student did not do well on the quiz, it is because they are not completing HW when assigned and/or not studying. They will be given the opportunity to do corrections for 1/2 credit on Friday. The grade that you will see is the grade with corrections.
Google Site Address – Students were asked a week ago to create a Google site and to upload it to a Google doc on my webpage. Only five students completed this task. Therefore, I will award "participation points (20) to those who complied by Monday. If you see a zero, it means that your student did not complete the task.
Pennies Activity- Students will complete this activity in class and the report will be turned in and graded for accuracy. f you see a zero, it means that your student did not complete the task.
CLT PowerPoint HW. Students were assigned to do a guided PowerPoint assignment for HW. All students participated in the HW review presentation and therefore all received credit.
Again, I need your support in stressing the importance of completing homework. Homework is practice and is not meant to be done perfectly and mistake free. Actually, homework coupled with classwork is your child’s opportunity to experience learning by making and correcting mistakes. In class, we review the homework and students have the opportunity to ask questions. I do not collect HW daily, as these are college-bound students who need to understand that homework is beneficial to success on quizzes and tests; additionally, it helps to develop good study skills. HW quizzes are my way of “collecting” homework.
PreCalculus Webpage
Students should check this webpage daily. All assignments, quiz/dates, links to math resources, etc. will be located here.
Reminders
• EXCESSIVE TALKING: Please speak to your student about the importance of LISTENING and not SOCIALIZING in class.
• SUPPLIES: Students need to make sure that they have pencils, a TI Nspire calculator, several composition notebooks. colored pencils, personal pencil sharpener, tissue, and hand sanitizer.
• TI-NSPIRE: The TI Nspire is the preferred calculator of the school. You may purchase another type of calculator, however, your student will have to be the "expert" for that calculator.
• HOMEWORK: Homework is given daily. It may consist of reading, studying, notetaking, researching, doing problems, creating webguides, videos, etc. Whatever the case, students should spend at least 45 minutes of their time dedicated to math.
• WEBPAGE: I have created a webpage for each course that I teach. Students are expected to visit it daily and keep abreast of assignments and due dates. I will not be posting assignments in the classroom.
• TUTORIALS: Math Dept. tutorials are held on Tuesdays from 3:30-4:30. Tutorials are a privilege, not a right. Tutorials are by appointment only. Students may sign up via a a google doc on my webpage and must obtain a pass from me the Monday prior to tutorial. Students must come with their notebook and their specific questions. I will encourage study sessions in my tutorials as I prepare my students for college survival.
• TARDIES: Please remind students to come to class on time. Right now, the majority of tardies occur in First Period and after lunch.
• DRESS CODE: Many students are following the dress code, YAY!! However, some are getting in trouble for wearing multicolored shoes (shoes should be white, brown, blue, or black) and outerwear (sweaters and jackets) that is not in school colors (outer wear should be white (not beige), navy blue, or hunter green.
• LARGE BAGS: I know that large bags are stylish, however, they pose a safety threat. Large purses/handbags are not allowed in classrooms. If the bag is large enough to carry a book, it is considered a book bag and should be mesh or clear, otherwise it must remain in the locker.
Contact me!
Feel free to contact me if you have any questions or concerns! E-mail is my preferred way to communicate, however, all forms of communication are welcomed. | 1,050 | 4,912 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2019-04 | latest | en | 0.969814 |
https://www.sofolympiadtrainer.com/forum/questions/42763/pa-man-earns-rs-20-on-the-first-day-and-spends-rs-15-on-the-next-day-he-again-earns-rs-20-on-the-thi | 1,621,361,642,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991288.0/warc/CC-MAIN-20210518160705-20210518190705-00593.warc.gz | 1,061,132,017 | 6,600 | # User Forum
Subject :IMO Class : Class 9
A man earns Rs 20 on the first day and spends Rs 15 on the next day. He again earns Rs 20 on the third day and spends Rs 15 on the fourth day. If he continues to save like this, then how soon will he have Rs 60 in hand?
AOn 17th day
BOn 27th day
COn 30th day
DOn 24th day
It will take him 16 days to save Rs 40. Then on the 17th day, he will gain Rs 20, and thus, will have Rs 60.Therefore, the correct answer is (A) On 17th Day | 154 | 477 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-21 | latest | en | 0.953211 |
https://human.libretexts.org/Courses/Los_Medanos_College/Phil_100%3A_Introduction_to_Philosophy_(Haven)/01%3A_The_Existence_of_God/1.05%3A_The_Teleological_Argument | 1,723,056,578,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640707024.37/warc/CC-MAIN-20240807174317-20240807204317-00177.warc.gz | 227,511,113 | 35,235 | # 1.5: The Teleological Argument
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
## State of the Argument
I. Nor would it, I apprehend, weaken the conclusion, that we had never seen a watch made — that we had never known an artist capable of making one — that we were altogether incapable of executing such a piece of workmanship ourselves, or of understanding in what manner it was per- formed ; all this being no more than what is true of soma exquisite remains of ancient art, of some lost arts, and, to the generality of mankind, of the more curious productions of modern manufacture. Does one man in a million know how oval frames are turned ? Ignorance of this kind exalt our opinion of the unseen and unknown artist's skill, if he be unseen and unknown, but raises no doubt in our minds of the existence and agency of such an artist, at some former time and in some place or other. Nor can I perceive that it varies at all the inference, whether the question arise concerning a human agent or concerning an agent of a different species, or an agent possessing in some respects a different nature.
II. Neither, secondly, would it invalidate our conclusion, that the watch sometimes went wrong, or that it seldom went exactly right. The purpose of the machinery, the design, and the designer might be evident, and in the case supposed, would be evident, in whatever way we accounted for the irregularity of the movement, or whether we could account for it or not- It is not necessary that a machine be perfect, in order to show with what design it was made : still less necessary, where the only question is whether it were made with any design at all.
III. Nor, thirdly, would it bring any uncertainty into the argument, if there were a few parts of the watch, concerning which we could not discover or had not yet discovered in what manner they conduced to the general effect ; or even some parts, concerning which we could not ascertain whether they conduced to that effect in any manner whatever. For, as to the first branch of the case, if by the loss, or disorder, or decay of the parts in question, the movement of the watch were found in fact to be stopped, or disturbed, or retarded, no doubt would remain in our minds as to the utility or intention of these parts, although we should be unable to investigate the manner according to which, or the connection by which, the ultimate effect depended upon their action or assistance ; and the more complex the machine, the more likely is this obscurity to arise. Then, as to the second thing supposed, namely, that there were parts which might be spared without prejudice to the movement of the watch, and that we had proved this by experiment, these superfluous parts, even if we were completely assured that they were such, would not vacate the reasoning which we had instituted concerning other parts. The indication of contrivance remained, with respect to them, nearly as it was before.
IV. Nor, fourthly, would any man in his senses think the existence of the watch with its various machinery account- ed for, by being told that it was one out of possible combinations of material forms ; that whatever he had found in the place where he found the watch, must have contained some internal configuration or other ; and that this configuration might be the structure now exhibited, namely, of the works of a watch, as well as a different structure.
V. Nor, fifthly, would it yield his inquiry more satisfaction, to be answered that there existed in things a principle of order, which had disposed the parts of the watch into their present form and situation. He never knew a watch made by the principle of order ; nor can he even form to himself an idea of what is meant by a principle of order, distinct from the intelligence of the watchmaker.
VI. Sixthly, he would be surprised to hear that the mechanism of the watch was no proof of contrivance, only a motive to induce the mind to think so :
VII. And not less surprised to be informed, that the watch in his hand was nothing more than the result of the laws of metallic nature. It is a perversion of language to assign any law as the efficient, operative cause of any thing. A law presupposes an agent ; for it is only the mode according to which an agent proceeds : it implies a power ; for it is the order according to which that power acts. Without this agent, without this power, which are both distinct from itself, the law does nothing, is nothing. The expression, " the law of metallic nature," may sound strange and harsh to a philosophic ear ; but it seems quite as justifiable as some others which are more familiar to him, such as " the law of vegetable nature," "the law of animal nature," or, indeed, as " the law of nature" in general, when assigned as the cause of phenomena, in exclusion of agency and power, or when it is substituted into the place of these?.
VIII. Neither, lastly, would our observer be driven out of his conclusion or from his confidence in its truth, by being told that he knew nothing at all about the matter. He knows enough for his argument ; he knows the utility of the end ; he knows the subserviency and adaptation of the means to the end. These points being known, his ignorance of other points, his doubts concerning other points, affect not the certainty of his reasoning. The consciousness of knowing little need not beget a distrust of that which he does know.
## Application of the Argument
… For every indication of contrivance, every manifestation of design which existed in the watch, exists in the works of nature, with the difference on the side of nature of being greater and more, and that in a degree which exceeds all computation. I mean, that the contrivances of nature surpass the contrivances of art, in the complexity, subtlety, and curiosity of the mechanism ; and still more, if possible, do they go beyond them in number and variety ; yet, in a multitude of cases, are not less evidently mechanical, not less evidently contrivances, not less evidently accommodated to their end or suited to their office, than are the most perfect productions of human ingenuity.
I know no better method of introducing so large a subject, than that of comparing a single thing with a single tiling : an eye, for example, with a telescope. As far as the examination of the instrument goes, there is precisely the same proof that the eye was made for vision, as there is that the telescope was made for assisting it. They are made upon the same principles ; both being adjusted to the laws by which the transmission and refraction of rays of light are regulated. I speak not of the origin of the laws themselves ; but such laws being fixed, the construction in both cases is adapted to them. For instance, these laws require, in order to produce the same effect, that the rays of light, in passing from water into the eye, should be refracted by a more convex surface than when it passes out of air into the eye. Accordingly we find that the eye of a fish, in that part of it called the crystalline lens, is much rounder than the eye of terrestrial animals. What plainer manifestation of design can there be than this difference ? What could a mathematical instrument maker have done more to show his knowledge of bis principle, his application of that knowledge, his suiting of his means to his end — I will not say to display the com- pass or excellence of his skill and art, for in these all comparison is indecorous, hut to testify counsel, choice, consideration, purpose?
To some it may appear a difference sufficient to destroy all similitude between the eye and the telescope, that the one is a perceiving organ, the other an unperceiving instrument. The fact is that they are both instruments. And as to the mechanism, at least as to mechanism being employed, and even as to the kind of it, this circumstance varies not the analogy at all. For observe what the constitution of the eye is. It is necessary, in order to produce distinct vision, that an image or picture of the object be formed at the bot- tom of the eye. Whence this necessity arises, or how the picture is connected with the sensation or contributes to it, it may be difficult, nay, we will confess, if you please, impossible for us to search out. But the present question is not concerned in the inquiry. It may be true, that in this and in other instances we trace mechanical contrivance a certain way, and that then we come to something which is not mechanical, or which is inscrutable. But this affects not the certainty of our investigation, as far as we have gone. The difference between an animal and an automatic statue consists in this, that in the animal we trace the mechanism to a certain point, and then we are stopped ; either the mechanism being too subtle for our discernment, or something else ... besides the known laws of mechanism taking place ; whereas, in the automaton, for the comparatively few motions of which it is capable, we trace the mechanism throughout. But, up to the limit, the reasoning is as clear and certain in the one case as in the other. In the example before us it is a matter of certainty, because it is a matter which experience and observation demonstrate, that the formation of an image at the bottom of the eye is necessary to perfect vision The image itself can be shown. Whatever affects the distinctness of the image, affects the distinctness of the vision. The formation then of such an image being necessary — no matter how — to the sense of sight and to the exercise of that sense, the apparatus by which it is formed is constructed and put together not only with infinitely more art, but upon the selfsame principles of art, as in the telescope or the camera-obscura. The perception arising from the image may be laid out of the question ; for the production of the image, these are instruments of the same kind. The end is the same ; the means are the same. The purpose in both is alike ; the contrivance for accomplishing that purpose is in both alike. The lenses of the telescopes and the humors of the eye bear a complete resemblance to one another, in their figure, their position, and in their power over the rays of light, namely, in bringing each pencil to a point at the right distance from the lens ; namely, in the eye, at the exact place where the membrane is spread to receive it. How is it possible, under circumstances of such close affinity, and under the operation of equal evidence, to exclude contrivance from the one, yet to acknowledge the proof of contrivance having been employed, as the plainest and clearest of all propositions, in the other?
The resemblance between the two cases is still more accurate, and obtains in more points than we have yet represented, or than we are, on the first view of the subject, aware of. ...
Every observation which was made in our first chapter concerning the watch, may be repeated with strict propriety concerning the eye; concerning animals; concerning plants; concerning all the organized parts of the works of nature.
When we are inquiring simply after the existence of an intelligent Creator, imperfection, inaccuracy, liability to disorder, occasional irregularities, may subsist in a consider- able degree without inducing any doubt into the question ; just as a watch may frequently go wrong, seldom perhaps exactly right, may be faulty in some parts, defective in some, without the smallest ground of suspicion from thence arising that it was not a watch, not made, or not made for the purpose ascribed to it. When faults are pointed out, and when a question is started concerning the skill of the artist, or the dexterity with which the work is executed, then, indeed, in order to defend These qualities from accusation, we must be able, either to expose some intractableness and imperfection in the materials, or point out some invincible difficulty in the execution, into which imperfection and difficulty the matter of complaint may be resolved ; or, if we cannot do this, we must adduce such specimens of consummate art and contrivance proceeding from the same hand as may convince the inquirer of the existence, m the case before him, of impediments like those which we have mentioned, although, what from the nature of the case is very likely to happen, they be unknown and unperceived by him. This we must do in order to vindicate the artist's skill, or at least the perfection of it ; as we must also judge of his intention, and of the provisions employed in fulfilling that intention, not from an instance in which they fail, but from the great plurality of instances in which they succeed. But, after all, these are different questions from the question of the artist's existence ; or, which is the same, whether the thing before us be a work of art or not ; and the questions ought always to be kept separate in the mind. So likewise it is in the works of nature Irregularities and imperfections are of little or no weight in the consideration, when that consideration relates simply to the existence of a Creator. When the argument respects his attributes, they are of weight ; but are then to be taken in conjunction — the attention is not to rest upon them, but they are to be taken in conjunction, with the unexceptionable evidences which we possess of skill, power, and benevolence displayed in other instances ; which evidences may, in strength, number, and variety, be such, and may so overpower apparent blemishes, as to induce us, upon the most reasonable ground, to believe that these last ought to be referred to some cause, though we be ignorant of it, other than defect of knowledge or of benevolence in the author.
1.5: The Teleological Argument is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. | 4,658 | 18,153 | {"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} | 3.5625 | 4 | CC-MAIN-2024-33 | latest | en | 0.193818 |
https://forums.studentdoctor.net/threads/qr-and-orgo-questions.647794/ | 1,632,847,235,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780060877.21/warc/CC-MAIN-20210928153533-20210928183533-00157.warc.gz | 304,513,243 | 28,438 | # QR and Orgo questions..
#### PAT30DAT30
##### Full Member
how to solve for y for this question,
y = (x+2)/(x-3).
and
AR-X, is it a meta or ortho/para director?
one of the question in the ADA sample test said it is para not meta, why?
#### nze82
##### Full Member
how to solve for y for this question,
y = (x+2)/(x-3).
and
AR-X, is it a meta or ortho/para director?
one of the question in the ADA sample test said it is para not meta, why?
Halogens are ring DEACTIVATORS that are Ortho/Para directors. Read any organic chemistry textbook and they will clearly explain why this is the case.
#### PAT30DAT30
##### Full Member
thanks, can you also help me on the y=...
#### nze82
##### Full Member
thanks, can you also help me on the y=...
Are you sure they want you to solve for Y?
I look at this problem, and I see that Y is already solved for in terms of X. So, I'm not sure how to solve for Y, when Y is already equal to something in terms of X.
#### PAT30DAT30
##### Full Member
Are you sure they want you to solve for Y?
I look at this problem, and I see that Y is already solved for in terms of X. So, I'm not sure how to solve for Y, when Y is already equal to something in terms of X.
sorry, i mean x not y. my bad.
#### dentrilla
##### Full Member
10+ Year Member
Multiply both sides by (x-3) to get
yx-3y=x+2 (collect x's on one side to get...
yx-x=3y+2
x(y-1)=3y+2
x=(3y+2)/(y-1)
#### nze82
##### Full Member
how to solve for y for this question,
y = (x+2)/(x-3).
Cross-Multiply:
xy - 3y = x + 2
Bring all the terms with x to one side:
xy - x = 2 + 3y
Factor out x:
x(y - 1) = 2 + 3y
x = (2+3y)/(y-1)
and
AR-X, is it a meta or ortho/para director?
one of the question in the ADA sample test said it is para not meta, why?
Hope this helps!
#### dentrilla
##### Full Member
10+ Year Member
beat ya 2 it nze
This thread is more than 12 years old.
Your message may be considered spam for the following reasons: | 590 | 1,955 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2021-39 | latest | en | 0.922992 |
https://www.scribd.com/document/59103436/An-448 | 1,569,007,739,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514574058.75/warc/CC-MAIN-20190920175834-20190920201834-00536.warc.gz | 1,017,358,684 | 63,418 | You are on page 1of 5
# INTEGRATED CIRCUITS
AN448 Determining baud rates for 8051 UARTs and other UART issues
Greg Goodhue June 1993
Philips Semiconductors
Philips Semiconductors
Application note
Determining baud rates for 8051 UARTs and other UART issues
Author: Greg Goodhue
The purpose of this note is to expand upon and clarify some aspects of determining baud rates and crystal frequencies for using a standard 8051 or 80C51 UART for ordinary RS-232 type serial communication. The standard baud rate equation is simplified here and is restated to allow solving for other variables such as the crystal frequency and timer reload values. The following discussion assumes that the reader has some knowledge of the 8051/80C51 UART and timers. This should be considered a supplement to the information presented in the Philips 80C51 Family Microcontroller Data Book sections on Timer/Counters and the Standard Serial Interface. Since this discussion assumes the use of a standard UART for RS-232 serial communications, the UART will be used in modes 1 or 3 (variable baud rates) and timer 1 will be used in mode 2 (8-bit auto-reload mode) as the baud rate generator. All of the equations shown here give an option for two clock divisors depending on whether the SMOD bit is used on a CMOS microcontroller. For an NMOS device, always use the default value (SMOD is not = 1). The basic equation for a timer reload value can be stated as: TH1 = 256 Crystal Frequency/384 (or 192 if SMOD = 1) Baud Rate
AN448
The equation can also be solved to derive the baud rate or the crystal frequency from the other information as follows: Baud Rate = Crystal Frequency/384 (or 192 if SMOD = 1) 256 TH1
Minimum crystal frequency for a = Baud Rate 384 (or 192 if SMOD = 1) given baud rate
Thus, the minimum crystal frequency that may be used for 19.2k baud communication on a CMOS part with SMOD = 1 would be 19200 192, which gives 3.6864 MHz. When using this equation, the timer reload value TH1 for the maximum baud rate is always 255 (256 1) or FF hexadecimal. Of course, any even multiple of the frequency obtained in this manner will also support the same baud rate with a different timer reload value. For instance, four times 3.6864 MHz is 14.7456 MHz. At that crystal frequency, 19.2k baud is attained with a timer reload value that gives one fourth of the timer overflow rate: 252 (256 4) or FC hexadecimal.
Example: To obtain a timer reload value for a 9600 baud serial data rate with an 11.0592 MHz crystal: 256 11,059,200/384 = 256 3 = 253, or FD hexadecimal 9600
June 1993
2535
Philips Semiconductors
Application note
Determining baud rates for 8051 UARTs and other UART issues
AN448
## CRYSTAL FREQUENCIES USED FOR STANDARD BAUD RATES
The following chart shows possible crystal frequencies for use with the 80C51 UART at standard baud rates. The chart assumes use of the UART in modes 1 or 3 (variable baud rates) and timer mode 2 (8-bit auto-reload mode). The chart also assumes a minimum requirement of at least 9600 baud (including the use of SMOD for baud rate doubling). More crystal frequencies are available if a lower maximum baud rate is required. The minimum timer count column indicates how many timer counts are required at the stated crystal frequency in order to obtain the Maximum Standard Crystal (MHz) 1.8432 3.6864 5.5296 7.3728 9.2160 11.0592 12.9024 14.7456 16.5888 18.4320 20.2752 22.1184 23.9616 25.8048 27.6840 29.4912 31.3344 33.1776 35.0208 36.8640 Maximum Baud Rate 9600 19200 9600 38400 9600 19200 9600 76800 (2 38400) 9600 19200 9600 38400 9600 19200 9600 153600 (4 38400) 9600 19200 9600 38400
maximum baud rate shown. The last column shows the timer reload value that is used to obtain the minimum timer count. This is simply 256 minus the minimum timer count. Timer reload values for other baud rates at the same crystal frequency are determined by multiplying the minimum timer count by two successively and calculating a new reload value as previously mentioned. For instance, for 4800 baud at 1.8432 MHz, the timer count would be 2 (twice what it is for 9600 baud), giving a timer reload value of 254 (256 2) or FE hexadecimal.
Timer Count 1 1 3 1 5 3 7 1 9 5 11 3 13 7 15 1 17 9 19 5
## Timer Reload Value (in hex) FF FF FD FF FB FD F9 FF F7 FB F5 FD F3 F9 F1 FF EF F7 ED FB
June 1993
2536
Philips Semiconductors
Application note
Determining baud rates for 8051 UARTs and other UART issues
AN448
## THE EFFECT OF USING OFF-FREQUENCY CRYSTALS
Occasionally, one may wish to use an off-frequency crystal in a design, but still want to make use of the UART for debug purposes. Since most terminals (or other RS-232 devices) will communicate with another device that has a baud rate that is off by several percent, this can often be done successfully. WARNING: running the UART off-frequency is NOT recommended if part of the applications normal operation involves communication with other RS-232 devices. There is no exact limit on how much frequency error is tolerable, since this depends on the devices communicating, the baud rates, precise frequencies used by both devices, etc. However, a rule of thumb may be used that the communication is likely to work if the frequency is off by less than 5%. This somewhat arbitrary number was arrived at as follows: for a ten-bit serial code (one start, 8 data bits, one stop), a 10% data rate error will put the receiver off by about plus or minus one bit time at the end of one data frame. A one bit-time error seems rather excessive if one wants fairly reliable communications. So, consider using half of that value (5%) as a rule of thumb. The consequence of all this is that one may often find a more standard off-the-shelf crystal frequency to use in an application, if the UART is being used for debugging, factory testing, etc. As an example, consider the well-known color burst crystal. At 3.579545 MHz, this crystal is only about 3% slower than the 3.6864 MHz crystal that may be desired for baud rate generation. As such, this lower cost crystal could be used in place of the less standard one in some cases. Another obvious replacement is to use the standard 14.31818 MHz crystal in place of the not-so-standard 14.7456 MHz crystal that appears in the table. This replacement also yields a less than 3% error and may be handy because it gives a fast instruction execution rate for the 80C51, whereas 3.58 MHz may be too slow for many applications.
It should also be remembered that RS-232 communications are most robust if characters are not transmitted back-to-back. This can become more important when the UART is deliberately used out of spec as described here. When data is sent at full speed, there is no chance for the receiver to re-synchronize to the transmitted frames if it once gets out of synch. However, when there is a short pause between characters (about 2 to 3 bit times or longer), the receiver will generally be able to correctly locate start bits without framing errors. In the worst case, a pause of one byte-time or longer in a transmission should ALWAYS re-synchronize any receiver no matter how out of synch it has become.
## A LITTLE KNOWN PHENOMENON
In the UART setup code for most applications, the actual timer count register (TL1) is not initialized. In many applications, this DOES have an affect on the way the UART behaves on the first character sent, although the chances of this being noticed are slight. This can be seen by trying to observe the first character sent from the UART on a logic analyzer that is being triggered by the end of microcontroller reset. The first character will begin so far down the time line that it will not be seen at any resolution on the logic analyzer that would show any of the individual bits. This effect occurs because TL1 has to time-out once before the first character is transmitted. If TL1 is not initialized in the program, it will have a reset value of 0. This could give the first timeout a duration of up to 255 normal bit times, depending on the reload value for TH1 (which again depends on the baud rate and crystal frequency). Again, in most applications, this would never be an issue. In fact, it may often be an advantage to have a delay before the first serial character is sent after power-up. But if the first serial character should start sooner, TL1 may be initialized to some value other than zero. For no delay, the same value used in TH1 should be used.
June 1993
2537
## Philips Semiconductors Products
Product specification
Determining baud rates for 8051 UARTs and other UART issues
AN448
Philips Semiconductors and Philips Electronics North America Corporation reserve the right to make changes, without notice, in the products, including circuits, standard cells, and/or software, described or contained herein in order to improve design and/or performance. Philips Semiconductors assumes no responsibility or liability for the use of any of these products, conveys no license or title under any patent, copyright, or mask work right to these products, and makes no representations or warranties that these products are free from patent, copyright, or mask work right infringement, unless otherwise specified. Applications that are described herein for any of these products are for illustrative purposes only. Philips Semiconductors makes no representation or warranty that such applications will be suitable for the specified use without further testing or modification. LIFE SUPPORT APPLICATIONS Philips Semiconductors and Philips Electronics North America Corporation Products are not designed for use in life support appliances, devices, or systems where malfunction of a Philips Semiconductors and Philips Electronics North America Corporation Product can reasonably be expected to result in a personal injury. Philips Semiconductors and Philips Electronics North America Corporation customers using or selling Philips Semiconductors and Philips Electronics North America Corporation Products for use in such applications do so at their own risk and agree to fully indemnify Philips Semiconductors and Philips Electronics North America Corporation for any damages resulting from such improper use or sale. Philips Semiconductors 811 East Arques Avenue P.O. Box 3409 Sunnyvale, California 940883409 Telephone 800-234-7381 Copyright Philips Electronics North America Corporation 1997 All rights reserved. Printed in U.S.A. | 2,461 | 10,448 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-39 | latest | en | 0.835437 |
https://edurev.in/studytube/RD-Sharma-Solutions-Chapter-19-Visualising-Shapes-/dbdb54af-fc8d-45ae-9165-a5786c6a2a18_t | 1,653,282,354,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662555558.23/warc/CC-MAIN-20220523041156-20220523071156-00645.warc.gz | 285,848,536 | 56,749 | # RD Sharma Solutions - Chapter 19 - Visualising Shapes (Part - 1), Class 8, Maths Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
## Class 8: RD Sharma Solutions - Chapter 19 - Visualising Shapes (Part - 1), Class 8, Maths Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8
The document RD Sharma Solutions - Chapter 19 - Visualising Shapes (Part - 1), Class 8, Maths Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8
PAGE NO 19.9:
Question 1:
What is the least number of planes that can enclose a solid? What is the name of the solid?
The least number of planes that can enclose a solid is 4.Tetrahedron is a solid with four planes (faces).
Question 2:
Can a polyhedron have for its faces:
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
(i)No, because in order to complete a polyhedron, we need at least four triangular faces.
(ii)Yes, a polyhedron with 4 triangular faces is a tetrahedron.
(iii)Yes, with the help of a square bottom and four triangle faces, we can form a pyramid.
Question 3:
Is it possible to have a polyhedron with any given number of faces?
Yes, it is possible to have a polyhedron with any number of faces.
The only condition is that there should be at least four faces.
This is because there is no possible polyhedron with 3 or less faces.
Question 4:
Is a square prism same as a cube?
Yes, a square prism and a cube are the same.Both of them have 6 faces, 8 vertices and 12 edges.
The only difference is that a cube has 6 equal faces, while a square prism has a shape like a cuboid with two squarefaces, one at the top and the other at the bottom and with, possibly, 4 rectangular faces in between.
Question 5:
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
No, because every polyhedron satisfies Euler's formula, given below: F + V = E + 2
Here, number of faces F = 10
Number of edges E = 20
Number of vertices V = 15
So, by Euler's formula:
LHS: 10 + 15 = 25
RHS: 20 + 2 = 22,
which is not true because 25≠22
Hence, Eulers formula is not satisfied and no polyhedron may be formed.
Question 6:
Verify Euler's formula for each of the following polyhedrons:
(i)In the given polyhedron:Edges E = 15
Faces F = 7
Vertices V = 10
(i)In the given polyhedron:Edges E = 15
Faces F = 7
Vertices V = 10
Now, putting these values in Euler's formula:
LHS: F + V = 7 + 10 = 17
LHS: E + 2 = 15 + 2 = 17
LHS = RHS
Hence, the Euler's formula is satisfied.Now, putting these values in Euler's formula:
LHS: F + V = 7 + 10 = 17
LHS: E + 2 = 15 + 2 = 17
LHS = RHS
Hence, the Euler's formula is satisfied.
(ii)In the given polyhedron:Edges E = 16
Faces F = 9
Vertices V = 9
(ii)In the given polyhedron:Edges E = 16
Faces F = 9
Vertices V = 9
Now, putting these values in Euler's formula:
RHS: F + V = 9 + 9 = 18
LHS: E + 2 = 16 + 2 = 18
LHS = RHS
Hence, Euler's formula is satisfied.
Now, putting these values in Euler's formula:
RHS: F + V = 9 + 9 = 18
LHS: E + 2 = 16 + 2 = 18
LHS = RHS
Hence, Euler's formula is satisfied.
(iii)In the following polyhedron:Edges E = 21
Faces F = 9
Vertices V = 14
(iii)In the following polyhedron:Edges E = 21
Faces F = 9
Vertices V = 14
Now, putting these values in Euler's formula:
LHS: F + V = 9 + 14 = 23
RHS: E + 2 = 21 + 2 = 23
This is true.
Hence, Euler's formula is satisfied.Now, putting these values in Euler's formula:
LHS: F + V = 9 + 14 = 23
RHS: E + 2 = 21 + 2 = 23
This is true.
Hence,
Euler's formula is satisfied.
(iv)In the following polyhedron:Edges E = 8
Faces F = 5
Vertices V = 5
(iv)In the following polyhedron:Edges E = 8
Faces F = 5
Vertices V = 5
Now, putting these values in Euler's formula:
LHS: F + V = 5 + 5 = 10
RHS: E + 2 = 8 + 2 = 10
LHS = RHS
Hence, Euler's formula is satisfied.Now, putting these values in Euler's formula:
LHS: F + V = 5 + 5 = 10
RHS: E + 2 = 8 + 2 = 10
LHS = RHS
Hence, Euler's formula is satisfied.
(v)In the following polyhedron:
Edges E = 16
Faces F = 9
Vertices V = 9(v)
In the following polyhedron:Edges E = 16
Faces F = 9
Vertices V = 9
Now, putting these values in Euler's formula:
LHS: F + V = 9 + 9 = 18
RHS: E + 2 = 16 + 2 = 18
LHS = RHS
Hence, Euler's formula is satisfied.
PAGE NO 19.10:
Question 7:
Using Euler's formula find the unknown:
Faces ? 5 20 Vertices 6 ? 12 Edges 12 9 ?
We know that the Euler's formula is: F + V = E + 2
(i) The number of vertices V is 6 and the number of edges E is 12.
Using Euler's formula:
F + 6 = 12 + 2
F + 6 = 14
F = 14 - 6
F = 8
So, the number of faces in this polyhedron is 8.
(ii)Faces, F = 5
Edges, E = 9.
We have to find the number of vertices.
Putting these values in Euler's formula:
5 + V = 9 + 25 + V = 11
V = 11 - 5
V = 6
So, the number of vertices in this polyhedron is 6.
(iii)Number of faces F = 20
Number of vertices V = 12
Using Euler's formula:
20 + 12 = E + 2
32 = E + 2
E + 2 = 32
E = 32 - 2
E = 30.
So, the number of edges in this polyhedron is 30.
The document RD Sharma Solutions - Chapter 19 - Visualising Shapes (Part - 1), Class 8, Maths Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8
Use Code STAYHOME200 and get INR 200 additional OFF
## RD Sharma Solutions for Class 8 Mathematics
88 docs
### Top Courses for Class 8
Track your progress, build streaks, highlight & save important lessons and more!
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
; | 2,213 | 5,830 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-21 | latest | en | 0.700641 |
http://www.hellenicaworld.com/Science/Mathematics/en/Naturalprocessvariation.html | 1,632,803,162,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00555.warc.gz | 91,832,577 | 3,849 | ### - Art Gallery -
Natural process variation, sometimes just called process variation, is the statistical description of natural fluctuations in process outputs.
Equations
The following equations are used for an x-bar-control chart:
$${\bar x}=\sum _{{i=1}}^{n}x_{i}/n$$
$$\sigma _{{{\bar x}}}=\sigma /{\sqrt n}$$
In the example, with n = 10 samples, the targeted mean, $${\bar {x}}$$, and standard error of the mean, $$\sigma _{{{\bar x}}}$$ are:
$${\bar x}=1$$
$$\sigma _{{{\bar x}}}=0.1/{\sqrt 1}0=0.0316$$
That is, independent 10-sample means should themselves have a standard deviation of 0.0316. It is natural that the means vary this much, for by the central limit theorem the means should have a normal distribution, regardless of the distribution of the samples themselves.
The importance of knowing the natural process variation becomes clear when we apply statistical process control. In a stable process, the mean is on target; in the example, the target is the filling, set to 1 litre. The variation within the upper and lower control limits (UCL and LCL) is considered the natural variation of the process.
Usage
When a sample average (size n = 10 in this case) is located outside the control limits, then this is an indication that the process is out of (statistical) control. To be more specific:
The Western Electric rules conclude that the process is out of control if:
One point plots outside the 3σ-limits (the UCL and LCL).
Two out of three consecutive points plot beyond a 2σ-limit.
Four out of five consecutive points plot at a distance of 1σ or beyond from the centerline.
Eight consecutive points plot on one side of the center line.
Goal
The most important goal of understanding the principle of natural process variation is to consider the natural variance in the output before we make any changes to the process. Since SPC tends to minimize the process variations in time, as we better understand the process and have more experience with running it, we try to reduce the variation of it. The knowledge of the principle of natural variance helps us avoid making any unnecessary changes to the process, which might add variance to the process, instead of removing it.
References
Douglas C. Montgomery, George C. Runger. Applied Statistics and Probability for Engineers, 4/e. Wiley, 2006. ISBN 978-0-471-74589-1.
An Introduction to Understanding Variation
Respecting Natural Variation | 563 | 2,428 | {"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} | 3.828125 | 4 | CC-MAIN-2021-39 | latest | en | 0.907988 |
https://windowssecrets.com/forums/showthread.php/68472-Date-Calculation-Discussions-(1-00) | 1,508,235,230,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187821017.9/warc/CC-MAIN-20171017091309-20171017111309-00665.warc.gz | 854,247,124 | 17,162 | # Thread: Date Calculation Discussions (1.00)
1. ## Date Calculation Discussions (1.00)
This thread has been created for the purpose of continuing the Date Calculation discussions started in the Star Post thread at <post#=249902>post 249902</post#>
2. ## Re: Date Calculation Discussions (1.00)
Phil,
I still have not gotten it yet as I did what you suggested but now the date is showing as May 12, 2004 even though my clock on Windows is showing the correct date for today (12/4/04).
As well their were four instances of the word date so I changed each individually and even all four but that still did not fix it.
I've attached a PDF file I created showing what I have for the field data.
Thanks again...
Curtis
3. ## Re: Date Calculation Discussions (1.00)
Hi Curtis,
The problem you're now having is because you're using a US date format, whereas the document uses non-US date formatting. This issue is discussed in the intro. To get the result you want, change:
'dd*10^6+mm'
on the last line of the field to:
'mm*10^6+dd'
Cheers
4. ## Re: Date Calculation Discussions (1.00)
(Edited by HansV to make provide link to post - see <!help=19>Help 19<!/help>)
Hi Macropod
Thanks for the help with date calculation - <post#=431960>post 431960</post#>
I am trying to format the output of the forward date calculated in Post 431960 in the form e.g. 31st June 2005 but with the 'st' in superscript. I can't see how I can combine the code in that section of your download with the code created to generate the date and generate the printed output.
Best regards
5. ## Re: Date Calculation Discussions (1.00)
Hi Duncan,
Change the last line from:
{=mm*10^6+dd*10^4+yy # "00'-'00'-'0000"} @ "dddd, MMMM d yyyy"}
(I'm guessing that you're using a 'dddd, MMMM d yyyy' output format) to:
{=mm*10^6+dd*10^4+yy # "00'-'00'-'0000"} @ "dddd, MMMM d
6. ## Re: Date Calculation Discussions (1.00)
Hi Macropod
Thank you again - Contrary to how it may seem, I am actually doing other bits under my own steam thanks to your help.
Best regards
7. ## Re: Date Calculation Discussions (1.00)
Hi Macropod
I've been testing the date calculations at extremes again before releasing the document and there seems to be a further problem with February.
If 6 months is added to Aug 29th the answer is 29-02-2005. Word formating recognises the problem and it does not display properly. The same is true for other years except leap years - when Feb 29th does exist. It is not August specific and 28th Feb is displayed correctly when the 30th and 31st of the month are entered. Also on leap year if 31st of Aug 04 has 42 months added the date reverts to 29th Feb 08 which is correct.
Have you any suggestions?
Thanks and regards
Duncan
8. ## Re: Date Calculation Discussions (1.00)
Hi Duncan,
Sorry 'bout that. The '>29' in the 'SET dd' expression should have been '>28' <img src=/S/stupidme.gif border=0 alt=stupidme width=30 height=30>.
Cheers
9. ## Re: Date Calculation Discussions (1.00)
Hi Macropod
Have now done wonders in docs thanks to your date help
Am not sure if the attachment is of any use to anyone or if I reinvented a wheel.
The * Cadtext switch does not properly create a printed output for money as an example. I crated the attachment that seems to work and wondered if it might be of use to others and if perhaps you wanted to check it and let others see it?
Regards
Duncan
10. ## Re: Date Calculation Discussions (1.00)
Hi,
First, I think you mean * Cardtext.
Second, have you tried * DollarText?
11. ## Re: Date Calculation Discussions (1.00)
Hi Duncan,
Your field can be both simplified and extended, as per second example in the attached in which I've implemented a solution using a FILLIN field that you could easily replace with your mergefield. This will deal with pounds to 9 digits and pennies, both as positive and negative values.
For more on Word field maths and numeric picture switches, see <post#=365442>post 365442</post#>.
Cheers
12. ## Re: Date Calculation Discussions (1.00)
Hi Duncan,
The code in the Date Calc document (see <post#=249902>post 249902</post#>) has now been updated, with a new and simpler algorithm for applying the 'February' test. The relevant code portion is now:
{SET dd{=IF(({DATE @ d}>28)*(mm=2)=1,28+((MOD(yy,4)=0)+(MOD(yy,400)=0)-(MOD(yy,100)=0)),IF((mm=4)+(mm=6)+(mm=9)+(mm=11)+( {DATE @ d}>30)>1,30,{DATE @ d}))}}
Cheers
13. ## Re: Date Calculation Discussions (1.00)
I'm looking to calculation the last day of the previsous month with a "MMMM d yyyy" format. Please help.
14. ## Re: Date Calculation Discussions (1.00)
Hi Macropod -- Thanks for the quick reply. Here's what I have and it still comes up as dddd, d MMMM yyyy. Please help. Looking for MMMM dd yyyy. Thanks a bunch.
15. ## Re: Date Calculation Discussions (1.00)
<P ID="edit" class=small>(Edited by macropod on 26-Apr-05 08:37. Corrected INT syntax error in SET yy field.)</P>Hi gogetter,
You can do this by modifying the field found under 'Calculate the day & date of the last or nth-to-last day of this month' in the DateCalc document (<post#=249902>post 249902</post#>). The steps are as follows:
. After the embedded field '{SET Subtract 0}', insert a new field coded as '{SET MAdjust -1}'
. Change the '{SET yy{DATE @ yyyy}}' field to '{SET yy{={DATE @ yyyy}+INT(({DATE @ M}+MAdjust)/12)}}'
. Change the '{SET mm{DATE @ M}}' field to {SET mm{=MOD({DATE @ M}+MAdjust-1,12)+1}}
. Change the 'dd*10^6+mm*10^4+yy' string to 'mm*10^6+dd*10^4+yy'
. Change the '"dddd, d
Page 1 of 4 123 ... Last
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 1,567 | 5,699 | {"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} | 2.765625 | 3 | CC-MAIN-2017-43 | latest | en | 0.897062 |
https://discuss.leetcode.com/topic/62765/sharing-my-code-java | 1,516,327,701,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887692.13/warc/CC-MAIN-20180119010338-20180119030338-00304.warc.gz | 655,001,029 | 8,602 | # Sharing my code... JAVA
• ``````public class Solution {
public List<List<String>> solveNQueens(int n) {
List<List<String>> result = new ArrayList<List<String>>();
if (n==0) return result;
int[] positions = new int[n]; //position in each row
Arrays.fill(positions, -1);
int row = 0;
while (row>=0) {
if (row==n) {
row--;
continue;
}
boolean forward = false;
for (int i=positions[row]+1; i<n; i++) {
if (isValid(positions, i, row)) {
positions[row] = i;
forward = true;
break;
}
}
if (forward) row++;
else {
positions[row]=-1;
row--;
}
}
return result;
}
private List<String> genSolution(int[] positions, int n) {
List<String> solution = new ArrayList<String>(n);
char[] a = new char[n];
Arrays.fill(a, '.');
for (int position: positions) {
a[position] = 'Q';
a[position] = '.';
}
return solution;
}
private boolean isValid(int[] positions, int x, int y){
for (int row = 0; row < y; row++) {
int position = positions[row];
if (position == x) return false;
if (y-row == Math.abs(x-position)) return false;
}
return true;
}
}
``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 313 | 1,129 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2018-05 | latest | en | 0.422215 |
https://www.biostars.org/p/9461844/ | 1,632,756,763,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058456.86/warc/CC-MAIN-20210927151238-20210927181238-00037.warc.gz | 695,808,384 | 6,185 | Interpret Bedtools Overlap?
1
0
Entering edit mode
6 months ago
kstangline ▴ 30
I have a fairly simple question regarding bedtools.
I've been asked to find the intersections between two types of sample peaks (ChIP-seq peaks). The goal is to see if they're similar or not (i.e. can we use our new method if it gives similar results/peaks to our old method).
I've used the following formula to find the reproducibility:
bedtools intersect -u -a sample1.bed -b sample2.bed -wa | wc -l
I then took the intersection value and divided it by the total of -a (sample1) to get the reproducibility rate. In other words, I'm showing the % of peaks in sample 1 that are reproduced in sample 2.
How would I interpret these results to a wet lab scientist if the reproducibility (overlap) is > 60%?
From my understanding, anything > than 60% (overlap) reproducibility is considered a good score because it's less likely to have occurred by chance?
Would I need to calculate a p value to show that there is a really good overlap?
bed • 253 views
1
Entering edit mode
6 months ago
Think about it this way: Is 50% a surprising chance to win a coin toss? How about having a 50% chance to win the lottery?
The point I am trying to make is that the value of an observation, interpreted as novel information, relates to how unlikely (aka informative) it is.
60% is only meaningful if you also knew how unlikely it was to get 60% by chance alone. In a sense, that likelihood is what p-values try to capture.
In your case, you would need to quantify how likely is that you could get 60% overlap even if the phenomena of interest (that you associate with overlap) would not be present. Or what fraction would overlap if you picked ChIP-seq data for similar tissues and states but conditions that contradict your hypotheses. With that, you can build up a confidence level as to what is credible overlap and what are accidental, systemic similarities.
Also, I would not call this "reproducibility", that means something else in my opinion. What you observe is replication, your replicates recapitulate some but not all the information. | 496 | 2,122 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2021-39 | longest | en | 0.976814 |
https://blog.csdn.net/shanliangliuxing/article/details/17608975 | 1,566,513,911,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027317516.88/warc/CC-MAIN-20190822215308-20190823001308-00227.warc.gz | 383,040,829 | 21,711 | python中保留两位小数
>>> a=13.949999999999999
>>> round(a, 2)
13.949999999999999
>>> print "%.2f" % a
13.95
还可以使用decimal
decimal.Decimal类型是Python中满足高精度计算的一种数据类型，使用进需要导入decimal包
1 无法使用赋字面值的方式定义
2 定义方式如下：
>>> import decimal >>> x = decimal.Decimal(87345) >>> x Decimal('87345') >>> x = decimal.Decimal('123.3344332566334') >>> x Decimal('123.3344332566334') 可以传递给Decimal整型或者字符串参数，但不能是浮点数据，因为浮点数据本身就不准确
>>> x = decimal.Decimal.from_float(127.3323)
>>> x
Decimal('127.332300000000003592504072003066539764404296875')
I have 3 questions pertaining to decimal arithmetic in Python, all 3 of which are best asked inline:
1)
>>> from decimal import getcontext, Decimal
>>> getcontext().prec = 6
>>> Decimal('50.567898491579878') * 1
Decimal('50.5679')
>>> # How is this a precision of 6? If the decimal counts whole numbers as
>>> # part of the precision, is that actually still precision?
>>>
and
2)
>>> from decimal import getcontext, Decimal
>>> getcontext().prec = 6
>>> Decimal('50.567898491579878')
Decimal('50.567898491579878')
>>> # Shouldn't that have been rounded to 6 digits on instantiation?
>>> Decimal('50.567898491579878') * 1
Decimal('50.5679')
>>> # Instead, it only follows my precision setting set when operated on.
>>>
3)
>>> # Now I want to save the value to my database as a "total" with 2 places.
>>> from decimal import Decimal
>>> # Is the following the correct way to get the value into 2 decimal places,
>>> # or is there a "better" way?
>>> x = Decimal('50.5679').quantize(Decimal('0.00'))
>>> x # Just wanted to see what the value was
Decimal('50.57')
>>> foo_save_value_to_db(x)
>>>
本机测试用例：
>>> import decimal
>>> x = decimal.Decimal(87345)
>>> x
Decimal('87345')
>>> print x
87345
>>> from decimal import getcontext, Decimal
>>> x = Decimal('0.998531571219').quantize(Decimal('0.00'))
>>> x
Decimal('1.00')
>>> print x
1.00
>>> x = Decimal('0.998531571219').quantize(Decimal('0.0000'))
>>> x
Decimal('0.9985')
>>> print x
0.9985
>>> y = Decimal.from_float(0.998531571219)
>>> y
Decimal('0.99853157121900004700165709436987526714801788330078125')
>>> y = Decimal.from_float(0.998531571219).quantize(Decimal('0.0000'))
>>> y
Decimal('0.9985')
>>> print y
0.9985
>>> f1 = 0.998531571219
>>> f1
0.998531571219
>>> type(f1)
<type 'float'>
>>> f2 = str(f1)
>>> f2
'0.998531571219'
>>> type(f2)
<type 'str'>
>>> | 779 | 2,340 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2019-35 | latest | en | 0.447684 |
https://groups.yahoo.com/neo/groups/primenumbers/conversations/topics/4200 | 1,394,435,386,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010683198/warc/CC-MAIN-20140305091123-00084-ip-10-183-142-35.ec2.internal.warc.gz | 624,691,028 | 16,493 | • ## A goldbach conjecture for twin primes
(8)
• NextPrevious
• There has been so much discussion about the Goldbach conjecture and also about twin primes that I can t resist adding a conjecture which sort of combines them.
Message 1 of 8 , Nov 29, 2001
View Source
• 0 Attachment
There has been so much discussion about the Goldbach conjecture and also
about twin primes that I can't resist adding a conjecture which sort of
combines them.
Define a t-prime to be a prime which has a twin.
Conjecture: Every sufficiently large even number is the sum of two
t-primes.
More exact: This is true for all even numbers greater than 4208. There are
only a few even numbers less than or equal to 4208 for which this is not
true.
Harvey Dubner
• To: primenumbers From: Harvey Dubner Date sent: Thu, 29 Nov 2001
Message 2 of 8 , Nov 29, 2001
View Source
• 0 Attachment
From: "Harvey Dubner" <hdubner1@...>
Date sent: Thu, 29 Nov 2001 23:15:40 -0500
Send reply to: "Harvey Dubner" <hdubner1@...>
Subject: [PrimeNumbers] A goldbach conjecture for twin primes
> There has been so much discussion about the Goldbach conjecture and also
> about twin primes that I can't resist adding a conjecture which sort of
> combines them.
>
> Define a t-prime to be a prime which has a twin.
>
> Conjecture: Every sufficiently large even number is the sum of two
> t-primes.
1)
Couldn't this conjecture be extended to any constellation?
2)
It seems your conjecture implies both the twin prime conjecture
and the goldbach conjecture.
Michael Hartley : Michael.Hartley@...
Sepang Institute of Technology
+---Q-u-o-t-a-b-l-e---Q-u-o-t-e----------------------------------
"Research without development is impossible - because research inspires development.
Development without research is impossible - because research inspires development."
• Harvey Dubner conjectured that ... which seems to have a good heuristic. As Michael Hartley observed, a comparable heuristic should work, in practice, for any
Message 3 of 8 , Nov 30, 2001
View Source
• 0 Attachment
Harvey Dubner conjectured that
> Every sufficiently large even number is the sum of two t-primes.
which seems to have a good heuristic.
As Michael Hartley observed, a comparable heuristic should
work, in practice, for any constellation with presumed
O(1/log(N)^k) density, be it k=1 for the primes in Goldbach,
k=2 for the twins in Harvey's conjecture, or what you will.
For reference, these (I think!)
are the k=2 exceptions that Harvey had in mind:
[ 2, 4,
94, 96, 98,
400, 402, 404,
514, 516, 518,
784, 786, 788,
904, 906, 908,
1114, 1116, 1118,
1144, 1146, 1148,
1264, 1266, 1268,
1354, 1356, 1358,
3244, 3246, 3248,
4204, 4206, 4208]
I like it that Harvey and Michael have combined
two of the great unprovens into one unproven.
David
• ... So did nobody read my mail from the day before either of the above? Phil Don t be fooled, CRC Press are _not_ the good guys. They ve taken Wolfram s money
Message 4 of 8 , Nov 30, 2001
View Source
• 0 Attachment
On Fri, 30 November 2001, d.broadhurst@... wrote:
> I like it that Harvey and Michael have combined
> two of the great unprovens into one unproven.
So did nobody read my mail from the day before either of the above?
Phil
Don't be fooled, CRC Press are _not_ the good guys.
They've taken Wolfram's money - _don't_ give them yours.
http://mathworld.wolfram.com/erics_commentary.html
Find the best deals on the web at AltaVista Shopping!
http://www.shopping.altavista.com
• ... This conjecture goes back a way. The sequence is Sloane s A007534. It is listed as finite , which would imply the conjecture. Normally he doesn t put
Message 5 of 8 , Nov 30, 2001
View Source
• 0 Attachment
At 02:22 PM 11/30/2001 +0000, d.broadhurst@... wrote:
>Harvey Dubner conjectured that
>
> > Every sufficiently large even number is the sum of two t-primes.
>[ 2, 4, ...
>4204, 4206, 4208]
This conjecture goes back a way. The sequence is Sloane's A007534. It is
listed as "finite", which would imply the conjecture. Normally he doesn't
put "finite" in there unless it is known to be finite, but that doesn't
seem to be the case here. Also see the end of:
http://mathworld.wolfram.com/TwinPrimes.html
%I A007534 M1306
%S A007534 2,4,94,96,98,400,402,404,514,516,518,784,786,788,904,906,908,1114,
%T A007534
1116,1118,1144,1146,1148,1264,1266,1268,1354,1356,1358,3244,3246,3248,
%U A007534 4204,4206,4208
%N A007534 Even numbers not the sum of a pair of twin primes.
%D A007534 D. Wells, The Penguin Dictionary of Curious and Interesting
Numbers. Penguin Books, NY, 1986, 132.
%H A007534 <a
href="http://www.research.att.com/~njas/sequences/Sindx_G.html#Goldbach">Index
entries for sequences related to Goldbach conjecture</a>
%H A007534 E. W. Weisstein, <a
The World of Mathematics.</a> (Currently unavailable)
%e A007534 The twin primes < 100 are 3, 5, 7, 11, 13, 17, 19, 29, 31, 41,
43, 59, 61, 71, 73. 94 is in the sequence because no combination of any two
numbers from the set just enumerated can be summed to make 94.
%t A007534 p = Select[ Range[ 4250 ], PrimeQ[ # ] && PrimeQ[ # + 2 ] & ]; q
= Union[ Join[ p, p + 2 ] ]; Complement[ Table[ n, {n, 2, 4250, 2} ],
Union[ Flatten[ Table[ q[ [ i ] ] + q[ [ j ] ], {i, 1, 223}, {j, 1, 223} ]
] ] ]
%Y A007534 Cf. A051345.
%K A007534 nonn,nice,fini
%O A007534 1,1
%A A007534 njas, Robert G. Wilson v (rgwv@...)
%E A007534 Conjectured to be complete.
+---------------------------------------------------------+
| Jud McCranie |
| |
| Programming Achieved with Structure, Clarity, And Logic |
+---------------------------------------------------------+
• Jud, Thanks for the information and references about the sum of twin primes. I was not aware of the previous work. The conjecture that every even number
Message 6 of 8 , Nov 30, 2001
View Source
• 0 Attachment
Jud,
Thanks for the information and references about the sum of twin primes. I
was not aware of the previous work. The conjecture that every even number
greater than 4208 is the sum of two t-primes is actually a consequence of
the main thrust of my paper.
Define a "middle number" to be the even number sandwiched between a pair of
twin primes. The main thrust of my paper is the conjecture that every
middle number greater than 6 is the sum of two middle numbers.
Harvey
• Hello all Harvey s conjecture ... than 4208. could be stated thusly: Every even number over 4208 can be written at least once as the sum of two primes, each
Message 7 of 8 , Nov 30, 2001
View Source
• 0 Attachment
Hello all
Harvey's conjecture
> Define a t-prime to be a prime which has a twin.
> Conjecture: Every sufficiently large even number is the sum of two
> t-primes. More exact: This is true for all even numbers greater
than 4208.
could be stated thusly:
Every even number over 4208 can be written at least once as the sum
of two primes, each prime of which is exactly two units from another
prime.
I can't resist another conjecture, and it is this: Every even number
over 8 can be written at least once as the sum of two primes, each
prime of which is exactly six units from another prime.
I have used my proprietary, massively parallel computer system (which
very much resembles a human's neural network) to confirm or refute
this. Up to 2n = 80 the conjecture holds.
An almost identical but stronger conjecture: Every even number over 8
can be written at least once as the sum of two primes, each of the
two primes being exactly six units more than another prime, or each
of the two primes being exactly six units less than another prime.
For instance, 68 = 7 + 61 = (13-6) + (67-6).
40 = 11+ 29 = (5+6) + (23+6).
The conjecture is very likely true since from from 5 to 113 the
number 71 is the only prime that is not 6 units away from another
prime. Also, primes separated by 6 (not necessarily consecutive
primes)should be on average twice as common as primes separated by
two.
Mark
--- In primenumbers@y..., "Harvey Dubner" <hdubner1@c...> wrote:
> There has been so much discussion about the Goldbach conjecture and
also
> about twin primes that I can't resist adding a conjecture which
sort of
> combines them.
>
> Define a t-prime to be a prime which has a twin.
>
> Conjecture: Every sufficiently large even number is the sum of two
> t-primes.
>
> More exact: This is true for all even numbers greater than 4208.
There are
> only a few even numbers less than or equal to 4208 for which this
is not
> true.
>
> Harvey Dubner
• ... also ... sort of ... There are ... is not ... I think primes satisfy GC not because of their primality but because of their random enough
Message 8 of 8 , Dec 2, 2001
View Source
• 0 Attachment
--- In primenumbers@y..., "Harvey Dubner" <hdubner1@c...> wrote:
> There has been so much discussion about the Goldbach conjecture and
also
> about twin primes that I can't resist adding a conjecture which
sort of
> combines them.
>
> Define a t-prime to be a prime which has a twin.
>
> Conjecture: Every sufficiently large even number is the sum of two
> t-primes.
>
> More exact: This is true for all even numbers greater than 4208.
There are
> only a few even numbers less than or equal to 4208 for which this
is not
> true.
>
> Harvey Dubner
I think "primes" satisfy GC not because of their "primality" but
because of their "random enough" distribution. In fact, with ever
larger even numbers, ever less percent of primes is needed to satisfy
GC. With my computer power, less than 1% of the primes would suffice.
Defining g(i) as the product of (1-2/p) for all prime p<=sqrt(n), the
number of Golbach pairs for the even n is almost (n/4)*g(i).
Similarly, the number of t-primes between p^2 and (p+2)^2 is almost
2p*g(i), which means t-prime distribution is far denser than what is
needed to satisfy GC. In fact, every set of random odd numbers with a
spacing of the order n^1/3 is enough to make all evens with their
paired sums, while t-prime spacing is of the order log(n)^2.
For the same reason, the GC-like conjecture for the triplet-primes is
also eventually true.
Kaveh
Your message has been successfully submitted and would be delivered to recipients shortly. | 2,892 | 10,117 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2014-10 | longest | en | 0.917054 |
https://www.hackmath.net/en/example/1208 | 1,484,920,705,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280835.22/warc/CC-MAIN-20170116095120-00122-ip-10-171-10-70.ec2.internal.warc.gz | 921,151,492 | 14,558 | # RT 11
Calculate the area of right tirangle if its perimeter is p = 46 m and one cathethus is 18 m long.
Result
S = 73.93 m2
#### Solution:
Try calculation via our triangle calculator.
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Be the first to comment!
## Next similar examples:
1. Hypotenuse
Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
2. Inscribed circle
XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
3. Median
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
4. ISO Triangle V2
Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
5. Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
6. Isosceles III
The base of the isosceles triangle is 24 cm area 416 cm2. Calculate the perimeter of this triangle.
7. RT 10
Area of right triangle is 17 cm2 and one of its cathethus is a=8 cm. Calculate perimeter of the triangle ABC.
8. Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
9. Circle's chords
In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
10. Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
11. Equilateral triangle v2
Equilateral triangle has a perimeter 36 dm. What is its area?
12. ISO trapezoid v2
bases of Isosceles trapezoid measured 12 cm and 2 cm and its perimeter is 18 cm. What is the are of a trapezoid?
13. Circumscribing
Determine the radius of the circumscribed circle to the right triangle with legs 6 cm and 3 cm.
14. Folded square
ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
15. Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry? | 706 | 2,620 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2017-04 | longest | en | 0.846057 |
http://www.school-for-champions.com/science/gravity_feedback.cfm?tab=gravity_work_by_gravity&next=10&start=31 | 1,516,419,247,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084888878.44/warc/CC-MAIN-20180120023744-20180120043744-00092.warc.gz | 549,701,252 | 9,323 | # Feedback Comments on Gravity
by Ron Kurtus
A total of 78 comments and questions have been sent in on Gravity. They are listed according to date.
You can read them to further your understanding of the subject.
## List of next 10 letters
### Country
Overview of Gravity Is the definition of gravity correct? K.S.A
Artificial Gravity Science fiction on artifical gravity USA
Overview of Gravity Is gravity why we don't fly off into space? USA
Work Against Gravity and Inertia Wants formula to lift with a motor India
Equivalence Principle of Gravity Confused about gravitation with a small object USA
Gravity I think that the calculations are wrong USA
Gravity How does gravity affect the human body? USA
Gravity Is there a point in the Universe with zero gravitation? USA
Gravity A force to counter gravity in aircraft flight UK
Gravity Should use SI units USA
Next 10
First 10 letters
## Is the definition of gravity correct?
Topic: Overview of Gravity
### Question
December 20, 2012
Hello,
I was wondering, we learned that gravity is the force that pulls all objects together. And basically, we are pulled more to the Earth than to each other because the Earth just has an extremely bigger mass, that our attraction to each other, then seems negligible. You, though, defined gravity as "the force that pulls us to the planets". How true is this theory, you think, that gravity pulls us all towards each other? I mean, how trusted can it be since it depends on the big bang theory? What are your thoughts, since you, yourself, chose to ignore that theory in your definition?
Thank you.
P.S. I realize this was just an "overview", but still your neglecting that theory made me wonder.
- K.S.A
23075
### Answer
There is a difference between gravity and gravitation that is often not explained in science courses. Sometimes the expression "gravity" is carelessly used for both terms.
Gravitation is the force of attraction between objects. It is most often seen in the attraction of large objects in space, although it even exists between small objects.
Gravity, on the other hand, is the attraction of object toward the Earth. There is also gravity of the Moon and gravity of Mars, and so on. Gravity is an approximation of gravitation for small objects near a large one, such as the Earth. See Overview of Gravitation for more information.
The Big Bang Theory concerned gravitational forces.
Back to top
## Science fiction on artifical gravity
Topic: Artificial Gravity
### Question
November 12, 2012
Greetings, I am a science fiction writer, and I'd like to postulate a hypothesis for your notions and feedback. If one were to create a form of crankshaft that spins energy through magnetic coils in a spiraling circuit, allowing for hyper-acceleration of particles for the production of anti-matter, similar to what is used in super-colliders, and this tube structure itself were to be spinning, further increasing the momentum of the charged particles generated within, could this spinning collision device be used to both produce anti-matter and generate artificial gravity if used in the core of a large space ship? Furthermore, this anti-matter could be funneled to one end of the cylinder and recombined with positive matter for propulsion. If this hypothesis were to hold true, would it not reduce the amount of mass needed to generate gravity, and allow for better streamlining of a space vessel, since it would also be generating fuel for propulsion?
Alternatively, if a circular super-collider were to be used for the outer rim of a disc-shaped vessel, could it's function in accelerating matter at beyond light speed alone create the momentum needed for artificial gravity, while again producing anti-matter which could be used as fuel for propulsion?
DJ - USA
23032
### Answer
You've got some complex ideas.
For some reason, most matter in the Universe is right-handed and has certain charges. Anti-matter is simply a particle with the opposite charge and perhaps spins in a left-handed direction. Radioactive decay and high energy collisions can result in antiparticles being emitted.
See Antimatter and Antiparticles.
Also so-called artificial gravity is simply caused by inertia. It has been used many times in science fiction.
Some better topics to consider are dark matter and dark energy. They are only theory but explain many things in the Universe. It is a good topic for science fiction, since you can almost create your own special properties from these items. For example, if someone could convert to dark matter, he would be invisible to normal people.
Best wishes in your writing. Keep in touch on your progress.
Back to top
## Is gravity why we don't fly off into space?
Topic: Overview of Gravity
### Question
October 30, 2012
i was just thinking gravity is the reason we do not fall from the earth, as does not water and all objects on this planet..its weird but plausible....
judy - USA
23011
### Answer
Yes, gravity is what pulls everything toward the Earth. The rotation of the Earth causes a centrifugal force that would cause objects to fly off into space, but it is too small to overcome the force of gravity. Thus, we are held down.
Back to top
## Wants formula to lift with a motor
Topic: Work Against Gravity and Inertia
### Question
October 27, 2012
WHAT IS THE FORMULA OR R.P.M NEEDED TO LIFT A SMALL BOX MADE UP OF THERMOCOL?IF THE WEIGHT OF THE BOX IS HALF KILOGRAM AND THE ROTOR OR FAN IS FITED IN THE BASE OF THE BOX. THE BOX IS NOT VERY BIG IT IS A SMALLER ONE.
ADITYA - India
23005
### Answer
I'm sorry, but we do not have that information.
Back to top
## Confused about gravitation with a small object
Topic: Equivalence Principle of Gravity
### Question
July 26, 2012
I am having difficulty with this concept.
Regarding falling bodies it is my understanding that
F = m1*a = G*m1*me/r^2 --> a = G*me/r^2 for object 1,
'me' being the mass of the earth.
As both objects are actually accelerating the earth's acceleration would be based on
F = me*a = G*m1*me/r^2 --> a = G*m1/r^2 for the earth.
For a 1 kg object at 1 kilometer and estimating G at 7*10^-11 N(Kg/m)^2, the earth's acceleration would be
a = (7*10^-11)(1)(10^-6)= 7*10^-17.
For a 2 kg object it would be 14 * 10^-17.
So small a difference as to be the same for practical purposes? Sure, until the mass of the other object approaches that of the earth sized object. I don't mean to be thick headed, but I could really use some help here. People regularly mention cancelling out the earth's gravitation when viewing it from the perspective that the other object is accelerating, while ignoring the perspective that the earth is accelerating. Its only in the past century and a half (speaking somewhat loosely) that we've been able to measure such small differences. If you could point me at some modern experiments I would be overjoyed.
Thanks for your time.
Alex - USA
22806
### Answer
At distances relatively close the the Earth, Newton's Universal Gravitation equation F = GMm/R^2 can be approximated as F = mg. Gravity Constant Factors has a chart showing that at distances above 6 km from the Earth's surface, the error in using F = mg instead of Newton's equations is less that 0.1%.
When dealing with small objects relative to the mass of the Earth and at distances relatively close to the surface of the Earth, the gravity equation is used. When dealing with large distances and astronomical bodies, you use the gravitation equations. That is why the section has been divided into those two areas.
Another factor in gravitation calculations concerns the center of mass between two objects.
I hope this helps your understanding.
Back to top
## I think that the calculations are wrong
Topic: Gravity
### Question
March 15, 2012
I think that the calculations are wrong if a meter is 3.3 feet then the 32.2 fps2 is wrong it should be 32.3631 and if you wanted to round up like they said they did then 32.3631 would be 32.4 not 32.2 so I was just wondering would that change the 9.8 newtons that g= in f=mg
Edward - USA
22514
### Answer
Actually, 1 m = 3.28 ft. See our English-to-Metric tool link on each page.
If we start with g = 9.807 m/s^2 from Overview of the Force of Gravity and multiply 9.807 X 3.28 = 32.167 ft/s^2. That rounds out to 32.2 ft/s^2.
Back to top
## How does gravity affect the human body?
Topic: Gravity
### Question
February 26, 2012
I'm interested in how gravity affects the human body; standing erect, bending forward, leaning to one side. Are there equations for these angles relating to the gravitational force on the human body?
Gay - USA
22449
### Answer
Gravity pulls all the atoms in the body toward the ground. You can consider the human body a solid object with a center of gravity (CG) according to the orientation and configuration of the body. See Center of Gravity.
If a person was bending over, there would be a tendency of the body to tip over, rotating about the fixed point where the feet are on the ground. What happens is that your muscles change the angle slightly and stabilize the body to prevent it from falling over.
There are no real equations to use. It is mainly done by geometric drawings, similar to those in the lesson.
Back to top
## Is there a point in the Universe with zero gravitation?
Topic: Gravity
### Question
February 22, 2012
In advance, Please forgive me for my spelling, grammer and rambling on.
Is there any such space in the known universe where there is zero gravity (meaning absolutely no gravitational pull or effect)all the time?
My understanding is that all MATTER has some form of gravitational pull. Also, all MATTER in the universe is in motion.
Therefore, is everything in the universe effected by gravity and have an effect on everything else?
Example; If a major star, planet or object was suddenly erased completely, would the entire universe be effected?
One theory I have is that the entire universe is like an "ecosystem". Meaning in some way it is all connected and self-dependant on everything in it. Any change will have some effect on the rest of it; big or small.
I feel this supports inteligent design. The Universe was Created and set in motion on purpose, and for a purpose. There can not possibly be this many "coincidences" coming so perfectly togeather.
I really would love and appreciate your views on this?
Thank you,
John Blackinton
John - USA
22440
### Answer
If the Big Bang Theory that matter in the Universe exploded from some center point is correct, I would imagine that point could have zero net gravitational pull on it, since matter is probably equally distributed around that point.
A good way of thinking about it is like a form of ecosystem.
As far as supporting Intelligent Design, see Big Bang Theory and Religion.
Back to top
## A force to counter gravity in aircraft flight
Topic: Gravity
### Question
February 9, 2012
I am looking at the principles of flight, particularly lift. Given the aircraft has thrust that contributes to lift in a climb, some of the weight is catered for by this thrust (other than aeodynamic - wing - lift). Now in straight and level flight the plane is effectively climbing (must have angle of attack). I am concerned, though I agree with the content here on gravity, that another force than lift exists to counteract gravity. With a plane we are talking not about a solid streamlined object, like a bullet, but something that has vertical wind resistance, which you will agree, changes the rate of descent. Also the plane has power constantly applied, unlike the bullet. With this powered forwards motion is the plane effectively seen to be lighter than it would be on the ground (ignoring inverse square law etc due to height above C of G)? It seems I am talking in the time domain, where a vehicle crossing a weak bridge at speed might get across, where at slow speed the bridge would collapse. Thanks for reading my question.
Michael - UK
22417
### Answer
Gravity can be considered a constant force toward the ground. For relatively short distances, it is straight down. But if the object is moving in a straight line. over a great distance, the curvature of the Earth must be taken into account. The inertia of the flying object make it want to go in a straight line, which is counter to gravity when the curvature is taken into consideration.
See Gravity and Newton's Cannon. As the cannonball moves faster, it will soon travel in a line into space. If the ball or object were continually propelled, the effect would be more dramatic.
Back to top
## Should use SI units
Topic: Gravity
### Question
February 7, 2012
This is a great resource but it would be more useful in SI units since that's the standard for science nowadays.
Brendan - USA
22411
### Answer
Since so many non-scientific people in the U.S. still use the English system of measurement, I've tried to use both English and SI in all the Gravity lessons. Some example problems are in feet/sec, while others are in meters/sec.
However, in the Gravitation section, only the SI units are used.
Back to top
Next 10
## Summary
Hopefully, this reader feedback has helped provide information about Gravity issues.
Appreciate what you have
## Resources and references
The following are some resources on this topic.
### Websites
Gravity Resources
### Books
Top-rated books on Gravity
## Questions and comments
Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.
Feel free to establish a link from your website to pages in this site.
## Where are you now?
School for Champions
Gravity topics
## Gravitation
### Let's make the world a better place
Be the best that you can be.
Use your knowledge and skills to help others succeed.
Don't be wasteful; protect our environment.
### Live Your Life as a Champion:
Take care of your health
Seek knowledge and gain skills
Do excellent work
Be valuable to others
Have utmost character
#### Be a Champion!
The School for Champions helps you become the type of person who can be called a Champion. | 3,168 | 14,235 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2018-05 | latest | en | 0.947935 |
https://math.stackexchange.com/questions/tagged/logic?sort=votes&pageSize=50 | 1,558,934,142,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232261326.78/warc/CC-MAIN-20190527045622-20190527071622-00112.warc.gz | 535,199,885 | 34,825 | # Questions tagged [logic]
Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the following tags as well, if they fit the question: (model-theory), (set-theory), (computability), and (proof-theory). This tag is not for logical puzzles, use (puzzle).
17,988 questions
18k views
Are there some proofs that can only be shown by contradiction or can everything that can be shown by contradiction also be shown without contradiction? What are the advantage/disadvantages of proving ...
7k views
4k views
### Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on
Popular mathematics folklore provides some simple tools enabling us compactly to describe some truly enormous numbers. For example, the number $10^{100}$ is commonly known as a googol, and a googol ...
18k views
### How is a system of axioms different from a system of beliefs?
Other ways to put it: Is there any faith required in the adoption of a system of axioms? How is a given system of axioms accepted or rejected if not based on blind faith?
14k views
### In what sense are math axioms true?
Say I am explaining to a kid, $A +B$ is the same as $B+A$ for natural numbers. The kid asks: why? Well, it's an axiom. It's called commutativity (which is not even true for most groups). How do I "...
5k views
### Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture
In the most recent numberphile video, Marcus du Sautoy claims that a proof for the Riemann hypothesis must exist (starts at the 12 minute mark). His reasoning goes as follows: If the hypothesis is ...
39k views
### Why is “the set of all sets” a paradox, in layman's terms?
I've heard of some other paradoxes involving sets (ie, "the set of all sets that do not contain themselves") and I understand how paradoxes arise from them. But this one I do not understand. Why is "...
24k views
### “Which answer in this list is the correct answer to this question?”
I received this question from my mathematics professor as a leisure-time logic quiz, and although I thought I answered it right, he denied. Can someone explain the reasoning behind the correct ...
13k views
### Does mathematics require axioms?
I just read this whole article: http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf which is also discussed over here: Infinite sets don't exist!? However, the paragraph which I found most ...
11k views
### Infinite sets don't exist!?
Has anyone read this article? This accomplished mathematician gives his opinion on why he doesn't think infinite sets exist, and claims that axioms are nonsense. I don't disagree with his arguments, ...
6k views
### Why is $\omega$ the smallest $\infty$?
I am comfortable with the different sizes of infinities and Cantor's "diagonal argument" to prove that the set of all subsets of an infinite set has cardinality strictly greater than the set itself. ...
18k views
### What is a simple example of an unprovable statement?
Most of the systems mathematicians are interested in are consistent, which means, by Gödel's incompleteness theorems, that there must be unprovable statements. I've seen a simple natural language ...
5k views
### Why is compactness in logic called compactness?
In logic, a semantics is said to be compact iff if every finite subset of a set of sentences has a model, then so to does the entire set. Most logic texts either don't explain the terminology, or ...
7k views
### Does mathematics become circular at the bottom? What is at the bottom of mathematics? [duplicate]
I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign)...
5k views
### Proving the existence of a proof without actually giving a proof
In some areas of mathematics it is everyday practice to prove the existence of things by entirely non-constructive arguments that say nothing about the object in question other than it exists, e.g. ...
10k views
### Is “The empty set is a subset of any set” a convention?
Recently I learned that for any set A, we have $\varnothing\subset A$. I found some explanation of why it holds. $\varnothing\subset A$ means "for every object $x$, if $x$ belongs to the empty set,...
6k views
### Optimal strategy for cutting a sausage?
You are a student, assigned to work in the cafeteria today, and it is your duty to divide the available food between all students. The food today is a sausage of 1m length, and you need to cut it into ...
14k views
### Why do people lose in chess?
Zermelo's Theorem, when applied to chess, states: "either white can force a win, or black can force a win, or both sides can force at least a draw [1]" I do not get this. How can it be proven? ...
25k views
### Implies vs. Entails vs. Provable
Consider A $\Rightarrow$ B, A $\models$ B, and A $\vdash$ B. What are some examples contrasting their proper use? For example, give A and B such that A $\models$ B is true but A $\Rightarrow$ B is ...
8k views
### Is there such a thing as proof by example (not counter example)
Is there such a logical thing as proof by example? I know many times when I am working with algebraic manipulations, I do quick tests to see if I remembered the formula right. This works and is ...
5k views
### What is a proof?
I am just a high school student, and I haven't seen much in mathematics (calculus and abstract algebra). Mathematics is a system of axioms which you choose yourself for a set of undefined entities, ...
6k views
### How is the Gödel's Completeness Theorem not a tautology?
As a physicist trying to understand the foundations of modern mathematics (in particular Model Theory) $-$ I have a hard time coping with the border between syntax and semantics. I believe a lot would ...
5k views
### Doesn't the unprovability of the continuum hypothesis prove the continuum hypothesis? [duplicate]
The Continuum Hypothesis say that there is no set with cardinality between that of the reals and the natural numbers. Apparently, the Continuum Hypothesis can't be proved or disproved using the ...
6k views
### Is it possible that “A counter-example exists but it cannot be found”
Then otherwise the sentence "It is not possible for someone to find a counter-example" would be a proof. I mean, are there some hypotheses that are false but the counter-example is somewhere we ...
8k views
### Are proofs by contradiction really logical?
Let's say that I prove statement $A$ by showing that the negation of $A$ leads to a contradiction. My question is this: How does one go from "so there's a contradiction if we don't have $A$" to ...
3k views
### Is it possible to prove a mathematical statement by proving that a proof exists?
I'm sure there are easy ways of proving things using, well... any other method besides this! But still, I'm curious to know whether it would be acceptable/if it has been done before?
3k views
### What does it take to divide by $2$?
Theorem 1 [ZFC, classical logic]: If $A,B$ are sets such that $\textbf{2}\times A\cong \textbf{2}\times B$, then $A\cong B$. That's because the axiom of choice allows for the definition of ...
10k views
### An easy example of a non-constructive proof without an obvious “fix”?
I wanted to give an easy example of a non-constructive proof, or, more precisely, of a proof which states that an object exists, but gives no obvious recipe to create/find it. Euclid's proof of the ...
6k views
### Is there any conjecture that we know is provable/disprovable but we haven't found a proof of yet?
I know that there are a lot of unsolved conjectures, but it could possible for them to be independent of ZFC (see Could it be that Goldbach conjecture is undecidable? for example). I was wondering if ...
25k views
### In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True?
Provided we have this truth table where "$p\implies q$" means "if $p$ then $q$": \begin{array}{|c|c|c|} \hline p&q&p\implies q\\ \hline T&T&T\\ T&F&F\\ F&T&T\\ F&...
12k views
### Understanding Gödel's Incompleteness Theorem
I am trying very hard to understand Gödel's Incompleteness Theorem. I am really interested in what it says about axiomatic languages, but I have some questions: Gödel's theorem is proved based on ...
22k views
### First-Order Logic vs. Second-Order Logic
Wikipedia describes the first-order vs. second-order logic as follows: First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic ...
5k views
### Say $a=b$. Is “Do the same thing to both sides of an equation, and it still holds” an axiom? [duplicate]
Recently I have started reviewing mathematical notions, that I have always just accepted. Today it is one of the fundamental ones used in equations: If we have an equation, then the equation holds ...
4k views
### Why can we use induction when studying metamathematics?
In fact I don't understand the meaning of the word "metamathematics". I just want to know, for example, why can we use mathematical induction in the proof of logical theorems, like The Deduction ...
3k views
### What do logicians mean by “type”?
I enjoy reading about formal logic as an occasional hobby. However, one thing keeps tripping me up: I seem unable to understand what's being referred to when the word "type" (as in type theory) is ...
29k views
### Good books on mathematical logic?
I just started to learn mathematical logic. I'm a graduate student. I need a book with relatively more examples. Any recommendation? | 2,324 | 9,869 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2019-22 | latest | en | 0.911005 |
https://skill-lync.com/profiles/Adithya-C-Vinod-744 | 1,679,972,610,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00526.warc.gz | 619,492,933 | 30,649 | Executive Programs
Workshops
Projects
Blogs
Careers
Find Jobs
Corporate Training
Hire from US
All Courses
Choose a category
All Courses
All Courses
Automobile Enthusiast
Skills Acquired at Skill-Lync :
• MATLAB-BASICS
• HEV-FUNDAMENTALS
• MATLAB
• STRUCTURAL-MESHING
• ANSA
• FEA
• HYPER-MESH
Introduction
SolidWorks Professional | Automobile Enthusiast
12 Projects
Simulink Model of a Washing machine using Stateflow
Objective:
Aim: Model of a Washing machine using Stateflow in Simulink with given conditions. Conditions: If the power supply is available, the system gets activated If the Water supply is not available, stop the process & indicate through LED Soaking time should be 200s followed by Washing time of 100s. Then rinsing…
04 Mar 2020 06:50 AM IST
Program to simulate the transient behaviour of a simple pendulum and to create an animation of it's motion.
Objective:
Aim To simulate the transient behaviour of a simple pendulum and to create an animation of it's motion. Introduction Second-order linear differential equations are used to model many situations in physics and engineering. It finds application in Springs, Pendulums etc. In this very problem we are using ODE to…
13 Feb 2020 12:49 AM IST
Parsing NASA Thermodynamic Data
Objective:
Aim: To parse the NASA thermodynamic data file and then calculate thermodynamic properties of various gas species. Introduction Parsing in computer languages refers to syntactic analysis of the input code into its components parts in order to facilitate the writing of compilers and interpreters. It can be used to…
21 Feb 2020 03:46 AM IST
Stalagmite Function Optimization using Matlab
Objective:
Aim To optimise the given stalagmite function and find the global maxima of the function. Introduction to Stalagmites & Stalactites Stalactites are structures formed from mineral deposits that hang from caves. These formations hold tightly to the ceiling and hang down. As opposed to hanging…
20 Feb 2020 11:00 PM IST
Matlab program to simulate forward kinematics of a 2R Robotic Arm
Objective:
Introduction A robotic arm is a mechanical arm (with 2 or more links) which can be programmed to do a particular function similiar to human hand. The function can be painting, welding,polishing,wrapping and a lot more. It's prominent application is seen in automotive field, mainly in body welding and painting. …
11 Feb 2020 04:24 AM IST
Gear Shift Indicator using Stateflow
Objective:
Aim: Make a Simulink chart for the 'Gear shift' logic as per given conditions. Conditions: Speed Range(kmph) Gear 0 to 15 …
04 Mar 2020 05:33 AM IST
Matlab Program to output PV diagram & Efficiency Of Otto Cycle
Objective:
Aim: To produce PV diagram & Efficiency for Otto Cycle Introduction The Otto cycle is an air-standard cycle which describes the processes in petrol engine. It constitutes two isentropic & two constant volume processes namely, Isentropic Compression Constant Volume Heat Absorption Isentropic…
11 Feb 2020 06:01 AM IST
Simulink model of Thermistor to sense the temperature of a heater & trigger a fan.
Objective:
Aim: Create a simulink model of thermistor to sense the temperature of a heater & turn on or turn off the fan. Conditions: Temperature source: 20 °C from 0 to 10 seconds, 27 °C from 10 to 30 seconds, 23 °C from 30 to 50 seconds. Fan conditions: ON if the temperature above 25 °C,…
03 Mar 2020 04:52 AM IST
Linear and Cubic Polynomial Curve fitting for Temperature-Cp Data
Objective:
Introduction Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in…
13 Feb 2020 02:08 AM IST
• MATLAB
Simulink Model of Doorbell using solenoid block
Objective:
Aim: Make a Simulink model of Doorbell using solenoid block. Conditions: Switch is closed for 2 seconds and then released. Blocks used in model: Pulse Generator Switch Battery Solenoid Ideal Translational Motion Sensor Mechanical Translational Reference Electrical Reference Scope Simulink Model: Model Explanation:…
03 Mar 2020 04:18 AM IST
Assignment 1
Objective:
Part 1 Switching to mixed topology view to find what all needs to be fixed while geometry cleanup. Zooming to the right side of the model shown above, a missing face & unwanted face was observed. Fixing the missing face using filler surface option under quick edit & splitting the unwanted face using trim with surface…
20 Jan 2021 12:34 PM IST
Assignment 2
Objective:
Question 1: Speed Of sound in rail Speed of sound, c = `sqrt (E/rho)` where E is Youngs modulus of material & `rho` is density of the material, E= 210000 MPa & `rho`= 0.0078 `g/(mm)^3` c= `sqrt((210000/0.0078)` = 5188.7452 ~ 5188.75 mm/s _______________________________________________________________________…
22 Jan 2021 09:52 AM IST
Showing 1 of 12 projects
2 Course Certificates
MATLAB for Mechanical Engineers
Certificate UID: 2cfyhli91p3zue7b
Introduction to Physical Modeling using Simscape
Certificate UID: zew0gqj27vs63xla
Showing 1 of 2 certificates
B.Tech
Saintgits College of Engineering (Autonomous), Kottayam
01 Jun 2015 - 01 Jun 2019
12th
MMARS
01 Jun 2014 - 01 Mar 2015
10th
MMARS
01 Jun 2012 - 01 Mar 2013
Schedule a counselling session
Firstname is required
Lastname is required
Here are the courses that I have enrolled
4.8
5 Hours of Content
Recently launched
18 Hours of Content
Recently launched
21 Hours of Content
Recently launched
10 Hours of Content
Similar Profiles
Apoorv Ranjan
Ladder of success cannot be climbed with hands in pocket. | 1,442 | 5,783 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2023-14 | latest | en | 0.769682 |
https://forums.azbilliards.com/threads/imagine-the-worlds-best-most-powerful-breaker-on-an-endless-pool-table-how-long-does-the-cue-ball-travel.551292/page-3 | 1,695,682,128,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510100.47/warc/CC-MAIN-20230925215547-20230926005547-00870.warc.gz | 291,605,397 | 20,535 | # Imagine the world's best/most powerful breaker on an endless pool table... how long does the cue ball travel?
#### Bob Jewett
##### AZB Osmium Member
Staff member
Gold Member
Silver Member
But, I mean.. why would you even need to start at a pool table? Just shoot it off any table, or a couch, or off a mat, or anything.
You can set up at a customary height and situation. If the table has the end rail off, why not?
#### hang-the-9
##### AzB Silver Member
Silver Member
I checked with ChatGPT and it estimated 20 to 30 feet for a 25mph hit. I think that estimate is pretty low.
From OpenAI:
The distance a cue ball would travel if struck at 25 mph would depend on several factors such as the type of table surface, the ball's initial trajectory, the presence of other balls on the table, and the level of friction and air resistance.
However, as a rough estimate, on a standard billiard table with a smooth, level surface, a cue ball struck at 25 mph might travel approximately 20 to 30 feet before coming to a stop, assuming no other balls are present on the table and there is no significant air resistance. This is just a rough estimate and actual distances may vary widely based on the specific conditions.
This sounds correct for a table when rails are involved with a slower cloth and slower rails than new. I know on the tables I most often play at with old rails I can get 3 or so table lengths of cueball travel with a hard hit, which is around this estimate. I think the AI was thinking about the constraints of a normal table not an open-ended table.
#### Nick8400
##### AzB Gold Member
Gold Member
Silver Member
All I know is the cue ball goes quite a long ways across the pool room after I jump it off the table.
Last edited:
#### Brookeland Bill
##### AzB Silver Member
Silver Member
It travels as far as it wants to.
Are you related to justnum?
Justnum and Numnuts.
#### Brookeland Bill
##### AzB Silver Member
Silver Member
I've heard of being bored but wtf.
After you get through playing with yourself there’s not a lot to think about is there?
#### Bob Jewett
##### AZB Osmium Member
Staff member
Gold Member
Silver Member
A pool ball doesn't go nearly that far on a pool table because it loses roughly 75% of its energy (50% of its speed) each time it makes fullish contact with a cushion. If you can get five lengths with your break speed (25MPH), you would have to hit the ball twice as fast (50MPH) to get six lengths.
Because distance increases directly with energy, every time you hit a cushion directly, your potential distance is reduced by a factor of 4.
#### Black-Balled
##### AzB Silver Member
Silver Member
A description of the experiment is in Byrne's Advanced Technique book. Byrne (his table and his garage), Shamos, Annigoni, Simon and Jewett were the experimenters. The balls -- including ivory -- landed on the driveway within a few yards of the end of the table.
Insanity
#### Banger
##### AzB Silver Member
Silver Member
Amarillo Slim once bet someone that he could drive a golf ball a mile. He then proceeded to tee it up on the shore of a frozen lake, and gave it a good whack. The golf ball went flying, and he won that bet. Or so the story goes.
#### Bob Jewett
##### AZB Osmium Member
Staff member
Gold Member
Silver Member
... d = v^2 / (g * (r+k))
I have the others (r=0.01) but how is k defined?
#### Bob Jewett
##### AZB Osmium Member
Staff member
Gold Member
Silver Member
Amarillo Slim once bet someone that he could drive a golf ball a mile. He then proceeded to tee it up on the shore of a frozen lake, and gave it a good whack. The golf ball went flying, and he won that bet. Or so the story goes.
The same story is told of Titanic Thompson.
Staff member
Gold Member
Silver Member
#### Fatboy
##### AzB Silver Member
Silver Member
Amarillo Slim once bet someone that he could drive a golf ball a mile. He then proceeded to tee it up on the shore of a frozen lake, and gave it a good whack. The golf ball went flying, and he won that bet. Or so the story goes.
Yes, that’s what I was thinking when I made my post.
I used to know Slim in Vegas, seen him at the pool room a few times and of course at the poker room.
#### Brookeland Bill
##### AzB Silver Member
Silver Member
If a cue ball flys off the table and hits a hardwood floor but no ones around, does it make a sound?
#### Fatboy
##### AzB Silver Member
Silver Member
A body in motion stays in motion until acted on by a outside force
That’s a principal in physics.
Friction is the only thing stopping the CB. The more friction, the faster the CB will stop. How hard it is initially hit determines how fast an infinite roll would happen in a frictionless environment (impossible), not how far.
Or something like that
Fatboy
#### Rocket354
##### AzB Silver Member
Silver Member
A pool ball doesn't go nearly that far on a pool table because it loses roughly 75% of its energy (50% of its speed) each time it makes fullish contact with a cushion. If you can get five lengths with your break speed (25MPH), you would have to hit the ball twice as fast (50MPH) to get six lengths.
Because distance increases directly with energy, every time you hit a cushion directly, your potential distance is reduced by a factor of 4.
On a 9' table 5 full lengths would be 500" = 41.67 ft. 41.67 x 2^5 = 1333.33 ft, so, yes, the drastic reduction in distance travelled from a real pool table to a theoretical infinite pool table does seem to check out. Thanks.
#### MitchAlsup
##### AzB Silver Member
Silver Member
Let's assume 30MPH for the break -- a few players can reach that with some control.
Simonis has the equivalent friction of an uphill slope of 1 in 100 or maybe 1/120 on a brand new cloth. (This is easy to measure from tournament videos.)
A ball moving 30MPH has the speed of a ball dropped from a height of 30 feet, unless I slipped a decimal. Multiply that height by the slope factor of 100 to get 3000 feet. Or 3600 on brand new cloth.
This ignores wind resistance, so the test is best done in a vacuum.
This is at least in the ball park.
#### Black-Balled
##### AzB Silver Member
Silver Member
If only your powers could be used for good, bob.
Mind-blowing Hahaha
#### Bob Jewett
##### AZB Osmium Member
Staff member
Gold Member
Silver Member
This is at least in the ball park.
They must have some big ball parks in your parts.
#### Patrick Johnson
##### Fish of the Day
Silver Member
...why would you even need to start at a pool table?
Why do it at all? What useful info were Byrne, Shamos, Annigoni, Simon and Jewett looking for?
pj <- were alcoholic beverages involved?
chgo
#### Cornerman
##### Cue Author...Sometimes
Gold Member
Silver Member
A description of the experiment is in Byrne's Advanced Technique book. Byrne (his table and his garage), Shamos, Annigoni, Simon and Jewett were the experimenters. The balls -- including ivory -- landed on the driveway within a few yards of the end of the table.
That jibes with my post above. | 1,698 | 7,013 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2023-40 | latest | en | 0.94601 |
https://stackoverflow.com/questions/66445983/create-a-divisors-list-and-indetify-primary-numbers | 1,624,242,266,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488259200.84/warc/CC-MAIN-20210620235118-20210621025118-00222.warc.gz | 485,532,760 | 35,765 | # Create a divisors list and indetify primary numbers
I tackled a beginners' exercise: "asks the user for a number and then prints out a list of all the divisors of that number."
NB - I reviewed similar questions in this forum but decided to post the following as they didn't address my needs.
The workflow I established is: input an integer number, say x add a variable which value is x/2, say y declare a divisors list
if the x is greater than 4 iterate between 2 and y+1 if the remainder is zero append it the the divisors list
if divisors list is empty or if the input number is smaller than 4 return: this is a primary number.
else, return divisors list
I ended up with the following solution. It does the job, but isn't good enough, as it has the following issues:
1. What is the python's input number limit? Currently, I have no limit which is wrong as it beyond the computational capacities of any computer.
2. I suspect my else statement isn't tidy enough. It can be shorter... but how?
3. If the number is lower than 4, the script returns twice the message "the number you entered is a primary number". I could fix it with an ad-hoc solution - but it should be solved through an algorithm not in a manual manner (...at least if I try to learn coding).
4. I ended up iterating in range of 2 and y+2 rather y+1 as I thought. I solved it manually but I don't understand why it isn't y+1.
``````num = int(input("Please select a number between: "))
y = num/2
if not y==0:
y=int(y-0.5)
list_range = list(range(2,y+2))
divisors_list = []
if num < 4:
print("The number you entered is a primary number")
else:
for i in list_range:
if num%i ==0:
divisors_list.append(i)
if not divisors_list:
print("The number you entered is a primary number")
else:
print(divisors_list)
`````` | 449 | 1,792 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2021-25 | latest | en | 0.913479 |
http://stackoverflow.com/questions/7556574/how-to-get-sign-of-a-number | 1,405,104,088,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776428735.82/warc/CC-MAIN-20140707234028-00054-ip-10-180-212-248.ec2.internal.warc.gz | 129,793,834 | 20,273 | # How to get sign of a number?
Is there a (simple) way to get the "sign" of a number (integer) in PHP comparable to `gmp_sign`Docs:
• -1 negative
• 0 zero
• 1 positive
I remember there is some sort of compare function that can do this but I'm not able to find it at the moment.
I quickly compiled this (Demo) which does the job, but maybe there is something more nifty (like a single function call?), I would like to map the result onto an array:
``````\$numbers = array(-100, 0, 100);
foreach(\$numbers as \$number)
{
echo \$number, ': ', \$number ? abs(\$number) / \$number : 0, "\n";
}
``````
(this code might run into floating point precision problems probably)
-
Why not install `gmp`? – Orbling Sep 26 '11 at 14:34
@Tomalak Geret'kal: Sometimes you're looking for feedback, right? ;) – hakre Sep 26 '11 at 14:41
@hakre: Try codereview.SE :) – Lightness Races in Orbit Sep 26 '11 at 14:43
@Orbling: Good question, maybe because it's already installed? Let me try :) – hakre Sep 26 '11 at 14:43
A variant to the above in my question I tested and which works as well and has not the floating point problem:
``````min(1, max(-1, \$number))
``````
Edit: The code above has a flaw for float numbers (question was about integer numbers) in the range greater than `-1` and smaller than `1` which can be fixed with the following shorty:
``````min(1, max(-1, \$number == 0 ? 0 : \$number * INF))
``````
That one still has a flaw for the float `NAN` making it return `-1` always. That might not be correct. Instead one might want to return `0` as well:
``````min(1, max(-1, (is_nan(\$number) or \$number == 0) ? 0 : \$number * INF))
``````
-
this is ok for integers, but if somebody pastes this solution for floats he will get into trouble. – rocksportrocker Sep 26 '11 at 19:03
@rocksportrocker: Especially for NAN and INF values. And for integers there is overflow as well. – hakre Sep 26 '11 at 20:36
don't works for `0.3` (or all numbers from `-1` to `1`) – Yukulélé Apr 4 '13 at 15:10
@hakre: in this case, all number from -1 to 1 return 0, not their sign – Yukulélé Apr 4 '13 at 15:21
@Yukulélé: Edited the post. Hope this is more helpful. Keep in mind that the question asks for integer numbers, not floating point numbers. – hakre Apr 4 '13 at 15:46
show 1 more comment
You can nest ternary operators:
``````echo \$number, ': ', (\$number >= 0 ? (\$number == 0 ? 0 : 1) : -1 )
``````
This has no problem with floating point precision and avoids an floating point division.
-
yeah, but the manual says you should avoid stacking them. – Gordon Sep 26 '11 at 15:29
What's wrong with this form?
``````if ( \$num < 0 )
{
//negative
}
else if ( \$num == 0 )
{
//zero
}
else
{
//positive
}
``````
or ternary:
``````\$sign = \$num < 0 ? -1 : ( \$num > 0 ? 1 : 0 );
``````
Not sure of the performance of `abs` vs value comparison, but you could use:
``````\$sign = \$num ? \$num / abs(\$num) : 0;
``````
and you could turn any of them into a function:
``````function valueSign(\$num)
{
return \$sign = \$num < 0 ? -1 : ( \$num > 0 ? 1 : 0 );
//or
return \$sign = \$num ? \$num / abs(\$num) : 0;
}
``````
I suppose you could be talking about `gmp_cmp`, which you could call as `gmp_cmp( \$num, 0 );`
-
The expression should represent a value of: `(-1, 0, 1)`. – hakre Sep 26 '11 at 14:30
@hakre, i'm not sure what you mean by that. – zzzzBov Sep 26 '11 at 14:38
@hakre, forgot about that part, added a zero check. – zzzzBov Sep 26 '11 at 14:40
Here's a cool one-liner that will do it for you efficiently and reliably:
``````function sign(\$n) {
return (\$n > 0) - (\$n < 0);
}
``````
-
This really is cool. Are there no exploits for it? – Tomáš Zato Apr 21 at 18:03
Well, you won't run into integer overflow issues or float precision issues since no arithmetic is performed on `\$n`. Moreover, IEEE floats do follow the law of excluded middle (`¬(A > B) ⇒ A ≤ B`, `¬(A < B) ⇒ A ≥ B`), so you won't get a nonzero number satisfying both conditions and yielding an incorrect sign of `0`. Finally, both `-0` and `0` are treated as equal to zero by IEEE specs, so will both return false under both conditions, yielding a sign of `0`. It's going to work for all numeric inputs. Feeding `NAN` into the function yields `1 - 1 = 0` which is as good an answer as any I suppose. – Milosz Apr 21 at 20:16
Here's one without loop:
``````function sign(\$number){
echo \$number, ': ', \$number ? abs(\$number) / \$number : 0, "\n";
}
\$numbers = array(-100, 0, 100);
array_walk(\$numbers, 'sign');
``````
-
``````echo \$number, ': ', strcmp(\$number, 0), "\n";
Cool! The docs is a little unprecise if it's always `-1, 0 or 1`, however, I will try it in the code. Thanks! – hakre Sep 26 '11 at 14:40
I now have tested this for some hours. If the `\$number` actually is a string (and representing zero, like `"n/a"`), this won't work (min(max) works here). Just noting, it's a side-case, just leaving this for the note. It generally worked pretty well, but not for string variables representing the numerical value `0` as we know it in PHP. @rocksportrocker: There are not really actual types like string or intever in PHP, so the conversion argument seems bogus in my eyes. Would be micro-optimizing for nothing anyway to that closely watch at it. – hakre Sep 27 '11 at 10:00 | 1,629 | 5,304 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2014-23 | latest | en | 0.90024 |
https://www.pw.live/question-answer/prove-that-the-diagonals-of-a-parallelogram-bisect-each-other-52150 | 1,675,064,967,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00364.warc.gz | 957,691,970 | 18,872 | # . Prove that the diagonals of a parallelogram bisect each other
Explanation:
We must show that the diagonals of the parallelogram ABCD cross each other.
OA = OC & OB = OD, in other words.
Now AD = BC [opposite sides are equal] in ΔAOD and ΔBOC.
[alternative interior angle] ∠ADO = ∠CBO in ΔAOD and ΔBOC.
Similarly, ∠AOD = ∠BOC by ΔDAO = ΔBCO (ASA rule)
As a result, OA = OC and OB = OB [according to CPCT]. | 132 | 415 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2023-06 | latest | en | 0.935833 |
https://study.com/academy/answer/solve-the-initial-value-problem-y-sqrt-1-y-2-quad-y-0-0.html | 1,544,784,064,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376825512.37/warc/CC-MAIN-20181214092734-20181214114234-00004.warc.gz | 745,857,766 | 21,709 | # Solve the initial value problem y'=\sqrt{1-y^2}, \quad y(0)=0
## Question:
Solve the initial value problem {eq}\displaystyle y'=\sqrt{1-y^2}, \quad y(0)=0 {/eq}
## Separation of Variables:
One of the methods of finding solutions of differential equations is separation of variables.
As its name suggests, this technique finds the solution of a differential equation by separating the variables into the two sides of the equation.
If we integrate it, the solution can be obtained.
We split first the variables {eq}x {/eq} and {eq}y {/eq}:
{eq}\begin{align*} \displaystyle y' & =\sqrt{1-y^2}\\ \frac{\mathrm{d}y}{\mathrm{d}x}&...
Become a Study.com member to unlock this answer! Create your account | 196 | 707 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2018-51 | latest | en | 0.71189 |
http://nrich.maths.org/public/leg.php?code=12&cl=3&cldcmpid=754 | 1,503,263,804,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886106990.33/warc/CC-MAIN-20170820204359-20170820224359-00471.warc.gz | 315,000,781 | 9,986 | # Search by Topic
#### Resources tagged with Factors and multiples similar to Small Change:
Filter by: Content type:
Stage:
Challenge level:
### There are 92 results
Broad Topics > Numbers and the Number System > Factors and multiples
### Divisively So
##### Stage: 3 Challenge Level:
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
### X Marks the Spot
##### Stage: 3 Challenge Level:
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
### Helen's Conjecture
##### Stage: 3 Challenge Level:
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
### One to Eight
##### Stage: 3 Challenge Level:
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
### LCM Sudoku II
##### Stage: 3, 4 and 5 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
### Remainder
##### Stage: 3 Challenge Level:
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
### LCM Sudoku
##### Stage: 4 Challenge Level:
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
### Mathematical Swimmer
##### Stage: 3 Challenge Level:
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
### Thirty Six Exactly
##### Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
### Data Chunks
##### Stage: 4 Challenge Level:
Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .
### Hot Pursuit
##### Stage: 3 Challenge Level:
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
### Inclusion Exclusion
##### Stage: 3 Challenge Level:
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
### Eminit
##### Stage: 3 Challenge Level:
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
### Factoring Factorials
##### Stage: 3 Challenge Level:
Find the highest power of 11 that will divide into 1000! exactly.
### AB Search
##### Stage: 3 Challenge Level:
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
### Counting Cogs
##### Stage: 2 and 3 Challenge Level:
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
### Diagonal Product Sudoku
##### Stage: 3 and 4 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
### Remainders
##### Stage: 3 Challenge Level:
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
### Star Product Sudoku
##### Stage: 3 and 4 Challenge Level:
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
### Powerful Factorial
##### Stage: 3 Challenge Level:
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
### Sieve of Eratosthenes
##### Stage: 3 Challenge Level:
Follow this recipe for sieving numbers and see what interesting patterns emerge.
### Gabriel's Problem
##### Stage: 3 Challenge Level:
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
### Diggits
##### Stage: 3 Challenge Level:
Can you find what the last two digits of the number $4^{1999}$ are?
### Oh! Hidden Inside?
##### Stage: 3 Challenge Level:
Find the number which has 8 divisors, such that the product of the divisors is 331776.
### Gaxinta
##### Stage: 3 Challenge Level:
A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?
### Factor Track
##### Stage: 2 and 3 Challenge Level:
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
### N000ughty Thoughts
##### Stage: 4 Challenge Level:
How many noughts are at the end of these giant numbers?
### Counting Factors
##### Stage: 3 Challenge Level:
Is there an efficient way to work out how many factors a large number has?
##### Stage: 3 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
### For What?
##### Stage: 4 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
### Times Right
##### Stage: 3 and 4 Challenge Level:
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
### Common Divisor
##### Stage: 4 Challenge Level:
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
### Even So
##### Stage: 3 Challenge Level:
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
### A Biggy
##### Stage: 4 Challenge Level:
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
### Sixational
##### Stage: 4 and 5 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
### How Old Are the Children?
##### Stage: 3 Challenge Level:
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
### Factorial
##### Stage: 4 Challenge Level:
How many zeros are there at the end of the number which is the product of first hundred positive integers?
### Different by One
##### Stage: 4 Challenge Level:
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
### Really Mr. Bond
##### Stage: 4 Challenge Level:
115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
### Factoring a Million
##### Stage: 4 Challenge Level:
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
### Power Crazy
##### Stage: 3 Challenge Level:
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
### Substitution Transposed
##### Stage: 3 and 4 Challenge Level:
Substitution and Transposition all in one! How fiendish can these codes get?
### Digat
##### Stage: 3 Challenge Level:
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
### Take Three from Five
##### Stage: 4 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
### Transposition Cipher
##### Stage: 3 and 4 Challenge Level:
Can you work out what size grid you need to read our secret message?
### Two Much
##### Stage: 3 Challenge Level:
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
### Ewa's Eggs
##### Stage: 3 Challenge Level:
I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?
### What a Joke
##### Stage: 4 Challenge Level:
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
### What Numbers Can We Make?
##### Stage: 3 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? | 2,342 | 9,054 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-34 | latest | en | 0.875714 |
https://www.electrondepot.com/electrodesign/rgb-led-colour-mixing-118534-.htm | 1,695,284,662,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233505362.29/warc/CC-MAIN-20230921073711-20230921103711-00660.warc.gz | 846,513,907 | 10,551 | # RGB LED colour mixing
• posted
I'm going to drive a Kingbright SMT RGB LED from a PIC with the intent to be able to display an apparent full colour spectrum. Plan is to "white balance" the thing using the current limit resistors and then PWM each channel, with 8 bit resolution if required. I'm wondering how many actual colours you need to display to make the thing scan through a convincing spectrum from a subjective human viewpoint. Also is there any algorithm that lets me calculate advance how to mix these colours, or have I just got to experiment to get a particular mixed colour? I'm aware that there are big differences in emission characteristics between the 3 LED's on the chip. I also wonder how much the linearity there is with respect to PWM drive level and output, and whether this varies between colours. All of this could make the output colour pretty arbitrary I guess.
Steve
• posted
On 09/01/2006 the venerable Steve etched in runes:
You need to start off with an understanding of the CIE chromaticity chart and how the human eye responds to colour stimulus. There are a couple of good references here:
and here:
Then plot your three primary wavelengths on the chart and you can reproduce any colour within that triangle. A study of the photopic curves will reveal a large negative lobe in the red sensitivity and a much smaller one in the green. In the early days of colour TV development we spent a long time looking for the elusive 'sucking phosphors' (try saying that after a glass or two of Merlot) to reproduce the gamut correctly. The answer of course was to do it electronically in the camera with a linear matrix.
Unfortunately colour reproduction is very subjective as at least 1 in 6 of the male population suffers from red/green colour blindness. Also for many years the unit of colour measurement was the JND or 'just noticable difference'! How scientific is that?
Anyway to answer your question, I think that for your project 64 steps for each of R, G & B would be more than adequate but the steps will not be linear and a look-up table for the PWM durations would be a good idea. Aim at a repetition rate of at least 70Hz and most of all have fun.
```--
John B
Delete \'spam blocker\' to reply direct```
• posted
Thanks for that John, I'll read the references, good to know 64 levels might do it. Will certainly have fun, indeed this one is purely a fun thing, it's going under my ice boots :-).
Steve
of R, G & B would
the PWM durations
have fun.
• posted
FWIW, I'm currently approaching completion of the first of a series of pre-programmed microcontrollers that will do PWM (BAM actually, to avoid patents) mixing of LEDs with 12 bits of resolution and at least 125Hz refresh. The first chip drives up to 21 LEDs (7 RGBs) from a 28-DIP, but the next version will drive 3 or 4 LEDs (RGB or RGBW) in an 8-DIP. They're controlled via I2C, but I can easily make versions that color-cycle internally, if people have specific cycles in mind.
Email me if you're interested in these chips.
TTYL, Omega aka Erik Walthinsen
• posted
I wrote quite a few routines for doing color analysis; and also have CIE data tables for the various sensitivities at differing resolutions (nm widths.) I can provide some thoughts based on my experiences and reading, too. But unless folks are interested in having a discussion and data tables and code bandied around here, perhaps we should take it to private email? (Mine is not obfuscated.)
Of course, none of this is particularly relevant if your main approach will be to simply work out what works from practice with your own vision. And for your use, that may be fine, with all the modeling and math more of an exploratory side-route than a direct path. Still, it can be fun to play with.
If you were putting these LEDs closely side by side into a grid and driving them, you may find the need to calibrate each one. It turns out that manufacturers haven't got processes or assembly processes tweaked well enough to guarantee that the emission bands are sufficiently close to each other for each die, or the dispersions similar enough, so that even at the same drive currents they do not emit the same optical amplitudes with the same dispersion distributions over angle and at the same wavelengths. Enough so that folks do notice differences in uncalibrated, gridded situations like outdoor LED displays supporting NTSC inputs.
Jon
• posted
Thanks Johathan,
Interested to hear of the issues for those needing to match colour output accurately. This application is pretty basic, it just needs to look like I'm displaying a spectrum to the casual viewer. I have mailed you with a bit more detail!
Steve
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners. | 1,056 | 4,879 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2023-40 | latest | en | 0.94326 |
https://www.snexplores.org/blog/eureka-lab/intel-sts-finalist-uses-math-predict-breast-cancer-spread | 1,726,662,573,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651895.12/warc/CC-MAIN-20240918100941-20240918130941-00015.warc.gz | 924,695,318 | 47,644 | # Intel STS finalist uses math to predict breast cancer spread
Inspired by her grandmother, Esha Maiti put statistics to use in medicine
Esha Maiti, 17, decided she wanted to study cancer after her grandmother passed away from misdiagnosed breast cancer. But at first she wasn’t sure where to start. Esha hit on her method in 10th grade. “I was in statistics class, and there was one of those Fun Fact boxes in my text book that talked about Monte Carlo simulations,” she says, “and I was thinking of cancer when I read that box, so I thought, ‘Oh! Maybe I could use a probabilistic method.’”
The senior at California High School in San Ramon, Calif., brought her mathematical predictions to the Intel Science Talent Search. The annual contest, run by Society for Science & the Public, brings 40 of the country’s brightest high school seniors to Washington, D.C., to show off the results of their research.
Cancers like breast cancer usually begin as a single tumor. The cells in the tumor have mutated, so they can no longer stop growing and dividing. When a tumor spreads, some of the cancer cells break off and move to other areas of the body, such as the lymph nodes or lungs. There the tumor cells take up residence and become secondary tumors, growing on their own.
At first, many of these secondary tumors, called metastases, are very small, less than a tenth of an inch (two millimeters). Most scans that doctors use cannot detect something that small. By the time the tumors grow big enough to detect, options for treating the cancer may be limited. And those secondary tumors can then start making new tumors of their own.
Esha wanted to see if she could use statistics to predict where breast cancer might spread. She tried the Monte Carlo method. It uses a computer program to pick random numbers from a particular number set over and over. The distribution of the numbers shows how likely a particular outcome is. In this case, Esha had the computer program select random numbers that reflected the probability of cancer spreading to the lymph nodes, to other areas in the body or not spreading at all.
“This model means that from the earliest stages of breast cancer, people could have a way to probabilistically tell where their tumors are likely to be,” Esha explains. While her math can’t attack cancer directly, she hopes that it will help patients to know more about their diagnosis. It could also help doctors. If they know where the cancer is most likely to spread, they can figure out the best course of treatment.
Esha is going to continue pursuing her passion, and hopes to study computational mathematics. She has always loved statistics and probability. “I love the idea of calculating to figure out exactly how important something is relative to anything else,” she says. Esha is off to a great start, she has published her work in a scientific journal, the Physical Review E.
### Power Words
cancer The rapid, uncontrolled growth of abnormal cells. It can lead to tumors, pain and death.
computational mathematics A branch of mathematics that uses computer programs to describe what is known about numbers and their relationships to each other, to predict or calculate the properties of other numbers.
lymph A colorless fluid produced by lymph glands. This secretion, which contains white blood cells, bathes the tissues and eventually drains into the bloodstream.
lymph glands (or lymph nodes) Organs that are part of the lymphatic system, small nodules located in the armpits, groin and stomach. They produce lymph and also serve as a storage place for cells in the immune system.
metastasis The spread of cancer from one organ to another. Cancer cells separate from the original tumor and can use the lymphatic system or blood vessels to move around the body, where they can form tumors in other organs.
Monte Carlo method A series of computational methods that repeatedly sample a set of numbers. By picking numbers at random over and over again, the Monte Carlo method can predict something unknown, such as the shape of a pictured object or the risk of cancer spreading to other areas of the body.
probability A measure of how likely something is to occur.
statistics The science of interpreting data, and in particular of reducing or estimating errors attributable to random variation.
tumor A mass of cells characterized by atypical and often uncontrolled growth. Benign tumors will not spread; they just grow and cause problems if they press against or tighten around healthy tissue. Malignant tumors will ultimately shed cells that can seed the body with new tumors. Malignant tumors are also known as cancers. | 954 | 4,675 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2024-38 | latest | en | 0.957988 |
https://astronomy.stackexchange.com/questions/27552/code-for-getting-the-pixel-coordinates-of-an-object-with-known-ra-dec-not-workin | 1,726,779,998,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652067.20/warc/CC-MAIN-20240919194038-20240919224038-00153.warc.gz | 92,628,918 | 36,865 | # Code for getting the pixel coordinates of an object with known RA DEC not working
I’m working on a project of which one of its functions is determining the XY pixel coordinates of an object given the object RA DEC coordinates and a platesolved image (this assumes that the target is near the image center).
I didn’t base this code on any algorithm, I thought it would just be basic vector manipulation. I’m aware that this basic approach doesn’t correct field flatness and stuff, I need it to be only roughly accurate.
'PS_DEC,PS_RA,PS_NORTH_ANGLE,PS_PIXEL_SCALE are retrieved from a platesolve
'Target_dec and Target_ra are the coordinates of the target
'VectorRotate(vector,angle) is a function that rotates a vector
'PS_DEC = 3.3026014754
'PS_RA = 278.7921661190
'Target_dec = 3.136138
'Target_ra = 278.65
'PS_NORTH_ANGLE = 99.89
'PS_PIXEL_SCALE = 3.15
Dim lengthTotal As Double = (90 - PS_DEC) * 3600 / PS_PIXEL_SCALE ' gets the length of the vector towards the celestial north pole in pixel
Dim InitVector As PointF
InitVector.X = 0
InitVector.Y = -CSng(lengthTotal) 'Casts the length to a vector
Dim FirstRotation As PointF = VectorRotate(InitVector, PS_NORTH_ANGLE * -1) 'rotates the vector towards the celestial north pole using north angle from the Plate Solve
Dim FlipVector As PointF
FlipVector.X = FirstRotation.X * -1
FlipVector.Y = FirstRotation.Y * -1 'flips the vector so that it points from the north pole to the image center
Dim Multiplier As Single = CSng((90 - Target_dec) / (90 - PS_DEC)) 'multiplier for applying the DEC difference
Dim FlipVectorTrim As PointF
FlipVectorTrim.X = FlipVector.X * Multiplier
FlipVectorTrim.Y = FlipVector.Y * Multiplier 'after this the vector should have the length of the Target dec
Dim Finalvector As PointF = VectorRotate(FlipVectorTrim, (target_Ra - PS_RA)) 'rotates the vector by the difference of the target ra and the ra from the plate solve
Dim Pixeloffset As Point
Pixeloffset.X = CInt(Finalvector.X - FlipVector.X)
Pixeloffset.Y = CInt(Finalvector.Y - FlipVector.Y) ' by subtracting the vectors I should get the relative offset from the image center in pixels
When I use the coordinates from the star marked green I get the yellow circle as a result, to the bottom left of the star.
Fiddling around with the code I found out that if I multiply the RA correction angle by 0.67 the target is correctly found.
Dim Finalvector As PointF = VectorRotate(FlipVectorTrim, (target_Ra - PS_RA) * 0.67)
I’ve tried this on another star where I got the same results. What I figure from this is that DEC is correctly handled, but the RA rotation is for some reason too much, by about one third.
I’ve looked at other possible error sources(placement of the circle in the image, star coordinates, the plate solve itself) and I’m confident that they are all correct, so the error has to be somewhere in this code.
I can use the fix I found, but I’d much rather know what I’m doing wrong.
Here is a link to the platesolved image.
• astrometry.net may be helpful as may be this question I asked in photo.SE: photo.stackexchange.com/questions/6111/…
– user21
Commented Sep 4, 2018 at 19:49
• @barrycarter the image has already solved with the (online) astrometry.net. The solved image includes the SIP distortion polynomial transformation which will make your task of mapping the World co-ordinates (RA, Dec) to pixel co-ordinates. Assuming your field is small (look like it), if you re-upload your image and set 'Tweak=0' under the Advanced Options, do you get more sensible results. In general, what you are trying to do is implement WCS e.g. docs.astropy.org/en/stable/wcs/index.html; this is a very general system which is often best left to libraries to do Commented Sep 4, 2018 at 23:47 | 937 | 3,756 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-38 | latest | en | 0.780044 |
https://dsp.stackexchange.com/questions/20539/how-to-plot-full-spectrum-with-negative-frequencies | 1,618,452,924,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00434.warc.gz | 330,282,822 | 42,287 | # How to plot Full spectrum with negative frequencies
I'm trying to do frequency analysis on signal of a rotating shaft. The signal is generated in two measurement planes i,e X-position and Y-Position. I was able to use fft and transform into frequency domain for individual planes. The plot I get for each place is only Half spectra. What I'm looking for is a full spectra which could combine both the planes. I did some research and found the following description online.
Full spectrum: The full spectrum is an additional diagnostic tool and is also called the spectrum of an orbit. It shows the same information as an orbit but in a different format. It helps to determine the degree of ellipticity (or flattening) associated with the various machinery conditions along with the precessional direction for all the frequency components present. To obtain the full spectrum, the orthogonal X and Y transducer signals are fed into the direct and quadrature parts of the FFT input. The positive and negative vibration components for each frequency are obtained. Positive is defined to be the forward precession and the negative component as the reverse precession. These components yield the following ellipticity and precessional information for a given orbit of any particular frequency (1× or 2× or …):
• The sum of two components, forward and reverse, is the length of the orbit major axis. • The difference between the two components is the length of the orbit minor axis. • The larger of the two components, positive or negative, determines the direction of precession that is forward or reverse.
One of the possible applications of full spectrum is analysis of the rotor runout caused by mechanical, electrical or magnetic irregularities. Depending on the periodicity of such irregularities observed by the X–Y proximity probes, different combinations of forward and reverse components are observed. The method forms the basis for many useful machinery diagnostics.
The full spectrum (just like the normal FFT) can be obtained in a steady-state analysis (a single FFT or waterfall) and even in transient analysis, which would then be called the full spectrum cascade (Figure attached).
Could anyone help how the 2 half spectra is converted into full spectra plot. Does anyone have any idea about this? Any hints or suggestions please!!
• don't you just take the fft of x+i*y? – endolith Feb 15 '15 at 19:00
• @endolith did that but the question now is how to derive the phase angle? drive.google.com/file/d/0Byib6yrCQ9vnRUM2Yi1sMklXeFk/… – Agni Feb 15 '15 at 19:44
• the same way you derive the phase angle for any complex number: en.wikipedia.org/wiki/… the FFT gives you a bunch of complex numbers, and typically you work with the magnitude and phase of each one. – endolith Feb 15 '15 at 20:56
• @endolith But that would give only one complex number So now I can only derive one phase angle. But if you can see in the figure I have shared in my previous comment. There are 2 phase angles alpha and beta. So How to deal with the other phase angle? Or since the X and Y sensors are orthogonal positioned, so assume that one angle is whatever I get from the complex number and the other is (90-phase angle)? – Agni Feb 16 '15 at 6:02
• I don't see any alpha and beta in your figures. As you said in your post "The positive and negative vibration components for each frequency are obtained. Positive is defined to be the forward precession and the negative component as the reverse precession." I'm not sure what the question is. – endolith Feb 17 '15 at 17:03 | 779 | 3,573 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-17 | longest | en | 0.929026 |
https://brainmass.com/math/calculus-and-analysis/higher-order-derivatives-of-f-x-2-2-x-1-13631 | 1,709,205,030,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474808.39/warc/CC-MAIN-20240229103115-20240229133115-00084.warc.gz | 143,832,373 | 7,526 | Purchase Solution
# Higher Order Derivatives of f(x) = [2^(2^x)] + 1
Not what you're looking for?
Differential Calculus
Fermat Numbers
Higher Order Derivatives of f(x) = [2^(2^x)] + 1
The function f(x) = [2^(2^x)] + 1 represents Fermat numbers when x = 1,2,3,...
Find the higher order derivative of the function f(x) = [2^(2^x)] + 1.
##### Solution Summary
This solution is comprised of a detailed explanation of the higher order derivatives of Fermat numbers. It contains step-by-step explanation to find the higher order derivative of the function f(x) = [2^(2^x)] + 1. Solution contains detailed step-by-step explanation.
Solution provided by:
###### Education
• BSc, Manipur University
• MSc, Kanpur University
###### Recent Feedback
• "Thanks this really helped."
• "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
• "Very nice thank you"
• "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
• "You are awesome. Thank you"
##### Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
##### Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them. | 367 | 1,541 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-10 | latest | en | 0.896183 |
https://www.enotes.com/homework-help/find-dimensions-largest-rectangle-whose-perimeter-426006 | 1,624,469,047,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488539764.83/warc/CC-MAIN-20210623165014-20210623195014-00368.warc.gz | 673,659,884 | 18,082 | # find the dimensions of the largest area rectangle whose perimeter is 3600 feet. (enter the dimensions from smalles to largest) side: side:
Let us say length is X and width is Y.
Perimeter `= 2(X+Y) = 3600`
`2(X+Y) = 3600`
`X+Y = 1800`
`Y = 1800-X`
Area` (A) = X*Y = X(1800-X) = 1800X-X^2`
For maximum/minimum area dA/dX = 0
dA/dx = 1800-2X
When `(dA)/(dX) = 0` ;
`1800-2X = 0`
`X = 900`
If X = 900 has a maximum then `(d^2A)/(dX^2)` at X = 900 would be negative.
`(dA)/dx = 1800-2X`
`(d^2A)/dx^2 = -2 ` (negative)
So we have a maximum for the area.
X = 900
Y = 1800-900 = 900
So the dimensions would be a square with 900ft each side.
Approved by eNotes Editorial Team | 268 | 688 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2021-25 | latest | en | 0.813414 |
https://math.stackexchange.com/questions/649701/gradient-descent-on-non-convex-function-works-how | 1,638,666,814,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363134.25/warc/CC-MAIN-20211205005314-20211205035314-00335.warc.gz | 479,043,905 | 36,673 | # Gradient descent on non-convex function works. How?
For Netflix Prize competition on recommendations one method used a stochastic gradient descent, popularized by Simon Funk who used it to solve an SVD approximately. The math is better explained here on pg 152. A rating is predicted by
$$\hat{r}_{ui} = \mu + b_i + b_u + q_i^Tp_u$$
Regularized square error is
$$\min_{b*,q*,p*} \sum_{u,i} (r_{ui} - \mu - b_i - b_u - q_i^Tp_u)^2 + \lambda_4 (b_i^2 + b_u^2 + ||q_i||^2 + ||p_u||^2)$$
If partial derivatives are taken according to each variable, and through a constant for the update rule we have equations such as
$$b_u \leftarrow b_u + \gamma (e_{ui} - \lambda_4 \cdot b_u)$$
[The rest is skipped]. My question is this, paper here (Wayback Machein) states square error function above non-convex because of $$q_i^Tp_u$$ and both variables here are unknown which, of course, is correct. Then how do we guarantee stochastic gradient descent scheme described in all papers will find a global minimum? I read somewhere SGD can be used to solve non-convex functions, I'd like to hear about some details on how. SGD SVD method described in the links works well in practice.
Also, alternating least squares can be applied to solve the SVD problem described above according to IEEE Koren paper. This method alternates between holding one or the other variable constant thereby creating convex problems in the process. I wonder if SGD, while it goes through dimensions, data points one-by-one also, in a way, creates convex sub-problems as it proceeds.
Maybe the answer is simply this presentation by LeCun, stochastic gradient on non-convex functions have no theoretical guarantees, but this doesn't mean we should not use them. "When Empirical Evidence suggests a fact for which we don't have theoretical guarantees, it just means the theory is inadequate".
I was able to reach Brandyn Webb (aka S. Funk) and he clarified some of my questions. The ideas that led to SGD SVD can be found in this paper
http://courses.cs.washington.edu/courses/cse528/09sp/sanger_pca_nn.pdf
where Sanger, building on work of Oja
http://users.ics.aalto.fi/oja/Oja1982.pdf
talks about finding N top eigenvectors through a method called Generalized Hebbian Algorithm (GHA) using a neural network with probability 1. That is, training this particular network ends up doing PCA (very cool).
Webb was researching NNs at the time (way before Netflix);
I was looking at a reciprocal arrangement between neurons in cortex and had worked out an implied learning algorithm which struck me as something that might have an analytical solution. [..] My original incremental formulation (not too different) from a few years before that was, rather than a gradient, just an expansion of matrix multiplication based on the matrix in question being the sum of outer products of individual sample vectors, and was, therefore, exactly the same as a common numeric approach to finding eigenvectors (just keep squaring the matrix until it settles to many copies of your first eigenvector [i.e. the power method]; then repeat with that one removed, and so on) -- for sufficiently small learning rate, anyway... The result is practically the same as the gradient derivation; it is my assumption that it has the same properties.
Later Gorrell and Webb realized the formulation looked like it was solving an SVD problem (again before Netflix Prize). Webb first started using the SGD derivation for Netflix, he mentioned that he "went for the direct gradient method on the spur of the moment because it was faster to derive that on a napkin than to find my old paper".
The question can be asked "how much SVD is Funk SVD?". Some on the Net call it "Funk's heuristic approach to SVD" and "in missing data form it's a factor model not SVD". Another says "in the case of a partially observed matrix [..] the factorized solution U V'is not truely an SVD – there is no constraint that the matrices U and V be orthogonal".
Webb does not agree, to the first two
I'd personally probably just call it incremental approximate SVD. Factor model is a broad category; it's useful to retain reference to the connection to SVD even if it's no longer SVD since it helps (down the road) to understand some of the properties.
for the last,
Any regularization, whether implicit or explicit (implicit via not over-training) likely violates orthogonality, but if the underlying algorithm is run to convergence with adequately low learning rate and no regularization, it will settle on orthogonal matrices. Look to Sanger's GHA proof for this, but it's trivially understandable as reverse inhibition removing projections of existing vectors from the dataset which means the residual gradient necessarily slides into a subspace that lacks any projection on the other vectors (i.e., orthogonal).
Once you add regularization, or any of the non-linearities that the incremental approach allows you to conveniently insert, then all bets are off. However, assuming the primary gradient is still the majority influence, you can guarantee a degree of orthogonality, ergo the "approximate SVD" depiction.
Overall, we can say there are connections between GHA, the so-called "iterative power method", gradient solution and SVD; It is because of this, perhaps, Webb could delve into a solution without being scared off by the non-convexity of the problem.
No matter what route was taken during the invention of this method however, we can look at the error function for recommendations, and through its gradients one can see SGD can minimize it, which is proven by empirical tests. The error function is non-convex, however as Bottou and LeCun suggest absence of theory should not stop us using a method. Plus people started to look at stochastic approaches, their theoretical guarantees much closer now, as seen here
http://arxiv.org/pdf/1308.3509
The paper above also talks about power method and SGD connection BTW.
Note: power method is used to find a single eval/evec, that is evec for the largest eval, however it can be used to find all other evecs by "removing" the newlyfound evec from matrix A (through a process called deflation), and re-running the power method on A again which finds the second eigenvector, and so on.
http://www.maths.qmul.ac.uk/~wj/MTH5110/notes/MAS235_lecturenotes1.pdf
http://heim.ifi.uio.no/~tom/powerandqrslides.pdf
• Glad I found this Q/A, as I'm having the same question these days (posted here: bit.ly/1R7qsmV), wondering why SGD actually works for matrix factorization, because each update is carried out on just one part of the entire loss function, and I think each update of parameter $p_u$ using just one data point (say $r_{ui}$) will optimize $(r_{ui} - q_i^Tp_u)$, but this update might worsen $(r_{uj} - q_j^Tp_u)$ Mar 20 '16 at 12:11
• Sadly, I don't quite understand the answer above (my poor english :-( ), could please give me more/clear hint on why SGD works? Mar 20 '16 at 12:14 | 1,618 | 6,979 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2021-49 | latest | en | 0.908862 |
https://oeis.org/A280215 | 1,606,614,555,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141195967.34/warc/CC-MAIN-20201129004335-20201129034335-00420.warc.gz | 408,276,427 | 4,113 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280215 Number of nX5 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards. 1
6, 307, 4382, 49328, 474433, 4245153, 36290440, 298709773, 2400798535, 18900933338, 146535311611, 1121019997031, 8483337931994, 63591088869355, 472819500109525, 3490412406841210, 25604337866580661, 186765973876472967 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Column 5 of A280217. LINKS R. H. Hardin, Table of n, a(n) for n = 1..250 EXAMPLE Some solutions for n=4 ..0..0..0..0..0. .0..0..1..0..0. .0..0..0..0..0. .0..0..0..1..1 ..1..1..0..0..0. .1..1..1..0..0. .0..1..1..0..0. .0..0..0..1..2 ..1..2..2..2..2. .1..1..0..2..1. .1..1..2..2..0. .2..0..0..2..2 ..2..2..2..2..0. .1..0..0..1..1. .2..2..2..2..0. .0..0..0..2..2 CROSSREFS Cf. A280217. Sequence in context: A229148 A333482 A104003 * A015103 A282373 A123181 Adjacent sequences: A280212 A280213 A280214 * A280216 A280217 A280218 KEYWORD nonn AUTHOR R. H. Hardin, Dec 29 2016 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 November 28 20:47 EST 2020. Contains 338755 sequences. (Running on oeis4.) | 651 | 1,881 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2020-50 | longest | en | 0.76329 |
https://mathinsight.org/plotting_line_graphs_in_r | 1,685,372,253,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644867.89/warc/CC-MAIN-20230529141542-20230529171542-00798.warc.gz | 419,185,120 | 5,112 | # Math Insight
### Plotting line graphs in R
#### The basic plot command
Imagine that in R, we created a variable $t$ for time points and a variable $z$ that showed a quantity that is decaying in time.
> t=0:10
> z= exp(-t/2)
The simplest R command to plot $z$ versus $t$ is
> plot(t,z)
Without any other arguments, R plots the data with circles and uses the variable names for the axis labels. The plot command accepts many arguments to change the look of the graph. Here, we use type="l" to plot a line rather than symbols, change the color to green, make the line width be 5, specify different labels for the $x$ and $y$ axis, and add a title (with the main argument).
> plot(t,z, type="l", col="green", lwd=5, xlab="time", ylab="concentration", main="Exponential decay")
#### A line plot with multiple series
Imagine that you wanted to plot not only $z$ but also a variable $w$ that was increasing with time.
> w = 0.1*exp(t/3)
One way to plot separate lines for both $z$ and $w$ is to first plot $z$ with the plot and then add a line for $w$ with the lines command.
> plot(t,z, type="l", col="green", lwd=5, xlab="time", ylab="concentration")
> lines(t, w, col="red", lwd=2)
> title("Exponential growth and decay")
> legend(2,1,c("decay","growth"), lwd=c(5,2), col=c("green","red"), y.intersp=1.5)
The last two lines add a title (since it wasn't added with a main argument of the plot command) and a legend. The first two arguments to the legend command are its position, the next is the legend text, and the following two are just vectors of the same arguments of the plot and lines commands, as R requires you to specify them again for the legend. (The last y.intersp argument just increases the vertical spacing of the legend.)
Notice that the range of the plot does not expand to include all of the line plotted by the lines command. By default, the plot sets the axis limits to fit the data given it. If you can manual specify the axis limits with the xlim or ylim arguments. Adding the argument ylim = range(w,z) will ensure that the $y$-axis limits include all the data from both $z$ and $w$. The following commands will show all the data of $w$. These commands also show how to add both points as well as lines by specifying type="b". The symbols used for the points are specified by the pch (plotting character) argument.
> plot(t,z, type="b", col="green", lwd=5, pch=15, xlab="time", ylab="concentration", ylim=range(w,z))
> lines(t, w, type="b", col="red", lwd=2, pch=19)
> title("Exponential growth and decay")
> legend(0,2.8,c("decay","growth"), lwd=c(5,2), col=c("green","red"), pch=c(15,19), y.intersp=1.5) | 730 | 2,644 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2023-23 | latest | en | 0.853083 |
https://www.jiskha.com/display.cgi?id=1361761181 | 1,516,349,592,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00556.warc.gz | 940,875,854 | 3,345 | Calculus
posted by .
Use logarithmic differentiation:
F(x)= (3x+6)^4 (x^3 -2)^5
• Calculus -
F'(x)=
Similar Questions
1. Calculus
I need to find the derivative of the following problem via logarithmic differentiation, but I'm getting stuck. I know how to solve via logarithmic differentiation, but I can't figure out how to re-write the exponent(s) as logs. Could …
2. Calculus
Use logarithmic differentiation to determine the derivative of the function defined by f(x)=x^5(x-3)^9/(x^2+2)^4
3. calculus
y = (ln x)^(cos4x) Use logarithmic differentiation to find the derivative of the function.
4. calculus
Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x).
5. calculus
Use logarithmic differentiation: F(x)= (3x+6)^4 (x^3 -2)^5 f'(x)=
6. calculus
use logarithmic differentiation to differentiate the function f(x)=2^x(x^2+2)^3(x^3-3)^7/(x^2+4)^1/2
7. Calculus Help
Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)
8. Calculus 1
Use logarithmic differentiation to find the derivative of the function. y = x^(8cosx)
9. Calculus 1
Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x
10. calculus
use logarithmic differentiation to find dy/dx for: [(x^2)(e^2)(x)] / [3√(2x-5)]
More Similar Questions | 382 | 1,301 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2018-05 | latest | en | 0.815602 |
http://www.mywordsolution.com/question/explain-estimating-probability-with-the-given/919446 | 1,484,621,876,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279410.32/warc/CC-MAIN-20170116095119-00218-ip-10-171-10-70.ec2.internal.warc.gz | 598,356,563 | 8,250 | +1-415-315-9853
info@mywordsolution.com
## Statistics
describe Estimating probability with the given data.
The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? describe your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt "just on this trip"?
Statistics and Probability, Statistics
• Category:- Statistics and Probability
• Reference No.:- M919446
Have any Question?
## Related Questions in Statistics and Probability
### Best ribs wishes to pay off a debt of 40000 in 7 years what
Best Ribs wishes to pay off a debt of \$40,000 in 7 years. What amortization payment would they need to make each six months, at 6% interest compounded semiannually? (Use Table 12-2 from your text) \$3,541.05 \$3,910.63 \$2, ...
### Mrjassica manager of appliances for midtown department
Mr.jassica, Manager of appliances for midtown department store feels that her inventory levels of stoves have been running higher than necessary. Before revising the inventory policy for stoves she records the number sol ...
### According to a recent poll 29 of adults in a certain area
According to a recent poll, 29% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major conce ...
### Goofys fast food center wishes to estimate the proportion
Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.07. If 475 are sampled, what is the probability that the sample proportio ...
### Describe the following game with incomplete information as
Describe the following game with incomplete information as an extensive-form game. There are two players N = {I, II}. Each player has three types, TI = {I 1 , I 2 , I 3 } and TII = {II 1 , II 2 , II 3 }, with common prio ...
### Discuss the beginnings of the cold war from the position
Discuss the beginnings of the Cold War. From the position of a Soviet ruler, how might you have viewed the situation following WWII? How did the Truman administration attempt to handle it? (Include as many of the followi ...
### According to harpers index 55 of all federal inmates are
According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 15 federal inmates is selected. (a) What is the probability that 9 or more are serving time for drug dealing? ...
### Entertainment software association would like to test if
Entertainment Software Association would like to test if the average age of "gamers" (those that routinely play video games) is more than 30 years old. A random sample of 33 gamers was selected and their ages were record ...
### A statisticsnbspinstructor at a large western university
A statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She ran ...
### Tell whether each of the following relationships reflects a
Tell whether each of the following relationships reflects a positive or a negative correlation: a. the amount of stress in people's lives and the number of colds they get in the winter b. the amount of time that people s ...
• 13,132 Experts
## Looking for Assignment Help?
Start excelling in your Courses, Get help with Assignment
Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.
### Section onea in an atwood machine suppose two objects of
SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless
### Part 1you work in hr for a company that operates a factory
Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl
### Details on advanced accounting paperthis paper is intended
DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac
### Create a provider database and related reports and queries
Create a provider database and related reports and queries to capture contact information for potential PC component pro
### Describe what you learned about the impact of economic
Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen | 1,017 | 4,744 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2017-04 | longest | en | 0.922218 |
http://www.cfd-online.com/W/index.php?title=Introduction_to_turbulence/Statistical_analysis&oldid=5739 | 1,477,525,533,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00499-ip-10-171-6-4.ec2.internal.warc.gz | 366,939,246 | 13,395 | # Introduction to turbulence/Statistical analysis
## Foreword
Much of the study of turbulence requires statistics and stochastic processes, simply because the instanteous motions are too complicated to understand. This should not be taken to mean that the govering equations (usually the Navier-Stokes equations) are stochastic. Even simple non-linear equations can have deterministic solutions that look random. In other words, even though the solutions for a given set of initial and boundary conditions can be perfectly repeatable and predictable at a given time and point in space, it may be impossible to guess from the information at one point or time how it will behave at another (at least without solving the equations). Moreover, a slight change in the intial or boundary conditions may cause large changes in the solution at a given time and location; in particular, changes that we could not have anticipated.
Here will be introduced the simple idea of the ensemble average
Most of the statistical analyses of turbulent flows are based on the idea of an ensemble average in one form or another. In some ways this is rather inconvenient, since it will be obvious from the definitions that it is impossible to ever really measure such a quantity. Therefore we will spendlast part of this chapter talking about how the kind of averages we can compute from data correspond to the hypotetical ensemble average we wish we could have measured. In later chapters we shall introduce more statistical concepts as we require them. But the concepts of this chapter will be all we need to begin a discussion of the averaged equations of motion in Chapter 3
## The ensemble and Ensemble Average
### The mean or ensemble average
The concept of an ensebmble average is based upon the existence of independent statistical event. For example, consider a number of inviduals who are simultaneously flipping unbiased coins. If a value of one is assigned to a head and the value of zero to a tail, then the average of the numbers generated is defined as
$X_{N}=\frac{1}{N} \sum{x_{n}}$ (2)
where our $n$ th flip is denoted as $x_{n}$ and $N$ is the total number of flips.
Now if all the coins are the same, it doesn't really matter whether we flip one coin $N$ times, or $N$ coins a single time. The key is that they must all be independent events - meaning the probability of achieving a head or tail in a given flip must be completely independent of what happens in all the other flips. Obviously we can't just flip one coin and count it $N$ times; these cleary would not be independent events
Unless you had a very unusual experimental result, you probably noticed that the value of the $X_{10}$'s was also a random variable and differed from ensemble to ensemble. Also the greater the number of flips in the ensemle, thecloser you got to $X_{N}=1/2$. Obviously the bigger $N$ , the less fluctuation there is in $X_{N}$
Now imagine that we are trying to establish the nature of a random variable $x$. The $n$th realization of $x$ is denoted as $x_{n}$. The ensemble average of $x$ is denoted as $X$ (or $\left\langle x \right\rangle$ ), and is defined as
$X = \left\langle x \right\rangle \equiv \frac{1}{N} \lim_{N \rightarrow \infty} \sum^{N}_{n=1} x_{n}$ (2)
Obviously it is impossible to obtain the ensemble average experimentally, since we can never an infinite number of independent realizations. The most we can ever obtain is the ariphmetic mean for the number of realizations we have. For this reason the arithmetic mean can also referred to as the estimator for the true mean ensemble average.
Even though the true mean (or ensemble average) is unobtainable, nonetheless, the idea is still very useful. Most importantly,we can almost always be sure the ensemble average exists, even if we can only estimate what it really is. The fact of its existence, however, does not always mean that it is easy to obtain in practice. All the theoretical deductions in this course will use this ensemble average. Obviously this will mean we have to account for these "statistical differenced" between true means and estimates when comparing our theoretical results to actual measurements or computations.
In general, the $x_{n}$ couldbe realizations of any random variable. The $X$ defined by equation 2.2 representsthe ensemble average of it. The quantity $X$ is sometimes referred to as the expacted value of the random variables $x$ , or even simple its mean.
For example, the velocity vector at a given point in space and time $x^{\rightarrow},t$ , in a given turbulent flow can be considered to be a random variable, say $u_{i} \left( x^{\rightarrow},t \right)$. If there were a large number of identical experiments so that the $u^{\left( n \right)}_{i} \left( x^{\rightarrow},t \right)$ in each of them were identically distributed, then the ensemble average of $u^{\left( n \right)}_{i} \left( x^{\rightarrow},t \right)$ would be given by
$\left\langle u_{i} \left( x^{\rightarrow} , t \right) \right\rangle = U_{i} \left( x^{\rightarrow} , t \right) \equiv \lim_{N \rightarrow \infty} \frac{1}{N} \sum^{N}_{n=1} u^{ \left( n \right) }_{i} \left( x^{\rightarrow} , t \right)$ (2)
Note that this ensemble average, $U_{i} \left( x^{\rightarrow},t \right)$ , will , in general, vary with independent variables $x^{\rightarrow}$ and $t$. It will be seen later, that under certain conditions the ensemble average is the same as the average wich would be generated by averaging in time. Even when a time average is not meaningful, however, the ensemble average can still be defined; e.g., as in non-stationary or periodic flow. Only ensemble averages will be used in the development of the turbulence equations here unless otherwise stated.
It is often important to know how a random variable is distributed about the mean. For example, figure 2.1 illustrates portions of two random functions of time which have identical means, but are obviuosly members of different ensembles since the amplitudes of their fluctuations are not diswtributed the same. it is possible to distinguish between them by examining the statistical properties of the fluctuations about the mean (or simply the fluctuations) defined by:
$X^{'}= x- X$ (2)
It is easy to see that the average of the fluctuation is zero, i.e.,
$\left\langle x^{'} \right\rangle = 0$ (2)
On the other hand, the ensemble average of the square of the fluctuation is not zero. In fact, it is such an important statistical measure we give it a special name, the variance, and represent it symbolically by either $var \left[ x \right]$ or $\left\langle \left( x^{'} \right) ^{2} \right\rangle$ | 1,560 | 6,663 | {"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": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2016-44 | latest | en | 0.927277 |
https://ebrary.net/32747/environment/computer_simulation | 1,679,325,311,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943484.34/warc/CC-MAIN-20230320144934-20230320174934-00542.warc.gz | 274,125,346 | 8,982 | # Computer Simulation
By applying heat and mass conservation, as shown in Eq. 3.17, it is possible to determine the outlet conditions of both the air and desiccant solution based upon the inlet boundary conditions, geometry of the heat and mass exchanger and calculated heat and mass transfer coefficients.
ma and ms0 are the respective air and solution mass flow rates in kg s-1. The left- hand side of Eq. 3.17 represents the total enthalpy change (temperature and mass) of the air and the right-hand side represents the total enthalpy change of the desiccant solution. Engineering Equation Solver (EES) has been used to complete a one dimensional computer simulation to determine the thermal performance of the dehumidifier and regenerator. Some simplifying assumptions were made, and are as follows:
• • The heat and mass transfer processes are considered steady-state.
• • The dehumidification/regeneration processes are adiabatic; heat loss to surroundings is negligible.
• • There is perfect wetting and coverage of the membrane material with desiccant solution, with ideal contact between the air and desiccant solution.
• • The membrane material poses no resistance to heat and mass transfer i.e. direct contact is assumed.
• • Air and desiccant solution physical and thermal properties are consistent between channels.
• • No desiccant carry-over to the airstream occurred.
• • The latent heat of sorption is absorbed by the desiccant solution.
The above assumptions have been adopted by previous researches in numerical studies, and have been found to have negligible effect on the overall desiccant system performance (Liu 2008; Jradi and Riffat 2014a).
The outlet air temperature is determined for each channel using Eq. 3.18.
dqair is the heat transfer on the air side in J, and is defined in Eq. 3.1 and &>a is air absolute humidity in kgvapour/kgdryair.
The outlet desiccant solution temperature is determined for each channel using Eq. 3.19.
dqsoiution is the heat transfer on the solution side in J, and is defined in Eq. 3.2. The heat transferred to the solution includes the sensible heat due to the temperature difference plus the latent heat of water vapour absorption. dqair and dqsolution will be positive during dehumidification and negative during regeneration.
The outlet air absolute humidity in kgvapour/kgdrya;r is determined for each channel using Eq. 3.20
The outlet desiccant solution mass concentration is determined using Eq. 3.21
dm is the mass of water vapour absorbed/desorbed in kg s-1 and is defined in Eq. 3.8. dm will be positive during dehumidification and negative during regeneration.
The liquid desiccant simulation work has been carried out using EES where air and water property routines are in-built validated functions. Appendix B provides the equations used to determine the thermodynamic properties of moist air as a reference. The thermophysical properties of the desiccant solution are determined from linear regression curve fits to published empirical data (James 1998; Melinder 2007). Section 3.3.3 provides the evaluation metrics used to analyse the performance of the dehumidifier and regenerator. | 691 | 3,168 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-14 | latest | en | 0.908363 |
http://www.chegg.com/homework-help/questions-and-answers/cars-equal-mass-collide-90-degree-intersection-momentum-car-120x10-5-kg-km-h-east-momentum-q488892 | 1,369,128,851,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699856050/warc/CC-MAIN-20130516102416-00092-ip-10-60-113-184.ec2.internal.warc.gz | 391,653,966 | 7,822 | ## Puzzled
Two cars of equal mass collide at a 90 degree intersection. If the momentum of car A is 1.20x10^5 kg km/h east and the momentum of car B is 8.50x10^4 kg km/h north, what is the resulting momentum of the final mass?
## Answers (1)
• the momentum of car A is p = 1.20x10^5kg km/h
the momentum of car B is p ' = 8.50x10^4 kg km / h
Total momentum of the two cars before collision P =√[ p 2 + p ' 2 ]
from law of conservation of momentum, resulting momentum ofthe final mass = P
substitue values weget answer
Get homework help
More than 200 experts are waiting to help you now... | 184 | 594 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2013-20 | latest | en | 0.787608 |
http://www.physicsforums.com/showthread.php?t=487981 | 1,411,156,480,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1410657132007.18/warc/CC-MAIN-20140914011212-00107-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | 724,523,488 | 10,185 | # Does the clock aboard a GPS ...
by vector22
Tags: aboard, clock
P: 56 sattelite tick slower than an earth bound clock. Lets say an atomic clock. From what Ive gathered so far, the clock aboard the GPS sattelite ticks slower The sattelite is in free fall so the clock aboard the sattelite is in zero G. Is the zero G condition the only condition that cause the sattelite clock to tick slower?
Emeritus Sci Advisor PF Gold P: 5,598 http://www.lightandmatter.com/html_b...ch02/ch02.html Use your browser's search function to find the text "Let's determine the directions and relative strengths of the two effects in the case of a GPS satellite."
Mentor
P: 12,017
Does the clock aboard a GPS ...
Quote by vector22 sattelite tick slower than an earth bound clock. Lets say an atomic clock. From what Ive gathered so far, the clock aboard the GPS sattelite ticks slower The sattelite is in free fall so the clock aboard the sattelite is in zero G. Is the zero G condition the only condition that cause the sattelite clock to tick slower?
In one case you have the clocks speeding up since they are experiencing less gravity than clocks on earth are. On the other hand they are at a high velocity which will slow them down relative to ours here on earth. The two equal out to being a bit slower than earth clocks i believe.
P: 1,480
Quote by Drakkith In one case you have the clocks speeding up since they are experiencing less gravity than clocks on earth are. On the other hand they are at a high velocity which will slow them down relative to ours here on earth. The two equal out to being a bit slower than earth clocks i believe.
The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with earth clocks
Mentor
P: 12,017
Quote by yogi The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with earth clocks
Of course. I meant that the clocks WOULD run slower, but as you pointed out they are corrected to run with the correct time.
P: 3,188
Quote by yogi The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with earth clocks
Sorry that is half wrong, the effect of gravitation is just the other way round. For clarity, please allow me to correct your statement:
The effect due to gravitational potential is more significant than the velocity effect - GPS clocks are preset before launch to run slower so that in orbit they run approximately synchronous with earth clocks.
Without that adjustment they would tick very slightly faster than earth clocks.
See the already provided references for details.
Emeritus
PF Gold
P: 5,598
Quote by harrylin Without that adjustment they would tick very slightly faster than earth clocks.
Yes.
P: 56 So i gather the GPS clocks tick faster than earth bound clocks - any links to reference materials on that. So evidently, zero gravity (free fall) is not the only condition. The current science suggests that there is more than one condition that can effect a clock's timing . If there is more than one condition, are the conditions dependant on each other? Oh i found the above link - time dialation looks like pretty exotic stuff
P: 1,480
Quote by harrylin Sorry that is half wrong, the effect of gravitation is just the other way round. For clarity, please allow me to correct your statement: The effect due to gravitational potential is more significant than the velocity effect - GPS clocks are preset before launch to run slower so that in orbit they run approximately synchronous with earth clocks. Without that adjustment they would tick very slightly faster than earth clocks. See the already provided references for details.
Yes -quite right
Mentor
P: 12,017
Quote by vector22 So i gather the GPS clocks tick faster than earth bound clocks - any links to reference materials on that. So evidently, zero gravity (free fall) is not the only condition. The current science suggests that there is more than one condition that can effect a clock's timing . If there is more than one condition, are the conditions dependant on each other? Oh i found the above link - time dialation looks like pretty exotic stuff
Free fall has nothing to do with time dilation. The gravitational pull at whatever distance the satellites are at, and their velocity relative to ours here on earth are the only factors. The satellites further up or lower in orbit have different rates of time dilation due to different gravitational pull and velocities compared to the GPS satellites.
Imagine a spaceship hovering stationary at a height equal to the GPS satellites. It has the same gravitational effects on its time that the GPS satellites have. However, since it is not moving at a high speed, it does not have the same effects from velocity.
Emeritus
PF Gold
P: 5,598
Quote by Drakkith Free fall has nothing to do with time dilation. The gravitational pull at whatever distance the satellites are at, and their velocity relative to ours here on earth are the only factors. The satellites further up or lower in orbit have different rates of time dilation due to different gravitational pull and velocities compared to the GPS satellites.
Actually it's the gravitational potential that matters, not the gravitational force.
Quote by Drakkith Imagine a spaceship hovering stationary at a height equal to the GPS satellites. It has the same gravitational effects on its time that the GPS satellites have. However, since it is not moving at a high speed, it does not have the same effects from velocity.
Experiments of this type have actually been done with atomic clocks, one in a valley and one at the top of a nearby mountain.
Mentor
P: 12,017
Quote by bcrowell Actually it's the gravitational potential that matters, not the gravitational force.
Oh. What's the difference?
Experiments of this type have actually been done with atomic clocks, one in a valley and one at the top of a nearby mountain.
Sure. I was just relating it to the current topic of GPS.
Emeritus
PF Gold
P: 5,598
Quote by Drakkith
Quote by bcrowell Actually it's the gravitational potential that matters, not the gravitational force.
Oh. What's the difference?
Gravitational potential is potential energy per unit mass.
Mentor
P: 12,017
Quote by bcrowell Gravitational potential is potential energy per unit mass.
Exactly what does that mean in regards to time dilation?
Emeritus
PF Gold
P: 5,598
Quote by Drakkith Exactly what does that mean in regards to time dilation?
The ratio of the rate of flow of time between two points is equal to $e^{\Delta\phi}$, where $\Delta\phi$ is the gravitational potential difference.
Mentor
P: 12,017
Quote by bcrowell The ratio of the rate of flow of time between two points is equal to $e^{\Delta\phi}$, where $\Delta\phi$ is the gravitational potential difference.
So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?
Emeritus | 1,601 | 7,419 | {"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} | 2.71875 | 3 | CC-MAIN-2014-41 | latest | en | 0.900903 |
https://en.wikipedia.org/wiki/Mixture_distribution | 1,721,602,953,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517796.21/warc/CC-MAIN-20240721213034-20240722003034-00611.warc.gz | 194,875,033 | 31,552 | # Mixture distribution
In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.
In cases where each of the underlying random variables is continuous, the outcome variable will also be continuous and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other distribution functions and density functions. The individual distributions that are combined to form the mixture distribution are called the mixture components, and the probabilities (or weights) associated with each component are called the mixture weights. The number of components in a mixture distribution is often restricted to being finite, although in some cases the components may be countably infinite in number. More general cases (i.e. an uncountable set of component distributions), as well as the countable case, are treated under the title of compound distributions.
A distinction needs to be made between a random variable whose distribution function or density is the sum of a set of components (i.e. a mixture distribution) and a random variable whose value is the sum of the values of two or more underlying random variables, in which case the distribution is given by the convolution operator. As an example, the sum of two jointly normally distributed random variables, each with different means, will still have a normal distribution. On the other hand, a mixture density created as a mixture of two normal distributions with different means will have two peaks provided that the two means are far enough apart, showing that this distribution is radically different from a normal distribution.
Mixture distributions arise in many contexts in the literature and arise naturally where a statistical population contains two or more subpopulations. They are also sometimes used as a means of representing non-normal distributions. Data analysis concerning statistical models involving mixture distributions is discussed under the title of mixture models, while the present article concentrates on simple probabilistic and statistical properties of mixture distributions and how these relate to properties of the underlying distributions.
## Finite and countable mixtures
Given a finite set of probability density functions p1(x), ..., pn(x), or corresponding cumulative distribution functions P1(x), ..., Pn(x) and weights w1, ..., wn such that wi ≥ 0 and Σwi = 1, the mixture distribution can be represented by writing either the density, f, or the distribution function, F, as a sum (which in both cases is a convex combination):
${\displaystyle F(x)=\sum _{i=1}^{n}\,w_{i}\,P_{i}(x),}$
${\displaystyle f(x)=\sum _{i=1}^{n}\,w_{i}\,p_{i}(x).}$
This type of mixture, being a finite sum, is called a finite mixture, and in applications, an unqualified reference to a "mixture density" usually means a finite mixture. The case of a countably infinite set of components is covered formally by allowing ${\displaystyle n=\infty \!}$ .
## Uncountable mixtures
Where the set of component distributions is uncountable, the result is often called a compound probability distribution. The construction of such distributions has a formal similarity to that of mixture distributions, with either infinite summations or integrals replacing the finite summations used for finite mixtures.
Consider a probability density function p(x;a) for a variable x, parameterized by a. That is, for each value of a in some set A, p(x;a) is a probability density function with respect to x. Given a probability density function w (meaning that w is nonnegative and integrates to 1), the function
${\displaystyle f(x)=\int _{A}\,w(a)\,p(x;a)\,da}$
is again a probability density function for x. A similar integral can be written for the cumulative distribution function. Note that the formulae here reduce to the case of a finite or infinite mixture if the density w is allowed to be a generalized function representing the "derivative" of the cumulative distribution function of a discrete distribution.
## Mixtures within a parametric family
The mixture components are often not arbitrary probability distributions, but instead are members of a parametric family (such as normal distributions), with different values for a parameter or parameters. In such cases, assuming that it exists, the density can be written in the form of a sum as:
${\displaystyle f(x;a_{1},\ldots ,a_{n})=\sum _{i=1}^{n}\,w_{i}\,p(x;a_{i})}$
for one parameter, or
${\displaystyle f(x;a_{1},\ldots ,a_{n},b_{1},\ldots ,b_{n})=\sum _{i=1}^{n}\,w_{i}\,p(x;a_{i},b_{i})}$
for two parameters, and so forth.
## Properties
### Convexity
A general linear combination of probability density functions is not necessarily a probability density, since it may be negative or it may integrate to something other than 1. However, a convex combination of probability density functions preserves both of these properties (non-negativity and integrating to 1), and thus mixture densities are themselves probability density functions.
### Moments
Let X1, ..., Xn denote random variables from the n component distributions, and let X denote a random variable from the mixture distribution. Then, for any function H(·) for which ${\displaystyle \operatorname {E} [H(X_{i})]}$ exists, and assuming that the component densities pi(x) exist,
{\displaystyle {\begin{aligned}\operatorname {E} [H(X)]&=\int _{-\infty }^{\infty }H(x)\sum _{i=1}^{n}w_{i}p_{i}(x)\,dx\\&=\sum _{i=1}^{n}w_{i}\int _{-\infty }^{\infty }p_{i}(x)H(x)\,dx=\sum _{i=1}^{n}w_{i}\operatorname {E} [H(X_{i})].\end{aligned}}}
The jth moment about zero (i.e. choosing H(x) = xj) is simply a weighted average of the jth moments of the components. Moments about the mean H(x) = (x − μ)j involve a binomial expansion:[1]
{\displaystyle {\begin{aligned}\operatorname {E} [(X-\mu )^{j}]&=\sum _{i=1}^{n}w_{i}\operatorname {E} [(X_{i}-\mu _{i}+\mu _{i}-\mu )^{j}]\\&=\sum _{i=1}^{n}w_{i}\sum _{k=0}^{j}\left({\begin{array}{c}j\\k\end{array}}\right)(\mu _{i}-\mu )^{j-k}\operatorname {E} [(X_{i}-\mu _{i})^{k}],\end{aligned}}}
where μi denotes the mean of the ith component.
In the case of a mixture of one-dimensional distributions with weights wi, means μi and variances σi2, the total mean and variance will be:
${\displaystyle \operatorname {E} [X]=\mu =\sum _{i=1}^{n}w_{i}\mu _{i},}$
{\displaystyle {\begin{aligned}\operatorname {E} [(X-\mu )^{2}]&=\sigma ^{2}\\&=\operatorname {E} [X^{2}]-\mu ^{2}&(\mathrm {standard} \ \mathrm {variance} \ \mathrm {reformulation} )\\&=\left(\sum _{i=1}^{n}w_{i}(\operatorname {E} [X_{i}^{2}])\right)-\mu ^{2}\\&=\sum _{i=1}^{n}w_{i}(\sigma _{i}^{2}+\mu _{i}^{2})-\mu ^{2}&(\mathrm {from} \ \sigma _{i}^{2}=\operatorname {E} [X_{i}^{2}]-\mu _{i}^{2},\mathrm {therefore} \,\operatorname {E} [X_{i}^{2}]=\sigma _{i}^{2}+\mu _{i}^{2}.)\end{aligned}}}
These relations highlight the potential of mixture distributions to display non-trivial higher-order moments such as skewness and kurtosis (fat tails) and multi-modality, even in the absence of such features within the components themselves. Marron and Wand (1992) give an illustrative account of the flexibility of this framework.[2]
### Modes
The question of multimodality is simple for some cases, such as mixtures of exponential distributions: all such mixtures are unimodal.[3] However, for the case of mixtures of normal distributions, it is a complex one. Conditions for the number of modes in a multivariate normal mixture are explored by Ray & Lindsay[4] extending earlier work on univariate[5][6] and multivariate[7] distributions.
Here the problem of evaluation of the modes of an n component mixture in a D dimensional space is reduced to identification of critical points (local minima, maxima and saddle points) on a manifold referred to as the ridgeline surface, which is the image of the ridgeline function
${\displaystyle x^{*}(\alpha )=\left[\sum _{i=1}^{n}\alpha _{i}\Sigma _{i}^{-1}\right]^{-1}\times \left[\sum _{i=1}^{n}\alpha _{i}\Sigma _{i}^{-1}\mu _{i}\right],}$
where ${\displaystyle \alpha }$ belongs to the ${\displaystyle (n-1)}$-dimensional standard simplex: ${\displaystyle {\mathcal {S}}_{n}=\{\alpha \in \mathbb {R} ^{n}:\alpha _{i}\in [0,1],\sum _{i=1}^{n}\alpha _{i}=1\}}$ and ${\displaystyle \Sigma _{i}\in R^{D\times D},\,\mu _{i}\in R^{D}}$ correspond to the covariance and mean of the ith component. Ray & Lindsay[4] consider the case in which ${\displaystyle n-1 showing a one-to-one correspondence of modes of the mixture and those on the ridge elevation function ${\displaystyle h(\alpha )=q(x^{*}(\alpha ))}$ thus one may identify the modes by solving ${\displaystyle {\frac {dh(\alpha )}{d\alpha }}=0}$ with respect to ${\displaystyle \alpha }$ and determining the value ${\displaystyle x^{*}(\alpha )}$.
Using graphical tools, the potential multi-modality of mixtures with number of components ${\displaystyle n\in \{2,3\}}$ is demonstrated; in particular it is shown that the number of modes may exceed ${\displaystyle n}$ and that the modes may not be coincident with the component means. For two components they develop a graphical tool for analysis by instead solving the aforementioned differential with respect to the first mixing weight ${\displaystyle w_{1}}$ (which also determines the second mixing weight through ${\displaystyle w_{2}=1-w_{1}}$) and expressing the solutions as a function ${\displaystyle \Pi (\alpha ),\,\alpha \in [0,1]}$ so that the number and location of modes for a given value of ${\displaystyle w_{1}}$ corresponds to the number of intersections of the graph on the line ${\displaystyle \Pi (\alpha )=w_{1}}$. This in turn can be related to the number of oscillations of the graph and therefore to solutions of ${\displaystyle {\frac {d\Pi (\alpha )}{d\alpha }}=0}$ leading to an explicit solution for the case of a two component mixture with ${\displaystyle \Sigma _{1}=\Sigma _{2}=\Sigma }$ (sometimes called a homoscedastic mixture) given by
${\displaystyle 1-\alpha (1-\alpha )d_{M}(\mu _{1},\mu _{2},\Sigma )^{2}}$
where ${\displaystyle d_{M}(\mu _{1},\mu _{2},\Sigma )={\sqrt {(\mu _{2}-\mu _{1})^{T}\Sigma ^{-1}(\mu _{2}-\mu _{1})}}}$ is the Mahalanobis distance between ${\displaystyle \mu _{1}}$ and ${\displaystyle \mu _{2}}$.
Since the above is quadratic it follows that in this instance there are at most two modes irrespective of the dimension or the weights.
For normal mixtures with general ${\displaystyle n>2}$ and ${\displaystyle D>1}$, a lower bound for the maximum number of possible modes, and – conditionally on the assumption that the maximum number is finite – an upper bound are known. For those combinations of ${\displaystyle n}$ and ${\displaystyle D}$ for which the maximum number is known, it matches the lower bound.[8]
## Examples
### Two normal distributions
Simple examples can be given by a mixture of two normal distributions. (See Multimodal distribution#Mixture of two normal distributions for more details.)
Given an equal (50/50) mixture of two normal distributions with the same standard deviation and different means (homoscedastic), the overall distribution will exhibit low kurtosis relative to a single normal distribution – the means of the subpopulations fall on the shoulders of the overall distribution. If sufficiently separated, namely by twice the (common) standard deviation, so ${\displaystyle \left|\mu _{1}-\mu _{2}\right|>2\sigma ,}$ these form a bimodal distribution, otherwise it simply has a wide peak.[9] The variation of the overall population will also be greater than the variation of the two subpopulations (due to spread from different means), and thus exhibits overdispersion relative to a normal distribution with fixed variation ${\displaystyle \sigma ,}$ though it will not be overdispersed relative to a normal distribution with variation equal to variation of the overall population.
Alternatively, given two subpopulations with the same mean and different standard deviations, the overall population will exhibit high kurtosis, with a sharper peak and heavier tails (and correspondingly shallower shoulders) than a single distribution.
### A normal and a Cauchy distribution
The following example is adapted from Hampel,[10] who credits John Tukey.
Consider the mixture distribution defined by
F(x) = (1 − 10−10) (standard normal) + 10−10 (standard Cauchy).
The mean of i.i.d. observations from F(x) behaves "normally" except for exorbitantly large samples, although the mean of F(x) does not even exist.
## Applications
Mixture densities are complicated densities expressible in terms of simpler densities (the mixture components), and are used both because they provide a good model for certain data sets (where different subsets of the data exhibit different characteristics and can best be modeled separately), and because they can be more mathematically tractable, because the individual mixture components can be more easily studied than the overall mixture density.
Mixture densities can be used to model a statistical population with subpopulations, where the mixture components are the densities on the subpopulations, and the weights are the proportions of each subpopulation in the overall population.
Mixture densities can also be used to model experimental error or contamination – one assumes that most of the samples measure the desired phenomenon, with some samples from a different, erroneous distribution.
Parametric statistics that assume no error often fail on such mixture densities – for example, statistics that assume normality often fail disastrously in the presence of even a few outliers – and instead one uses robust statistics.
In meta-analysis of separate studies, study heterogeneity causes distribution of results to be a mixture distribution, and leads to overdispersion of results relative to predicted error. For example, in a statistical survey, the margin of error (determined by sample size) predicts the sampling error and hence dispersion of results on repeated surveys. The presence of study heterogeneity (studies have different sampling bias) increases the dispersion relative to the margin of error.
## Notes
1. ^ Frühwirth-Schnatter (2006, Ch.1.2.4)
2. ^ Marron, J. S.; Wand, M. P. (1992). "Exact Mean Integrated Squared Error". The Annals of Statistics. 20 (2): 712–736. doi:10.1214/aos/1176348653., http://projecteuclid.org/euclid.aos/1176348653
3. ^ Frühwirth-Schnatter (2006, Ch.1)
4. ^ a b Ray, R.; Lindsay, B. (2005), "The topography of multivariate normal mixtures", The Annals of Statistics, 33 (5): 2042–2065, arXiv:math/0602238, doi:10.1214/009053605000000417
5. ^ Robertson CA, Fryer JG (1969) Some descriptive properties of normal mixtures. Skand Aktuarietidskr 137–146
6. ^ Behboodian, J (1970). "On the modes of a mixture of two normal distributions". Technometrics. 12: 131–139. doi:10.2307/1267357. JSTOR 1267357.
7. ^ Carreira-Perpiñán, M Á; Williams, C (2003). On the modes of a Gaussian mixture (PDF). Published as: Lecture Notes in Computer Science 2695. Springer-Verlag. pp. 625–640. doi:10.1007/3-540-44935-3_44. ISSN 0302-9743.
8. ^ Améndola, C.; Engström, A.; Haase, C. (2020), "Maximum number of modes of Gaussian mixtures", Information and Inference: A Journal of the IMA, 9 (3): 587–600, arXiv:1702.05066, doi:10.1093/imaiai/iaz013
9. ^ Schilling, Mark F.; Watkins, Ann E.; Watkins, William (2002). "Is human height bimodal?". The American Statistician. 56 (3): 223–229. doi:10.1198/00031300265.
10. ^ Hampel, Frank (1998), "Is statistics too difficult?", Canadian Journal of Statistics, 26: 497–513, doi:10.2307/3315772, hdl:20.500.11850/145503 | 4,137 | 16,301 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 40, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2024-30 | latest | en | 0.939155 |
http://www.scribd.com/doc/34753744/Suku-Banyak-Dan-Teorema-Faktor | 1,429,442,391,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246638820.85/warc/CC-MAIN-20150417045718-00212-ip-10-235-10-82.ec2.internal.warc.gz | 782,505,894 | 34,428 | Welcome to Scribd, the world's digital library. Read, publish, and share books and documents. See more
Standard view
Full view
of .
0 of .
Results for:
P. 1
Suku Banyak Dan Teorema Faktor
# Suku Banyak Dan Teorema Faktor
Ratings: (0)|Views: 903|Likes:
Published by: puji_n10tangsel on Jul 23, 2010
### Availability:
Read on Scribd mobile: iPhone, iPad and Android.
download as PPT, PDF, TXT or read online from Scribd
See more
See less
07/03/2013
pdf
text
original
1
Suku BanyakDanTeorema Faktor
2
Setelah menyaksikantayangan ini anda dapat
Menentukanfaktor, akar-akar serta jumlah dan hasil kaliakar-akar persamaan sukubanyak
3
eorema Faktor
J
ika f(x) adalah sukubanyak;(x ±
) merupakan faktor dari P(x) jika dan hanya jika P(
) = 0
## Activity (20)
You've already reviewed this. Edit your review. | 269 | 813 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2015-18 | longest | en | 0.352441 |
http://gridlab-d.shoutwiki.com/wiki/Tech:Multizone_ETP_Linearization | 1,620,425,826,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988828.76/warc/CC-MAIN-20210507211141-20210508001141-00430.warc.gz | 20,133,062 | 11,828 | *** WORKING DRAFT ***
Please review, edit and comment as necessary.
Tech:Multizone_ETP_Linearization - Linearized solution of the Equivalent Thermal Parameters method for modeling multizone commercial buildings
## Introduction
TODO: Describe purpose of multizone ETP solver and reason for linearization.
### Nomenclature
$C_n$
The heat capacity of $n$th node (Btu/degF).
$\Delta t$
The time-step taken for the next iteration (h).
$\Delta T_n$
The difference between the observed temperature and the setpoint temperature of the $n$th node, if controlled.
$k$
The proportional control gain of the HVAC control system (unitless).
$N$
The number of nodes in a thermal network (integer).
$n$
A reference to the $n$th of $N$ nodes (integer).
$m$
A reference to the $m$th of $N$ nodes (integer).
$Mode_n$
The HVAC mode of the system interacting with the $n$th zone (heat, cool, etc.).
$Q_n$
The HVAC heat flow into (positive for heating) or out of (negative for cooling) the $n$th node, if controlled (Btu/h).
$Q_{nm}$
The heat flow from the $n$th to $m$th nodes (Btu/h).
$Q_{mode-cap,n}$
The heating (positive) or cooling (negative) capacity of the HVAC system interacting with the $n$th node, if controlled (Btu/h).
$T_n$
The temperature of the $n$th node (degF).
$T_{cool,n}$
The cooling setpoint temperature of the $n$th node, if controlled (degF).
$T_{heat,n}$
The heating setpoint temperature of the $n$th node, if controlled (degF).
$U_{nm}$
The thermal conductance of the path from the $n$th and $m$th nodes (Btu/degF/h).
## Methodology
Figure 1. 6-Node Thermal Network
Known parameter values and boundary conditions are shown in red. Illustrated in Figure 1 is an arbitrary six-node thermal network. Note that the top horizontal branch is the original ETP circuit model, where $T_0$ is the outdoor air temperature (known boundary condition), $T_1$ is the indoor air temperature, and $T_2$ is the mass temperature. Node 3 might represent an unconditioned atrium space. Nodes 4 and 5 are present to illustrate series solutions of massless nodes, and might also represent an atrium with an additional buffer space to the outdoors.
Two additional massless paths are added to illustrate additional circumstances. A node n is characterized by its temperature Tn, its mass $C_n$ (which can be zero), and an exogenous heat gain $Q_n$ (from solar, internal, and/or HVAC, which is a boundary condition that can also be zero).
Nodes $m$ and $n$ are connected by conductance’s $U_{mn}$. A conductance might represent the UA of a building, an air flow rate between two nodes, or the product of a convective surface heat transfer coefficient and the surface area, for example.
To solve this circuit explicitly, the heat flow from any node $m$ through the conductance to any other node $n$ at the time $t$is denoted as $Q_{mn}(t)$. Thus
$Q_{mn}(t)=U_{mn}\left[T_m(t)-T_n(t)\right]$
(1)
Note that this implies a sign convention for heat flow into a node as positive. Thus, by definition, $Q_{mn}=-Q_{nm}$.
Assume a "small" time step $\Delta t$ during which all temperatures change by a "small" amount relative to the temperature differences between the nodes, i.e. $Q_{mn}$ can be considered a constant. This is the linearizing assumption. The maximum time-step $\Delta t$ permissible that satisfies the linearizing assumption is limited by two considerations:
(1) How long until an HVAC $Mode_n$ changes or internal gains $Q_n$ change?
This is determined by the time to the next expected change in mode, which can be estimated for each node based on the type of control (bang-bang or proportional).
(2) How long until the change in the temperature difference between a two nodes $n$ and $m$ exceeds a preset limit?
This is determined by computing the rate of change of the temperature difference and estimating the time until that rate of change exceeds a preset limit.
### Step 1: Compute temperatures of all massive nodes
Then the heat balance on a massive node $n$, i.e., $C_n \gt 0$, from a set of connected nodes $m=1$ to $M$, from time $t$ to time $t+\Delta t$ is:
$Q_n(t)+\sum_{m=1}^M Q_{mn}(t)=\frac{C_n\left[T_n(t+\Delta t)-T_n(t) \right]}{\Delta t}$
(2)
where $Q_n(t)$ is assumed to be constant boundary condition over the interval.
Solving this for the temperature of the node at the next time step:
$\frac{C_n T_n(t+\Delta t)}{\Delta t} = Q_n(t)+\sum_{m=1}^M Q_{nm}(t)+\frac{C_n T_n(t)}{\Delta t}$
(3)
$T_n(t+\Delta t) = \frac{\Delta t}{C_n} \left[Q_n(t)+\sum_{m=1}^M Q_{nm}(t)\right] + T_n(t)$
(4)
Substituting the definition for $Q_{nm}$ from Equation (1):
$T_n(t+\Delta t) = \frac{\Delta t}{C_n} \left[Q_n(t)+\sum_{m=1}^M U_{mn}\left[T_m(t)-T_n(t)\right]\right] + T_n (t)$
(5)
or
$T_n(t+\Delta t) = \frac{\Delta t}{C_n} Q_n(t) + \frac{\Delta t}{C_n} \sum_{m=1}^M U_{mn} T_m(t) + T_n(t) \left[1-\frac{\Delta t}{C_n}\sum_{m=1}^M U_{mn}\right]$
(6)
### Step 2: Compute temperatures of all massless nodes
If node $n$ is massless, i.e., $C_n = 0$, then it must be in thermal equilibrium with all adjacent nodes at any time. For massless nodes, Equation (2) reduces to
$Q_n(t)+\sum_{m=1}^M Q_{nm}(t+\Delta t)=0$
(7)
where over the time interval from $t$ to $t+\Delta t$ $Qn$ is a constant boundary condition.
Substituting the definition for $Q_{mn}$ from Equation (1):
$Q_n(t)+\sum_{m=1}^M U_{mn} \left[ T_m(t+\Delta t)-T_n(t+\Delta t) \right]=0$
(8)
Solving for the temperature of the node at time t+Δt:
$T_n(t+\Delta t)=\frac{Q_n(t)+\sum_{m=1}^M U_{mn}T_m(t+\Delta t)}{\sum_{m=1}^M U_{mn}}$
(9)
Figure 2. Reduced equivalent of 6-node thermal network
Computing the temperature of massless nodes in the thermal network assumes all temperatures of adjacent nodes are known at the end of a time-step, either as boundary conditions, or because they are massive and have had their temperatures computed in Step 1.
The simplest way to resolve this is to reduce the network to an equivalent network when massless nodes are in series, parallel, or "wye" configuration.
#### Series massless nodes configurations
Figure 3a - Series massless node reduction
A series configuration of two nodes, such as the thermal network in Figure 1, can be reduced as shown in Figure 2, where Node 5 is eliminated and the equivalent series conductance from Node 0 to Node 4 is
$U_{xy} = \frac{U_{xw} + U_{wy}}{U_{xw} U_{wy}}$
(10a)
#### Parallel massless nodes configurations
Figure 3b - Parallel thermal path reduction
A parallel configuration of two nodes can be reduced to a single node thus:
$U_{xy} = U_{A} + U_{B} \!$
(10b)
#### Delta massless nodes configurations
A "delta" configuration of 3 nodes $(x, y, z)$ can be transformed to a "wye" configuration of four nodes $(x,y,z,w)$ as follows:
\begin{align} U_{xw} &= U_{xy}U_{xz}\left[ \frac{1}{U_{xy}} + \frac{1}{U_{yz}} + \frac{1}{U_{xz}} \right] \\ U_{yw} &= U_{xy}U_{yz}\left[ \frac{1}{U_{xy}} + \frac{1}{U_{yz}} + \frac{1}{U_{xz}} \right] \\ U_{zw} &= U_{xz}U_{yz}\left[ \frac{1}{U_{xy}} + \frac{1}{U_{yz}} + \frac{1}{U_{xz}} \right] \end{align}
(10c)
Note that for the general "star-mesh" case, the transformation is:
$U_{ij} = U_iw U_jw \sum_{n=1}^N \frac{1}{U_n} \!$
(10d)
where $N=1$ is the dangling node case (which eliminates the node), $N=2$ is the series node case (see above) and $N=3$ is the "delta-wye" transformation case. The "star-mesh" transformation has no general inverse without additional constraints, so all mesh configurations must be simplified using a series of appropriate wye-delta transformations.
In such all cases, the temperature of the new node, $w$ is calculated as follows:
$T_w = \frac{\sum_{n=1}^N U_{nw} T_n}{\sum_{n=1}^N U_{nw}} \!$
(10e)
#### Special Case for "Bang-Bang" HVAC Control
Nodes whose temperature is used to control $Q_n$ (typically heating or cooling from the HVAC system) must have a modified calculation procedure, because $Q_n$ is no longer a boundary condition but rather a function of the node temperature, $T_n$, and the thermostat setpoints $T_{cool,n}$ and $T_{heat,n}$.
Define $Q_n$ as the sum of the HVAC energy input (heating positive, cooling negative), and the sum of internal heat gains and solar heat gains, to Node $n$:
$Q_n = Q_{hvac,n}+Q_{gains,n} \quad$
(11)
Let $Q_{cool-cap,n}$ and $Q_{heat-cap,n}$ be the net cooling and heating capacity available to supply the zone, respectively (net of the fan power). Let $Q_{fan,n}$ be the fan power when the HVAC is off (i.e. if the fan runs continually then $Q_{fan,n} \gt 0$).
Assume a heating and cooling thermostat with setpoints centered in a deadband with range $+\Delta T_n$ on either side of the setpoint. Note that setpoints must not overlap:
$T_{cool,n} - \Delta T_n \gt T_{heat,n} + \Delta T_n \quad$
(12)
The thermostat sets $Q_{hvac,n}$, which persists in subsequent time steps until changed by the thermostat:
When $T_n \lt T_{heat,n} - \Delta T_n$
$Mode_n = On \quad ; \quad Q_{hvac,n} = Q_{heat-cap,n}$.
(13)
When $T_n \gt T_{cool,n} + \Delta T_n$
$Mode_n = On \quad ; \quad Q_{hvac,n} = Q_{cool-cap,n}$.
(14)
When $Mode_n=On$ and $T_{heat,n}+ \Delta T_n$$T_n$$T_{cool,n} - \Delta T_n$
$Mode_n = Off \quad ; \quad Q_{hvac,n} = Q_{fan,n}$.
(15)
Then the node temperature at time $t+\Delta t$ can be calculated from Equation (6). Note that all HVAC control nodes with On/Off control must be massive. If one were massless, Equation (9) indicates there is no way to maintain a setpoint without proportional control of $Q_{hvac,n}$.
#### Special case for Proportional-Differential (PD) HVAC Control
In the case of proportional control for $Q_{hvac,n}$, then a proportional-differential control scheme:
When $T_{heat,n} - \Delta T_n \lt T_n(t) \lt T_{heat,n} + \Delta T_n \quad$
$Q_{hvac,n}(t) = Q_{heat-cap,n}(t) \left[ \frac{T_{heat,n}+\Delta T_n-T_n(t)}{2\Delta T_n} - \frac{k}{2\Delta T_n} \left[ T_n(t)-T_n(t-\Delta t)\right]\right]$.
(16)
When $T_{cool,n} - \Delta T_n \lt T_n(t) \lt T_{cool,n} + \Delta T_n \quad$
$Q_{hvac,n}(t) = Q_{cool-cap,n}(t) \left[ \frac{T_n(t) - T_{cool,n} + \Delta T_n}{2 ∆T_n} - \frac{k}{2\Delta T_n} \left[ T_n(t-\Delta t)-T_n(t) \right] \right]$.
(17)
When $T_{heat,n} + \Delta T_n \le T_n(t) \le T_{cool,n} - \Delta T_n$
$Q_{hvac,n}(t) = Q_{fan,n} \quad$.
(18)
where $k$ is the proportional gain for the controller.
### Step 3: Compute temperatures of reduced nodes
Massless nodes that have been reduced from the network are unnecessary to the simulation model of the network if
1. the temperature of the node does not affect some non-linear aspect such as a thermostatic control, and
2. the temperature is not needed as an output variable for some purpose.
In general, it may be best to assume that if the user specified “unneeded” nodes, that there was some purpose in mind, and their temperatures should be computed from Equation (9) as a final step.
## Validation
TODO: Describe how to validate a numerical implementation of this method.
## Authors
This method was developed by Robert G. Pratt and Lucy Huang at Pacific Northwest National Laboratory | 3,276 | 11,029 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-21 | latest | en | 0.774914 |
hibikii.com | 1,545,001,825,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827998.66/warc/CC-MAIN-20181216213120-20181216235120-00088.warc.gz | 114,943,983 | 9,966 | Opps, you've got an error!
click me to close
List of Categories List of Knowledges
# What is Amp, Watt, Volt and Ohm
## What is Amp, Watt, Volt and Ohm
The three most basic units in electricity are:- voltage (V), current (I, uppercase “i”) and resistance (r). Voltage is measured involts, current is measured in amps and resistance is measured in ohms. Electrical power is measured in watts. In an electrical system power(P) is equal to the voltage multiplied by the current. P = VI
It is important to measure how much lighting is added to an electric circuit. How to measure electricity is the tip that we hope will help you to maintain a safe and nicely lighted environment.
Watts = Amps * Volts
The fuse on the circuit will tell you how many amps that circuit will carry, usually 15 or 20 amps. Examples:
1. 110 volts times 15 amps equals 1650 watts
2. 110 volts times 20 amps equals 2200 watts
When lights are going to be left on for more than an hour, a safety factor should be used to offset heat build-up. Eighty percent of the total line wattage should be used as the maximum safe line wattage in these situations (for 153amp circuit: 1650 watts x .80 safety factor = 1320 watts, for 203 amp circuit: 2200 watts x .80 safety factor = 1760 watts).
Amps = Watts / Volts
Examples: How many amps does 1500 watts equal?
It all depends on the supply voltage.
1. If supply voltage is 240V, amps would be 1500w/240v = 6.25A.
2. If supply voltage is 110v, amps would be 1500w/110v = 13.64A.
Example: 15 AMP equal to how many watts?
1. Most fuses or thermal circuit breakers are designed to hold (not trip or melt open) 80% of their rated load.
2. 80% or 15 amps is 12 amps. You should try and not exceed this current on any circuit for the value of breaker or fuse protecting it.
3. The number of outlet plugs is immaterial as each plug may have different loads. Look at the devices you plan to connect to any particular outlet. It should give you a volt amp, watt, or at least current rating for the device. Lamps depend on what wattage bulb you have in them.
4. A 15 amp circuit can reliably hold 12 amps of current. 12 times 120V is 1,440 watts.
5. Your 15 amp breaker could only hold about 14 lamps if they had 100 watt bulbs in them. If you exceed the 80% rating, the breaker may occasionally trip for no apparent reason. The more you exceed the 80% rating the more often it will trip. When your exceed the full 100% of it’s rating it should trip reliably.
6. If you want the full capacity of a circuit breaker, get a magnetic or hydraulic breaker. The will hold reliably until their rating has been reached. | 693 | 2,618 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2018-51 | longest | en | 0.893098 |
https://socratic.org/questions/how-do-you-solve-the-system-3x-2y-4-and-4x-3y-7#581653 | 1,632,277,776,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057303.94/warc/CC-MAIN-20210922011746-20210922041746-00561.warc.gz | 575,586,848 | 6,148 | # How do you solve the system 3x+2y=4 and 4x+3y=7?
Mar 25, 2018
$x = - 2$ and $y = 5$
#### Explanation:
You can begin by subtracting the first equation from the second, which simplifies your operations. Doing so leaves you with $x + y = 3$.
You can write $x$ as $x = 3 - y$ and substitute in whichever equation you prefer:
$4 \left(3 - y\right) + 3 y = 7$
$12 - 4 y + 3 y = 7$
$12 - y = 7$
$- y = 7 - 12 = - 5$
$y = 5$
After finding $y$ you can return to $x = 3 - y$ and substitute $y$.
$x = 3 - 5$
$x = - 2$
So your solution is $S = \left\{\left(- 2 , 5\right)\right\}$ | 228 | 578 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2021-39 | latest | en | 0.77311 |
https://man.linuxtool.net/centos7/u3/man/3_catanhf.html | 1,627,933,686,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154356.39/warc/CC-MAIN-20210802172339-20210802202339-00206.warc.gz | 385,577,318 | 2,292 | # CATANH
NAME
SYNOPSIS
DESCRIPTION
VERSIONS
ATTRIBUTES
CONFORMING TO
EXAMPLE
COLOPHON
## NAME
catanh, catanhf, catanhl − complex arc tangents hyperbolic
## SYNOPSIS
#include <complex.h>
double complex catanh(double complex z);
float complex catanhf(float complex
z);
long double complex catanhl(long double complex
z);
## DESCRIPTION
The catanh() function calculates the complex arc hyperbolic tangent of z. If y = catanh(z), then z = ctanh(y). The imaginary part of y is chosen in the interval [−pi/2,pi/2].
One has:
catanh(z) = 0.5 * (clog(1 + z) − clog(1 − z))
## VERSIONS
These functions first appeared in glibc in version 2.1.
## ATTRIBUTES
For an explanation of the terms used in this section, see attributes(7).
C99.
## EXAMPLE
#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>
int
main(int argc, char *argv[])
{
double complex z, c, f;
if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);
exit(EXIT_FAILURE);
}
z = atof(argv[1]) + atof(argv[2]) * I;
c = catanh(z);
printf("catanh() = %6.3f %6.3f*i\n", creal(c), cimag(c));
f = 0.5 * (clog(1 + z) − clog(1 − z));
printf("formula = %6.3f %6.3f*i\n", creal(f2), cimag(f2));
exit(EXIT_SUCCESS);
} | 399 | 1,222 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2021-31 | latest | en | 0.419249 |
https://www.section.io/engineering-education/big-decimal-and-primitive-data-type-in-java/ | 1,701,822,143,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100575.30/warc/CC-MAIN-20231206000253-20231206030253-00096.warc.gz | 1,063,531,656 | 14,082 | # BigDecimal and Primitive Data Types in Java
##### September 30, 2021
Because of their inaccuracy, floating-point data types cannot be used in financial calculations. This is why Java provides a separate class named BigDecimal for executing operations. BigDecimal reduces the chances of calculation errors.
On double numbers, the BigDecimal class provides arithmetic, scale management, rounding, comparison, format conversion, and hashing functions. It compensates for the time complexity by handling large and small floating-point integers with exceptional precision.
These basic arithmetic operations can be performed on BigDecimal, and between BigDecimal and primitive data types. This is what we will cover in this article.
While both `BigInteger` and `BigDecimal` support arbitrary-precision integers, BigDecimal only supports arbitrary-precision, fixed-point numbers. BigDecimal/BigInteger is not advisable if you are constructing a low-latency application where every microsecond counts.
Let us look at our first example of adding, subtracting, and multiplying two large decimal integers with a Java program:
``````import java.io.*;
import java.math.BigDecimal;
class Example {
public static void main(String[] args)
{
// Declaration of the BigDecimal numbers
BigDecimal first1 = new BigDecimal("25.35557");
BigDecimal sec2 = new BigDecimal("55.3767");
// Actual arithmetic addition operation
System.out.println("Adding first1 and sec2 = "
// Actual arithmetic subtraction operation
System.out.println("Subtracting first1 and sec2 = "
+ (first1.subtract(sec2)));
// Actual arithmetic multiplication operation
System.out.println(
"Multiplying first1 and sec2 = "
+ (first1.multiply(sec2)));
}
}
``````
Output:
``````Adding first1 and sec2 = 80.73227
Subtracting first1 and sec2 = -30.02113
Multiplying first1 and sec2 = 1404.107793
``````
We have done three operations on our two declared BigDecimals; subtraction, addition, and multiplication operations.
There is a point to note here, we did not perform the division operation because the division of the two numbers is non-terminating.
This throws an error. Yet we know that BigDecimal was established to provide the highest level of precision.
We will fix it in the following code, where we will divide the same integers, but this time the data type will be double. Thus, there should be no errors.
Let us have the second example below:
``````import java.io.*;
class Example {
public static void main(String[] args)
{
double first1 = 25.35557;
double sec2 = 55.3767;
System.out.println("Dividing first1 and sec2 = "
+ (sec2 / first1));
}
}
``````
Output:
``````Dividing first1 and sec2 = 0.45787434
``````
### Primitive data types
We have done several operations on our BigDecimal objects. Now, we’ll attempt to do the same with primitive data types.
Let us now look at our third example:
``````import java.io.*;
import java.math.BigDecimal;
class Example {
public static void main(String[] args)
{
// Declaring an integer number and BigDecimal object
BigDecimal first1 = new BigDecimal("15");
int sec2 = 20;
// Adding both of them
System.out.println("Adding first1 and sec2 ="
}
}
``````
Upon running the code above, an error stating that `int` cannot be converted to `BigDecimal` will be thrown.
The error that occurs happens since the operation can only be performed on BigDecimal objects. Our primitive data type must be converted into a BigDecimal object using the BigDecimal class’s constructor.
We are constructing a new object of class BigDecimal with the same value as `sec2` and providing it directly to the `add()` method as an argument.
The code below resolves the problem in the following way:
``````import java.io.*;
import java.math.BigDecimal;
class Example {
public static void main(String[] args)
{
// Declaring a BigDecimal object and integer number
BigDecimal first1 = new BigDecimal("15");
int sec2 = 20;
System.out.println(
"Adding first1 and sec2 = "
}
}
``````
Output:
``````Adding first1 and sec2 = 35
``````
Lastly, look at the following example showing the arithmetic operations between `BigDecimal` and `int` to understand it better:
``````import java.io.*;
import java.math.BigDecimal;
class Example {
public static void main(String[] args)
{
// Declaring an integer number and a BigDecimal object
BigDecimal first1 = new BigDecimal("15");
int sec2 = 20;
System.out.println(
"Adding first1 and sec2 = "
System.out.println(
"Subtracting first1 and sec2 = "
+ first1.subtract(new BigDecimal(sec2)));
System.out.println(
"Multiplying first1 and sec2 = "
+ first1.multiply(new BigDecimal(sec2)));
System.out.println(
"Dividing first1 and sec2 = "
+ first1.divide(new BigDecimal(sec2)));
}
}
``````
Output:
``````Adding first1 and sec2 = 35
Subtracting first1 and sec2 = -5
Multiplying first1 and sec2 = 300
Dividing first1 and sec2 = 0.75
``````
No null values are allowed in a database, application, or view. Everything is initialized with new BigDecimal(0). Or, you execute null checks on every use of nullable values.
### Need for BigDecimal
There is a lot of fun to be had with floating-point numbers. A double type is commonly used for quantities unless the value is an integer, in which case an int type is usually acceptable.
Also, a float, or a long can be used, depending on the size of a value’s `value` type.
It should be noted that these kinds are the very worst thing you can use when dealing with money. They do not provide the correct value, but rather one that can be stored in a binary format.
### About primitive data types
They are the simplest types. It is possible to design your complicated kinds by using primitive types as a starting point for development.
Primitive types are easier to use in applications since they boost the performance by a large amount. Object-based implementation of primitive types would result in a considerable performance.
As a result of their name, they can relate to a wide range of objects. The non-primitive data types in Java, however, are built by programmers.
For the same reason, primitive types are more efficient when compared to instances of wrapper classes.
### Primal and non-primitive data types
Primal and non-primitive data types differ primarily in their underlying data types. This means that Java comes with a set of primitive types that are already specified.
In contrast, primitive types cannot be used to call methods to execute particular actions.
While a primitive type always has a value, other types can be null.
### Conclusion
A BigDecimal is a means to represent numbers that are accurate. Having a `double` gives you a certain level of precision in your game.
When working with doubles of varying magnitudes, the smaller one could be dropped from the sum because the magnitude difference is so huge. This would not happen with BigDecimal.
BigDecimal has the drawback of being slower, and more difficult to write algorithms with. | 1,520 | 6,953 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2023-50 | latest | en | 0.822014 |
https://wiki.zcubes.com/index.php?title=Manuals/calci/IMSQRT&oldid=196786 | 1,653,653,587,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662647086.91/warc/CC-MAIN-20220527112418-20220527142418-00277.warc.gz | 692,223,884 | 6,886 | Manuals/calci/IMSQRT
IMSQRT(z)
• is the complex number is of the form
Description
• This function gives square root of a complex number.
• IMSQRT(z), where z is the complex number is in the form of "x+iy".
• where x&y are the real numbers. imaginary unit ..
• The square root of a complex number is defined by:
$\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}$
• where is the modulus of .
• And is the argument of . $\displaystyle θ=tan^{-1}(y/x)$ also $\displaystyle θ∈(-pi(),pi()]$ .
• We can use COMPLEX function to convert real and imaginary number in to a complex number.
Examples
1. =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
2. =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
3. =IMSQRT("7")=2.64575131106459
4. =IMSQRT("8i")=2+2i | 287 | 811 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 3} | 3.75 | 4 | CC-MAIN-2022-21 | latest | en | 0.647023 |
https://hurew.com/quickanswer/what-subjects-are-on-the-ged-test | 1,685,401,629,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644913.39/warc/CC-MAIN-20230529205037-20230529235037-00756.warc.gz | 349,431,566 | 27,154 | # what subjects are on the ged test
You’re presently in: which topics are within the ged check In Hurew.com
## Which topics participate within the Ged check?
The GED® The examination consists of 4 topics divided into separate exams: Mathematical pondering, argumentation by means of language artwork, social research and science. You do not have to take all 4 exams directly – you’ll be able to clear them out and go at your personal tempo.
## Which topics are included in GED?
The GED examination is taken on the pc and contains 4 topics: mathematical pondering, argumentation by means of language artwork, social research and science.
## What sort of math is on the GED check?
The GED Math check consists of 46 questions that cowl the sense of numbers, Quantity operations, algebra, capabilities and patterns, measurement and geometry, statistics, information evaluation and chance. There are usually not solely a number of selection questions.
## Is the GED check tough to cross?
The GED check is hard as a result of it’s below loads of time stress. However in case you put together with good sources, the GED is fairly easy. The GED check offers you a restricted period of time (from 70 to 150 minutes, relying on the topic) for about 35-40 questions per topic.
## What are the 5 topics for GED?
The GED check covers 5 core matters: Arithmetic, social research, pure sciences, studying and writing.
## What number of modules are within the GED check?
The GED check® contains 5 Testing of modules within the fields of writing, social research, science, studying and arithmetic. Every module requires normal information and pondering expertise.
## Is algebra on the GED check?
The GED math check covers a number of the extra vital math matters that anybody incomes their GED ought to concentrate on. The overall matters of the GED arithmetic check are Primary Arithmetic, Geometry, Primary Algebra and Graphs & Capabilities.
## What number of questions are you able to miss about GED arithmetic?
The GED® Math check takes 115 minutes and has about 45 to 49 questions divided into 4 principal classes. A calculator can be utilized for the second a part of the maths check, and a math method sheet is supplied. To cross the GED Math check, it is advisable to reply between 30 and 32 of the questions right.
## Is the GED tougher than the SAT?
Some individuals suppose that the GED is a bit simpler than the SAT or ACT, however to take the GED and obtain leads to the college-ready areas could be very difficult, particularly for college kids who sometimes received unhealthy grades throughout their highschool years and left college early.
## Is GED A number of Alternative?
The GED is a computer-aided check. The sorts of questions you will see embody A number of Alternative, fill within the clean, drop-down, and superior response, amongst different issues. Every examination has a doable level vary of 100-200 factors, with a handed rating of 145.
## How exhausting is GED Math?
On a scale of 100 to 200, it’s essential to rating not less than 145 factors to cross every skilled check. And for the GED as an entire, the minimal rating is 580. Of the 4 topic checks, individuals have been Generally, you discover arithmetic essentially the most tough. The truth is, it’s the departmental check that college students most frequently fail.
## What grade degree is the GED check?
It was primarily based on a check {that a} majority of scholars might cross firstly of highschool, not on the finish. Analysis means that the present model of the GED check will increase information of a ninth or tenth grade degree.
## What rating do I have to cross GED?
145 or
Though a rating from 145 or higher is taken into account a handed rating on the GED, a college-ready rating is taken into account to be simply over 164. College students who rating 165-174 factors present that they’ve the talents they should begin college-level programs and could be exempted from placement checks or remedial programs (with out credit score) in school.
## What’s on the 2021 GED check?
The brand new GED check consists of 4 separate content material areas: Argumentation by means of language artwork (RLA), mathematical pondering, pure sciences and social research. The check is designed as a highschool equivalence check – in case you cross the GED, it’s going to assume that you’ve got an schooling equal to a typical highschool graduate.
## Can you employ a calculator on the GED?
The GED math check consists of two sections. On the primary part, which consists of 5 Questions, you aren’t allowed to make use of a calculator. For the second part, which accommodates 41 questions, you should use a calculator. Please notice that it’s essential to convey your personal TI-30XS calculator.
## Is the GED time-controlled?
The GED® is a time-controlled check, and also you solely have a sure period of time for every part. To finish the complete examination, it is advisable to pace your self up.
## What number of occasions can I repeat the GED check?
There isn’t a restrict to what number of occasions you’ll be able to take a GED check. You have to comply with your state’s ready time pointers and should pay the complete check charge once more after the check thrice.
## Are you able to cheat on the GED check?
Absolute. It is a very strict check, and in case you might someway handle to cheat, it will have massive penalties. There is a motive why it is now thought-about equal to a highschool diploma. It’s taken significantly partially due to its legitimacy.
## Can I take the GED check on-line?
In most states, college students can Take the 4 GED subtests on-line from the consolation of your personal residence or in an official check centre. To qualify for on-line checks, college students should obtain a “inexperienced” rating on the GED Prepared check, the official GED follow check.
## How a lot is every query price on the GED?
How does GED Scoring work? To cross the GED, you want a scaled rating of not less than 145 out of 200 on every topic check, which equates to a complete of not less than 580. So each check particular person check is off 200 factors
## How are GED checks evaluated?
Every GED topic check is rated on a scale of 100-200 factors. To cross the GED, it’s essential to earn not less than 145 factors in every of the 4 topic checks for a complete of not less than 580 factors (out of a doable 800). … Your finest outcomes on every try shall be added collectively to get your whole rating to qualify you to your GED qualification.
## What occurs if I do not end the GED?
In case you failed one in every of your GED® Topics, you might be for 2 consecutive repeat checks, with out restrictions between repetitions. In case you fail the third or a subsequent retest, you’ll have to wait 60 days for The subsequent try. Extra authorities necessities might apply.
## Does Harvard settle for GED?
The reply to the query of whether or not Harvard accepts GED graduates is: merely YES. Harvard accepts GED graduates. The actual fact is that Harvard doesn’t require a highschool or GED diploma for admission.
## What’s the highest rating you will get on a GED check?
800
GED-Factors system
The utmost achievable rating within the 4 modules is 800 and it is advisable to earn a minimum of 580 factors throughout the board. The 4 checks could be accomplished individually, so a rating of 580 is barely good if in case you have achieved a rating of 145 in every of the 4 sections.
## What occurs after you cross all 4 components of the GED?
Upon getting handed all 4 GED subtests, You’ll obtain your diploma and it’ll stay legitimate eternally! Which means that when you attain your GED, the diploma can be utilized to get a greater employment alternative or to proceed your educational schooling at a university or college.
## Do it’s a must to take all 5 GED checks on the identical time?
The GED® The check consists of 5 topics divided into separate exams. If You do the check on the pc, you do not have to do all 5 checks directly. As a substitute, you’ll be able to distribute them because it fits you and go at your personal tempo.
## What number of questions are there about GED 2021 Language Arts?
The GED® Reasoning by means of Language Arts Take a look at (RLA) assesses your studying and writing expertise. You’ve got 2.5 hours for over 46 questions that require you to: reply questions primarily based on particular person passages and on passages which might be paired with one another (studying and pondering expertise);
## Can I cross GED with out studying?
Go the GED in 2 months.
It would not matter while you left college. … To begin with, it is advisable to know that passing the GED check® with out finding out isn’t for everybody. In case your studying comprehension expertise are robust, chances are high you’ll be able to cross the GED subtests social research, science, and RLA (literacy).
## What science is on the GED?
The GED® The scientific check measures your information of Life Sciences, Bodily Sciences, and Earth and House Sciences.
## How do I examine at residence for the GED?
10 Surefire Methods to Put together for GED
1. Select the absolute best check date. …
3. Research textbooks. …
4. Join a GED check preparation course. …
5. Schedule time to review. …
6. Familiarize your self with the pc. …
7. Put together your self in your thoughts for the check ofr. …
8. Get well within the week earlier than the check.
## What’s the lowest rating for GED?
145
A handed check result’s 145. GED® Take a look at Rating Necessities are: Required minimal normal rating of 145 on every check (Max doable: 200) Required whole rating of 580.
## Does a GED correspond to a grade of 12?
Your GEDcredential®is to be obtained the equal of a *Grade 12 certificates. … Along with your GED®, you are able to do the identical issues as somebody who graduated in twelfth grade. All of the work is on-line and also you study from residence on the Web. They’re able to proceed studying like everybody else.
## What number of questions are there on the GED?
GED: Format of the check
Part Variety of questions Protocol
Half I: A number of Alternative 50 questions 75 minutes
Half II: Essay 1 Essay 45 minutes
Civics 50 questions 70 minutes
Science 50 questions 80 minutes
## How I handed the G.E.D. check was principally not a course of examine!
Associated Searches
which topics are within the ged check 2021
which topics are within the ged check 2020
ged Curriculum 2021 pdf
What are the 5 ged topics
ged necessities
ged check on-line
What are the 4 ged topics
Extra articles could be discovered within the class: FREQUENTLY ASKED QUESTIONS | 2,427 | 10,722 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2023-23 | latest | en | 0.920196 |
https://math.stackexchange.com/questions/tagged/infinite-graphs | 1,653,124,313,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662539049.32/warc/CC-MAIN-20220521080921-20220521110921-00708.warc.gz | 460,282,158 | 74,011 | # Questions tagged [infinite-graphs]
The study of graphs with an infinite number of vertices.
55 questions
Filter by
Sorted by
Tagged with
27 views
### Example of a locally finite graph without a uniform degree bound
We call an infinite graph locally finite if every vertex of it is of finite degree. A locally finite graph is said to have a uniform degree bound if the degree of every vertex of it is bounded by some ...
39 views
### Finding an isomorphism between an infinite tree and a subgraph of $\mathbb{Z}^3$
I was wondering if there exists a construction of an infinite tree, with some properties, that is isomorphic to subgraph of $\mathbb{Z}^3$. Notation Let $\Gamma_n$ denote the tree's vertices at ...
• 1,956
96 views
### Infinite core graphs
Let $G$ be an infinite graph (directed, loops okay, no multi-edges, so essentially a set with a binary relation). $G$ is called core if every one of its endomorphisms is surjective. Does this ever ...
• 1,193
88 views
### Compactness argument for countable subgraphs and beyond
I am interested whether there exists a certain generalization of so-called compactness argument in graph theory. First let me define what I mean by "compactness argument" Let $G = (V, E)$ be ...
1 vote
35 views
### Vertex sets separated only by infinitely many vertices imply an infinite number of disjoint paths between them.
In Reinhard Diestel's book "Graph Theory" (5th ed.) there is a chapter on infinite graphs (chapter 8). In that chapter Diestel states the following fact related to Menger's Theorem: ...
1 vote
34 views
### Infinite game (Ehrenfeucht-Fraïssé?) for Linear Temporal Logics
Imagine we have two LTL formulae: A and B. I would like to prove whether they are equivalent or not (the formulae can have the "Globally" operator, so the game is infinite). To do so I have ...
• 141
114 views
### Is there a locally finite tree having every other locally finite tree as a subgraph?
Is there a locally finite tree $T$ such that any locally finite tree is isomorphic to a subgraph of $T$?
• 39
1 vote
41 views
### Differentiating condition for two infinite graphs
From the tiling of $\mathbb{R}^2$ with squares I get an infinite graph where each node has 4 neighbors. I can create an infinite tree by attaching 4 nodes to a root node and then keep attaching 3 new ...
• 549
1 vote
352 views
### Infinite recursive graphs and different ways to build them
Infinite directed graphs (graphs with countably many nodes and edges) have a number of different applications. They can be identified with binary relations, in other words as elements of the power set ...
• 341
66 views
42 views
### Does every infinite graph contain a maximal clique?
The original problem is stated in terms of the tolerance relation (reflexive and symmetric, but not necessarily transitive): Is every tolerance subset contained in a maximal tolerance subset? For a ...
• 23
48 views
### Determining set and Automorphism group of a graph
Let $G$ be a simple graph. A set $S\subset V(G)$ is said to be determining set of $G$, if for any two Automorphisms $f,g \in Aut(G)$ whenever $f(s)=g(s)$ for all $s\in S$, then $f=g$. That is, an ...
• 572
62 views
### Finite automorphism group of a graph
Let $G$ be a simple graph and $Aut(G)$ denotes the automorphism group. Then prove or disprove, Suppose $Aut(G)$ and $diam(G)$ are finite for a graph $G$. Then $|V(G)|$ is finite. I know $Aut(G)$ ...
• 572
65 views
### Eccentricity in infinite tournaments
Definitions. A tournament is an oriented complete graph, that is, it's what you get by taking a (finite or infinite) complete graph and assigning a unique direction to each edge. If $T$ is a ...
• 70.1k
216 views
• 1,829
1 vote
497 views
### Does Kőnig's theorem hold for infinite bipartite graphs?
Kőnig's theorem states that in a bipartite graph the size of the maximal matching equals the size of the minimal vertex cover. I learned it as an equivalence to Hall's theorem and we proved it using ...
• 50
264 views
### Visual example of an infinite planar graph with degree sequence $(4^4,6^\infty)$
After reading some graph theory and talking with experts, I was intrigued. I would like to construct and visualise an infinite planar graph with degree sequence: $$D=(4^4,6^\infty)$$ where the ...
• 725
379 views
### Finite Unions of Dendrites [closed]
The question is a bit specific, but seems to be the most general question to ask after handling some obvious counterexamples. Initially, I was wondering the following. Let $X$ be a one-dimensional ...
• 601
66 views
### Is there a name for graphs with this property?
The property of the graph is the following: it's countable, undirected, simple, and for any infinite subset of vertices there are two vertices connected(by infinite Ramsey theorem this is in fact ...
• 1,251
1 vote
32 views
• 15.3k
293 views
### Hamilton Cycle Theorem?!
I've come across this link, where the author states: "Hamilton Cycle Theorem fails for infinite graphs unless ..." Please help me on this, what does he mean by "Hamilton Cycle Theorem"? I studied a ...
1k views
### There exists no zero-order or first-order theory for connected graphs
Prove that no zero-order theory (i.e. propositional calculus, without quantification) or first-order theory can describe the "connected graph" (i.e. from any point one can reach each other point in ...
• 2,950
1 vote
176 views
### Given a path between 2 vertices of a graph, there is only a finite number of vertices in the path?
Let us have a weighted graph $G=(V,E)$ with set of vertices $V$ and set of edges $E$, with a function $E\to V\times V$, a weight function $w:E\to\mathbb{R}_{>0}$ etc. Take the topological ...
• 871 | 1,427 | 5,716 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2022-21 | latest | en | 0.916203 |
https://or.stackexchange.com/questions/8324/how-to-formulate-cumulative-sum-of-lpvariable-in-pulp-python | 1,701,368,554,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100229.44/warc/CC-MAIN-20231130161920-20231130191920-00612.warc.gz | 497,577,344 | 33,023 | # How to formulate cumulative sum of LpVariable in Pulp Python
I have a Multiple product LP optimization problem in which the product(B1,B2,D) will be received in variable quantity with respect to date column.
The Optimizer should LP variable Output as Assy Out B1, Assy Out B2, Assy Out D, Open Assy Line (Binary decision to produce or not in given date).
The target is to maximize the assembly output per day.
The constraints are material receipt for each date and not allowed to produce more than material available in each date
here is my data:
I used the code below:
dfs=dfs.set_index(dfs['t'])
x=np.arange(1,10)
Assy_B1=pulp.LpVariable.dicts('Assy_B1',x,0,None,'Integer')
Assy_B2=pulp.LpVariable.dicts('Assy_B2',x,0,None,'Integer')
Assy_D=pulp.LpVariable.dicts('Assy_D',x,0,None,'Integer')
Open_Line=pulp.LpVariable.dicts('Open_Line',x,0,None,'Binary')
model=LpProblem('Assembly_Plan',LpMaximize)
model +=lpSum([ Assy_B1[t] + Assy_B2[t] + Assy_D[t] for t in x])
for i in x:
model+=(Assy_B1[i]+Assy_B2[i]+Assy_D[i])<=(dfs.loc[i,'Max_Capacity ']*Open_Line[i])
model+=lpSum(Assy_B1[i])<=dfs.loc[i,'INPUT B1']
model+=lpSum(Assy_B2[i])<=dfs.loc[i,'INPUT B2']
model+=lpSum(Assy_D[i])<=dfs.loc[i,'INPUT D']
model.solve()
The Model Solution is Optimal and output as below:
Everything is fine except the last date, the model should have capacity to produce 100 but utilized less (date 5/5/2022 cumulative produced is 60 and still 40 of model D can be produced on that day).
Similarly if the input material is available and capacity is less than cumulative material available the model should fit in next best available date for the same.
I am not able to fix this Constrain/Relaxation in Pulp.
• I think providing a reproducible example would increase your chances of getting answers. I can't imagine anyone is willing to type out the data from your image in order to run your code snippet.
– joni
Apr 28, 2022 at 11:33
• On 5/5, your constraint model+=lpSum(Assy_D[i])<=dfs.loc[i,'INPUT D'] forces Assy_D[i] to be 0 since dfs.loc[i,'INPUT D'] is 0 for that date. There isn't much point to the model as is though, since inputs have no weights, you could just select however much available INPUT and sum up to 100 if available. No ILP needed. Apr 28, 2022 at 12:26
• Hi Andy if i remove that constraint the model is filling 100 as output on non material available date also , example for Date 4/30 input of is 0 but the model will fill value for Assy Out D on that date , so to restrict that i need to give this lock Apr 28, 2022 at 12:37
• There is no more input left over for 5/5, hence it does not sum up to 100. It uses up 20 and 40 for B1 and B2 respectively. Apr 28, 2022 at 20:29
• The Cumulative available qty of B2 and D is not utilized fully , example Input D cumulative 220 and Assy_Out D 100 only , at least in last day (5/5) there is a available capacity of 40 and it can be untilized Apr 29, 2022 at 1:00
This is one way you can formulate/model the problem: \begin{align*} x_{i,t} &\in R^{+} \text{ variable denoting amount of raw material i processed/out in time t}\\ q_{i,t} &\in R^{+} \text{ variable denoting leftover raw material i at end of time t}\\ I_{i,t} &\in R^{+} \text{ Parameter denoting amount of raw material i that is provided in time t} \end{align*} Quantity of raw material $$i$$ processed/out in time $$t$$ is less than available inventory & left over inventory needs to carry-forward \begin{align*} x_{i,t}+q_{i,t} &= I_{i,t} \qquad \qquad \forall i,t | t= 0 \\ x_{i,t}+q_{i,t} &= q_{i,t-1} + I_{i,t} \quad \forall i,t|t> 0 \end{align*} Limit on processing capacity \begin{align*} \sum_{i} x_{i,t} &\le C^{\text{max}} \qquad \qquad \forall t \end{align*} Objective is minimize left over of each week to get the behaviour required for total quantity processed across all materials & times $$\text{minimize} \sum_{i,t} q_{i,t}$$ Note: As per your formulation, openLine[i] can always take 1 for each time period and binary is not needed as per requirement. | 1,163 | 4,011 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2023-50 | longest | en | 0.828293 |
https://www.kevinoninvesting.com/2017/ | 1,726,235,806,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651523.40/warc/CC-MAIN-20240913133933-20240913163933-00875.warc.gz | 773,487,208 | 12,986 | ## Thursday, April 27, 2017
### Monitor Your CD Maturity Dates
This is a quick reminder to those of you with CDs to monitor your CD maturity dates. I have an IRA CD maturing at a credit union in mid-May, and the rates there aren't great. So I logged on, and used online chat to request that the proceeds be deposited into my IRA savings account instead of being rolled into a new IRA CD (which is the default at most banks and credit unions). Within a few seconds, the rep responded that it had been done, and followed up with an email confirmation.
Typically there's a 10-day grace period after the maturity date during which time you can cancel the renewal, but I prefer to do it in advance if possible. It turned out to be very easy at this credit union. Now I'll be hunting for a good IRA CD at a bank or credit union at which I don't already have an IRA CD (I typically put enough in these to get close to the federal deposit insurance limit, which I don't want to exceed). We've been seeing some pretty good deals in recent months, so I'm optimistic.
## Tuesday, April 25, 2017
### Bond Basics: Part 7 (Duration)
Toward the end of the last post in this series, Bond Basics: Part 6, we saw that the change in the price of a bond, for a given change in yield, was related to the bond's term to maturity, and I mentioned that this was related to the bond concept of duration. In this post I'll discuss the concept of duration, especially as it relates to bond funds, which is the way you probably own bonds if you own them at all.
In a nutshell, duration provides a way to calculate an approximate value for the change in bond or bond fund price for a given a change in bond or bond fund yield. In the previous posts in this series, we discussed how bond price and yield move in opposite directions--when one goes up, the other goes down, and vice versa. Duration gives us a simple way to quantify this relationship--at least approximately.
## Monday, January 23, 2017
### Bond Basics: Part 6
In Part 5 of this series on bond basics, I derived the formula to calculate the price of a one-year bond in terms of its yield. I started by developing a formula to calculate something more familiar: the amount you end up with in a savings account after one year. In this part of the series I'll derive the formula to calculate the price of a bond with a term to maturity of more than one year, and again, I'll start with the more familiar concept of compound interest in a savings account.
## Saturday, January 7, 2017
### Bond Basics: Part 5
Much of the discussion in this series on bond basics has been about the inverse relationship between bond yield and bond price: when one goes up, the other goes down, and vice versa. My goal in this post is to help you begin to understand the mathematical formula that specifies bond price in terms of bond yield, since understanding this can facilitate a deeper understanding of bond fundamentals. We can start by considering something familiar: earning interest in a savings account. We can develop the simple formula that describes this, then with some elementary algebra, we can build on it to develop the formula that gives us bond price in terms of bond yield.
## Wednesday, January 4, 2017
### Bond Basics: Part 4
I had planned to start digging into the mathematical formula that relates bond price and bond yield in this post, but first I want to discuss one more example related to the topic discussed in Part 3 of this series. In that part, I explained that we can't make precise statements about the general relationship between interest rates and bond prices, because the yield (and price) of each bond changes differently depending on the bond market's assessment of the term risk and credit risk of that particular bond. Confusion about this is often exposed by questions about the impact of increases to the federal funds rate (FFR) on the prices of bond funds. So following is a brief discussion of this, and then in Part 5 I'll pick up on deriving the formula for bond pricing. | 880 | 4,050 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2024-38 | latest | en | 0.959442 |
http://chronicle.com/blognetwork/castingoutnines/2009/02/18/spreadsheets-and-calculus-proceed-with-caution/ | 1,472,155,844,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982294097.9/warc/CC-MAIN-20160823195814-00218-ip-10-153-172-175.ec2.internal.warc.gz | 49,762,899 | 13,652 | Previous The iPod touch: Keeping new parents sane since 2009 Next "This is a science course. Lasers are not voodoo."
Spreadsheets and calculus: Proceed with caution
February 18, 2009, 2:51 pm
Spreadsheets are one of the most underrated tools available for doing and learning mathematics, especially calculus. At my college we include spreadsheets as a central tool for our Calculus I course and use them every chance we get. But as with all technology, there is the possibility of encountering a seemingly inexplicable glitch when using them even in a very tame situation.
Here’s one I encountered this week when setting up a spreadsheet to do an average velocity/instantaneous velocity problem. We started with a falling object whose position from the start point at time t is given in the following table:
The eventual goal is to compute the average velocity from t=2 to t=3, then t=2.5 and t=3, then t=2.9 and t=3, and so on, finally estimating the instantaneous velocity right at t=3. Actually, this is where the glitches started. The “25″ in the third cell was supposed to be a “20″ because I wanted to position data to be fit, exactly, by the function $$s = 5t^2$$, which we were going to use to generate the position data not in the table. I caught this after an initial edit but decided it would be more interesting to proceed with the 25 there, then use my spreadsheet to get a power function trendline through the data, and go from there.
Go from there I did, and here’s the chart with the trendline:
Pretty close to $$s = 5t^2$$, right? Well… not exactly. Here’s what we get when we use the trendline formula to generate the position data for value of time approaching t=3 from the left, and then the average velocity from those times to t=3:
What’s supposed to happen is that the position values approach the position attained by the book at t=3, and the average velocities stabilize toward a single number which represents the instantaneous velocity at t=3. But the little deviation in the t=2 position from the original table (25 instead of 20) throws the trendline off so that the position as time approaches 3 overshoots the actual position at t=3, and so we end up with average velocities that are spinning out of control. (-1781 m/sec is roughly 4000 miles per hour, for reference, and the direction is wrong to boot).
But, you say, this is no surprise, because the mistake in the original table had the position off by 5 meters from where you intended. But what’s funny is that if you go back and make the mistake in the original table smaller, even a lot smaller, you encounter the same effect. If you change the 25 in the t=2 cell to 20.1 — that’s just a difference of less than 4 inches from the intended position of 20 meters — the trendline changes to $$y = 5.0089x^{1.9992}$$, and here’s what you get as time approaches 3:
As we close in on t=3, we still get the object rocketing upward!
What we learn here is that if you use a trendline for calculations, you really shouldn’t mix data from the trendline with data from the table which produced the trendline. In fact, the original trendline created using s(2) = 25 would predict s(3) ≈ 46.813, and when that value is used instead of 45 in the average velocity calculations you see the averages stabilize, although slowly, towards something like 31.2 m/sec.
But even then, if you took that trendline formula and found $$y’(3)$$ using the Power Rule (as we typically end up doing later in the course to tie algebraic diferentiation rules back to table calculations), you get $$y’(3) \approx 30.634$$, which is not what the average velocities are approaching in the table.
So spreadsheets are useful tools for learning mathematics, but for the kind of infinitesimal, close-up work that we have to do with calculus, error propagation becomes a viable course topic as the students are learning about limits.
Note: I used Numbers 09 for the charts and trendlines. I think Excel uses the same algorithm to produce power function trendlines as does Numbers, so this isn’t an Apple vs. Microsoft issue.
This entry was posted in Calculus, Math, Teaching, Technology and tagged , , , , . Bookmark the permalink.
• The Chronicle of Higher Education
• 1255 Twenty-Third St., N.W.
• Washington, D.C. 20037 | 1,003 | 4,284 | {"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} | 4.28125 | 4 | CC-MAIN-2016-36 | latest | en | 0.929139 |
https://puzzling.stackexchange.com/questions/101486/in-trouble-with-the-law/101602 | 1,717,041,537,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059418.31/warc/CC-MAIN-20240530021529-20240530051529-00885.warc.gz | 396,840,551 | 40,711 | # In trouble with the law
My suffix is insanity
My infix is grassy
My whole is false
There is a little joke here bonus points if you can find it
Hints
Crossreference
How many fingers am I holding up?
Monopoly money
COUNTERFEIT
A counter is a response
My suffix is insanity
Feit is pronounced as "fit", as in a fit of madness or insanity
My infix is grassy
Terf is pronounced the same as "turf", an upper layer of grassy ground
My whole is false
Counterfeits are fake
This also fits with some other clues, because
Counterfeit money will get you in trouble with the law, and another term for counterfeit/fake bills is "Monopoly money"
• If the infix can overlap the prefix and/or suffix that opens a lot more possibilities!
– TTT
Aug 28, 2020 at 21:22
• Bingo!!!! well done
– PDT
Aug 29, 2020 at 0:05
This doesn't fit all the clues, but perhaps some of this will help others:
kleptomania
Details:
Title: "In trouble with the law" - if you're a kleptomaniac, your're probably going to get caught stealing eventually.
Prefix: k = this just might be the single most popular reply in all texts and chats.
Suffix: mania = insanity
Infix: lepto - symptoms of the disease might be "gassy" (vomiting and diarrhea). Close enough to "grassy"? Hehe.
I don't have a match for the rest, but here are some ideas: "How many fingers am I holding up?" might refer to the book 1984, where Winston sees 4 fingers but is trying to be convinced (via drugs and torture) that there are actually 5 fingers, and the goal of this exercise is to make Winston "sane". Maybe there's a big brother reference in this puzzle somewhere? For monopoly money, when you start the game you have 1500, and the entire game comes with 20,580, in case either of those numbers are relevant somehow.
Acknowledge?
Ack is fundamentally a reply - it is used for nothing else. There's a certain infamous grassy knoll. One might indeed stand on the precipice of insanity, on the thin ledge before the fall. I...suspect that this isn't truly the answer, because it doesn't seem to fit the rest of the riddle all that well, but it fit those first parts well enough that I wished to share. Unless the joke is that by "whole" you meant "hole", and you're saying that "allege" is false?
• No, wrong answer, a little hint... You need to 'acknowledge' the title of this puzzle more than what your answer suggests
– PDT
Aug 27, 2020 at 17:51
• It seems you are unfamiliar with the comic strip Cathy, whose protagonists uses "Ack!" as an unprompted interjection pretty much all the time. Aug 28, 2020 at 20:25 | 656 | 2,579 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2024-22 | latest | en | 0.950244 |
http://thetopsites.net/article/53476164.shtml | 1,601,434,210,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402101163.62/warc/CC-MAIN-20200930013009-20200930043009-00108.warc.gz | 119,863,757 | 6,730 | ## I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm
optics: ordering points to identify the clustering structure
ordered clustering
optics clustering in r
I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm.
I Would be grateful if someone gives a logical and intuitive explanation of the ordering and also explain what `res\$order` does in the following code and what is the reahability plot(which can be obtained by the command 'plot(res)').
```library(dbscan)
set.seed(2)
n <- 400
x <- cbind(
x = runif(4, 0, 1) + rnorm(n, sd=0.1),
y = runif(4, 0, 1) + rnorm(n, sd=0.1)
)
plot(x, col=rep(1:4, time = 100))
res <- optics(x, eps = 10, minPts = 10)
res
res\$order
plot(res)
```
res\$order gives the following output:
[1] 1 363 209 349 337 301 357 333 321 285 281 253 241 177 153 57 257 29 77 169 105 293 229 145 181 385 393 377 317 381 185 117 [33] 101 9 73 237 397 369 365 273 305 245 249 309 157 345 213 205 97 49 33 41 193 149 17 83 389 25 121 329 5 161 341 217 [65] 189 141 85 53 225 313 289 261 221 173 69 61 297 125 81 133 129 197 109 137 59 93 165 89 21 13 277 191 203 379 399 375 [97] 351 311 235 231 227 71 11 299 271 291 147 55 23 323 219 275 47 263 3 367 331 175 87 339 319 251 247 171 111 223 51 63 [129] 343 303 207 151 391 359 287 283 215 143 131 115 99 31 183 43 243 199 79 27 295 67 347 255 239 195 187 139 107 39 119 179 [161] 395 371 201 123 159 91 211 355 103 327 95 7 167 35 267 155 387 383 335 315 259 135 15 113 279 373 4 353 265 127 45 37 [193] 19 276 224 361 260 288 336 368 348 292 268 252 120 108 96 88 32 16 340 156 388 372 356 332 304 220 188 168 136 124 56 236 [225] 28 244 392 184 76 380 232 100 116 112 256 72 8 280 64 52 208 172 152 148 360 352 192 160 144 284 216 48 84 92 36 20 [257] 212 272 264 200 128 80 180 364 196 12 132 40 324 308 176 164 68 316 312 384 300 344 328 248 204 140 296 24 320 228 60 44 [289] 233 65 400 376 240 163 104 396 307 75 14 325 269 262 234 382 294 206 198 374 310 362 318 386 358 330 278 210 298 282 122 98 [321] 34 26 174 142 46 6 62 118 190 202 114 322 286 38 242 394 342 266 162 130 30 182 2 74 314 290 246 194 170 126 158 378 [353] 350 254 226 214 70 18 10 366 354 186 150 86 306 102 338 346 134 250 138 94 78 390 274 58 42 258 66 90 146 370 222 218 [385] 326 82 110 270 334 178 166 398 22 50 238 106 154 302 230 54
and the 'plot' produces a reachability plot which I am not able to post because this is my first question on StackExchange...but if you run the R code you can easily get it.
[PDF] OPTICS: Ordering Points To Identify the Clustering Structure, input parameters which are hard to determine but have a significant the result of the clustering algorithm describes the intrinsic cluster- algorithm OPTICS to create an ordering of a data set with re- mal definitions for this notion of a clustering are shortly for getting a clear understanding of the structure of the data. Its. It is a 2D plot, with the ordering of the points as processed by OPTICS on the x-axis and the reachability distance on the y-axis. Since points belonging to a cluster have a low reachability distance to their nearest neighbor, the clusters show up as valleys in the reachability plot.
A detailed description is included in the R packages.
```library("dbscan")
vignette("dbscan")
```
See Section 2.2. OPTICS: Ordering Points To Identify Clustering Structure
OPTICS provides an augmented ordering. The algorithm starting with a point and expands it’s neighborhood like DBSCAN, but it explores the new point in the order of lowest to highest core-distance. The order in which the points are explored along with each point’s core- and reachability-distance is the final result of the algorithm.
Clustering Using OPTICS, There is a relative of DBSCAN, called OPTICS (Ordering Points to Identify Cluster only if you would like to try and speed up computation time. First, I will explain a little how this algorithm works, how it can include in-line Although the MinPts parameter is used in these calculations, the idea is that it Prerequisites: DBSCAN Clustering. OPTICS Clustering stands for Ordering Points To Identify Cluster Structure. It draws inspiration from the DBSCAN clustering algorithm. It adds two more terms to the concepts of DBSCAN clustering. They are:-Core Distance: It is the minimum value of radius required to classify a given point as a core point. If
It is a reordering (permutation) of your data set, such that nearby points usually are close in the order.
[PDF] OPTICS: Ordering Points To Identify the Clustering Structure, input parameters which are hard to determine but have a significant the result of the clustering algorithm describes the intrinsic cluster- algorithm OPTICS to create an ordering of a data set with re- mal definitions for this notion of a clustering are shortly fcp\ for getting a clear understanding of the structure of the data. OPTICS: Ordering Points to Identify the Clustering Structure. run-time of the algorithm OPTICS is nearly the same as the run- used by the OPTICS clustering algorithm to determine the clus-
(PDF) OPTICS: Ordering Points to Identify the Clustering Structure, sis which is intended to help a user to understand the natural gorithms require values for input parameters which are hard to algorithm OPTICS to create an ordering of a data set with re- nected by a line of few points having a small inter-object dis- The key idea of density-based clustering is that for each object. sic notions of density-based clustering are defined and our new algorithm OPTICS to create an ordering of a data set with re-spect to its density-based clustering structure is presented. The application of this cluster-ordering for the purpose of cluster analysis is demonstrated in section 4. Both, automatic as well
OPTICS algorithm, Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major we need to assume to have p and o belong to the same cluster. I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm. I Would be grateful if someone gives a logical and intuitive explanation of the ordering and also explain
Optics ordering points to identify the clustering structure, (Paper Presentation) OPTICS-Ordering Points To Identify The Clustering Structure. Such parameter settings are usually empirically set and difficult to determine. OPTICS works in principle like such an extended DBSCAN algorithm Having generated the augmented cluster-ordering of a database with Possible duplicate of I am having a hard time understanding the concept of Ordering in OPTICS Clustering algorithm – onofricamila Oct 16 '19 at 2:02 add a comment | 1 Answer 1 | 2,022 | 6,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2020-40 | latest | en | 0.258284 |
http://mathhelpforum.com/geometry/30204-geometry-problem.html | 1,526,855,700,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863689.50/warc/CC-MAIN-20180520205455-20180520225455-00153.warc.gz | 182,000,159 | 10,020 | 1. ## Geometry(?) Problem
I'm pretty sure I've done this in grade 8, but sadly I threw out last year's Math notes... Reminder anybody? Please and thank you's.
In the diagram, triangle XYZ is right-angled at X, with YX = 60 and XZ = 80. W is the point on YZ so that WX is perpendicular to YZ. Determine the length of WZ.
2. Hello, anh1tran!
In the diagram, triangle $\displaystyle XYZ$ is right-angled at $\displaystyle X$,
with $\displaystyle YX = 60$ and $\displaystyle XZ = 80$.
$\displaystyle XW$ is perpendicular to $\displaystyle YZ$.
Determine the length of $\displaystyle WZ$.
Code:
X
*
*| *
60 * | * 80
* | *
* | *
* | *
* * * * * * * * * * *
Y W Z
: - - - - - 100 - - - - - - - :
Using Pythagorus: .$\displaystyle YZ^2 \:=\:60^2+80^2 \:=\:100,000\quad\Rightarrow\quad YZ = 100$
Since $\displaystyle \Delta WXZ \sim \Delta XYZ$, we have: .$\displaystyle \frac{WZ}{XZ} \:=\:\frac{XZ}{YZ}$
Hence: .$\displaystyle \frac{WZ}{80}\:=\:\frac{80}{100}\quad\Rightarrow\q uad WZ \:=\:\frac{6400}{100} \:=\:\boxed{64}$
3. Oh my.. Thank you so much! | 392 | 1,159 | {"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} | 4.0625 | 4 | CC-MAIN-2018-22 | latest | en | 0.66306 |
http://gmatclub.com/forum/fractions-and-powers-88336.html | 1,430,748,502,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1430454443858.51/warc/CC-MAIN-20150501042723-00026-ip-10-235-10-82.ec2.internal.warc.gz | 83,845,227 | 46,867 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 04 May 2015, 06:08
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Fractions and Powers
Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 29 Nov 2009
Posts: 22
Location: Toronto
Followers: 0
Kudos [?]: 6 [1] , given: 5
Fractions and Powers [#permalink] 22 Dec 2009, 14:58
1
KUDOS
2
This post was
BOOKMARKED
00:00
Difficulty:
(N/A)
Question Stats:
96% (02:07) correct 4% (01:56) wrong based on 51 sessions
Hi everyone,
I did the GMATPrep exam yesterday and here was my first question. Kind of threw me off . Any thoughts?
$$(\frac{1}{5})^m (\frac{1}{4})^{18} = \frac{1}{2(10)^m}$$
m=
a.17
b.18
c.34
d.35
e.36
[Reveal] Spoiler:
D. 35
Kaplan Promo Code Knewton GMAT Discount Codes Veritas Prep GMAT Discount Codes
Intern
Joined: 13 Dec 2009
Posts: 11
Followers: 0
Kudos [?]: 4 [2] , given: 7
Re: Fractions and Powers [#permalink] 22 Dec 2009, 18:18
2
KUDOS
split the 10 into 5^m * 2^m
(1/5)^m * (1/4)^18 = 1/2 * (1/5^m *1/2^m)
1/5^m cancels on both sides
and (1/4)^18 can be written as (1/2)^36
so
(1/2)^36 = 1/2 * 1/2^m
1/2^35 = 1/2^m
M = 35
Manager
Joined: 23 Nov 2009
Posts: 55
Followers: 1
Kudos [?]: 11 [0], given: 1
Re: Fractions and Powers [#permalink] 22 Dec 2009, 19:31
M=35
Split the right side
_________________
A kudos would greatly help
Tuhin
Manager
Joined: 13 Oct 2009
Posts: 115
Location: USA
Schools: IU KSB
Followers: 4
Kudos [?]: 55 [1] , given: 66
Re: Fractions and Powers [#permalink] 22 Dec 2009, 19:49
1
KUDOS
brentbrent wrote:
Hi everyone,
I did the GMATPrep exam yesterday and here was my first question. Kind of threw me off . Any thoughts?
$$(\frac{1}{5})^m (\frac{1}{4})^{18} = \frac{1}{2(10)^m}$$
m=
a.17
b.18
c.34
d.35
e.36
[Reveal] Spoiler:
D. 35
$$(\frac{2*2^m *5^m}{5^m})= 2^{2*18}$$
$$2^{m+1}=2^{36}$$
$$m+1=36$$
$$m=35$$
Intern
Joined: 29 Nov 2009
Posts: 22
Location: Toronto
Followers: 0
Kudos [?]: 6 [0], given: 5
Re: Fractions and Powers [#permalink] 22 Dec 2009, 20:34
*...is seen smacking palm on face*
thanks guys.
Manager
Joined: 09 May 2009
Posts: 204
Followers: 1
Kudos [?]: 111 [0], given: 13
Re: Fractions and Powers [#permalink] 22 Dec 2009, 20:39
[(1/5)^m]*[1/4]^18=[(1/2)*(1/10^m)]
(1/5)^m * (1/2)^36 - [ (1/2)*(1/2^m)*(1/5^m)]=0
(1/5)^m[(1/2)^36-(1/2)^m+1]=0
(1/2)^36=(1/2)^m+1
---->m+1=36
m=35
_________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME
Re: Fractions and Powers [#permalink] 22 Dec 2009, 20:39
Similar topics Replies Last post
Similar
Topics:
3 solving fraction's power 3 12 Nov 2010, 16:33
1 fractions and powers 2 08 Oct 2009, 10:40
Fractions 2 25 Feb 2007, 10:37
Fraction 3 15 Feb 2007, 09:11
Display posts from previous: Sort by
# Fractions and Powers
Question banks Downloads My Bookmarks Reviews Important topics
Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 1,348 | 3,688 | {"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} | 4.03125 | 4 | CC-MAIN-2015-18 | longest | en | 0.845701 |
https://yourwiseadvices.com/how-can-you-tell-if-triangles-are-congruent/ | 1,726,624,399,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.68/warc/CC-MAIN-20240918000844-20240918030844-00335.warc.gz | 993,612,948 | 14,167 | How can you tell if triangles are congruent?
How can you tell if triangles are congruent?
ASA stands for “angle, side, angle” and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
What is SSS SAS ASA AAS?
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side)
What are the 4 ways to prove triangles are congruent?
Two triangles are said to be congruent if and only if we can make one of them superpose on the other to cover it exactly. These four criteria used to test triangle congruence include: Side – Side – Side (SSS), Side – Angle – Side (SAS), Angle – Side – Angle (ASA), and Angle – Angle – Side (AAS).
What lines are congruent?
When two line segments exactly measure the same, they are known as congruent lines. For example, two line segments XY and AB have a length of 5 inches and are hence known as congruent lines. When two angles exactly measure the same, they are known as congruent angles.
Is AAS congruent?
The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
What is the condition of congruency?
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object.
How do you tell if a triangle is SAS or SSA?
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.
How do you know if it’s AAS or ASA?
If two triangles are congruent, all three corresponding sides are congruent and all three corresponding angles are congruent. This shortcut is known as angle-side-angle (ASA). Another shortcut is angle-angle-side (AAS), where two pairs of angles and the non-included side are known to be congruent.
How do you know if its AAS or ASA?
While both are the geometry terms used in proofs and they relate to the placement of angles and sides, the difference lies in when to use them. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.
What does AAS mean math?
angle-angle-side
AAS (angle-angle-side) Two angles and a non-included side are congruent.
How do you write congruent lines?
For line segments, ‘congruent’ is similar to saying ‘equals’. You could say “the length of line AB equals the length of line PQ”. But in geometry, the correct way to say it is “line segments AB and PQ are congruent” or, “AB is congruent to PQ”. In the figure above, note the single ‘tic’ marks on the lines.
What are the Five Ways to prove triangles congruent?
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL. SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. For example: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
What are three ways that triangles are congruent?
What are the methods to prove triangles are congruent? SSS (side, side, side) SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. SAS (side, angle, side) ASA (angle, side, angle) AAS (angle, angle, side) HL (hypotenuse, leg)
How would prove these triangles are congruent?
SSS (side,side,side) SSS stands for “side,side,side” and means that we have two triangles with all three sides equal.
• SAS (side,angle,side)
• ASA (angle,side,angle)
• AAS (angle,angle,side)
• HL (hypotenuse,leg)
• How do you prove that two triangles are similar?
Use the angle-angle theorem for similarity. Once you have identified the congruent angles, you can use this theorem to prove that the triangles are similar. State that the measures of the angles between the two triangles are identical and cite the angle-angle theorem as proof of their similarity. | 1,062 | 4,496 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2024-38 | latest | en | 0.948318 |
https://www.scribd.com/document/351254738/geography-assignment | 1,566,123,074,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313747.38/warc/CC-MAIN-20190818083417-20190818105417-00347.warc.gz | 975,089,102 | 58,331 | You are on page 1of 5
# 1) Describe three types of scattering that occur in the earths atmosphere.
## Scattering is the process by which small particles suspended in a medium of different
index of refraction diffuse a portion of incident radiation in all direction. With scattering
there is no energy transformation, but a change in spatial distribution of the energy. Three
types of scattering includes, Rayleigh scattering, Mie scattering and non-selective
scattering.
Rayleigh scattering mainly consist of scattering from atmosphere gases. The process has
been named in honour of Lord Rayleigh, who in 1871 published a paper describing this
phenomenon. Rayleigh scattering can be considered to be elastic scattering since the
photon energies of the scattered photons is not changed. According to Gibson,(2012),
Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can
be extended to scattering from particles up to about a tenth of the wavelength of the light
This occurs when the particles causing the scattering are smaller in size than the
wavelength of radiation in contact with them. This type of scattering is therefore
wavelength dependent. As the wavelength decreases, the amount of scattering increases.
This type of scattering is also known as clear sky scattering because it is the one that
explains why the sky is blue. The blue color of the sky is caused by the scattering of
sunlight off the molecules of the atmosphere. This scattering, called Rayleigh scattering,
is more effective at short wavelengths, the blue end of the visible spectrum. Therefore the
light scattered down to the earth at a large angle with respect to the direction of the sun's
light is predominantly in the blue end of the spectrum.
Mie scattering occurs when particles causing the scattering are much larger than the
wavelength of radiation in contact with them. It is the first type of scattering examined as
it is equally applicable to spheres of all sizes, refractive indices and for radiation at all
wavelengths. It is caused by pollen, dust, smoke, water droplets and other particles in the
lower portion of the atmosphere. Mie scattering tends to occur in the presence of water
vapor and dust and will dominate in overcast or humid conditions. This type ofscattering
explains the reddish hues of the sky following a forest fire or volcanic eruption,Lockwood
G.J,(2015). Mie scattering is responsible for the white appearance of the clouds. Mie
scattering is not strongly wavelength dependent and produces the almost white glare
around the sun.The Mie scattering has a strong forward lobe and increases as you
approach the sun's direction when a lot of particulate material is present in the air. Mie
scattering is greatly increased when the atmosphere is slightly overcast.
Non-selective scattering is another type of scattering that occurs in the lower portion of
the atmosphere. It occurs when the particles are much larger than the incident radiation.
Non-selective scattering is not wavelength dependent and is the primary cause of
haze,(Kenneth R,(2015). Non-selective scattering scatters all visible light evenly - hence
the term non-selective. In the visible wavelength light is scattered evenly, hence fog and
clouds appear white. Since clouds scatter all wavelengths of light this means that clouds
block all energy from reaching the Earth's surface. Clouds appear white because equal
quantities of blue, green and red light are being scattered.
## 2) Why is the sky blue.
The blueness of the sky is the result of a particular type of scattering which is known
as Rayleigh scattering .Rayleigh scattering refers to the selective scattering of light off
particles that are not bigger than one-tenth the wavelength of the light. Rayleigh
scattering is heavily dependent on the wavelength of light, with lower wavelength
light being scattered most. In the lower atmosphere, tiny oxygen and nitrogen
molecules scatter short-wavelength light, such as blue and violet light, to a far greater
degree than long-wavelength light, such as red and yellow. Schimid,(2013) states that
the sky is blue because blue light in the Sun's rays bends more than red light so as we
look in a direction of the sky away from the Sun, we see those wavelengths that bent
the most. Though the atmospheric particles scatter violet more than blue (450-nm
light), the sky appears blue, because our eyes are more sensitive to blue light and
because some of the violet light is absorbed in the upper atmosphere. Michael
(2013)Blue light has a short wavelength, and the particles in the air scatter it around,
making the sky appear blue. The light of day is actually a complex spectrum of many
different wavelengths, but it is dominated by light with wavelengths between 400
nanometers violet and 450 nanometers blue.
## 3). Define the following:
i).Spatial resolution refers to the size of the instantaneous field of view (IFOV) or
the ground pixel. Spatial resolution is a measure of the area or size of the smallest
dimension on the Earths surface over which an independent measurement can be
made by the sensor Kumar,(2014). The IFOV is the area on the ground that is viewed
by the sensor at a given instant in time. As such, it usually represents the ground area
that is represented by each pixel in a remotely sensed image. Spatial resolution has
important implications for how we define objects on the surface; the scale of analysis;
locational precision and accuracy as well as areal accuracy. Spatial resolution is
usually given as "nominal" spatial resolution which refers to the resolution for a
sample obtained from the nadir viewing position at the specified altitude of the
satellite. Spatial Resolution describes how much detail in a photographic image is
visible to the human eye. The ability to resolve or separate, small details is one way of
describing what we call spatial resolution. Spatial resolution of images acquired by
satellite sensor systems is usually expressed in meters. Based on the spatial resolution,
satellite systems can be classified as follows, low resolution systems, medium
resolution systems, high resolution systems and very high resolution systems. Remote
sensing systems with spatial resolution more than 1km are generally considered as
low resolution systems. MODIS and AVHRR are some of the very low resolution
sensors used in the satellite remote sensing. When the spatial resolution is 100m
1km, such systems are considered as moderate resolution systems, Dorji P,(2017).
Remote sensing systems with spatial resolution approximately in the range 5-100m
are classified as high resolution for example Landsat ETM+ (30m). Very high
resolution systems are those which provide less than 5m spatial resolution such as
GeoEye (0.45m for Panchromatic.
(ii). Radiometric resolution is often called contrast ,it can be defined as the
sensitivity of a remote sensing detector to differentiate in signal strength as it records
the radiant flux reflected or emitted from the terrain. It refers to the dynamic range, or
number of possible data-file values in each band. It describes the ability of the sensor
to measure the signal strength (acoustic reflectance) or brightness of
objects.According to Mathew,(2014),The more sensitive a sensor is to the reflectance
of an object as compared to its surroundings, the smaller an object that can be
detected and identified. Radiometric resolution specifies how well the differences in
brightness in an image can be perceived. This is measured through the number of the
grey value levels, and the maximum number of values is defined by the number of
bits. The finer or the higher the radiometric resolution is, the better small differences
in reflected or emitted radiation can be measured, and the larger the volume of
measured data. Radiometric resolution depends on the wavelengths and the type of
the spectrometer.
## (iii).Spectral resolution is defined as the ability of a sensor to define fine wavelength
intervals or the ability of a sensor to resolve the energy received in a spectral
bandwidth to characterize different constituents of earth surface. The finer the spectral
resolution, the narrower the wavelength range for a particular channel or band. In
remote sensing, different features are identified from the image by comparing their
responses over different distinct spectral bands Kumar,(2016). Broad classes, such as
water and vegetation, can be easily separated using very broad wavelength ranges like
visible and near-infrared. However, for more specific classes vegetation type or rock
classification, much finer wavelength ranges and hence finer spectral resolution are
required. a sensor's spectral resolution specifies the number of spectral bands in which
the sensor can collect reflected radiance. Brian(2012) further argues that the number
of bands is not the only important aspect of spectral resolution. The position of bands
in the electromagnetic spectrum is important, too.
## (iv)Temporal resolution is defined as the amount of time needed to revisit and
acquire data for the exact same location. When applied to remote sensing, this amount
of time depends on the orbital characteristics of the sensor platform as well as sensor
characteristics. The temporal resolution is high when the revisiting delay is low and
vice-versa. Temporal resolution is usually expressed in days, (Jrme Thau,2012).
The actual temporal resolution of a sensor depends on a variety of factors, including
the satellite/sensor capabilities, the swath overlap, and latitude.
Brian.O(2012).National High Magnetic Field Laboratory;The Florida State
University.
Dorji P,(2017). Impact of the spatial resolution of satellite remote sensing sensors
in the quantification of total suspended sediment concentration. Cambridge:
Cambridge University Press.
## Gibson P.J(2012).Introductory Remote Sensing- Principles and Concepts
Routledge, London
Jerom,T(2012).Temporal resolution,Springer.
Frances. | 2,068 | 10,013 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2019-35 | latest | en | 0.940163 |
https://number.academy/250357 | 1,669,927,637,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00496.warc.gz | 474,333,066 | 12,397 | # Number 250357
Number 250,357 spell 🔊, write in words: two hundred and fifty thousand, three hundred and fifty-seven . Ordinal number 250357th is said 🔊 and write: two hundred and fifty thousand, three hundred and fifty-seventh. Color #250357. The meaning of number 250357 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 250357. What is 250357 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 250357.
## What is 250,357 in other units
The decimal (Arabic) number 250357 converted to a Roman number is (C)(C)(L)CCCLVII. Roman and decimal number conversions.
#### Weight conversion
250357 kilograms (kg) = 551937.0 pounds (lbs)
250357 pounds (lbs) = 113561.2 kilograms (kg)
#### Length conversion
250357 kilometers (km) equals to 155565 miles (mi).
250357 miles (mi) equals to 402911 kilometers (km).
250357 meters (m) equals to 821372 feet (ft).
250357 feet (ft) equals 76310 meters (m).
250357 centimeters (cm) equals to 98565.7 inches (in).
250357 inches (in) equals to 635906.8 centimeters (cm).
#### Temperature conversion
250357° Fahrenheit (°F) equals to 139069.4° Celsius (°C)
250357° Celsius (°C) equals to 450674.6° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
250357 seconds equals to 2 days, 21 hours, 32 minutes, 37 seconds
250357 minutes equals to 6 months, 5 days, 20 hours, 37 minutes
### Codes and images of the number 250357
Number 250357 morse code: ..--- ..... ----- ...-- ..... --...
Sign language for number 250357:
Number 250357 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Mathematics of no. 250357
### Multiplications
#### Multiplication table of 250357
250357 multiplied by two equals 500714 (250357 x 2 = 500714).
250357 multiplied by three equals 751071 (250357 x 3 = 751071).
250357 multiplied by four equals 1001428 (250357 x 4 = 1001428).
250357 multiplied by five equals 1251785 (250357 x 5 = 1251785).
250357 multiplied by six equals 1502142 (250357 x 6 = 1502142).
250357 multiplied by seven equals 1752499 (250357 x 7 = 1752499).
250357 multiplied by eight equals 2002856 (250357 x 8 = 2002856).
250357 multiplied by nine equals 2253213 (250357 x 9 = 2253213).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 250357
Half of 250357 is 125178,5 (250357 / 2 = 125178,5 = 125178 1/2).
One third of 250357 is 83452,3333 (250357 / 3 = 83452,3333 = 83452 1/3).
One quarter of 250357 is 62589,25 (250357 / 4 = 62589,25 = 62589 1/4).
One fifth of 250357 is 50071,4 (250357 / 5 = 50071,4 = 50071 2/5).
One sixth of 250357 is 41726,1667 (250357 / 6 = 41726,1667 = 41726 1/6).
One seventh of 250357 is 35765,2857 (250357 / 7 = 35765,2857 = 35765 2/7).
One eighth of 250357 is 31294,625 (250357 / 8 = 31294,625 = 31294 5/8).
One ninth of 250357 is 27817,4444 (250357 / 9 = 27817,4444 = 27817 4/9).
show fractions by 6, 7, 8, 9 ...
### Calculator
250357
#### Is Prime?
The number 250357 is not a prime number. The closest prime numbers are 250343, 250361.
#### Factorization and factors (dividers)
The prime factors of 250357 are 29 * 89 * 97
The factors of 250357 are 1 , 29 , 89 , 97 , 2581 , 2813 , 8633 , 250357
Total factors 8.
Sum of factors 264600 (14243).
#### Powers
The second power of 2503572 is 62.678.627.449.
The third power of 2503573 is 15.692.033.132.249.292.
#### Roots
The square root √250357 is 500,356873.
The cube root of 3250357 is 63,026024.
#### Logarithms
The natural logarithm of No. ln 250357 = loge 250357 = 12,430643.
The logarithm to base 10 of No. log10 250357 = 5,39856.
The Napierian logarithm of No. log1/e 250357 = -12,430643.
### Trigonometric functions
The cosine of 250357 is -0,942807.
The sine of 250357 is -0,333339.
The tangent of 250357 is 0,35356.
### Properties of the number 250357
Is a Friedman number: No
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 250357 in Computer Science
Code typeCode value
PIN 250357 It's recommendable to use 250357 as a password or PIN.
250357 Number of bytes244.5KB
CSS Color
#250357 hexadecimal to red, green and blue (RGB) (37, 3, 87)
Unix timeUnix time 250357 is equal to Saturday Jan. 3, 1970, 9:32:37 p.m. GMT
IPv4, IPv6Number 250357 internet address in dotted format v4 0.3.209.245, v6 ::3:d1f5
250357 Decimal = 111101000111110101 Binary
250357 Decimal = 110201102111 Ternary
250357 Decimal = 750765 Octal
250357 Decimal = 3D1F5 Hexadecimal (0x3d1f5 hex)
250357 BASE64MjUwMzU3
250357 MD547ab53593cdd2736d3563a25d79f4a05
250357 SHA146402cc298aa4fa343c825a839e9e93b084276a2
250357 SHA22462f793e4468d151c68b9759e9dfef73818183c914946695df5c9428a
250357 SHA256d74119efe871a0e55c24de4cfa385493074fd45701565261a5f2a825ff015fe6
250357 SHA384a67b29b2c25e0e7553a2a28cbf5a70568eaaf358516f1b98ea749c10fc2030f0dde3729b6c6e07fc6ff6d568377f2d92
More SHA codes related to the number 250357 ...
If you know something interesting about the 250357 number that you did not find on this page, do not hesitate to write us here.
## Numerology 250357
### Character frequency in number 250357
Character (importance) frequency for numerology.
Character: Frequency: 2 1 5 2 0 1 3 1 7 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 250357, the numbers 2+5+0+3+5+7 = 2+2 = 4 are added and the meaning of the number 4 is sought.
## Interesting facts about the number 250357
### Asteroids
• (250357) 2003 SN255 is asteroid number 250357. It was discovered by Spacewatch from Obs. US National at Kitt Peak on 9/27/2003.
## № 250,357 in other languages
How to say or write the number two hundred and fifty thousand, three hundred and fifty-seven in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 250.357) doscientos cincuenta mil trescientos cincuenta y siete German: 🔊 (Nummer 250.357) zweihundertfünfzigtausenddreihundertsiebenundfünfzig French: 🔊 (nombre 250 357) deux cent cinquante mille trois cent cinquante-sept Portuguese: 🔊 (número 250 357) duzentos e cinquenta mil, trezentos e cinquenta e sete Hindi: 🔊 (संख्या 250 357) दो लाख, पचास हज़ार, तीन सौ, सत्तावन Chinese: 🔊 (数 250 357) 二十五万零三百五十七 Arabian: 🔊 (عدد 250,357) مئتانخمسون ألفاً و ثلاثمائة و سبعة و خمسون Czech: 🔊 (číslo 250 357) dvěstě padesát tisíc třista padesát sedm Korean: 🔊 (번호 250,357) 이십오만 삼백오십칠 Danish: 🔊 (nummer 250 357) tohundrede og halvtredstusindtrehundrede og syvoghalvtreds Dutch: 🔊 (nummer 250 357) tweehonderdvijftigduizenddriehonderdzevenenvijftig Japanese: 🔊 (数 250,357) 二十五万三百五十七 Indonesian: 🔊 (jumlah 250.357) dua ratus lima puluh ribu tiga ratus lima puluh tujuh Italian: 🔊 (numero 250 357) duecentocinquantamilatrecentocinquantasette Norwegian: 🔊 (nummer 250 357) to hundre og femti tusen, tre hundre og femti-syv Polish: 🔊 (liczba 250 357) dwieście pięćdziesiąt tysięcy trzysta pięćdziesiąt siedem Russian: 🔊 (номер 250 357) двести пятьдесят тысяч триста пятьдесят семь Turkish: 🔊 (numara 250,357) ikiyüzellibinüçyüzelliyedi Thai: 🔊 (จำนวน 250 357) สองแสนห้าหมื่นสามร้อยห้าสิบเจ็ด Ukrainian: 🔊 (номер 250 357) двiстi п'ятдесят тисяч триста п'ятдесят сiм Vietnamese: 🔊 (con số 250.357) hai trăm năm mươi nghìn ba trăm năm mươi bảy Other languages ...
## Comment
If you know something interesting about the number 250357 or any natural number (positive integer) please write us here or on facebook. | 2,665 | 7,700 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2022-49 | latest | en | 0.653222 |
https://www.onlineclothingstudy.com/2021/08/how-to-convert-knitted-fabric-in-kg-to.html | 1,721,532,565,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517550.76/warc/CC-MAIN-20240721030106-20240721060106-00634.warc.gz | 789,552,623 | 39,062 | # How to convert knitted fabric in Kg to fabric in Yards (with online calculator)
In this post, I will show you how to convert knitted fabric in Kg to fabric in yards. In some parts of the world, fabric length is measured in meters but in some parts, people measure the length in yards. You may need to convert the fabric in Kg to fabric in Yards. This guide will be a handy resource for your daily job.
In another article, I have explained the method of converting knit fabric from Kg to meter. We will use the same method for converting fabric needs in Kg to fabric in the yard.
You need the following data for conversion
1) Total weight of the Fabric (Kg) - Total weight of the fabric that you have. And the fabric that you wanted to convert from Kg in Yards (length). Take the fabric weight in Kilogram (Kg)
2) Fabric width – You may have the fabric width in meters or centimeters or inches or in width. If you get the width measurement in other units, you need to convert in meters. Reason – fabric GSM is in a square meter.
3) Fabric GSM - GSM is the weight of the fabric per square unit (Normally fabric weight is represented per square meter in grams. (GSM) )
### Formula
The formula to know the approximate length of the roll from its weight
The weight of a fabric roll is calculated using this formula
Weight (in gram) = Fabric length (in meter) X fabric width (in meter) X Fabric GSM
Therefore, to convert kg to meter use the following formula
Fabric length (in meters) = [(Fabric weight in gram)/ (Fabric GSM *Fabric Width in meter)]
Fabric length (in meters) = (Fabric weight * 1000)/(Fabric GSM *Fabric Width in inch * 0.0254)
(when fabric width is given in inches)
First, convert the total fabric length into meters. After getting the total length in meters, convert into yards by using the below formula.
1 Meter = 1.09361 Yards
Example-1: Here is an example of conversion from Kg to yards when fabric width is given in centimeters.
• Weight: 12 Kg,
• GSM: 360 and
• Fabric width: 147 cm (1.47 meter)
Therefore, Fabric length = (12*1000)/(360*1.47) = 22.675737 Meters
Fabric length in Yards = 24.798 Yards (24.8 Yards)
Example-2: Here is an example of conversion from Kg to yards when fabric width is given in inches.
• Weight: 10 Kg,
• GSM: 200 and
• Fabric width: 64 inches
Therefore, Fabric length = (10*1000)/(200*64*0.0254) =30.76 Meters (Round off)
Fabric length in Yards = 30.76 x 1.09361 = 33.64 Yards
Use the following online calculator for converting fabric in Kg to Fabric in Yards.
Convert Knits Fabric in Kg to fabric in Yards
Parameter Enter Value Result (Yards)
Fabric Weight (Kg)
Fabric Width (Inches)
GSM
?
Note: The above formula will give you an approximate length of the fabric roll as the density of the fabric throughout the roll length may change. Secondly, if you include more than one roll in the calculation, the width of the fabric may also vary from roll to roll.
Related post: How to Convert Knitted Fabric Requirement from Meter to Kg (Kilogram)?
### Prasanta Sarkar
Prasanta Sarkar is a textile engineer and a postgraduate in fashion technology from NIFT, New Delhi, India. He has authored 6 books in the field of garment manufacturing technology, garment business setup, and industrial engineering. He loves writing how-to guide articles in the fashion industry niche. He has been working in the apparel manufacturing industry since 2006. He has visited garment factories in many countries and implemented process improvement projects in numerous garment units in different continents including Asia, Europe, and South Africa. He is the founder and editor of the Online Clothing Study Blog. | 871 | 3,669 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2024-30 | latest | en | 0.896307 |
http://wattonweb.it/kqez/phenotypic-ratio-calculator.html | 1,600,445,207,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00387.warc.gz | 153,107,675 | 21,232 | # Phenotypic Ratio Calculator
g 1:2:1 Phenotypic ratios : The ratio of different phenotypes in the offspring from a genetic cross. (eumelanin based) [**NOTE: the phenotypic color will depend on what is at the B, D, C and M Locus]; If the dog is E/E or E/e at the E locus, and at the K locus, it is "k^br/k^br" or "k^br/k" it will be brindled with the color of the phaeomelanin part of the brindling affected by the Agouti alleles present;. Our phenotype will show a 3:1 ratio. 25% of the offspring are expected to be red so the calculation would be. Using these probabilities, we can predict the phenotypic ratio we should see in the F2 generation. Mendel's law of segregation. Determine the genotypic and phenotypic ratios for the F 1 generation: All F 1 progeny will be heterozygous for both characters (WwDd) and will have white, disk-shaped fruit. 7/1000 Japanese, 0. genotypic contribution only explains a fraction of the total phenotypic variation between the individuals. Drugs and mechanisms that protect β-cells. 5714+5G>A, c. Increased levels of blood plasma urea were used as phenotypic parameter for establishing novel mouse models for kidney diseases on the genetic background of C3H inbred mice in the phenotype-driven Munich ENU mouse mutagenesis project. Phenotypic Ratio. What is the phenotypic ratio of the offspring in Figure 6. Figure 2: The image above shows a Punnett square for figuring out the genotypic ratio using 4 traits from each parent. If the ratio is 3:1 and the total number of observed individuals is 880, then the expected numerical values should be 660 green and 220 yellow. Worksheet: Dihybrid Crosses. Phenotypic ratios: 3/4 will have white fruit color and 1/4 will have yellow fruit color. Introduction. Simplify Ratios: Enter A and B to find C and D. 68%) and PubMed (18. Improvement in feed efficiency would reduce the amount of feed required for growth, the production cost and the amount of nitrogenous waste. So, we can conclude that when genotypic and phenotypic ratios are the same, the alleles show incomplete dominance. 42 ( 42% ) By also calculating the other four possibilities, we can construct a graph that shows the statistical distribution you would expect to see in a large population. It can also give out ratio visual representation samples. one parent is homozygous dominant for each trait and one parent is homozygous recessive for each trait. For example, the ratio $$1: 10$$ is read as "one is to ten" or "one per 10". Therefore, the cross is Cc Vv x Cc Vv. This is a 3:1. Write down the cross between F 1 progeny: WwDd (white, disk-shaped fruit) X WwDd (white, disk-shaped fruit) 5. phenotypic outcome of the traits she was observing to be in the following ratio 4 stripes only: 3 spots only: 9 both stripes and spots. For the purposes of a χ2-test, what would the calculated values of E be? a. In the first 45 minutes, discuss each of the biomarkers contained within Levine’s Biological Age calculator, Phenotypic Age. (or enter C and D to find A and B) The calculator will simplify the ratio A : B if possible. the genetic constitution determining the phenotype of an organism ) Supplement The genotypic ratio describes the number of times a genotype would appear in the offspring after a test cross. (c): In a genetic cross having recessive epistasis, F 2 phenotypic ratio would be 9:3 :4. For example, you calculate the relative frequency of prices between $3. • Calculate genotypic and phenotypic outcomes. This astonishing phenotypic diversity has been molded by two main phases of evolution: 1) the initial domestication from wolves more than 15,000 years ago, where dogs became adapted to life in closer proximity to humans and 2) the formation of distinct. Two black eyed lizards are crossed, and the result is 72 black eyed lizards, and 28 yellow. Category Phenotypic ratio Observed Expected Deviation d d2 d2 / e Hairy 1/2 82 1/2 x 169 = 84. We log e-transformed optical densities, and used the slope of the curve in the interval OD 420 nm = [0. 00 and the low price target for FLO is$21. The proportion of phenotypic variance that can be attributed to additive genetic variance. Write the genotype and phenotype ratios of the F2 offspring: Are the F2 offspring from bin A in the expected 3:1 phenotypic ratio? ____ Explain why there might be differences. 1 - Calculate and predict the genotypic and phenotypic ratio of offspring of dihybrid crosses involving unlinked autosomal genes. It supports up to different 4 genes/traits and displays both genotype and phenotype results as well as probabilites for each of them and their combination. It's easy to calculate that the genotypic ratio is 0. It is also poorly understood whether such phenotypic variations are shaped by early specification or regional cellular environment. 50 * (125 – 100) = 12. In this example: 2 – RR, 2 – Rr So the Genotypic Ratio is 2 RR / 2 Rr, which can be simplified to 1RR / 1Rr, this indicates that. values between 0 and 1 indicate partial interference. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2. How easily find ratio and genotypic and phenotypic ratio online calculator probability for exact genotype or phenotype with this. Excessive extracellular matrix (ECM) deposition is a hallmark feature in fibrosis and tissue remodelling diseases. If you actually collected 69 yellow seeds and 31 green seeds, is that close enough to what is expected that you can say your results are consistent with the theory — that the deviation. Levine, et al, entitled "An epigenetic biomarker of aging for lifespan and healthspan" describes a technique for combining nine blood-work values with calendar age to calculate your Mortality Score (probability of death in the next ten years) and your Phenotypic Age, i. The square is particularly useful to determine probabilities of phenotype and genotype ratios. To get phenotypes in ratio 1:1:1:1, there must be a cross between heterozygote for both traits and recessive homozygote for both traits. CL/P is relatively common, with an incidence of 1-2 per 1,000 births. Solve ratios for the one missing value when comparing ratios or proportions. A count of 3 from one group and 1 from the other would give a ratio of 3:1. Transmission ratio distortion (TRD) is defined as the allele transmission deviation from the heterozygous parent to the offspring from the expected Mendelian genotypic frequencies. References. 5; Multiplied 0. recessive individual. You can convert a value expressed as a percent to a ratio in a few short steps. 25, which is rounded to the whole number 116. d’adamo,e m. The recessive epistasis is illustrated by coat colour in mouse, the coat colour is determined by A/a pair, recessive allele b is epistatic over A/a. One-third of the round seeds and all of the wrinkled seeds in the F 2 generation were homozygous and produced only seeds of the same phenotype. The default is to test for dominance (a 2 df test). Phenotypic analysis of peripheral blood mononuclear cells was car- ried out by whole-blood staining with Optlyse C lysis solution. If the alleles in the parental genotype are dominant or recessive, probable outcomes can be predicted. The progeny of this cross has the phenotypic ratio 9:3:3:1, which is displayed on the interface. Euclidean phenotypic distances, calculated using a deep convolutional triplet network, demonstrate. Ratio to Fraction Calculator is a tool which makes calculations easy and fun. In the case shown, we are looking at a single phenotypic trait (pea flower color) that is determined by two independent genes. We also derive the fundamental condition for. Here the result is expressed in terms of phenotypic standard deviations per generation, and the subscripted log I is a reminder that the result is dependent on time scale (rates of most interest are H 0 where I = 1 generation and log I = 0). What are the genotypic and phenotypic ratios? To calculate a ratio, add up the total number of individuals for each category, then divide all of the totals by the lowest number to get ‘1’ as the smallest value in the ratio. Scientists used to infer mutations from phenotypic changes, such as the development of drug resistance. It can also give out ratio visual representation samples. But in this first experiment, there was a result that was not predicted by Mendel’s theory: all the white-eyed flies were male!. Increaser allele frequency: The frequency of the trait increasing allele is specified, 0 < p < 1. Conclusions: Phenotypic Age is a reliable predictor of all-cause and cause-specific mortality in multiple subgroups of the population. The authors found that taxane-treated breast cancer cells became more reliant on oxidative and non-oxidative glucose metabolism. Calculate the ACTUAL phenotypic ratio from the experimentally obtained data shown in the table below. We also derive the fundamental condition for. Gulf Coast State College | Gulf Coast State College, Florida. 25; 95% CI = 0. Calculate the dilution required to prepare a stock solution. References. Determine the genotypic and phenotypic ratios for the F 1 generation: All F 1 progeny will be heterozygous for both characters (WwDd) and will have white, disk-shaped fruit. When pure breeding red cows are bred with pure breeding white cows, the offspring are roan (a pinkish coat color). A pea plant that is heterozygous for round, yellow seeds is self fertilized, what are the phenotypic ratios of the resulting offspring? Step 1: Determine the parental genotypes from the text above, the word "heteroyzous" is the most important clue, and you would also need to understand that self fertilized means you just cross it with itself. Traditional anatomical analyses captured only a fraction of real phenomic information. 63 at 1 day after transduction, 0. 2, or 20%) and 50 were && (0. The phenotypically dominant mutant line HST014 was established and further analyzed. With a sample size of 20 gas stations, the relative frequency of each class equals the actual number of gas stations divided by 20. The general consensus is that biologists are not strong when it comes to statistics. How to Convert a Percentage to Ratio Form. A phenotypic array method, developed for quantifying cell growth, was applied to the haploid and homozygous diploid yeast deletion strain sets. Chi-square analysis can be used in any area, not just genetics. The negative inverse of the a verage information matrix gives us estimates 1 I A for the variance of the estimators var(x 1), var(x 1), and cov(x 12) but also the covariance between the various. phenotypic ratios, respectively. Thus, frequency of homozygous dominant (YY) genotype is equal to 0. 1-5 Relative increases in levels of the 2-hydroxylation pathway metabolites are associated with decreased risk. It's easy to calculate that the genotypic ratio is 0. Once the Punnett square for Question 13 is complete, calculate the ratio of purple and yellow kernels (recall that if the dominant trait is present, it will be expressed). genotypic ratio. In this example: 2 – RR, 2 – Rr So the Genotypic Ratio is 2 RR / 2 Rr, which can be simplified to 1RR / 1Rr, this indicates that. I’ve talked about “the breeder’s equation,” R = h2S, before. Invasiveness is generally linked to higher values of reproductive, physiological and growth-related traits of the invasives relative to the natives in the introduced range. values between 0 and 1 indicate partial interference. Whereas ketoconazole is often used to study the worst-case scenario for clinical pharmacokinetic drug-drug interactions (DDIs) for drugs that are primarily metabolized by CYP3A4, fluconazole is considered to be a moderate inhibitor of CYP3A4, providing assessment of the moderate-case scenario of CYP3A-based DDIs. The recessive epistasis is illustrated by coat colour in mouse, the coat colour is determined by A/a pair, recessive allele b is epistatic over A/a. Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection which he outlined in his 1930 book The Genetical Theory of Natural Selection which postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. Linkage Mapping in Drosophila written by J. Significantly improved crop varieties are urgently needed to feed the rapidly growing human population under changing climates. Phenotypic noise, defined here as trait variability among isogenic. , purple and white are produced and the normal dihybrid segregation ratio 9 : 3 : 3 : 1 is changed to 9 : 7 ratio in F 2 generation. P p P 1 2 p 3 4. This yields a phenotypic ratio for the dihybrid cross of 9:3:3:1 The genotypic ratios for dihybrid crosses require lots if individual calculations, but each one is very easy! Especially once you have the calculations for the monohybrid, genotypic ratios above: The probability of inheriting AA and BB would be 1/4 x 1/4 = 1/16. Shading in each Punnett Square represents matching phenotypes, assuming complete dominance and independant assortment of genes, phenotypic ratios are also presented. You know a ratio is a comparison that tells how two or more things relate. Patterns of genetic inheritance obey the laws of probability. I know the normal ratio is 9 3:1, but is there a particular ratio for linkage and another different ratio for epistasis? Also what does the 9 3:1 mean, like 9,3,3 and 1 of what?. What are the expected progeny ratios in the F 2? As previously calculated, we expect to get a ratio of gray to white o r 3:1 (3/4:1/4) for body color and a ratio of bicorn to unicorn of 3:1 (3/4:1/4) for horn number. Consider an example : Here , we have crossed a heterozygous ( the two alleles show dominant and recessive relationship vix T and. Phenotypic plasticity is a common and highly adaptive phenomenon where the same genotype produces different phenotypes in response to environmental cues. Write the genotype and phenotype ratios of the F2 offspring: Are the F2 offspring from bin A in the expected 3:1 phenotypic ratio? ____ Explain why there might be differences. 9%) had a reported diagnosis of cancer other than OAC. , there is dominance): BB = 3cm, Bb = 3cm and bb = 1cm. Probability of F1 pollen x Probability of F1 ovule = Probability of F2 genotype 1 2 R 1 2 R 1 4 RR 1 2 R 1 2 r 1 4 Rr 1 2 r 1 2 R 1 4 Rr 1 2 r 1 2 r 1 4 rr Note that there are two ways of producing “Rr” in the F2 generation. The F1 individuals, called dihybrid, were all round yellow. Chi-square analysis can be used in any area, not just genetics. Solve ratios for the one missing value when comparing ratios or proportions. This blood type calculator determines the possible blood type of a person based on the blood groups of his or her parents. , the Iberian pig). To advance therapeutics in ALS, we need easily accessible. Carbapenemase-producing Enterobacteriaceae (CPE) are difficult to identify among carbapenem non-susceptible Enterobacteriaceae (NSE). Thus, in the presence of bb, both A and aa give the same phenotype (albino). Generally interference decreases as the. 2 in DeWitt et al. The genotypic ratio would be 1:2:1 (1 AA, 2 Aa, 1 aa). _____ x _____ Phenotypic Ratio: 3) The father is type A heterozygous, the mother is type B heterozygous. • Explain the importance of genetic variability. Then, the expected phenotypic ratios of the two traits together can be calculated algebraically as a binomial distribution: (3Y + 1y) x (3R + 1r) = 9YR + 3Yr + 3Ry + 1 ry That is, we expect a characteristic 9:3:3:1 phenotypic ratio of round-yellow : wrinkled -yellow : round- green : wrinkled-green pea seeds. To produce the 3:1 ratio of normal to waltzing behavior, we expect the parents are all heterozygotes (Vv). With a sample size of 20 gas stations, the relative frequency of each class equals the actual number of gas stations divided by 20. Genotypic frequency is the frequency of the given genotype in the population. phenotypic values: the underlying polygenic distribution, which is continuous, and the visible phenotypic distribution, which is discontinuous, and the two scales are connected by the ‘threshold’–a point of discontinuity. Two black eyed lizards are crossed, and the result is 72 black eyed lizards, and 28 yellow. ) in their offspring. Wilson, D. For the purposes of a χ2-test, what would the calculated values of E be? a. 75 at 27 days after transduction, respectively. Learn about phenotypic plasticity Introduction: The traits of an organism are determined jointly by its genes and the environmental conditions it experiences. Dietary ratios of omega-3 (n-3) to omega-6 (n-6) polyunsaturated fatty acids (PUFAs) have been implicated in controlling markers of the metabolic syndrome, including insulin sensitivity, inflammation, lipid profiles and adiposity. Computational modeling predicted. In this video I will discuss setting up the ratios and percents of a punnett square. phenotypic ratio ~~18. Despite the fact that you cannot enter a ratio of 4/5 into this calculator, it accepts values such as 4:5, for example, 4/3 should be written as 4:3. INTERPRETING A PEDIGREE CHART Determine whether the disorder is dominant or recessive. All babies are tall, so the pheonotypic ratio is 1 tall : 0 short SAMPLE DIHYBRID PROBLEM: In pea plants, R=round seeds, and r=wrinkled seeds, while Y=yellow seeds, and y=green seeds. Feed cost constitutes about 70% of the cost of raising broilers, but the efficiency of feed utilization has not kept up the growth potential of today's broilers. To draw a square, write all possible allele combinations one parent can contribute to its gametes across the top of a box and all possible allele combinations from the other parent down the left side. Phenotypic ratio calculator. what phenotypic ratio would be expected in the F2 generation? 2. Computational modeling predicted. F2 phenotypic ratio: 12:3:1; Example: In summer squash fruit colour may be white, yellow or green. Among these techniques are methods that researchers can apply to just about any species. 2 in DeWitt et al. Calculate the percent chance of each blood type. Allele B makes B antigen. 001) for all patients (F-Ratio = 21. A testcross to a heterozygous individual should always yield about a 1:1 ratio of the dominant to recessive phenotype. Step One: Rewrite as a Decimal. Write the genotype and phenotype ratios of the F2 offspring: Are the F2 offspring from bin A in the expected 3:1 phenotypic ratio? ____ Explain why there might be differences. For Genotypic Ratio - Sum each genotype present and give ratio out of total present, reduce if necessary. These cell-based assay systems model adaptive immune cell microenvironment and T and B cell responses in a platform amenable to compound screening. In the example shown, the formulas in F6 and F7 are: = STDEV. AaBb and Aabb. The second ear of corn was the result of crossing two heterozygous ears of corn male purple (Pp x Pp). Calculate the Genotypic and Phenotypic Ratio for the Offspring. Gulf Coast State College | Gulf Coast State College, Florida. Genotypic ratios: The ratio of different genotype in the offspring from a genetic cross. the genetic constitution determining the phenotype of an organism ) Supplement The genotypic ratio describes the number of times a genotype would appear in the offspring after a test cross. Using Punnett Squares to Calculate Phenotypic Probabilities: IntroductionBackground Punnett Squares are a diagram which biologists use to determine the probability of an offspring having a particular trait. 68%) and PubMed (18. Category Phenotypic ratio Observed Expected Deviation d d2 d2 / e Hairy 1/2 82 1/2 x 169 = 84. I’ve talked about “the breeder’s equation,” R = h2S, before. Heritability, in a general sense, is the ratio of variation due to differences between genotypes to the total phenotypic variation for a character or trait in a population. Phenotypic information is of great significance for irrigation management, disease prevention and yield improvement. Besides gene duplication and de novo gene generation, horizontal gene transfer (HGT) is another important way of acquiring new genes. A pea plant that is heterozygous for round, yellow seeds is self fertilized, what are the phenotypic ratios of the resulting offspring? Step 1: Determine the parental genotypes from the text above, the word "heteroyzous" is the most important clue, and you would also need to understand that self fertilized means you just cross it with itself. 769-784C>T, and c. A phenotypic array method, developed for quantifying cell growth, was applied to the haploid and homozygous diploid yeast deletion strain sets. 5714+5G>A, c. "Fast phenotypic and genotypic ratios and classes calculation with any model of inheritance, easy to use, nice interface, great support and unique software of its kind. D antigen frequency is most common in Asians (99%) and is slightly less common in Blacks (92%) and Caucasians (85%). Using large numbers of crosses, Mendel was able to calculate probabilities, found that they fit the model of inheritance, and use these to predict the outcomes of other crosses. To remove a gene, select it in the list below, and press "Remove Selected Gene. For example, you calculate the relative frequency of prices between $3. 1-5 Relative increases in levels of the 2-hydroxylation pathway metabolites are associated with decreased risk. An excellent paper by M. Explain how two black guinea pigs can have a white offspring. Mendel's law of segregation. As an aside, the. 9 Green/Round : 3 Green/Wrinkled : 3 Yellow/Round : 3 Yellow/Wrinkled. Question: In pea plants tall is dominant to short and purple flowers are dominant to white flowers. Two fundamental calculations are central to population genetics: allele frequencies and genotype frequencies. The goal of all selective breeding programmes is to produce a true-breeding population. mannucci,c i. Heritability, in a general sense, is the ratio of variation due to differences between genotypes to the total phenotypic variation for a character or trait in a population.$ He decided to perform chi- square analysis using two different null hypotheses: (a) the data fit a 3: 1 ratio; and (b) the data fit a 1: 1 ratio. To draw a square, write all possible allele combinations one parent can contribute to its gametes across the top of a box and all possible allele combinations from the other parent down the left side. Phenotypic Ratio. Typical coils of copper tubing Question:We have some bent coils of 1/8-inch (3. Levine, et al, entitled "An epigenetic biomarker of aging for lifespan and healthspan" describes a technique for combining nine blood-work values with calendar age to calculate your Mortality Score (probability of death in the next ten years) and your Phenotypic Age, i. , purple and white are produced and the normal dihybrid segregation ratio 9 : 3 : 3 : 1 is changed to 9 : 7 ratio in F 2 generation. Latham et al. Hypertrophic cardiomyopathy (HCM) is the most prevalent genetic cardiovascular disease, affecting one in every 200 individuals. Phenotypic ratio: Genotypic ratio: b. The correlation will be denoted by r and is determined as r = 1 2 12 xx x. The default is to test for dominance (a 2 df test). Test cross to determine the genotype of a shorthaired cat. Check your textbook and lecture notes for the details of how to structure the punnet squares to calculate the phenotypic ratios. Two black eyed lizards are crossed, and the result is 72 black eyed lizards, and 28 yellow. In this example: 2 - RR, 2 - Rr So the Genotypic Ratio is 2 RR / 2 Rr, which can be simplified to 1RR / 1Rr, this indicates that 50% of offspring will have the genotype RR and 50% will have the genotype Rr. A phenotypic array method, developed for quantifying cell growth, was applied to the haploid and homozygous diploid yeast deletion strain sets. realized heritability Heritability measured by a response to selection. For example in the cross A / a ; b / b × A / a ; B / b, we might want to calculate the expected phenotypic ratio in the progeny. The adjusted sum of squares does not depend on the order the factors are entered into the model. What is the phenotypic ratio? Phenotype for Aabb = Ab; Phenotype for aabb = ab Now we know that that the phenotypic ratio is equal to the genotypic ratio = 1:1. -Calculator-Chi Square Table-Paper or Note Taking App. Record your answer as an integer. These values are consistent with excellent blood-brain-barrier penetration. These values were used to calculate the oxygen supply temperature quotient, fmaxQ 10. In a population, the ratio of the total genetic variance to the total phenotypic variance. Name the type of inheritance in which the genotypic ratio is the same as the phenotypic ratio. A count of 3 from one group and 1 from the other would give a ratio of 3:1. As an aside, the. The phenotypic variation among organisms or cells is a theme of growing importance in biology. The numbers in the boxes below indicate the proportion of progeny of each phenotype expected to result from a mating of the shorthaired of unknown genotype to a homozygous recessive longhaired. Simplify Ratios: Enter A and B to find C and D. , purple and white are produced and the normal dihybrid segregation ratio 9 : 3 : 3 : 1 is changed to 9 : 7 ratio in F 2 generation. 24, adjusted for a number of health, disease, and social characteristics predictive of 5-year mortality. Now consider that BB and Bb have the same phenotype (i. Excessive extracellular matrix (ECM) deposition is a hallmark feature in fibrosis and tissue remodelling diseases. We studied the impact of grazing and substrate supply on the size structure of a freshwater bacterial strain ( Flectobacillus sp. The genotypic ratio would be 1:2:1 (1 AA, 2 Aa, 1 aa). Conversely, for 34 of 50 (68%) H63D homozygotes, abnormalities of iron metabolism were not associated with a known aetiology. Every genetics problem, from those on an exam to one that determines what coat color your dog’s puppies may have, can be solved in the same manner. Twelve of these patients had a phenotypic diagnosis of HH (table 3). Mendel performed this experiment for a number of times and based on the results; it was confirmed that a ratio could be formulated according to the phenotype of the F2 generation that is 3:1. Feb 4, 2013 • ericminikel. Determine the genotypic and phenotypic ratios for the F 1 generation: All F 1 progeny will be heterozygous for both characters (WwDd) and will have white, disk-shaped fruit. The Punnett square is a useful tool for predicting the genotypes and phenotypes of offspring in a genetic cross involving Mendelian traits. phenotypic ratios in our cross and what is expected by Mendelian theory. Conclusions: Phenotypic Age is a reliable predictor of all-cause and cause-specific mortality in multiple subgroups of the population. Chi-square analysis can be used in any area, not just genetics. The scaling behavior of chromatin packing regulates phenotypic plasticity through intercellular transcriptional heterogeneity. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of Heliconius erato and Heliconius melpomene. To advance therapeutics in ALS, we need easily accessible. Characterizing phenotypes in germplasm collections and making data publicly available is crucial to ensure the utilization of the accessions in breeding programs. The authors found that taxane-treated breast cancer cells became more reliant on oxidative and non-oxidative glucose metabolism. What is the ratio of kernels based on the Punnett square? (2 points) How does this compare to the ratio obtained from counting the corn kernels? (2 points) What are the genotypic and phenotypic ratios for kernel color and kernel texture for a dihybrid cross between PpSS x Ppss? (4 points) genotypic ratio; phenotypic ratio. What are the genotypic and phenotypic ratios? To calculate a ratio, add up the total number of individuals for each category, then divide all of the totals by the lowest number to get ‘1’ as the smallest value in the ratio. In the first 45 minutes, discuss each of the biomarkers contained within Levine’s Biological Age calculator, Phenotypic Age. genotypic ratio. Example: Convert the ratio 2:4 into a percentage: 2 : 4 can be written as 2 / 4 = 0. The phenotypically dominant mutant line HST014 was established and further analyzed. The gene for smooth peas (S) is dominant over its allele for wrinkled peas (s). What if you bred some snap dragons and crossed a homozygous red plant (RR) with a homozygous white plant (rr)? In botony, "true breeding" means homozygous. Phenotypic noise, defined here as trait variability among isogenic. There are more than 400 breeds of domestic dog, which exhibit characteristic variation in morphology, physiology and behavior. generation) what will be the genotypic and phenotypic ratios of the F 2 generation? a. According to the results of the likelihood ratios of the phenotypic tests, the best equilibrium between positive and negative ratios is achieved by the characterization at species level in the phenotypic microbiological procedures (LR+ = 5. The number of neutral mutations that are fixed over a given period of time can be predicted, and these can be used to estimate evolutionary relationships. Do not squeeze the eggs. A geneticist, in assessing data that fell into two phenotypic classes, observed values of $250: 150. Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection which he outlined in his 1930 book The Genetical Theory of Natural Selection which postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. m of 3 independent experiments. 002) and yield-stability index (YSI; 0. Genotype is the *genetic make-up * of an organism. Hendrix Learning Objectives Upon completing the exercise, each student should be able: • to understand the developmental cycle of Drosophila melanogaster;. Variance component estimates are use. carbon isotope ratio: variance) in a phenotypic character in a population that is due to individual to find the variance of the set of numbers 4, 6, and 8, we first calculate the mean. Phenotypic plasticity is a common and highly adaptive phenomenon where the same genotype produces different phenotypes in response to environmental cues. All of this can be figured if there is no linkage. phenotypic ratios in our cross and what is expected by Mendelian theory. ) Antibody: Protein in plasma that reacts with specific antigens that enter the blood (usually something that isn't supposed to be there!). Write the amount of homozygous dominant (AA) and heterozygous (Aa) squares as one phenotypic group. Using these probabilities, we can predict the phenotypic ratio we should see in the F2 generation. Merits of Punnett Square: It is a lightweight portable Punnett Square calculator. _____ x _____ Phenotypic Ratio: 2) The father is type A homozygous, the mother is type B homozygous. Genotypic frequency is the frequency of the given genotype in the population. How does this compare to the ratio obtained from counting the corn kernels? (2 points) ~~17. To advance therapeutics in ALS, we need easily accessible. investigated why breast cancer cells treated with taxanes become resistant to the unrelated, routinely used doxorubicin. Phenotypic Ratio. Provide Your Calculated Values In The Corresponding Blank Boxes Below The Table. A quantitative trait locus (QTL) is a locus (section of DNA) that correlates with variation of a quantitative trait in the phenotype of a population of organisms. Bacterial cells have a remarkable ability to adapt to environmental changes, a phenomenon known as adaptive evolution. Negligible reports on the. On a separate chromosome, the allele for smooth peas (S) is dominant over the allele for wrinkled peas (s). two-thirds (372/565) of them produced both types of seeds in the F 3 and — once again — in a 3:1 ratio. Question: In pea plants tall is dominant to short and purple flowers are dominant to white flowers. Example: Convert the ratio 2:4 into a percentage: 2 : 4 can be written as 2 / 4 = 0. The second ear of corn was the result of crossing two heterozygous ears of corn male purple (Pp x Pp). Use sampling to determine phenotypic ratios of a visible trait in the corn. Explain how two black guinea pigs can have a white offspring. Tip: If the alleles are codominant, each phenotype is distinct (you can distinguish between tall, medium and short) and your job is easier. The correlation will be denoted by r and is determined as r = 1 2 12 xx x. 150 : 300 : 150. This is a 3:1. To remove a gene, select it in the list below, and press "Remove Selected Gene. Category Phenotypic ratio Observed Expected Deviation d d2 d2 / e Hairy 1/2 82 1/2 x 169 = 84. Chi-square analysis can be used in any area, not just genetics. Sample terms associated with content area. Phenotypic ratio: 3 Roller/Free : 3 Roller/Attached : 1 Non-roller/Free : 1 Non-roller/Attached Or, can also be represented as: Roller/Free = 3/8 Roller/Attached = 3/8 Non-roller/Free = 1/8 Non-roller/Attached = 1/8 TF Tf tF tf Tf TTFf TTff TtFf Ttff. The square root of each value to will yield q and r: square root of q 2 = 0. For the purposes of a χ2-test, what would the calculated values of E be? a. 73, while the genetic correlations ranged from 0. Therefore the cross is CC Vv x cc Vv. An F2 cross in our Vial II between White-Eyed Males (X w Y) and Wild Females (X + X +) will result in the same 1:1:1:1 genotype ratio, but a 1:1 phenotype ratio, 50% white-eyed (25% male, 25% female) and 50% wild (25% male, 25% female). "Fast phenotypic and genotypic ratios and classes calculation with any model of inheritance, easy to use, nice interface, great support and unique software of its kind. The correlation will be denoted by r and is determined as r = 1 2 12 xx x. If it is a 50/50 ratio between men and women the disorder is autosomal. The understanding of how. Shading in each Punnett Square represents matching phenotypes, assuming complete dominance and independant assortment of genes, phenotypic ratios are also presented. The Appendix gives examples of the possible crosses of genotypes and what one may expect when breeding particular individuals in terms of the ratio of genotypes within the litter as well as the ratio of color expression (phenotype) within the litter. Among these techniques are methods that researchers can apply to just about any species. Show the punnett square and phenotypic ratios for the following crosses: 1) Both the father and mother have type O blood. Obtain an ear of corn labeled Monohybrid Cross. ) I found the expected value of the smooth and wrinkled kernels using the total number of kernels and using the 3:1 expected ratio. o 205-day weaning weight o 305-day milk production record. According to the Chi-square test, did she get the predicted outcome? 4. genotypic and phenotypic ratios when you cross a purple radish with a white radish? 50% purple (RW) 50% white (WW) R W W RW WW W RW WW 2. calculate surface area to volume ratio; use scales for measuring; represent phenotypic ratios (monohybrid and dihybrid crosses) MS 0. To further highlight the utility of this assay for phenotypic screening, we profiled a small set of compounds known to modulate the hypertrophic response. To calculate expected DCO, actual distances from gene map should be used when available. However, we do not, suggesting gene linkage. Give the genotypic and phenotypic ratios in the F1 and F2 generations of a cross between an. According to the Chi-square test, did she get the predicted outcome? 4. Two fundamental calculations are central to population genetics: allele frequencies and genotype frequencies. Interest in the evaluation of phenotypes has grown with the goal of enhancing the quality of fruit trees. First treat the A gene. We also derive the fundamental condition for. The cell length varied from 2 to >40 μm and encompassed rods, curved cells, and long filaments. investigated why breast cancer cells treated with taxanes become resistant to the unrelated, routinely used doxorubicin. Can this trait be sex linked in. There is a male to female ratio of 3:2. Calculate phenotypic ratios for the following crosses: a. Mendel used dihybrid crosses in an effort to uncover more. Calculate the Genotypic and Phenotypic Ratio for the Offspring. Write down the cross between F 1 progeny: WwDd (white, disk-shaped fruit) X WwDd (white, disk-shaped fruit) 5. Ratio: In simple mathematics, relationship or comparison between two more numbers is known as ratios. For a given genetic model, it is possible to calculate risk ratios for relatives. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2. Representative areas of prostate carcinoma (n = 51) and of nodular prostate hyperplasia (n = 20) were analysed for hypoxia-inducible factor 1 alpha (HIF-1α), carbonic anhydrase IX (CAIX), lysyl oxidase. So, the observed ratio in the F2 generation is 9:7. Crosses between these F1s would result in a 1:2:1 ratio of 3cm:2cm:1cm beaks and the mean of the F2's (2) would be the same as the mean of the F1's and the mean of the two parents. We also derive the fundamental condition for. Interest in the evaluation of phenotypes has grown with the goal of enhancing the quality of fruit trees. genotypic and phenotypic ratio online calculator genotypic and phenotypic ratio online calculator genotypic and phenotypic ratio online calculator // im genes c. When reading a ratio, the colon (:) or fraction bar (-) is read as "is to" or "per". Antibody response plays an important role in host resistance to Newcastle disease, and selection for antibody. the genetic constitution determining the phenotype of an organism ) Supplement The genotypic ratio describes the number of times a genotype would appear in the offspring after a test cross. 723 (95% CI 0. Then, the expected phenotypic ratios of the two traits together can be calculated algebraically as a binomial distribution: (3Y + 1y) x (3R + 1r) = 9YR + 3Yr + 3Ry + 1 ry That is, we expect a characteristic 9:3:3:1 phenotypic ratio of round-yellow : wrinkled -yellow : round- green : wrinkled-green pea seeds. Calculate the$\chi^{2}$values for each hypothesis. What are the expected progeny ratios in the F 2? As previously calculated, we expect to get a ratio of gray to white o r 3:1 (3/4:1/4) for body color and a ratio of bicorn to unicorn of 3:1 (3/4:1/4) for horn number. Please note that in this calculator ratio a:b means a out of b. When analyzing two parents, it is easier to determine how many possible phenotypic and genotypic combinations of each gene pair, and then multiply them all together. A quantitative trait locus (QTL) is a locus (section of DNA) that correlates with variation of a quantitative trait in the phenotype of a population of organisms. – Step 1: Propose a hypothesis that allows us to calculate the expected values based on Mendel’s laws • The two traits are independently assorting – Step 3: Apply the chi square formula χ2 = (O 1 –E 1) 2 E 1 (O 2 –E 2)2 E 2 (O 3 –E 3) E 3 (O 4 –E 4)2 E 4 +++ – Step 2: Calculate the expected values of the four phenotypes. The software also provides the number of different phenotypic and genotypic classes and it works with any model of inheritance (linkage with crossing over frequency, epistatics, incomplete dominance, etc. We can further observe that the difference in the ratio of false negative between Wikipedia (21. Give the genotypic and phenotypic ratios in the F1 and F2 generations of a cross between an. When analyzing two parents, it is easier to determine how many possible phenotypic and genotypic combinations of each gene pair, and then multiply them all together. Let the dominant allele as “Y” and recessive allele as “y”. 1,B and C). Thus only two phenotypic classes, viz. one parent is homozygous dominant for each trait and one parent is homozygous recessive for each trait. Most of these ratios fall within the normal range of those for plasma VWF (1-0. Using the Punnett Sq, predict the phenotypic ratios in the offspring that result from a cross of two pea plants that are heterozygous for both seed color and shape. (PpSs x PpSs) involving two pairs of heterozygous genes resulting in a theoretical (expected) ratio of 9:3:3:1. -Calculator-Chi Square Table-Paper or Note Taking App. About Ratio to Percentage Calculator. The phenotypic ratio is the ratio of observed phenotypes, which may be different from the genotypic ratio due to interactions between alleles. The F1 individuals, called dihybrid, were all round yellow. Can a child have blood group O if his parents have blood group ‘A’ and. Despite the fact that you cannot enter a ratio of 4/5 into this calculator, it accepts values such as 4:5, for example, 4/3 should be written as 4:3. The cell length varied from 2 to >40 μm and encompassed rods, curved cells, and long filaments. What is the ratio of kernels based on the Punnett square? (2 points) How does this compare to the ratio obtained from counting the corn kernels? (2 points) What are the genotypic and phenotypic ratios for kernel color and kernel texture for a dihybrid cross between PpSS x Ppss? (4 points) genotypic ratio; phenotypic ratio. 50, then: R = 0. L1 activity. Developmental and Phenotypic Plasticity in Leaves Objectives: 1. A certain breed of dogs, a gene (D) codes for hair length. Negligible reports on the. The key difference between phenotype and genotype ratio is that the phenotype ratio is the relative number of or the pattern of the offspring manifesting the visible expression of a particular trait while the genotype ratio is the pattern of offspring distribution according to the genetic constitution. The ratio of the single-generation progress of selection to the selection differential of the parents. There were 133 affected males and 40 affected females, a male:female ratio of 3. It's easy to calculate that the genotypic ratio is 0. The second ear of corn was the result of crossing two heterozygous ears of corn male purple (Pp x Pp). In peas, a gene for tall plants (T) is dominant over its allele for short plants (t). Question: Calculate The ACTUAL Phenotypic Ratio From The Experimentally Obtained Data Shown In The Table Below. Yet, cells of a tissue do not behave similarly, and molecular studies on several organisms have shown that regulations can be highly stochastic, sometimes generating diversified cellular phenotypes within tissues. This online tool calculates Punnett Square diagram that can be used to to predict an outcome of a particular cross or breeding experiment. In The USA: 800-514-9672 Phone: 850-386-1145 Email: Use Contact Form.$ He decided to perform chi- square analysis using two different null hypotheses: (a) the data fit a 3: 1 ratio; and (b) the data fit a 1: 1 ratio. High-density genetic map construction associated with quantitative trait locus (QTL) mapping provides an effective way to facilitate trait. To calculate expected DCO, actual distances from gene map should be used when available. Animal Genetics Inc. Compare ratios and evaluate as true or false to answer whether ratios or fractions are equivalent. There were 133 affected males and 40 affected females, a male:female ratio of 3. 50, then: R = 0. These values were used to calculate the oxygen supply temperature quotient, fmaxQ 10. In assessing data that fell into two phenotypic classes, a geneticist observed values of 250:150. In a monohybrid cross, where the alleles present in both parents are known, each genotype shown in a Punnett Square is equally likely to occur. – The phenotypic and genotypic ratio of F 2 progeny in a monohybrid cross is 1 : 2 : 1. This assumes independent assortment. What is the phenotypic ratio of the offspring in Figure 6. If the alleles are dominant and recessive, we can't visually tell the homozygous AA from the heterozygous Aa genotypes (both are tall), so it's best to start with the homozygous recessive (short) aa individuals. one parent is homozygous dominant for each trait and one parent is heterozygous for each trait. What are the genotypic and phenotypic ratios for kernel color and kernel texture for a dihybrid cross between PpSS x Ppss? (4 points) c. Do not squeeze the eggs. In the case shown, we are looking at a single phenotypic trait (pea flower color) that is determined by two independent genes. help you calculate the genotypes of the F2 individuals resulting from this cross. Record Your Answer As An Integer. Independent assortment allows the calculation of genotypic and phenotypic ratios based on the probability of individual gene combinations. 30 (30 percent). Data Analysis: Thirty two control wells containing cells only, 24 wells containing Hyamine and 8 wells containing ALLN were included on each assay plate and used to calculate Z' value for each plate and to normalize the data on a per plate basis. It's easy to calculate that the genotypic ratio is 0. Using these probabilities, we can predict the phenotypic ratio we should see in the F2 generation. Give the genotypic and phenotypic ratios in the F1 and F2 generations of a cross between an. For example, a log R ratio of approximately 1 (log 2 of 50%. According to the results of the likelihood ratios of the phenotypic tests, the best equilibrium between positive and negative ratios is achieved by the characterization at species level in the phenotypic microbiological procedures (LR+ = 5. We studied residual feed intake (RFI) and feed conversion ratio (FCR) over two age periods to. $He decided to perform chi- square analysis using two different null hypotheses: (a) the data fit a 3: 1 ratio; and (b) the data fit a 1: 1 ratio. ) I found the expected value of the smooth and wrinkled kernels using the total number of kernels and using the 3:1 expected ratio. Below the form you can read more about blood antigens and determination and also about blood transfusions. What are the genotypes and phenotypes for the three options for canary coloring?. taddei masieri,a p. The Punnett square calculator allows you to estimate the possibility that certain genes will be inherited, and calculate the genotypic and phenotypic ratio of any trait. This blood type calculator determines the possible blood type of a person based on the blood groups of his or her parents. 2 mm) diameter copper tubing. In the first 45 minutes, discuss each of the biomarkers contained within Levine’s Biological Age calculator, Phenotypic Age. Name the type of inheritance in which the genotypic ratio is the same as the phenotypic ratio. 1-3 It is a global disease that occurs in many ethnic groups and in both sexes. In India, a great deal of public and private sectors’ investment has focused on developing pearl millet single cross hybrids based on the cytoplasmic-genetic male sterility (CMS) system, while in Africa most pearl millet production relies on open pollinated varieties. Round the other number to the nearest 10th of a decimal (0. To distinguish between the sexes, WorMachine uses morphological and brightness features that differentiate between hermaphrodites and males and, also, when fluorescent reporters are available, sex-specific expression. Human life span is a phenotype that integrates many aspects of health and environment into a single ultimate quantity: the elapsed time between birth and death. Heritability is the proportion of variance in a particular trait, in a particular population, that is due to genetic factors, as opposed to environmental influences or stochastic variation. A quantitative trait locus (QTL) is a locus (section of DNA) that correlates with variation of a quantitative trait in the phenotype of a population of organisms. This cross involves codominance and gene interaction resulting in a 9:3:3:1 phenotypic ratio of offspring. Question: In pea plants tall is dominant to short and purple flowers are dominant to white flowers. Existing assays for measuring ECM production are often low throughput and not disease relevant. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. You can easily tell the phenotypic ratio is 3:1 or 3/4 to 1/4. Phenotypic Ratio Calculator. Consider an example : Here , we have crossed a heterozygous ( the two alleles show dominant and recessive relationship vix T and. Determine the genotypic and phenotypic ratios for the F2 generation: Genotypic ratios: 1/4 will be homozygous dominant (WW), 1/2 will be heterozygous (Ww) and 1/4 will be homozygous recessive (ww). Use calculators to find and use power, exponential and. To advance therapeutics in ALS, we need easily accessible. Ratio to Fraction Calculator is an online tool to change ratio into fraction. Count the amount of homozygous recessive (aa) squares as another group. The square root of each value to will yield q and r: square root of q 2 = 0. Shell length is the length of the long axis within the shell outline and shell width is the length of an axis halfway along, and perpendicular to, the long axis (see fig. = 0 then interference is complete and no double crossovers are observed. 4/1000 American Blacks. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2. At another locus ‘Y’ for yellow fruits is dominant to its allele ‘y’ for green fruits. Calculate the ACTUAL phenotypic ratio from the experimentally obtained data shown in the table below. Affected individuals are homozygous recessive for the responsible allele and often die in childhood. Phenotypic ratio —> Red : Pink : White :: 1 : 2 : 1 Genotypic ratio —> RR : Rr: rr :. Coverage Ratio” to automatically calculate colony confluency value as “Ph-Mask Area Ratio”. Two fundamental calculations are central to population genetics: allele frequencies and genotype frequencies. You can convert a value expressed as a percent to a ratio in a few short steps. genotypic and phenotypic ratios when you cross a purple radish with a white radish? 50% purple (RW) 50% white (WW) R W W RW WW W RW WW 2. – Step 1: Propose a hypothesis that allows us to calculate the expected values based on Mendel’s laws • The two traits are independently assorting – Step 3: Apply the chi square formula χ2 = (O 1 –E 1) 2 E 1 (O 2 –E 2)2 E 2 (O 3 –E 3) E 3 (O 4 –E 4)2 E 4 +++ – Step 2: Calculate the expected values of the four phenotypes. For alleles that display incomplete dominance, the phenotypic ratio expected in the F2 generation of a monohybrid cross would be the same as the genotypic ratio. one parent is homozygous dominant for each trait and one parent is heterozygous for each trait. The ratios would be the same as for the incomplete dominance examples as well. You want to cross a plant that is heterozygous for both traits with a plant that has wrinkled green seeds. Fluconazole is also a moderate inhibitor of CYP2C9 and CYP2C19. According to the Chi-square test, did she get the predicted outcome? 4. Ex) A tall green pea plant (TTGG) is crossed with a short white pea plant. The T Cell Autoimmune Panel includes BioMAP systems comprised of complex co-cultures of immune and adherent human primary cell types. In the case shown, we are looking at a single phenotypic trait (pea flower color) that is determined by two independent genes. Among these techniques are methods that researchers can apply to just about any species. These values are consistent with excellent blood-brain-barrier penetration. Learn some ways to quantify morphology 2. Using large numbers of crosses, Mendel was able to calculate probabilities, found that they fit the model of inheritance, and use these to predict the outcomes of other crosses. Epistasis Gene Interaction: Type # 5. Let the dominant allele as “Y” and recessive allele as “y”. For example, you calculate the relative frequency of prices between$3. These values of were used to calculate MRQ 10 for the two temperature steps (17–22 and 22–28°C) for the replicate. This observed figures closely approximated a 9:3:3:1 ratio. How do I calculate this? I forgot if this statistic is called Percent Difference or something else, I remember learning it in Chemistry for actual vs. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2. The Punnett square calculator provides you with an answer to that and many other questions. Calculate the phenotypic ratio resulting from a cross between one pea plant homozygous recessive for both pea texture and color and another pea plant heterozygous for both. For example, a log R ratio of approximately 1 (log 2 of 50%. One-third of the round seeds and all of the wrinkled seeds in the F 2 generation were homozygous and produced only seeds of the same phenotype. You can quickly calculate phenotypic and genotypic ratios with ease. To calculate the standard deviation of a data set, you can use the STEDV. The EU considers an essential oil usage rate of 3% or less to be safe in wash-off products like soap. Phenotypic assays have proven generally useful in the discovery of first-in-class therapeutics , although not yet for fibrosis. High-density genetic map construction associated with quantitative trait locus (QTL) mapping provides an effective way to facilitate trait. What will be the genotypic. genotypic and phenotypic ratio online calculator genotypic and phenotypic ratio online calculator genotypic and phenotypic ratio online calculator // im genes c. 2 mm) diameter copper tubing. We log e-transformed optical densities, and used the slope of the curve in the interval OD 420 nm = [0. 1) while lowest for yield index (YI; 0. The hypothesis that the two genes are unlinked predicts the offspring phenotypic ratio will be 1:1:1:1. Introduction. We believe that this difference is mainly due to the forms of expression used in both sources, with Wikipedia being more discursive, as opposed to the scientific style of PubMed. In conclusion, 50% of the couple's children will be born with alleles Ab - that is curly, blond hair. Determine the genotypic and phenotypic ratios for the F2 generation: Genotypic ratios: 1/4 will be homozygous dominant (WW), 1/2 will be heterozygous (Ww) and 1/4 will be homozygous recessive (ww). Feb 4, 2013 • ericminikel. In the example shown, the formulas in F6 and F7 are: = STDEV. Conversely, for 34 of 50 (68%) H63D homozygotes, abnormalities of iron metabolism were not associated with a known aetiology. Heritability is the proportion of variance in a particular trait, in a particular population, that is due to genetic factors, as opposed to environmental influences or stochastic variation. 8601) and the lymphocyte/neutrophil ratio in combination with the PaO 2 /FiO 2 ratio. (USA) 3382 Capital Circle NE Tallahassee, FL 32308 USA. We designed phenotypic strategies giving priority to high sensitivity for screening putative CPE before further testing. Genotype is the *genetic make-up * of an organism. From a genome screen for hydroxyurea (HU) chemical-genetic interactions, 298 haploid deletion strains were selected for further. The square is particularly useful to determine probabilities of phenotype and genotype ratios. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2. both parents are heterozygous. Increased levels of blood plasma urea were used as phenotypic parameter for establishing novel mouse models for kidney diseases on the genetic background of C3H inbred mice in the phenotype-driven Munich ENU mouse mutagenesis project. Narrow sense heritability is a measure of the ratio of additive genetic variation to phenotypic variation in a given population for a given trait. Commonly used chemotherapies can lead to resistance to drugs with different modes of actions. Without grazers and with a sufficient substrate supply, bacteria grew mainly in the form of medium-sized rods (4 to 7. 2 mm) diameter copper tubing. Phenotypic ratio 18:5:4:2 2. Risk stratification by this composite measure is far superior to that of the individual measures that go into it, as well as traditional measures of health. Percentage values are often expressed as a whole number with a percent symbol (%) after the number while ratios are usually written using 2 numbers separated by a colon (:). Students may be tested on their ability to: estimate results to sense check that the calculated values are appropriate; MS 0. (a) Phenotypic integration of scent bouquets emitted by animals, flowers and leaves. Calculate phenotypic ratios for the following crosses: a. You know a ratio is a comparison that tells how two or more things relate. The negative inverse of the a verage information matrix gives us estimates 1 I A for the variance of the estimators var(x 1), var(x 1), and cov(x 12) but also the covariance between the various. Otherwise the calculator finds an equivalent ratio by multiplying each of A and B by 2 to. QTLs are mapped by identifying which molecular markers (such as SNPs or AFLPs) correlate with an observed trait. The above table, a Punnett square, illustrates the results of a cross between two F1 heterozygous individuals. The ratios VWF:RCo/VWF:Ag and CBA/VWF:Ag were 0. carbon isotope ratio: variance) in a phenotypic character in a population that is due to individual to find the variance of the set of numbers 4, 6, and 8, we first calculate the mean. The number of neutral mutations that are fixed over a given period of time can be predicted, and these can be used to estimate evolutionary relationships. Fairfax Cryobank is operating and available to answer questions! Call 1-800-338-8407 to order vials and receive 3 months of free storage! Learn how Fairfax supports families on our COVID-19 Resource page. 3 HCM has an autosomal dominant pattern of inheritance, and incomplete, age- and gene-dependent penetrance. These values are consistent with excellent blood-brain-barrier penetration. Genetic variance is a concept outlined by the English biologist and statistician Ronald Fisher in his fundamental theorem of natural selection which he outlined in his 1930 book The Genetical Theory of Natural Selection which postulates that the rate of change of biological fitness can be calculated by the genetic variance of the fitness itself. 2 in DeWitt et al. NS indicates not significant. According to the Chi-square test, did she get the predicted outcome? 4. Heterozygous/homozygous. expected genotypic ratio and the expected phenotypic ratio of their offspring. Figure 2: The image above shows a Punnett square for figuring out the genotypic ratio using 4 traits from each parent. A pea plant that is heterozygous for round, yellow seeds is self fertilized, what are the phenotypic ratios of the resulting offspring? Step 1: Determine the parental genotypes from the text above, the word "heteroyzous" is the most important clue, and you would also need to understand that self fertilized means you just cross it with itself. _____ x _____ Phenotypic Ratio: 2) The father is type A homozygous, the mother is type B homozygous. Phenotypic noise, defined here as trait variability among isogenic. According to the results of the likelihood ratios of the phenotypic tests, the best equilibrium between positive and negative ratios is achieved by the characterization at species level in the phenotypic microbiological procedures (LR+ = 5. Again the patient (F-Ratio = 2. 1,B and C). e) Green Green. Analysis of the causative mutation as well as the standardized, systemic. The second ear of corn was the result of crossing two heterozygous ears of corn male purple (Pp x Pp). What if you bred some snap dragons and crossed a homozygous red plant (RR) with a homozygous white plant (rr)? In botony, "true breeding" means homozygous. Determine the genotypic and phenotypic ratios for the F 1 generation: All F 1 progeny will be heterozygous for both characters (WwDd) and will have white, disk-shaped fruit. • Explain the importance of genetic variability. Changes of sex ratio have occurred as a correlated response in a selection experiment for high and low levels of blood pH ( Weir, 1960b). The fractional ratios for these four phenotypes are 9/16, 3/16, 3/16 and 1/16. To distinguish between the sexes, WorMachine uses morphological and brightness features that differentiate between hermaphrodites and males and, also, when fluorescent reporters are available, sex-specific expression. Question: Calculate The ACTUAL Phenotypic Ratio From The Experimentally Obtained Data Shown In The Table Below. (PpSs x PpSs) involving two pairs of heterozygous genes resulting in a theoretical (expected) ratio of 9:3:3:1. Questions: What is the expected genotypic ratio in the F2 generation? What is the expected phenotypic ratio in the F2 generation? Procedure 4: Monohybrid cross using Corn Material Monohybrid Corn Cob 1. It's easy to calculate that the genotypic ratio is 0. The Punnett square is a useful tool for predicting the genotypes and phenotypes of offspring in a genetic cross involving Mendelian traits. Variance component estimates are use. Show the punnett square and phenotypic ratios for the following crosses: 1) Both the father and mother have type O blood. The phenotype for a characteristic like eye colour is the result of the combination of alleles. 42 ( 42% ) By also calculating the other four possibilities, we can construct a graph that shows the statistical distribution you would expect to see in a large population. Mendel used dihybrid crosses in an effort to uncover more. Calculate phenotypic ratios for the following crosses: a. A testcross to a heterozygous individual should always yield about a 1:1 ratio of the dominant to recessive phenotype. | 14,635 | 62,118 | {"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} | 3.125 | 3 | CC-MAIN-2020-40 | latest | en | 0.890294 |
http://mathhelpforum.com/algebra/211778-number-sample-remain.html | 1,495,650,611,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607849.21/warc/CC-MAIN-20170524173007-20170524193007-00587.warc.gz | 240,381,453 | 10,575 | # Thread: number of sample remain
1. ## number of sample remain
The half-life of an element is 10 years. How much of a 20g sample will remain after 50 years?
Choices: 0.625g , 1.25g , 2.5g, 5g
my answer is 2.5g.
considering: 20g is a half life an element. since it is 50 yrs... then there are five 10 years in a 50 years. so in every 10 years there corresponds half life
5 time half life = 5 x 1/2 = 2.5 ...
please help me understand the problem. and hope somebody will correct or check my work. because im not sure of my answer
thanks
2. ## Re: number of sample remain
Sorry, this incorrect. Every 10 years the amount remaining is cut in half. At year 0 you have 20 grams, and ten years later at year 10 you have half of that, or 10 grams. At year 20 you have half of what you had at year 10, or 5 grams. Continue on in this manner, cutting the amount in half for each 10 year period, and what do you get at year 50?
To make an equation for this you can raise 1/2 to the number of half life periods to determine the fraction of material remaining. Since the half life is 10 years, and you want to know how much is remaining after 50 years, that's 5 half-life periods. So (1/2)^5 = 1/32, and hence 1/32nd of the original amount is remaining after 50 years. What's 1/32nd of 20 grams?
3. ## Re: number of sample remain
Originally Posted by ebaines
Sorry, this incorrect. Every 10 years the amount remaining is cut in half. At year 0 you have 20 grams, and ten years later at year 10 you have half of that, or 10 grams. At year 20 you have half of what you had at year 10, or 5 grams. Continue on in this manner, cutting the amount in half for each 10 year period, and what do you get at year 50?
To make an equation for this you can raise 1/2 to the number of half life periods to determine the fraction of material remaining. Since the half life is 10 years, and you want to know how much is remaining after 50 years, that's 5 half-life periods. So (1/2)^5 = 1/32, and hence 1/32nd of the original amount is remaining after 50 years. What's 1/32nd of 20 grams?
Therefore ... I got it is 0.625 in 50 years... Is this correct?
4. ## Re: number of sample remain
No, try again. 20/32 = ?? | 625 | 2,199 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2017-22 | longest | en | 0.954806 |
http://mathhelpforum.com/geometry/141692-circles-within-square-print.html | 1,508,241,399,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187821088.8/warc/CC-MAIN-20171017110249-20171017130249-00672.warc.gz | 210,965,158 | 3,756 | # Circles within a square
• Apr 27th 2010, 06:31 AM
BG5965
Circles within a square
http://i301.photobucket.com/albums/n...5965/MASBc.png
This is part c) of a problem using circles within squares - the first 2 parts included information necessary for part c), which included the length of the rope if the total area "eatable" was $288m^2$. However, I don't know how to approach this part of the question. Please help! Thanks :)
• Apr 27th 2010, 07:44 AM
bjhopper
circles in square
Quote:
Originally Posted by BG5965
http://i301.photobucket.com/albums/n...5965/MASBc.png
This is part c) of a problem using circles within squares - the first 2 parts included information necessary for part c), which included the length of the rope if the total area "eatable" was $288m^2$. However, I don't know how to approach this part of the question. Please help! Thanks :)
Hello BG,
I think this problem belongs in trig. If you can handle geometry I can help by telling you i calculated the sector angle common to the two goats 55.2 deg. Rest is geometry.
bjh
• Apr 27th 2010, 10:00 AM
Wilmer
Well, removing the goats and company out of there, you've got
2 intersecting circles, one with center (0,24) and radius 19.15 [1],
the other with center (24,0) and radius 19.15 [2].
Their equations are:
(x - 0)^2 + (y - 24)^2 = 19.15^2 [1]
(x - 24)^2 + (y - 0)^2 = 19.15^2 [2]
Now you can easily (easily enough!) calculate the 2 intersecting points...
Get my drift?
• Apr 28th 2010, 05:32 AM
BG5965
Thanks all of your for your input, I've worked it out now.
Let the 4 corners be A, B, C, D and and the obtuse angles of the rhombus as E and F.
By pythagoras, the diagonal is 33.94m, and the 2 radii from either circle (length 19.15m) make a triangle with those dimensions. By cosine rule, the obtuse angle AED is 124.79 degrees, and as opposite angles are equal, so is the other side.
Therefore, each acute angle is 55.21 degrees, so the area of the sector EDF is $176.69m^2$. Similarly, the area of the triangle EDF is $150.59m^2$, therefore the extra circular area in the sector is equal to $26.1m^2$, which is half of the shared area, so the total shared area is $52.2m^2$.
Once again, thanks a lot for your help :) BG
• Apr 29th 2010, 08:43 AM
slovakiamaths
diff. ans
Dear BG5965, i worked out a diff. ans of your problem. Please check the attachment and give remarks
• Apr 29th 2010, 12:58 PM
bjhopper
Quote:
Originally Posted by slovakiamaths
Dear BG5965, i worked out a diff. ans of your problem. Please check the attachment and give remarks
Hi slovakiamaths,
The answers given by BG5965 are correct. Area in question consists of two back-back circular segments.No relation to ellipse.
bjh | 799 | 2,689 | {"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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2017-43 | longest | en | 0.92645 |
https://www.noodle.com/learn/details/52353/the-commutative-associative-properties-of-multiplication | 1,529,282,542,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267859904.56/warc/CC-MAIN-20180617232711-20180618012711-00326.warc.gz | 885,037,705 | 12,519 | ## At A Glance
### The Commutative & Associative Properties of Multiplication
Check out Bas Rutten's Liver Shot on MMA Surge: http://bit.ly/MMASurgeEp1 In this video, Mahalo math expert Allison Moffett shows you how to use the commutative and associative properties of multiplication. Commutative Property of Multiplication --------------------------------------------------------------------- This property states that if you have A times B, that is equal to B times A. The order doesn't matter as long as all the numbers involved are being multiplied to each other. Associative Property of Multiplication --------------------------------------------------------------------- This property states that if you have A times the quantity B times C, that is the same as the quantity A times B times C. It doesn't matter which two you associate together in the parentheses as long as all numbers involved are being multiplied to each other. Read more by visiting our page at: http://www.mahalo.com/the-commutative-and-associative-properties-of-multiplication/
Length: 01:44
## Contact
Questions about The Commutative & Associative Properties of Multiplication | 227 | 1,159 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2018-26 | latest | en | 0.867792 |
http://www.ck12.org/geometry/Area-and-Volume-of-Similar-Solids/?by=all&difficulty=all | 1,493,495,255,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917123560.51/warc/CC-MAIN-20170423031203-00314-ip-10-145-167-34.ec2.internal.warc.gz | 486,613,216 | 16,873 | # Area and Volume of Similar Solids
## Solve problems using ratios between similar solids.
Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.
## Area and Volume of Similar Solids
Find the ratios of surface areas and volumes of similar solids.
MEMORY METER
This indicates how strong in your memory this concept is
3
## Area and Volume of Similar Solids
This concept teaches students to use ratios between similar solids to solve for missing information.
MEMORY METER
This indicates how strong in your memory this concept is
5
## Understand Scale Relationships
by CK-12 //basic
Learn to understand scale relationships of area and volume.
MEMORY METER
This indicates how strong in your memory this concept is
3
## SLT 11 Determine the effect on volume of doubling or tripling one or more dimensions of a solid.
MEMORY METER
This indicates how strong in your memory this concept is
2
• PLIX
## Similar Solids
Area and Volume of Similar Solids Interactive
MEMORY METER
This indicates how strong in your memory this concept is
0
• Video
## Area and Volume of Similar Solids Principles
This video gives more detail about the mathematical principles presented in Area and Volume of Similar Solids.
MEMORY METER
This indicates how strong in your memory this concept is
1
• Video
## Area and Volume of Similar Solids Examples
This video shows how to work step-by-step through one or more of the examples in Area and Volume of Similar Solids.
MEMORY METER
This indicates how strong in your memory this concept is
0
• Video
## Similar Solids Principles - Basic
by CK-12 //basic
This video provides the student with a walkthrough on similar solids.
MEMORY METER
This indicates how strong in your memory this concept is
0
• Video
## Similar Solids Examples - Basic
by CK-12 //basic
This video provides the student with a walkthrough of one or more examples from the concept "Similar Solids".
MEMORY METER
This indicates how strong in your memory this concept is
0
• 0
• Critical Thinking
## Area and Volume of Similar Solids Discussion Questions
A list of student-submitted discussion questions for Area and Volume of Similar Solids.
MEMORY METER
This indicates how strong in your memory this concept is
0
• Real World Application
## Is There Life Out There?
Learn about Kepler-69c, a planet similar to Earth.
MEMORY METER
This indicates how strong in your memory this concept is
0
• Study Guide
## Surface Area and Volume Study Guide
This study guide looks at the definitions and postulates of surface area and volume, Cavalieri's principle, and composite solids.
MEMORY METER
This indicates how strong in your memory this concept is
1
• Flashcards
## Understand Scale Relationship
by Ellaine Chou //basic | 673 | 3,217 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2017-17 | latest | en | 0.903248 |
https://www.educationhub.tech/2020/05/electric-flux-by-aksinha.html | 1,726,437,959,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651668.26/warc/CC-MAIN-20240915220324-20240916010324-00298.warc.gz | 695,757,647 | 35,994 | # Electric Flux by A.K.Sinha
Electric Flux:
Electric Flux is a measure of total electric field lines crossing a particular area.
we can simply define it as dot product of Electric field and Area vector. It is represented by Φ such that
Here ds is an area vector.
( NOTE : The first equation in fig. represents dot product of two vectors and when we simply that equation we get the very next equation.)
Electric flux depends on the cosine of angle between electric field and area vector.
When E is along area vector i.e. θ =0°, Flux is Maximum & Φ = E ds , and when E is perpendicular to the area vector i.e. θ = 90°, Flux is Minimum & Φ = 0.
Electric Flux is a Scalar quantity.
SI Unit : N m2 C-1
Dimensional Formula : Your task ….Find and reply in comment ???
Area Vector:
In the concept of electric flux we consider area as a vector and consider its direction as perpendicular to the plane of the area going outside.
Here ds is a small area. And its direction is perpendicular to the plane of area ds.
Electric Flux Density :
Electric Flux Density is defined as the field lines produced across closed unit area.
Your task : ( Reply your answer in comment )
Q.1) If a body gives out 105 electrons every second, how much time is required to get a total charge of 1 C from it ?
Q.2) Two equal and opposite charges of 2 × 10-7 C are placed 1 mm apart. Find the magnitude and nature of force of interaction.
Notes here: GET PDF 👉
GET IMPORTANT QUESTIONS: CLICK HERE
GET YOUR RELATED TOPICS HERE : CLICK HERE
### 1 Comments
1. Dimensional formula of electric flux is
[ML^3T^-3A^-1]
If you have any doubt, please let me know. Leave a comment here... | 407 | 1,680 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-38 | latest | en | 0.901044 |
http://physics.stackexchange.com/questions/61967/if-theres-a-light-ray-and-its-turned-to-a-new-location-by-a-certain-angle | 1,469,772,366,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257829972.19/warc/CC-MAIN-20160723071029-00259-ip-10-185-27-174.ec2.internal.warc.gz | 198,350,030 | 18,288 | # If there's a light ray and it's turned to a new location by a certain angle
Imagine that there's a light ray, with source at point A, and it's directed towards point B (which is very far from point A) and it continues for a huge distance. How will an observer at point B perceive the light ray if it gets moved be a certain angle so that it's now directed towards point C.
If the distance AB is large enough, then according to theory of special relativity "something should happen" either with light ray (will it behave like a stream of water, i.e. like matter = matter at the 'end' of stream will fall behind the matter at the 'start') or with perception of the observer so that the speed of light is not exceeded.
-
Please clarify what you mean by "according to special relativity something should happen". – Brandon Enright Apr 25 '13 at 4:21
It's not totally clear what the situation is you're asking about, but it seems to be something like this:
If something is causing light to bend - a glass wedge, a gravitational field, magic unicorn powder, fuzzy green fog - then a ray (yellow) initially heading toward B will miss B. It will hit C if there happens to be such a thing in the right place. Anyone at B will not be aware of this yellow ray of light.
However, another ray (orange) leaving A at the right angle, after being bent by whatever, may end up heading just the right direction to arrive at B. An observer at B will see A, not in their view straight across (white dashed line) but appearing above the expected direction.
Also note that they won't see the exactly the right half of A, as expected if light weren't being bent, but rather have a view of the upper right part.
Special and general relativity have nothing to add to this basic geometry, although general relativity might explain the cause of the bend e.g. Schwarzchild geometry - the gravity around any massive object.
Further reading: search for Eddington, Einstein, Africa and eclipse. Try this site: http://undsci.berkeley.edu/article/natural_experiments
-
Okay, at the moment when something bends the light ray, should the observer at C notice it immediately? I mean, if i takes time t1 for the light ray to change its direction at the point of deflection and the distance BC is larger then t1 * c ? – Artur Udod Apr 23 '13 at 9:46
@Artur: The principle is the same as if you are looking at a torch in my hand and I turn the torch off. You don't find out about it until $x/c$ seconds later (ignoring relativistic effects and assuming we're in a vacuum etc etc). Photons currently travelling in your direction are unaffected by subsequent torch waggling. You may need to edit your question and add a diagram and a more careful explanation of what is puzzling you. – RedGrittyBrick Apr 23 '13 at 11:07 | 642 | 2,791 | {"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} | 3.109375 | 3 | CC-MAIN-2016-30 | latest | en | 0.942043 |
https://www.physicsforums.com/threads/series-solutions-to-tise.533921/ | 1,510,989,655,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934804666.54/warc/CC-MAIN-20171118055757-20171118075757-00798.warc.gz | 884,175,517 | 15,955 | # Series Solutions to TISE
1. Sep 26, 2011
### atomicpedals
1. The problem statement, all variables and given/known data
The eigenvalue problem H$\psi$=E$\psi$ for $\phi$ becomes
-$\phi$''+2x$\phi$'+((a(a-1))/x2)$\phi$+(1-2E)=0
assume that $\phi$(x)=$\sum$anxn+B, determine B.
2. The attempt at a solution
As a first step I took the first and second derivatives of $\phi$:
$\phi$'=$\sum$(n+B)anxn+B-1
$\phi$''=$\sum$(n+B-1)(n+B)anxn+B-2
and then substituted these back into -$\phi$''+2x$\phi$'+((a(a-1))/x2)$\phi$+(1-2E)=0; which is
-$\sum$(n+B-1)(n+B)anxn+B-2+2x($\sum$(n+B)anxn+B-1)+((a(a-1))/x2)($\sum$anxn+B)+(1-2E)=0
And it's at this point (assuming I'm working correctly up to here) that I stop-short mentally; how do I go about solving this monster for B?
2. Sep 26, 2011
### kreil
Try computing the terms for n=0, then n=1, n=2, and n=3 then grouping the terms by powers of x to see if any noticeable patterns emerge
3. Sep 26, 2011
### atomicpedals
I'm certainly getting the impression there's either a (x-1)2 or a(a-1) in the denominator...
Last edited: Sep 26, 2011
4. Sep 27, 2011
### vela
Staff Emeritus
Are you sure the (1-2E) term isn't multiplied by $\phi$?
5. Sep 27, 2011
### atomicpedals
Oh there is! Good catch!
6. Sep 27, 2011
### vela
Staff Emeritus
Look up the method of Frobenius in your math methods book. That's what you're doing here.
To find B, find the relation a0 must satisfy. This is called the indicial equation. By assumption, a0 is not equal to 0, so the relation will only hold for certain values of B.
7. Sep 27, 2011
### atomicpedals
Thanks for the help! I'll go look Frobenius up in Arfken. | 580 | 1,660 | {"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} | 3.796875 | 4 | CC-MAIN-2017-47 | longest | en | 0.850108 |
https://math.stackexchange.com/questions/1539564/orders-of-mean-value-theorem | 1,563,660,453,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526714.15/warc/CC-MAIN-20190720214645-20190721000645-00037.warc.gz | 459,038,691 | 37,674 | # Orders of mean value theorem?
Q. Use Mean Value Theorem of appropriate order to prove that $\sin(x)\gt x-\dfrac{x^3}{3!}$
Now, I know the stated inequality was proved in a previous post, viz. Proof for $\sin(x)\gt x-\frac{x^3}{3!}$ but my question here is what does the problem poser (aka my calculus professor) mean by "mean value theorem of appropriate order" ?
I'm sorry if this is a naive question, I'm a beginner at differential calculus. Thanks for any help!
Now let’s take an arbitrary function f that is n-times differentiable on an open interval containing $[x,x+h]$. To prove the mean value theorem, we subtracted a linear function so as to obtain a function that satisfied the hypotheses of Rolle’s theorem. Here, the obvious thing to do is to subtract a polynomial p of degree n to obtain a function that satisfies the hypotheses of our higher-order Rolle theorem.
The properties we need $p$ to have are that $p(x)=f(x)$, $p'(x)=f'(x)$, and so on all the way up to $p^{(n-1)}(x)=f^{(n-1)}(x)$, and finally $p(x+h)=f(x+h)$. It turns out that we can more or less write down such a polynomial, once we have observed that the polynomial $q_k(x)=(u-x)^k/k!$ has the convenient property that $q_k^{(j)}(x)=0$ except when $j=k$ when it is $1$. This allows us to build a polynomial that has whatever derivatives we want at $x$. So let’s do that. Define a polynomial $q$ by
$q(u)=f(x)+q_1(u)f'(x)+q_2(u)f''(x)+\dots+q_{n-1}(u)f^{(n-1)}(x)$
Then $q^{(k)}(x)=f^{(k)}(x)$ for $k=0,1,\dots,n-1$. A more explicit formula for $q(u)$ is
$\displaystyle f(x)+(u-x)f'(x)+\frac{(u-x)^2}{2!}f''(x)+\dots+\frac{(u-x)^{n-1}}{(n-1)!}f^{(n-1)}(x)$
Now $q(x+h)$ doesn’t necessarily equal $f(x+h)$, so we need to add a multiple of $(u-x)^n$ to correct for this. (Doing that won’t affect the derivatives we’ve got at $x$.) So we want our polynomial to be of the form
$p(u)=q(u)+\lambda(u-x)^n$
and we want $p(x+h)=f(x+h)$. So we want $q(x+h)+\lambda h^n$ to equal $f(x+h)$, which gives us $\lambda=h^{-n}(f(x+h)-q(x+h))$. That is,
$\displaystyle p(u)=q(u)+\frac{(u-x)^n}{h^n}(f(x+h)-q(x+h))$
A quick check: if we substitute in $x+h$ for $u$ we get $q(x+h)+(h^n/h^n)(f(x+h)-q(x+h))$, which does indeed equal $f(x+h)$.
For the moment, we can forget the formula for $p$. All that matters is its properties, which, just to remind you, are these.
$p$ is a polynomial of degree $n$. $p^{(k)}(x)=f^{(k)}(x) for k=0,1,\dots,n-1$. $p(x+h)=f(x+h)$. The second and third properties tell us that if we set $g(u)=f(u)-p(u)$, then $g^{(k)}(x)=0$ for $k=0,1,\dots,n-1$ and $g(x+h)=0$. Those are the conditions needed for our higher-order Rolle theorem. Therefore, there exists $\theta\in(0,1)$ such that $g^{(n)}(x+\theta h)=0$, which implies that $f^{(n)}(x+\theta h)=p^{(n)}(x+\theta h)$.
Let us just highlight what we have proved here.
Theorem. Let f be continuous on the interval $[x,x+h]$ and n-times differentiable on an open interval that contains $[x,x+h]$. Let $p$ be the unique polynomial of degree $n$ such that $p^{(k)}(x)=f^{(k)}(x)$ for $k=0,1,\dots,n-1$ and $p(x+h)=f(x+h)$. Then there exists $\theta\in(0,1)$ such that $f^{(n)}(x+\theta h)=p^{(n)}(x+\theta h)$.
Note that since $p$ is a polynomial of degree $n$, the function $p^{(n)}$ is constant. In the case $n=1$, the constant is $\frac{f(x+h)-f(x)}{h}$, the gradient of the line joining $(x,f(x))$ to $(x+h,f(x+h))$, and the theorem is just the mean value theorem.
• I'm lazy af right now to go through such mathematical detail at the moment, so would you do me a favor and show how this can be applied to prove the stated inequality? The answer in the linked page doesn't use this form of MVT but instead some MVT for integrals. – learner Nov 22 '15 at 7:36
• @learner Taylor's theorem is called the M.V.T. of $n^{\text{th}}$ order. – SchrodingersCat Nov 22 '15 at 19:06
• I see, well, would you be kind enough to show how does one use Taylor's Theorem here to prove the stated inequality? I know the infinite series expansion $\sin(x)=\sum\limits_{k=0}^\infty (-1)^k\dfrac{x^{2k+1}}{(2k+1)!}$ but I'm not sure how does one rigorous prove that inequality using Taylor's Theorem (I haven't covered that part yet). – learner Nov 24 '15 at 10:51
• You have stated the proof in your comment. It goes like this: $\sin x=\sum_{k=0}^{\infty} (-1)^k \frac{x^{2k+1}}{(2k+1)!}=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-...> x-\frac{x^3}{3!}$ since it is very obvious and can also be proven easily that $\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-...>0$. Hope this helps..:-) – SchrodingersCat Nov 24 '15 at 16:00
• it does but I was thinking there would be some rigorous proof at hand here. Nonetheless, thanks for all the help. :) – learner Nov 24 '15 at 17:03 | 1,579 | 4,735 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2019-30 | latest | en | 0.825297 |
https://spureconomics.com/revealed-preference-theory/ | 1,725,788,984,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650976.41/warc/CC-MAIN-20240908083737-20240908113737-00417.warc.gz | 529,316,505 | 57,939 | ## Revealed Preference Theory
Revealed preference provides an alternative viewpoint to consumer preferences as compared to cardinal or ordinal utility analysis.
## Ordinal utility analysis vs Revealed Preference
The ordinal utility analysis explains consumer choice based on indifference curves and budget constraints. That is, consumers’ choice of any combination of goods is determined by their preference (from indifference curves) and budget (from the budget line).
The theory of revealed preference reverses this phenomenon. It states that preferences are determined by a consumer’s choice of a combination of goods. In other words, preferences are revealed from the choices made by consumers.
Therefore, ordinal utility analysis determines consumer choice through preferences. Whereas revealed preference theory determines preferences through consumer choice.
## Theory
If a consumer chooses a combination of goods over other available combinations, it can be said that the consumer prefers that combination over others. Hence, consumers reveal their preferences in their choice of goods.
The diagram illustrates the basic idea of revealed preference. Lines B1 and B2 are budget lines showing various combinations of two goods or bundles that a consumer can purchase. If the consumer chooses combination ‘A’, then, he or she prefers combination ‘A’ over combination ‘B’ as they are on the same budget line (B1).
Suppose, the relative prices of goods change and the budget line shifts to B2. If the consumer purchases combination ‘B’ at this new budget line, we can conclude that combination ‘B’ is preferred over ‘C’. Hence, combination ‘A’ will also be preferred over ‘C’. This happens because of the transitivity of preferences as the consumer chose ‘A’ over ‘B’.
Therefore, the consumer prefers ‘A’ over all the combinations available. These are shown by the shaded region (in blue) below both the budget lines. The combinations which lie in the shaded region above ‘A’ (in green) will be preferred over ‘A’. These combinations provide higher utility to the consumer As a result, the indifference curve of the consumer passes through point A and must lie in the unshaded region.
## Extension: several budget lines and choices to determine preferences
The above analysis can be extended further with multiple budget lines and consumer choices. We already know that ‘A’ is preferred over ‘B’ because the consumer chose ‘A’. With changes in relative prices of goods, the budget line shifts again to budget line B3. If the consumer chooses the combination ‘D’ here, we know that he or she prefers ‘D’ over ‘A’. Similarly, if the consumer chooses ‘E’ on the budget line B4, then, the consumer prefers ‘E’ over ‘A’.
Therefore, the shaded region above ‘A’ shows all the combinations that will be preferred by the consumer over ‘A’. This is true because both ‘E’ and ‘D’ are chosen by the consumer. Hence, all points above line AE and AD will be preferred over ‘A’ (in orange) as the indifference curve associated with ‘A’ has to be convex and fall below points ‘E’ and ‘D’.
We also know that ‘A’ is preferred over all the combinations in the shaded region below budget lines B1 and B2 (in blue). The indifference curve associated with ‘A’, therefore, will lie in the unshaded region. Similarly, this analysis can still be extended by including more consumer choices and budget lines to further reveal the preferences of the consumer.
### Visualizing Data with Python
This website contains affiliate links. When you make a purchase through these links, we may earn a commission at no additional cost to you. | 730 | 3,624 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-38 | latest | en | 0.898484 |
https://yarsm.ru/how-to-solve-trigonometry-problems-6798.html | 1,620,601,523,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989018.90/warc/CC-MAIN-20210509213453-20210510003453-00621.warc.gz | 1,151,408,553 | 9,653 | # How To Solve Trigonometry Problems
Related Topics: More Lessons on Trigonometry Trigonometry Games The following diagram shows how SOHCAHTOA can help you remember how to use sine, cosine, or tangent to find missing angles or missing sides in a trigonometry problem. For example, divide an isosceles triangle into two congruent right triangles. Step 4: Mark the angles or sides you have to calculate.STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity.(x) = 1 STEP 7: Since this is one of the Pythagorean identities, we know it is true, and the problem is done.
Tags: Gcse English Coursework FrankensteinArchaeology Research PaperWoody Allen Earl Monroe EssayTexting While Driving Persuasive EssayCryptography Phd ThesisLiterature Review In Research PaperDietary Analysis Essay
Proving identities is a big part of any trigonometry class (or method of study).
Here, you will find a basic method that will work on every problem, an example of how to use it, and additional tips and tricks to save you some time.
As you gain more practice, you can skip or combine these steps when you recognize other identities.
STEP 1: Convert all sec, csc, cot, and tan to sin and cos.
STEP 3: Check for angle multiples and remove them using the appropriate formulas.
STEP 4: Expand any equations you can, combine like terms, and simplify the equations.The angle of elevation of a hot air balloon, climbing vertically, changes from 25 degrees at am to 60 degrees at am.The point of observation of the angle of elevation is situated 300 meters away from the take off point.The trick to solve trig identities is intuition, which can only be gained through experience.The more basic formulas you have memorized, the faster you will be.From the first equation, I get: However (and this is important!), I squared to get this solution, and squaring is an "irreversible" process. If you square something, you can't just square-root to get back to what you'd started with, because the squaring may have changed a sign somewhere.) So, to be sure of my results, I need to check my answers in the , which is the same almost-solution as before.STEP 5: Replace cos powers greater than 2 with sin powers using the Pythagorean identities.STEP 6: Factor numerators and denominators, then cancel any common factors.If you're behind a web filter, please make sure that the domains *.and *.are unblocked.Guide to Proving Trig Identitieswritten by: Kayla Griffin • edited by: Noreen Gunnell • updated: 3/26/2014IT MIGHT TAKE SOME TIME TO READ THIS BUT IT IS WORTH IT!
## Comments How To Solve Trigonometry Problems
• ###### What are the tips to solve trigonometry problems fast? - Quora
Original Reference How to Solve Trig Identities Essentials, Examples & Tips on Proving Trigonometry Identities } Guide to Proving Trig.…
• ###### Solve Trigonometry Problems
Trigonometry problems with detailed solution are presented. Problem 1 A person 100 meters from the base of a tree, observes that the angle between the.…
• ###### Trigonometric equations and identities Trigonometry Math.
Learn how to solve trigonometric equations and how to use trigonometric identities to solve various problems.…
• ###### Solving Simple to Medium-Hard Trig Equations Purplemath
Introduces techniques for solving trigonometric equations. Provides worked examples of solving some simpler to medium-hard equations.…
• ###### How to Solve Trigonometry Identity Proving Problems - Trig Math
For List of complete Trigonometry video tutorials. Trigonometry Identity are easy as well as difficult.…
Learn trigonometry for free—right triangles, the unit circle, graphs, identities, and more. Full curriculum of. Using trigonometric identities to solve problems.… | 844 | 3,767 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2021-21 | latest | en | 0.895563 |
www.freundeoesterreichs.ch | 1,601,152,837,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00566.warc.gz | 859,824,886 | 7,586 | # critical speed calculation ball mill 4229
### Critical Speed Calculation Of Ball Mill
Critical Speed Calculation Of Ball Mill Abstract. Calculate and Select Ball Mill Ball Size for In Grinding, selecting (calculate) the correct or optimum ball size that allows for the best and optimum/ideal or target grind size to be achieved by your ball mill is an important thing for a Mineral Processing Engineer AKA Metallurgist to do.
### Ball Mill Critical Speed Mineral Processing &
2020-8-5 · A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as speed varies. Use our online formula The mill speed is typically defined as the percent of the Theoretical
### calculate critical speed of ball mill practical
The effects of lifter configurations and mill speeds AIP Publishing. At 74% critical speed, the size distributions of the Rail and Hi Lo lifters were finer than at 70% Keywords: grinding mills, lifter shapes, mill speed, mill power draw, ball trajectory A practical range of the ideal ratio should be S/H ±1. . draw is then calculated from the force readings using the following equation: .
### Critical Speed Calculation Of Tumbling Machine For
Critical Speed Of Ball Mill Calculation Pdf. COMMON EQUATIONS FOR OPTIMAL PERFORMANCE ball mill calculations critical speed Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at 50 62 75 and 90 of the critical speed Six lifter bars of rectangular crosssection were used at equal
### Mill Critical Speed Calculation majestic-restaurant.de
1 天前 · Mill Critical Speed Calculation. Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at 50 62 75 and 90 of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overall motion of the balls at the end of five revolutions is shown in Figure 4
### Torque Speed Calculation For Ball Mill wir-sind
2020-8-11 · Torque Speed Calculation For Ball Mill. Torque Speed Calculation For Ball Mill:Torque Speed Calculation For Ball Mill Ball mil design calculation yahoo answersar 31 2008 the critical speed rpm is given by nc 4229 d where d is the internal diameter in metres ball mills are normally operated at around 75 of critical speed so a mill with diameter 5 metres will turn at around 14 rpm the mill is
### Mill Critical Speed Calculation
2020-8-5 · Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied. The mill was rotated at 50, 62, 75 and 90% of the critical speed. Six lifter bars of rectangular cross-section were used at equal spacing. The overall motion of the balls at the end of five revolutions is shown in Figure 4. As can be seen from the
### ball mill critical speed metric calculation
Critical Speed Of Ball Mill Calculation India stonecrushingmachine solution production line,TECHNICAL NOTES 8 GRINDING R P King The critical speed of the mill, c, is defined as the, Figure 83 Simplified calculation of the . Check price. SAGMILLING.COM .:. Mill Critical Speed Determination.
### designing calculation of critical speed of ball mill
Ball Mill Critical Speed Mineral Processing & 2019-5-7 · A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as
### SAGMILLING.COM .:. Mill Critical Speed Determination
Enter the width of a mill shell liner. Note this is not the width of a lifter! You may use the Mill Liner Effective Width calculation to determine this value. The mill critical speed will be calculated based on the diameter (above) less twice this shell liner width. Mill Actual RPM: Enter the measured mill rotation in revolutions per minute.
### critical speed ball mill calculation bakerspalace.co.za
The critical speed of the mill, &c, is defined as the speed at which a single ball will just . autogenous mills calculated using the formulas of Austin Rod and ball mills in Mular AL and Bhappu R B Editors Mineral Processing Plant Design.
### critical speed calculation ball mill 4229
Ball Mill Critical Speed Mineral Processing & Metallurgy. 2016/12/12· Ball Mill Power Calculation Example A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing ¼ inch (6350 microns).
### critical speed of ball mill formulae
formula critical speed ball mill greenmountainptaorg. critical speed calculation ball mill 4229 tecsolcoin formula for critical speed of ball mill YouTube Oct 15, 2013 formula for critical speed of ball mill More details Get the price of machines. 【Live Chat】 critical speed calculation formula of ball mill
### Formula of critical speed of ball mill Henan Mining
The critical speed of ball mill is given by, where R = radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of 15 rpm Therefore, the mill is operated at 100 x 15 307 = 4886 % of critical speed. View More Details.
### critical speed of cement mill peterohlenschlager.nl
Mill speed critical speed read more.What is crictal speed of cement grinding machine.Critical speed of ball mill calculation india.Technical notes 8 grinding r p king the critical speed of the mill c is defined as the figure 8 3 simplified calculation of the torque required to turn a mill to size a ball mill or rod mill.
### Critical Speed Of Ball Mill Nptel salento-kirchheim.de
The critical speed for a grinding mill is defined as the rotational speed where centrifugal forces equal gravitational forces at the mill shells inside surface.Ball mill slideshare.Nov 18, 2008.Introduction ball mill is an efficient tool for grinding many materials into fine.At a certain point, controlled by the mill speed.
### Ball Mill|Critical Speed Of Ball Mill From Wiki
22 rotation speed calculation of ball mill critical speed when the ball mill cylinder is rotated there is no relative slip between the grinding medium and the cylinder wall and it just starts to run in a state of rotation with the cylinder of the mill this instantaneous speed of the mill is as follows. Online Chat
### critical speed of ball mill formulae
critical speed of ball mill formulae csscontainers.be. The critical speed of the mill, &c, is defined as the speed at which a single ball, In equation 814, D is the diameter inside the mill liners and Le is the, Rod and ball mills in Mular AL and Bhappu R B Editors Mineral Processing Plant Designget price
### Small Ball Mill Henan Mining Machinery Co., Ltd
Small Ball Mill. We have Small Ball Mill,Browsing for small ball mill for sale the best online shopping experience is guaranteed 8730 small ball products from 2910 small ball suppliers on for sale are availabletalk with suppliers directly to customize your desired product and ask for the lowest price good discount and shipping fees
### why determination of critical speed of ball mill is
A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as speed varies.
### critical speed calculation ball mill 4229
Ball Mill Critical Speed Mineral Processing & Metallurgy. 2016/12/12· Ball Mill Power Calculation Example A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing ¼ inch (6350 microns).
### critical speed calculation ball mill 4229
Calculation of ball mill critical speed.Ball mill operating speed mechanical operations solved problems sep 11 2014 in a ball mill of diameter 2000 mm 100 mm dia steel balls are being used for aug 18 2016 ball mill rpm calculation mtm crusher the critical speed of ball mill is a mill ball mill ceramic ball mill critical speed
### critical speed of cement mill peterohlenschlager.nl
Mill speed critical speed read more.What is crictal speed of cement grinding machine.Critical speed of ball mill calculation india.Technical notes 8 grinding r p king the critical speed of the mill c is defined as the figure 8 3 simplified calculation of the torque required to turn a mill to size a ball mill or rod mill.
### Formula of critical speed of ball mill Henan Mining
The critical speed of ball mill is given by, where R = radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of 15 rpm Therefore, the mill is operated at 100 x 15 307 = 4886 % of critical speed. View More Details.
### critical speed of ball mill formulae
critical speed of ball mill formulae csscontainers.be. The critical speed of the mill, &c, is defined as the speed at which a single ball, In equation 814, D is the diameter inside the mill liners and Le is the, Rod and ball mills in Mular AL and Bhappu R B Editors Mineral Processing Plant Designget price
### Calculate Critical Ball johanklaps.be
Calculate ball mill critical speed. Calculate ball mill critical speed home calculate ball mill critical speed since november 1994 scambusters has helped over eleven million people protect themselves from scams scambusters is committed to helping you avoid getting read more from mill...
### mill critical speed Bouman Installatietechniek
CRITICAL SPEED OF THE BALL MILL VDChari. Aug 23 2018 · To maintain the position of the ball in the mill the condition C ≥ P should be satisfied if the angle becomes 90 o where D is in meters Generally the . Online Chat What it is the optimun speed for a ball mill.
### Torque Speed Calculation For Ball Mill wir-sind
2020-8-11 · Torque Speed Calculation For Ball Mill. Torque Speed Calculation For Ball Mill:Torque Speed Calculation For Ball Mill Ball mil design calculation yahoo answersar 31 2008 the critical speed rpm is given by nc 4229 d where d is the internal diameter in metres ball mills are normally operated at around 75 of critical speed so a mill with diameter 5 metres will turn at around 14 rpm the mill is
### Ball Mill|Critical Speed Of Ball Mill From Wiki
22 rotation speed calculation of ball mill critical speed when the ball mill cylinder is rotated there is no relative slip between the grinding medium and the cylinder wall and it just starts to run in a state of rotation with the cylinder of the mill this instantaneous speed of the mill is as follows. Online Chat
### porcelain ball mill charging calculation
2016/01/01 · A comparison of wear rates of ball mill grinding media.pdf Journal of Mining and Metallurgy 52 A (1) (2016 ) 110 # Corresponding author alex.jankovic . Chat Online; porcelain ball mill charging calculation. Porcelain Ball Mill Charging Calculation Porcelain Ball Mill Charging Calculation.
### critical speed calculation ball mill 4229
Ball Mill Critical Speed Mineral Processing & Metallurgy. 2016/12/12· Ball Mill Power Calculation Example A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing ¼ inch (6350 microns).
### critical speed calculation ball mill 4229
Calculation of ball mill critical speed.Ball mill operating speed mechanical operations solved problems sep 11 2014 in a ball mill of diameter 2000 mm 100 mm dia steel balls are being used for aug 18 2016 ball mill rpm calculation mtm crusher the critical speed of ball mill is a mill ball mill ceramic ball mill critical speed
### mill critical speed Bouman Installatietechniek
CRITICAL SPEED OF THE BALL MILL VDChari. Aug 23 2018 · To maintain the position of the ball in the mill the condition C ≥ P should be satisfied if the angle becomes 90 o where D is in meters Generally the . Online Chat What it is the optimun speed for a ball mill.
### Torque Speed Calculation For Ball Mill wir-sind
2020-8-11 · Torque Speed Calculation For Ball Mill. Torque Speed Calculation For Ball Mill:Torque Speed Calculation For Ball Mill Ball mil design calculation yahoo answersar 31 2008 the critical speed rpm is given by nc 4229 d where d is the internal diameter in metres ball mills are normally operated at around 75 of critical speed so a mill with diameter 5 metres will turn at around 14 rpm the mill is
### notes critical speed formula for ball mill in meters
critical speed of ball mill calculation ciitcoin (this point is called "Critical Speed" ball mills normally operate at 65% to by formula nC = 4229/vd (d is internal diameter in meters) a mill with diameter. notes critical speed formula for ball mill in meters.
### porcelain ball mill charging calculation
2016/01/01 · A comparison of wear rates of ball mill grinding media.pdf Journal of Mining and Metallurgy 52 A (1) (2016 ) 110 # Corresponding author alex.jankovic . Chat Online; porcelain ball mill charging calculation. Porcelain Ball Mill Charging Calculation Porcelain Ball Mill Charging Calculation.
### Calculation Of Grinding Media In Ball Mill In Delhi India
Critical Speed Of Ball Mill Calculation India ball mill circulating load ball mill critical speed calculation ball Ball Mill Charge Calculation In Hyderabad,India and Ball 19 Aug 2014 Cement Ball Mill Calculation Crusher In India 31 Oct 2014 Concement ball mill grinding media calculation The ball charge mill consists of unit
### calculation of wind mill for pumping water doc
what is the use of a coal ball mill. what is kraft mill silo calculation of wind mill for pumping water doc crushing what is kraft mill silo for mobile . Get Price. Water Pumping Windmills and Windmill Pumps are the low cost low wind speed solution for pumping large
### cost of a jaw crusher mining italy veiligheidsflitser.nl
crusher cost machineitaly Seaforth Lodge. Jaw Crusher Production Little Italylittle italy crusher and mill Manufacturer pe900 1200 jaw grinding alibaba Manufacturer pe900 1200 jaw below is the information about the supplier s.sellers of jaw crushers in nigeria Jaw crusher Sellers Of Crusher Plants In Italy Stone Crusher Cost in Germany a PE900 1200 Jaw Crusher,.
### SKD Crushing Equipment For Copper
Skd Gold Mining Equipment Ceramic Ball Mill Major mining equipment scale iron ore skd ball mill mc.Major mining equipment scale iron ore skd ball mill.As a leading global manufacturer of crushing and milling equipment, we offer advanced, rational solutions for any size-reduction requirements, including quarry, aggregate, grinding production | 3,303 | 15,082 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2020-40 | latest | en | 0.881703 |
http://www.brightstorm.com/qna/question/5316/ | 1,369,123,760,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699798457/warc/CC-MAIN-20130516102318-00023-ip-10-60-113-184.ec2.internal.warc.gz | 373,985,114 | 9,865 | Quick Homework Help
# 2yω - 16z ⚑ Flag
by patricia203 at June 04, 2010
2 y to the third
minus 16 z to the 3
So for this problem you have to take out 2 first so it would be 2(1y to the third - 8z to the third). After that, use the formula (x³-y³)= {x-y}*{x²+xy+y²} or (x³+y³)= {x+y}*{x²-xy+y²}. The final answer is 2{y-2z}*{y²+2yz+4z²}.
Harry_Singh June 05, 2010
Dont read the first one.First take out 2 first so it would be 2(y cube - 8 z cube). For these kind of questions you could use the formulas: (x cube - y cube)= {x-y}*{x square+xy + y square} or (x cube +y cube)= {x+y}*{x square-xy+y square}. The final answer is: 2{y-2z}*{y square+2yz+4z square}.
Harry_Singh June 05, 2010
2{y-2z}*{y square+2yz+4z square}.
gibby. June 06, 2010 | 314 | 759 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2013-20 | latest | en | 0.882106 |
https://aprove.informatik.rwth-aachen.de/eval/JAR06/JAR_TERM/TRS/nontermin/CSR/Ex8_BLR02.trs.Thm26:LPO:NO.html.lzma | 1,719,094,812,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862420.91/warc/CC-MAIN-20240622210521-20240623000521-00166.warc.gz | 85,806,498 | 2,038 | Term Rewriting System R:
[N, X, Y, XS]
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y)))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)
Termination of R to be shown.
` R`
` ↳Dependency Pair Analysis`
R contains the following Dependency Pairs:
FIB(N) -> SEL(N, fib1(s(0), s(0)))
FIB(N) -> FIB1(s(0), s(0))
FIB1(X, Y) -> FIB1(Y, add(X, Y))
SEL(s(N), cons(X, XS)) -> SEL(N, XS)
Furthermore, R contains three SCCs.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Argument Filtering and Ordering`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳Remaining`
Dependency Pair:
SEL(s(N), cons(X, XS)) -> SEL(N, XS)
Rules:
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y)))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)
The following dependency pair can be strictly oriented:
SEL(s(N), cons(X, XS)) -> SEL(N, XS)
There are no usable rules w.r.t. to the AFS that need to be oriented.
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
trivial
resulting in one new DP problem.
Used Argument Filtering System:
SEL(x1, x2) -> SEL(x1, x2)
s(x1) -> s(x1)
cons(x1, x2) -> cons(x1, x2)
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 4`
` ↳Dependency Graph`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳Remaining`
Dependency Pair:
Rules:
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y)))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)
Using the Dependency Graph resulted in no new DP problems.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳Argument Filtering and Ordering`
` →DP Problem 3`
` ↳Remaining`
Dependency Pair:
Rules:
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y)))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)
The following dependency pair can be strictly oriented:
There are no usable rules w.r.t. to the AFS that need to be oriented.
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
trivial
resulting in one new DP problem.
Used Argument Filtering System:
s(x1) -> s(x1)
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 5`
` ↳Dependency Graph`
` →DP Problem 3`
` ↳Remaining`
Dependency Pair:
Rules:
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y)))
sel(0, cons(X, XS)) -> X
sel(s(N), cons(X, XS)) -> sel(N, XS)
Using the Dependency Graph resulted in no new DP problems.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳AFS`
` →DP Problem 2`
` ↳AFS`
` →DP Problem 3`
` ↳Remaining Obligation(s)`
The following remains to be proven:
Dependency Pair:
FIB1(X, Y) -> FIB1(Y, add(X, Y))
Rules:
fib(N) -> sel(N, fib1(s(0), s(0)))
fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))) | 1,064 | 3,072 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-26 | latest | en | 0.628083 |
https://numberworld.info/123837 | 1,591,324,027,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348492427.71/warc/CC-MAIN-20200605014501-20200605044501-00294.warc.gz | 461,519,859 | 3,854 | Number 123837
Properties of number 123837
Cross Sum:
Factorization:
3 * 7 * 5897
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
1e3bd
Base 32:
3ott
sin(123837)
0.99156390671815
cos(123837)
-0.12961874437688
tan(123837)
-7.649849653188
ln(123837)
11.726721463724
lg(123837)
5.0928504225117
sqrt(123837)
351.90481667633
Square(123837)
Number Look Up
Look Up
123837 (one hundred twenty-three thousand eight hundred thirty-seven) is a amazing figure. The cross sum of 123837 is 24. If you factorisate the number 123837 you will get these result 3 * 7 * 5897. 123837 has 8 divisors ( 1, 3, 7, 21, 5897, 17691, 41279, 123837 ) whith a sum of 188736. 123837 is not a prime number. 123837 is not a fibonacci number. The number 123837 is not a Bell Number. The figure 123837 is not a Catalan Number. The convertion of 123837 to base 2 (Binary) is 11110001110111101. The convertion of 123837 to base 3 (Ternary) is 20021212120. The convertion of 123837 to base 4 (Quaternary) is 132032331. The convertion of 123837 to base 5 (Quintal) is 12430322. The convertion of 123837 to base 8 (Octal) is 361675. The convertion of 123837 to base 16 (Hexadecimal) is 1e3bd. The convertion of 123837 to base 32 is 3ott. The sine of the figure 123837 is 0.99156390671815. The cosine of 123837 is -0.12961874437688. The tangent of the number 123837 is -7.649849653188. The square root of 123837 is 351.90481667633.
If you square 123837 you will get the following result 15335602569. The natural logarithm of 123837 is 11.726721463724 and the decimal logarithm is 5.0928504225117. I hope that you now know that 123837 is very impressive number! | 622 | 1,785 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2020-24 | latest | en | 0.778084 |
http://nrich.maths.org/public/leg.php?code=-339&cl=2&cldcmpid=6862 | 1,505,971,067,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818687642.30/warc/CC-MAIN-20170921044627-20170921064627-00017.warc.gz | 251,423,712 | 8,778 | # Search by Topic
#### Resources tagged with Practical Activity similar to Reflector ! Rotcelfer:
Filter by: Content type:
Stage:
Challenge level:
### There are 183 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Practical Activity
### Making Maths: Indian Window Screen
##### Stage: 2 Challenge Level:
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
### Making Maths: Snowflakes
##### Stage: 2 Challenge Level:
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
### Making Maths: Five-point Snowflake
##### Stage: 2 Challenge Level:
Follow these instructions to make a five-pointed snowflake from a square of paper.
### Triangle Shapes
##### Stage: 1 and 2 Challenge Level:
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
### Turning Granny
##### Stage: 2 Challenge Level:
A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?
### World of Tan 11 - the Past, Present and Future
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of the telescope and microscope?
### World of Tan 7 - Gat Marn
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this plaque design?
### Little Boxes
##### Stage: 2 Challenge Level:
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
### World of Tan 9 - Animals
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this goat and giraffe?
### World of Tan 12 - All in a Fluff
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of these rabbits?
### World of Tan 18 - Soup
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
### World of Tan 19 - Working Men
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
### World of Tan 16 - Time Flies
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of the candle and sundial?
### World of Tan 15 - Millennia
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of the workmen?
### World of Tan 14 - Celebrations
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
### Fractional Triangles
##### Stage: 2 Challenge Level:
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
### World of Tan 20 - Fractions
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of the chairs?
### Making Maths: Test the Strength of a Triangle
##### Stage: 2 Challenge Level:
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
### Folding, Cutting and Punching
##### Stage: 2 Challenge Level:
Exploring and predicting folding, cutting and punching holes and making spirals.
### Making Maths: Make a Magic Circle
##### Stage: 2 Challenge Level:
Make a mobius band and investigate its properties.
### Triangle Relations
##### Stage: 2 Challenge Level:
What do these two triangles have in common? How are they related?
### Making Maths: Be a Mathemagician
##### Stage: 2 Challenge Level:
Surprise your friends with this magic square trick.
### Construct-o-straws
##### Stage: 2 Challenge Level:
Make a cube out of straws and have a go at this practical challenge.
### Square Corners
##### Stage: 2 Challenge Level:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
### Making Maths: Making a Tangram
##### Stage: 2 Challenge Level:
Follow these instructions to make a three-piece and/or seven-piece tangram.
### Making Maths: A-maze-ing
##### Stage: 2 Challenge Level:
Did you know mazes tell stories? Find out more about mazes and make one of your own.
### Making Maths: Rolypoly
##### Stage: 1 and 2 Challenge Level:
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
### World of Tan 22 - an Appealing Stroll
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of the child walking home from school?
### Jomista Mat
##### Stage: 2 Challenge Level:
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
### Two by One
##### Stage: 2 Challenge Level:
An activity making various patterns with 2 x 1 rectangular tiles.
### Hoops/rope
##### Stage: 2 Challenge Level:
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
### Let Us Reflect
##### Stage: 2 Challenge Level:
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
### Making Tangrams
##### Stage: 2 Challenge Level:
Here's a simple way to make a Tangram without any measuring or ruling lines.
### A Patchwork Piece
##### Stage: 2 Challenge Level:
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
### Advent Calendar 2006
##### Stage: 2 Challenge Level:
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
### Cutting Corners
##### Stage: 2 Challenge Level:
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
### It's a Tie
##### Stage: 2 Challenge Level:
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
### Sticks and Triangles
##### Stage: 2 Challenge Level:
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
### World of Tan 4 - Monday Morning
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
### World of Tan 6 - Junk
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this junk?
### World of Tan 26 - Old Chestnut
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
### World of Tan 25 - Pentominoes
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of these people?
### World of Tan 24 - Clocks
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of these clocks?
### Making Maths: Birds from an Egg
##### Stage: 2 Challenge Level:
Can you make the birds from the egg tangram?
### World of Tan 27 - Sharing
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Fung at the table?
### World of Tan 28 - Concentrating on Coordinates
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
### Two Squared
##### Stage: 2 Challenge Level:
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
### Two on Five
##### Stage: 1 and 2 Challenge Level:
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
### Making Maths: Stars
##### Stage: 2 Challenge Level:
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
### World of Tan 29 - the Telephone
##### Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this telephone? | 1,901 | 8,215 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2017-39 | latest | en | 0.838169 |
https://crypto.stackexchange.com/questions/87480/encryption-algorithms-that-require-more-work-to-decrypt-versus-encrypt | 1,713,745,315,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818067.32/warc/CC-MAIN-20240421225303-20240422015303-00127.warc.gz | 169,629,520 | 41,152 | # Encryption algorithms that require more work to decrypt versus encrypt?
Are there any encryption algorithms that require significantly more work to decrypt, versus the amount of work required to encrypt?
I'm looking for a method of fast encryption, but which will require much more CPU time to decrypt later, as a method of spam prevention (prevent people from decrypting too many files in a short amount of time).
One thing I should mention, is that the encryption key itself will be public knowledge.
I'm not trying to lock anyone out, I just want to force them to work before they can acquire data.
• Symmetric or asymmetric? Jan 12, 2021 at 8:16
• @forest Preferably symmetric, but I'm open to any ideas right now. (Early design stages.)
– poly
Jan 12, 2021 at 8:17
• This looks like an X/Y problem. What is the thing you're trying to do? Jan 12, 2021 at 8:19
• It looks like you should be looking for access control and rate control instead of increasing the work factor (which is almost sure to not work as well as you expect). Jan 12, 2021 at 9:23
• Bitcoin should have taught you that proof of work is a bad idea: motivated people will have enough work power, while normal users will be negatively impacted. It will most likely not solve your problem and just make your system use so much power that nobody in their right mind would want to use it. Jan 12, 2021 at 9:29
Since the encryption key is public knowledge, one simple method is to encrypt using a standard symmetric algorithm (such as AES), but randomize a portion of the encryption key.
For example, if you use AES-256, and the encryption key is published, but each individual encrypted file has 12 bits of the key overwritten with a random value (which is never saved or stored anywhere), so decrypting the file will require the decrypting device to brute-force the final 12 bits of the key.
The number of bits randomized, can be adjusted based on how quickly people are able to crack it, to hit whatever sweet-spot of required work you are looking for.
IMPORTANT:
It should be noted, as A. Hersean pointed out in the comments, that this method may have significant negative side effects:
... proof-of-work is a bad idea: motivated people will have enough work power, while normal users will be negatively impacted. It will most likely not solve your problem and just make your system use so much power that nobody would want to use it.
• Are you playing a game with your users? What the hell a normal user will want to this. Jan 12, 2021 at 9:19
• @kelalaka lol it's just a proof-of-work spam prevention methodology. If I design it well, the benefits will greatly outweigh the end-user costs.
– poly
Jan 12, 2021 at 9:21
• After users find out passwords for particular files, they would post passwords on some external web resource, so that the others benefit from it. Thus you will not slow your users down. Jan 12, 2021 at 17:23
• @mentallurg they would post passwords on some external web resource, so that the others benefit from it This would require universal cooperation from every single global user, and would provide no benefit with less than ~95% of users actively participating in the "password posting." (Even with 100% participation, the "benefit" is pretty minor.) As I mentioned in the main question comments, this work requirement is clearly not a complete solution, but just one layer of defense. Without additional safeguards alongside it, this probably won't provide the level of protection I'm looking for.
– poly
Jan 12, 2021 at 17:48 | 808 | 3,538 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-18 | latest | en | 0.954041 |
https://www.teacherspayteachers.com/Product/Parallel-and-Perpendicular-Lines-Quiz-3503507 | 1,513,273,341,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948545526.42/warc/CC-MAIN-20171214163759-20171214183759-00593.warc.gz | 789,515,831 | 23,639 | Total:
\$0.00
# Parallel and Perpendicular Lines Quiz
Subject
Resource Type
Product Rating
File Type
Word Document File
159 KB|2 pages
Share
Product Description
This quiz focuses on determining if lines are parallel, perpendicular, or neither and writing equations of lines that are parallel or perpendicular to a given line. The majority of the questions ask students to answer in slope intercept, one asks for standard, but this is a word document so you can edit if need be. A good majority of the questions are given in standard form so the students must put into slope intercept to find the slope.
Layout:There is a chart where students are listing the parallel and perpendicular slope, 2 questions each on writing equations of lines that are parallel and perpendicular, one question that wants equations for both scenarios, 6 problems that ask to identify the relationship, one question on the coordinate plane and students must find the relationship, and one questions with 3 lines that students must graph and identify their relationships.
I gauge this will take 35-40 minutes to complete.
Total Pages
2 pages
Not Included
Teaching Duration
N/A
Report this Resource
\$2.00
\$0.00
\$0.00
\$0.00
\$0.00
\$0.00
\$2.00 | 273 | 1,228 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2017-51 | longest | en | 0.904518 |
https://businessessayhelp.com/2022/09/12/a-market-trader-sells-ball-poi/ | 1,722,887,629,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640454712.22/warc/CC-MAIN-20240805180114-20240805210114-00538.warc.gz | 120,996,199 | 11,417 | # A market trader sells ball-poi
A market trader sells ball-point pens on his stall. He sells the pens for a different
fixed price, x pens, in each of six weeks. He notes the number of pens, y that he
sells in each of these six weeks. The results are shown in following table.
Week 1 2 3 4 5 6
Pens 10 15 20 25 30 35
Sells 68 60 55 48 38 32
a. Find the correlation coefficient between pens and sells and test the hypothesis
that there is no relation between these variables.
b. Find the regression equation of sells to pens
c. Estimate the weekly sells for 20 pens.
d. Estimate the Error.
# A market trader sells ball-poi
A market trader sells ball-point pens on his stall. He sells the pens for a differentfixed price, x pens, in each of six weeks. He notes the number of pens, y that hesells in each of these six weeks. The results are shown in following table.
Week 1 2 3 4 5 6 Pens 10 15 20 25 30 35 Sells 68 60 55 48 38 32
1. Find the regression equation of sells to pens
2. Estimate the weekly sells for 20 pens.
3. Estimate the Error.
# A market trader sells ball-poi
. 4 A market trader sells ball-point pens on his stall. He sells the pens for a different fixed price, x pens, in each of six weeks. He notes the number of pens, y that he sells in each of these six weeks. The results are shown in following table.
Week 1 2 3 4 5 6 Pens 10 15 20 25 30 35 Sells 68 60 55 48 38 32
1. Find the correlation coefficient between pens and sells and test the hypothesis that there is no relation between these variables.
2. Find the regression equation of sells to pens
3. Estimate the weekly sells for 20 pens.
4. Estimate the Error.
# A market trader sells ball-poi
A market trader sells ball-point pens on his stall. He sells the pens for a differentfixed price, x pens, in each of six weeks. He notes the number of pens, y that hesells in each of these six weeks. The results are shown in following table.
Week 1 2 3 4 5 6 Pens 10 15 20 25 30 35 Sells 68 60 55 48 38 32
1. Find the correlation coefficient between pens and sells and test the hypothesis that there is no relation between these variables.
2. Find the regression equation of sells to pens
3. Estimate the weekly sells for 20 pens.
4. Estimate the Error.
## Calculate the price of your order
550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)
# Our guarantees
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
### Money-back guarantee
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
### Zero-plagiarism guarantee
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
### Free-revision policy
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result. | 930 | 3,624 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2024-33 | latest | en | 0.90227 |
https://studyres.com/doc/9470856/level-2-3-test-2---st-wilfrids-community | 1,670,604,198,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711417.46/warc/CC-MAIN-20221209144722-20221209174722-00104.warc.gz | 574,251,299 | 8,619 | Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Document related concepts
Ethnomathematics wikipedia , lookup
Elementary mathematics wikipedia , lookup
Transcript
```St Wilfrid’s Catholic Primary School
2-3 Test 2
Maths Basic Skills
Level
Name ___________________________
Date______________________________
Class_____________________________
Section A: Counting and understanding numbers
Section B: Calculating
Section C: Using and applying
2.1
2.6
1. How many groups of five can be
2.2 2. Put these numbers in order,
starting with the smallest:
29 , 12 , 37 , 24
2.3 3. Write the missing numbers in
this sequence:
3 , 6 , 9 , ... , 15 , 18 , ...
11.
2.4
2.9
4. How many two pence coins are
equal to sixteen pence?
14. Joe saves 28p. His friend gives him
31p. How much does he have now?
2.5
2.10
5. How many halves are in 6 whole
ones?
15. 4 boys have 6 sweets each. How
many sweets do they have altogether?
3.1
3.7
6. What number is three less than five
hundred and one?
16. Divide 120 by 3.
3.2
3.8
7. What temperature is 6 degrees less
than 4 degrees Celsius?
17.
3.3
3.9
8. Write down the next two numbers.
22 , 27 , 32 , ... , ...
18. Subtract thirty-two from sixty-five.
3.4
3.10
9. What is one-third of twenty-four?
19. What must be added to eightythree to make one hundred?
3.6
3.11
10. Multiply six by three.
20. One orange costs sixteen pence.
How much will four oranges cost?
Total (A)
Test Total (A+B+C)
18 +
= 25
12. I think of a number and half it.
What was my number?
2.7
21. A film starts at three o’clock and
ends at five o’clock.
How many minutes does the film
last?
2.8
13. What must be added to 60 to
make one hundred?
7 x 6 = 30 + ?
Total (B)
R (0-9)
22. Susan has 54p.
Mary has 22p more than her.
How much do they have altogether?
23. How many millimetres are in
eight and a half centimetres?
24. I had one pound. I bought two
chocolate bars and got ten pence
change.
How much did each chocolate bar
cost?
25. Ben saved seventeen 10p
coins and two 20p coins.
How much money has Ben
saved?
Total (C)
Y (10-19)
G (20-25)
```
Related documents | 652 | 2,152 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2022-49 | longest | en | 0.909957 |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Integer_square_root | 1,621,307,325,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991650.73/warc/CC-MAIN-20210518002309-20210518032309-00380.warc.gz | 1,150,854,329 | 9,791 | # Integer square root
In number theory, the integer square root (isqrt) of a positive integer n is the positive integer m which is the greatest integer less than or equal to the square root of n,
${\displaystyle {\mbox{isqrt}}(n)=\lfloor {\sqrt {n}}\rfloor .}$
For example, ${\displaystyle {\mbox{isqrt}}(27)=5}$ because ${\displaystyle 5\cdot 5=25\leq 27}$ and ${\displaystyle 6\cdot 6=36>27}$ .
## Algorithm using Newton's method
One way of calculating ${\displaystyle {\sqrt {n}}}$ and ${\displaystyle {\mbox{isqrt}}(n)}$ is to use Newton's method to find a solution for the equation ${\displaystyle x^{2}-n=0}$ , giving the iterative formula
${\displaystyle {x}_{k+1}={\frac {1}{2}}\left(x_{k}+{\frac {n}{x_{k}}}\right),\quad k\geq 0,\quad x_{0}>0.}$
The sequence ${\displaystyle \{x_{k}\}}$ converges quadratically to ${\displaystyle {\sqrt {n}}}$ as ${\displaystyle k\to \infty }$ . It can be proven that if ${\displaystyle x_{0}=n}$ is chosen as the initial guess, one can stop as soon as
${\displaystyle |x_{k+1}-x_{k}|<1}$
to ensure that ${\displaystyle \lfloor x_{k+1}\rfloor =\lfloor {\sqrt {n}}\rfloor .}$
### Using only integer division
For computing ${\displaystyle \lfloor {\sqrt {n}}\rfloor }$ for very large integers n, one can use the quotient of Euclidean division for both of the division operations. This has the advantage of only using integers for each intermediate value, thus making the use of floating point representations of large numbers unnecessary. It is equivalent to using the iterative formula
${\displaystyle {x}_{k+1}=\left\lfloor {\frac {1}{2}}\left(x_{k}+\left\lfloor {\frac {n}{x_{k}}}\right\rfloor \right)\right\rfloor ,\quad k\geq 0,\quad x_{0}>0,\quad x_{0}\in \mathbb {Z} .}$
By using the fact that
${\displaystyle \left\lfloor {\frac {1}{2}}\left(x_{k}+\left\lfloor {\frac {n}{x_{k}}}\right\rfloor \right)\right\rfloor =\left\lfloor {\frac {1}{2}}\left(x_{k}+{\frac {n}{x_{k}}}\right)\right\rfloor ,}$
one can show that this will reach ${\displaystyle \lfloor {\sqrt {n}}\rfloor }$ within a finite number of iterations.
However, ${\displaystyle \lfloor {\sqrt {n}}\rfloor }$ is not necessarily a fixed point of the above iterative formula. Indeed, it can be shown that ${\displaystyle \lfloor {\sqrt {n}}\rfloor }$ is a fixed point if and only if ${\displaystyle n+1}$ is not a perfect square. If ${\displaystyle n+1}$ is a perfect square, the sequence ends up in a period-two cycle between ${\displaystyle \lfloor {\sqrt {n}}\rfloor }$ and ${\displaystyle \lfloor {\sqrt {n}}\rfloor +1}$ instead of converging. For termination, it suffices to check that either the number has converged or it has increased by exactly one from the previous step, in which case the new result is discarded.
### Domain of computation
Although ${\displaystyle {\sqrt {n}}}$ is irrational for many ${\displaystyle n}$ , the sequence ${\displaystyle \{x_{k}\}}$ contains only rational terms when ${\displaystyle x_{0}}$ is rational. Thus, with this method it is unnecessary to exit the field of rational numbers in order to calculate ${\displaystyle {\mbox{isqrt}}(n)}$ , a fact which has some theoretical advantages.
### Stopping criterion
One can prove that ${\displaystyle c=1}$ is the largest possible number for which the stopping criterion
${\displaystyle |x_{k+1}-x_{k}|
ensures ${\displaystyle \lfloor x_{k+1}\rfloor =\lfloor {\sqrt {n}}\rfloor }$ in the algorithm above.
In implementations which use number formats that cannot represent all rational numbers exactly (for example, floating point), a stopping constant less than one should be used to protect against roundoff errors.
## Digit-by-digit algorithm
The traditional pen-and-paper algorithm for computing the square root ${\displaystyle {\sqrt {n}}}$ is based on working from higher digit places to lower, and as each new digit pick the largest that will still yield a square ${\displaystyle \leq n}$ . If stopping after the one's place, the result computed will be the integer square root.
### Using bitwise operations
If working in base 2, the choice of digit is simplified to that between 0 (the "small candidate") and 1 (the "large candidate"), and digit manipulations can be expressed in terms of binary shift operations. With * being multiplication, << being left shift, and >> being logical right shift, a recursive algorithm to find the integer square root of any natural number is:
function integerSqrt(n):
if n < 0:
error "integerSqrt works for only nonnegative inputs"
else if n < 2:
return n
else:
# Recursive call:
smallCandidate = integerSqrt(n >> 2) << 1
largeCandidate = smallCandidate + 1
if largeCandidate*largeCandidate > n:
return smallCandidate
else:
return largeCandidate
function integerSqrt(n):
if n < 0:
error "integerSqrt works for only nonnegative inputs"
# Find greatest shift.
shift = 2
nShifted = n >> shift
# We check for nShifted being n, since some implementations
# perform shift operations modulo the word size.
while nShifted ≠ 0 and nShifted ≠ n:
shift = shift + 2
nShifted = n >> shift
shift = shift - 2
# Find digits of result.
result = 0
while shift ≥ 0:
result = result << 1
candidateResult = result + 1
if candidateResult*candidateResult ≤ n >> shift:
result = candidateResult
shift = shift - 2
return result
Traditional pen-and-paper presentations of the digit-by-digit algorithm include various optimisations not present in the code above, in particular the trick of presubtracting the square of the previous digits which makes a general multiplication step unnecessary. | 1,514 | 5,537 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 34, "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} | 4.6875 | 5 | CC-MAIN-2021-21 | latest | en | 0.739378 |
https://www.reference.com/web?q=easy+way+to+convert+kilometers+to+miles&qo=relatedSearchBing&o=600605&l=dir | 1,558,454,444,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256426.13/warc/CC-MAIN-20190521142548-20190521164548-00241.warc.gz | 907,247,615 | 14,638 | https://www.mnn.com/earth-matters/wilderness-resources/blogs/more-ways-to-convert-between-miles-and-kilometers
Sep 9, 2011 ... A few of you chimed in with your own cool tricks to convert between miles and kilometers. I want to share the best of them here, each are ...
Mar 10, 2016 ... Converting kilometers to miles in your head is easy if you know the trick!
https://www.thecalculatorsite.com/articles/units/convert-kilometers-to-miles.php
Jul 18, 2016 ... Learn the tricks for how to convert between kilometers and miles and check your figures with our converter.
Actual answer = 3.107 miles - close enough to 3.125 for me. 1.5k views ... What are some ways of converting kilometers to megameters? ... Since 10/16 = 10/(4×4 ), multiply by 10 (easy decimal shift) and divide by 4 twice.
https://www.wikihow.com/Convert-Kilometers-to-Miles
Apr 18, 2019 ... It's a fairly easy mathematical equation to convert kilometers to miles, or vice versa. ... There is a way you can do the calculation in your head.
https://www.quickanddirtytips.com/education/math/how-convert-miles-kilometers
Sep 27, 2011 ... Either way, it can be confusing. But the good news is that it's easy to do the unit conversion in your head...and this post contains ... To convert distances in miles into distances in kilometers (or speeds in miles per hour into ...
https://sciencing.com/convert-kilometers-miles-4424080.html
Oct 15, 2018 ... A simple km to miles formula is all it takes to convert kilometers into the ... The simplest way to do this is to perform the inverse of the operation ...
https://www.metric-conversions.org/length/kilometers-to-miles.htm
Kilometers to Miles (km to miles) conversion calculator for Length conversions with additional tables and formulas.
https://www.inchcalculator.com/convert/mile-to-kilometer/
Convert miles to kilometers (mi to km) with the length conversion calculator, and learn the mile to kilometer calculation formula.
https://www.inchcalculator.com/convert/kilometer-to-mile/
Convert kilometers to miles (km to mi) with the length conversion calculator, and learn the kilometer to mile calculation formula. | 524 | 2,143 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2019-22 | latest | en | 0.83535 |
https://quant.stackexchange.com/questions/tagged/wienerprocess?sort=active | 1,561,498,855,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999948.3/warc/CC-MAIN-20190625213113-20190625235113-00280.warc.gz | 577,466,766 | 29,680 | # Questions tagged [wienerprocess]
The tag has no usage guidance.
24 questions
68 views
### Can anyone explain to how Hull get's from the stock returns to continuously compounded stock returns?
I'm reading Chapter 13 of Hull's book and am stuck on how he got from stock returns to continuously compounded stock returns. As a recap, he built the generalized Wiener Process, which describes a ...
151 views
61 views
342 views
### Determine $E[W_p W_q W_r]$
Given prob space $(\Omega, \mathscr{F}, P)$ and a Wiener process $(W_t)_{t \geq 0}$, define filtration $\mathscr{F}_t = \sigma(W_u : u \leq t)$ Let 0 < p < q < r. Determine $E[W_p W_q W_r]$. ...
3k views
### How to calculate the expected value of a function of a standard brownian motion (Wiener process)
Have a problem regarding the expected value of the Wiener process inside a function, namely: Compute $E[cos(W_t)]$. To extend my question, what is the general method of computing these E´s when it ... | 250 | 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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2019-26 | latest | en | 0.816141 |
https://teamtreehouse.com/community/this-is-how-i-did-the-reverse-game-i-want-to-add-1-more-functionality-can-anyone-give-me-a-tip | 1,621,055,329,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989812.47/warc/CC-MAIN-20210515035645-20210515065645-00405.warc.gz | 587,524,756 | 23,701 | # This is how I did the reverse game! I want to add 1 more functionality. Can anyone give me a tip?
I made a loop. In the loop a random_number will be generated and tested if it is equal to my secret_number argument. If the guess is wrong I print out the random_number that the computer guessed and whether it is higher or lower than my secret_number. How can I depending on the first iteration make the computer guess a lower/higher random_number than the random_number in the next iteration?
```import random
def game(secret_number):
guesses_left = 5
print("Hey computer, can you beat me by guessing the nummer I have in mind? You will receive {} guesses, good luck!".format(guesses_left))
while guesses_left > 1:
random_number = random.randint(1, 10)
if random_number == secret_number:
print("Yo computer, {} is the correct answer! Good job!".format(random_number))
break
elif random_number < secret_number:
guesses_left -= 1
print("{} is lower than what I have in mind, try again! You have {} guesses left.".format(random_number, guesses_left))
else:
guesses_left -= 1
print("{} is higher than what I have in mind, try again! You have {} guesses left.".format(random_number, guesses_left))
else:
print("Game over! You didn't guess the number in the amount of guesses available.")
play_again = input("Fancy another game? Enter yes or no: ")
if play_again.lower() == "yes":
game(6)
else:
print("Okay! Have a nice day!")
game(6)
```
MOD
One way would be to track the range of targeted guesses with variables, such as, `lower_limit` and `upper_limit`.
• Initially set these values to the limits of your initial range: 1 and 10
• Then replace the random guess to use these limits: `random_number = random.randint(lower_limit, upper_limit)`
• Finally, based on the guess being too low or too high, use the previous guess to update the appropriate value of `lower_limit` or `upper_limit`
Post back if you have more questions. Good luck!!
Do I need to declare the lower and upper like this: lower_limit = 1 upper_limit = 10
then : random_number = random.randint(lower_limit, upper_limit)
Isn't that the same as passing 1, 10? I can't see how it will give me a lower or higher random number?
Also I have no idea how i can apply your third bulletpoint. Specifically I don't know how I can do something else with the next iteration.
```Do I need to declare the lower and upper like this: lower_limit = 1 upper_limit = 10 then : random_number = random.randint(lower_limit, upper_limit)```. Correct.
`Isn't that the same as passing 1, 10? I can't see how it will give me a lower or higher random number?` Be sure to place the original assignment to `lower_limit` and `upper_limit` outside of the loop. That way as these limits get changed, the random number will too.
`Also I have no idea how i can apply your third bulletpoint. Specifically I don't know how I can do something else with the next iteration.` If the random_number is less that the secret number set `lower_limit = random_number`. If the random number is higher, set `higher_limit = random_number`.
Awesome, it worked. the logic is still a bit vague to me though. I'm not sure how a lower/higher number is generated depending on the previous guess.
The random_number sometimes gives the same number but less/higher than the previous number. so i changed the operater accordingly.
thanks for the help! | 792 | 3,377 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-21 | latest | en | 0.845439 |
https://isabelle.in.tum.de/repos/testboard/comparison/21c0b3a9d2f8/src/HOL/List.thy | 1,632,778,616,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058552.54/warc/CC-MAIN-20210927211955-20210928001955-00413.warc.gz | 378,031,125 | 2,610 | src/HOL/List.thy
changeset 71656 21c0b3a9d2f8 parent 71647 d8fb621fea02 child 71781 4b1021677f15
equal inserted replaced
71655:ff6394cfc05c 71656:21c0b3a9d2f8
` 5170 `
` 5170 `
` 5171 lemma sorted_wrt_map:`
` 5171 lemma sorted_wrt_map:`
` 5172 "sorted_wrt R (map f xs) = sorted_wrt (\<lambda>x y. R (f x) (f y)) xs"`
` 5172 "sorted_wrt R (map f xs) = sorted_wrt (\<lambda>x y. R (f x) (f y)) xs"`
` 5173 by (induction xs) simp_all`
` 5173 by (induction xs) simp_all`
` 5174 `
` 5174 `
` `
` 5175 lemma`
` `
` 5176 assumes "sorted_wrt f xs"`
` `
` 5177 shows sorted_wrt_take: "sorted_wrt f (take n xs)"`
` `
` 5178 and sorted_wrt_drop: "sorted_wrt f (drop n xs)"`
` `
` 5179 proof -`
` `
` 5180 from assms have "sorted_wrt f (take n xs @ drop n xs)" by simp`
` `
` 5181 thus "sorted_wrt f (take n xs)" and "sorted_wrt f (drop n xs)"`
` `
` 5182 unfolding sorted_wrt_append by simp_all`
` `
` 5183 qed`
` `
` 5184 `
` `
` 5185 lemma sorted_wrt_filter:`
` `
` 5186 "sorted_wrt f xs \<Longrightarrow> sorted_wrt f (filter P xs)"`
` `
` 5187 by (induction xs) auto`
` `
` 5188 `
` 5175 lemma sorted_wrt_rev:`
` 5189 lemma sorted_wrt_rev:`
` 5176 "sorted_wrt P (rev xs) = sorted_wrt (\<lambda>x y. P y x) xs"`
` 5190 "sorted_wrt P (rev xs) = sorted_wrt (\<lambda>x y. P y x) xs"`
` 5177 by (induction xs) (auto simp add: sorted_wrt_append)`
` 5191 by (induction xs) (auto simp add: sorted_wrt_append)`
` 5178 `
` 5192 `
` 5179 lemma sorted_wrt_mono_rel:`
` 5193 lemma sorted_wrt_mono_rel:` | 646 | 1,628 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2021-39 | latest | en | 0.421251 |
https://yo.wikipedia.org/wiki/%E1%BA%B8y%E1%BB%8D_t%C3%ADk%C3%B2s%C3%AD | 1,721,447,978,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514981.25/warc/CC-MAIN-20240720021925-20240720051925-00110.warc.gz | 952,512,856 | 19,919 | Ẹyọ tíkòsí
Àwọn nọ́mbà nínú ìmọ̀ mathematiki
Basic
${\displaystyle \mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} }$
Nọ́mbà àdábáyé ${\displaystyle \mathbb {N} }$
Nọ́mbà alòdì
Nọ́mbà odidi ${\displaystyle \mathbb {Z} }$
Nọ́mbà oníìpín ${\displaystyle \mathbb {Q} }$
Nọ́mbà aláìníìpín
Nọ́mbà gidi ${\displaystyle \mathbb {R} }$
Nọ́mbà tíkòsí ${\displaystyle \mathbb {I} }$
Nọ́mbà tóṣòro ${\displaystyle \mathbb {C} }$
Nomba aljebra ${\displaystyle \mathbb {A} }$
Nọ́mbà tíkòlónkà
Complex extensions
Quaternions ${\displaystyle \mathbb {H} }$
Octonions ${\displaystyle \mathbb {O} }$
Sedenions ${\displaystyle \mathbb {S} }$
Cayley-Dickson construction
Split-complex numbers ${\displaystyle \mathbb {R} ^{1,1}}$
Bicomplex numbers
Biquaternions
Coquaternions
Tessarines
Hypercomplex numbers
Other extensions
Other
Nominal numbers
Serial numbers
Ordinal numbers
Cardinal numbers
Nomba akoko
Constructible numbers
Computable numbers
Integer sequences
Mathematical constants
Large numbers
π = 3.141592654…
e = 2.718281828…
i (Imaginary unit) ${\displaystyle i^{2}=-1}$
∞ (infinity)
This box: view talk edit
Ninu mathimatiki, ẹyọ tíkòsí (imaginary unit) n fun sistemu nomba gidi ${\displaystyle \mathbb {R} }$ laye lati fe de sistemu nomba sisoro ${\displaystyle \mathbb {C} }$ . O se ko sile pelu i tabi j tabi leta Greek iota. | 534 | 1,376 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/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-2024-30 | latest | en | 0.176227 |
http://mathhelpforum.com/calculus/164886-finding-area-enclosed-integral-x-axis.html | 1,524,794,524,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125948738.65/warc/CC-MAIN-20180427002118-20180427022118-00244.warc.gz | 188,708,408 | 9,983 | # Thread: Finding area enclosed by integral and x-axis
1. ## Finding area enclosed by integral and x-axis
Find the area enclosed by the graph of definite integral [4(x^3-3x^2+2x)dx] (a=0, b=2) and the x-axis. The first part of this question asked to evaluate the definite integral for which i got 0 and i thought you would find the area the same way but the last part asks you to explain why the two answers aren't the same!
2. If you graph the equation, you will see that an equal portion lies in the negative y axis and the positive. When you run the integral from 0 to 1 and 1 to 2, you will get the area correct.
See graph
3. Note that area,whether above or below the axis, is always positive.
Integrating $\displaystyle \int_a^b f(x)dx$ will give the area between the graph of f(x) and the x-axis only if f(x) is non-negative between a and b.
By the way, your phrasing is rather peculiar. This is not the area between an integral and the x-axis, it is the area between a graph and the x-axis. And not the "graph of the definite integral". A definite integral is always a number and has no "graph". You are asking for the area between the graph of y= 4(x^3-3x^2+2x) and the x-axis and you find that by taking the definite integral (and being careful of the sign as I say). | 334 | 1,283 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2018-17 | latest | en | 0.938217 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.