text
stringlengths 18
50k
| id
stringlengths 6
138
| metadata
dict |
|---|---|---|
Quarrying is necessary to provide much of the materials used in traditional hard flooring, such as granite, limestone, marble, sandstone, slate and even just clay to make ceramic tiles. However, like many other man-made activities, quarrying causes a significant impact on the environment. In particular, it is often necessary to blast rocks with explosives in order to extract material for processing but this method of extraction gives rise to including noise pollution, air pollution, damage to biodiversity and habitat destruction.
Dust from quarry sites is a major source of air pollution, although the severity will depend on factors like the local microclimate conditions, the concentration of dust particles in the ambient air, the size of the dust particles and their chemistry, for example limestone quarries produce highly alkaline (and reactive) dusts, whereas coal mines produce acidic dust.
The air pollution is not only a nuisance (in terms of deposition on surfaces) and possible effects on health, in particular for those with respiratory problems but dust can also have physical effects on the surrounding plants, such as blocking and damaging their internal structures and abrasion of leaves and cuticles, as well as chemical effects which may affect long-term survival.
Unfortunately, quarrying involves several activities that generate significant amounts of noise. It starts with the preparatory activities, such as establishing road or rail access, compound and even mineral processing facilities. Next is the process of exposing the mineral to be extracted and this is usually done by removing the top soil and other soft layers using a scraper, or hydraulic excavators and dump trucks. The excavation of the mineral itself will involve considerable noise, particularly is blasting methods are used. Following this, the use of powered machinery to transport the materials as well as possibly processing plants to crush and grade the minerals, all contribute even more noise to the environment.
Damage to Biodiversity
One of the biggest negative impacts of quarrying on the environment is the damage to biodiversity. Biodiversity essentially refers to the range of living species, including fish, insects, invertebrates, reptiles, birds, mammals, plants, fungi and even micro-organisms. Biodiversity conservation is important as all species are interlinked, even if this is not immediately visible or even known, and our survival depends on this fine balance that exists within nature.
Quarrying carries the potential of destroying habitats and the species they support. Even if the habitats are not directly removed by excavation, they can be indirectly affected and damaged by environmental impacts – such as changes to ground water or surface water that causes some habitats to dry out or others to become flooded. Even noise pollution can have a significant impact on some species and affect their successful reproduction. Nevertheless, with careful planning and management, it is possible to minimise the effect on biodiversity and in fact, quarries can also provide a good opportunity to create new habitats or to restore existing ones.
Again, like many other man-made activities, quarrying involves the production of significant amounts of waste. Some types of quarries do not produce large amounts of permanent waste, such as sand and gravel quarries, whereas others will produce significant amounts of waste material such as clay and silt. The good news is that they are generally inert and non-hazardous, unlike the waste from many other processes. However, there is still potential for damage to the environment, particularly with water contamination.
For example, suspended particles – even though they are chemically inert – may imbalance freshwater ecosystems. Large amounts of solids can also exacerbate flooding, if it is dumped on the flood plains. Lastly, the accumulation of waste by-products will still need to be stored and managed somewhere that will not affect the environment in an adverse manner. Furthermore, the treatment and disposal of the waste may produce more negative impacts on the environment.
While quarries can cause significant impact to the environment, with the right planning and management, many of the negative effects can be minimised or controlled and in many cases, there is great opportunity to protect and enhance the environment, such as with the translocation of existing habitats or the creation of new ones. | <urn:uuid:8fae07c8-9c8c-4977-ae2b-fc7f5497eda0> | {
"date": "2023-12-08T22:36:54",
"dump": "CC-MAIN-2023-50",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100779.51/warc/CC-MAIN-20231208212357-20231209002357-00756.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9483973979949951,
"score": 4.03125,
"token_count": 833,
"url": "https://sustainablebuild.co.uk/the-impact-of-quarrying/"
} |
# Node Voltage Analysis
## Homework Statement
Determine the node voltages, Va and Vb of this circuit:
http://img198.imageshack.us/i/circuitx.jpg/
## The Attempt at a Solution
Node a: 3 V - Va/4 + (Va - Vb)/2 = 0
3 - Va/4 + 2Va/4 - 2Vb/4 = 0
3 + Va/4 - 2Vb/4 = 0
--> 12 + Va - 2Vb = 0
Node b: Vb/3 - 4 - (Va - Vb)/2 = 0
2Vb/6 - 4 - 3Va/6 + 3Vb/6 = 0
---> -24 - 3Va + 5Vb = 0
Combining two equations yields:
-24 - 3Va + 5Vb
3(12 + Va - 2Vb)
12 - Vb = 0
Vb = 12 V
- 24 - 3Va + 5(12) = 0
Va = 12 V
According to the book, my answer is wrong. What am I doing wrong??
## Answers and Replies
gneill
Mentor
Your node equations are not being consistent with the assumed directions of currents (what sign to assign to incoming versus outgoing currents from a node).
I find it's easier to always assume that currents are flowing out of a node unless it is a current source that leaves one no choice. The mathematics takes care of sorting out the actual directions via the node voltages it determines. So, for example, I would write:
Node a: -3A - Va/4Ω - (Va - Vb)/2Ω = 0 ............ No choice for the -3A flowing out of Node a
Node b: +4A - Vb/3Ω - (Vb - Va)/2Ω = 0 ........... No choice for the +4A flowing into Node b
Note how the (Va - Vb) term changes "direction" when looking from Node b towards Node a, versus looking towards Node b from Node a.
So, at any given node, to write the "outgoing" current for a branch, simply take the node's voltage and subtract the voltage of the next node over, and divide by the intervening resistance. | crawl-data/CC-MAIN-2021-31/segments/1627046155188.79/warc/CC-MAIN-20210804205700-20210804235700-00596.warc.gz | null |
ARC Protection Explained
ARC protection is typically designed for electrical industry, specifically those workers who are involved in tasks that expose them to electrical hazards such as electricians, electrical engineers, linemen, and others who work with or around high-voltage electrical equipment.
ARC protection, also known as arc flash protection, is designed to protect workers from the thermal effects of an electric arc, which can generate extreme heat, intense light, and pressure waves that can cause serious injury or even death. The protection typically includes personal protective equipment (PPE) such as flame-resistant clothing, gloves, and face shields that can withstand the high temperatures and energy released during an arc flash incident. (Read more about what an ARC Flash is here)
Other industries where workers may also require ARC protection include the oil and gas industry, chemical plants, and other industrial settings where workers are exposed to electrical hazards.
ARC Protection Standards
Performance requirements for protective clothing against the thermal hazards of an electric arc is covered in the EN 61482 series . Divided into two methods:
EN 61482-1-1: Open ARC Method, popular in the American industries
EN 61482-1-2: Box Test Method, which is Mandatory for the European Market | <urn:uuid:22d1b60c-0e0d-4868-9dde-c16e8b8d820a> | {
"date": "2023-09-26T06:06:14",
"dump": "CC-MAIN-2023-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510149.21/warc/CC-MAIN-20230926043538-20230926073538-00558.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9396977424621582,
"score": 3.59375,
"token_count": 253,
"url": "https://apparelsupply.ie/electrical-knowledge-base-2/"
} |
Mass and length may not be fundamental properties of nature, according to new ideas bubbling out of the multiverse.
Though galaxies look larger than atoms and elephants appear to outweigh ants, some physicists have begun to suspect that size differences are illusory. Perhaps the fundamental description of the universe does not include the concepts of “mass” and “length,” implying that at its core, nature lacks a sense of scale.
This little-explored idea, known as scale symmetry, constitutes a radical departure from long-standing assumptions about how elementary particles acquire their properties. But it has recently emerged as a common theme of numerous talks and papers by respected particle physicists. With their field stuck at a nasty impasse, the researchers have returned to the master equations that describe the known particles and their interactions, and are asking: What happens when you erase the terms in the equations having to do with mass and length?
Nature, at the deepest level, may not differentiate between scales. With scale symmetry, physicists start with a basic equation that sets forth a massless collection of particles, each a unique confluence of characteristics such as whether it is matter or antimatter and has positive or negative electric charge. As these particles attract and repel one another and the effects of their interactions cascade like dominoes through the calculations, scale symmetry “breaks,” and masses and lengths spontaneously arise.
Similar dynamical effects generate 99 percent of the mass in the visible universe. Protons and neutrons are amalgams — each one a trio of lightweight elementary particles called quarks. The energy used to hold these quarks together gives them a combined mass that is around 100 times more than the sum of the parts. “Most of the mass that we see is generated in this way, so we are interested in seeing if it’s possible to generate all mass in this way,” said Alberto Salvio, a particle physicist at the Autonomous University of Madrid and the co-author of a recent paper on a scale-symmetric theory of nature.
In the equations of the “Standard Model” of particle physics, only a particle discovered in 2012, called the Higgs boson, comes equipped with mass from the get-go. According to a theory developed 50 years ago by the British physicist Peter Higgs and associates, it doles out mass to other elementary particles through its interactions with them. Electrons, W and Z bosons, individual quarks and so on: All their masses are believed to derive from the Higgs boson — and, in a feedback effect, they simultaneously dial the Higgs mass up or down, too.
The new scale symmetry approach rewrites the beginning of that story.
“The idea is that maybe even the Higgs mass is not really there,” said Alessandro Strumia, a particle physicist at the University of Pisa in Italy. “It can be understood with some dynamics.”
The concept seems far-fetched, but it is garnering interest at a time of widespread soul-searching in the field. When the Large Hadron Collider at CERN Laboratory in Geneva closed down for upgrades in early 2013, its collisions had failed to yield any of dozens of particles that many theorists had included in their equations for more than 30 years. The grand flop suggests that researchers may have taken a wrong turn decades ago in their understanding of how to calculate the masses of particles.
“We’re not in a position where we can afford to be particularly arrogant about our understanding of what the laws of nature must look like,” said Michael Dine, a professor of physics at the University of California, Santa Cruz, who has been following the new work on scale symmetry. “Things that I might have been skeptical about before, I’m willing to entertain.”
The Giant Higgs Problem
The scale symmetry approach traces back to 1995, when William Bardeen, a theoretical physicist at Fermi National Accelerator Laboratory in Batavia, Ill., showed that the mass of the Higgs boson and the other Standard Model particles could be calculated as consequences of spontaneous scale-symmetry breaking. But at the time, Bardeen’s approach failed to catch on. The delicate balance of his calculations seemed easy to spoil when researchers attempted to incorporate new, undiscovered particles, like those that have been posited to explain the mysteries of dark matter and gravity.
Instead, researchers gravitated toward another approach called “supersymmetry” that naturally predicted dozens of new particles. One or more of these particles could account for dark matter. And supersymmetry also provided a straightforward solution to a bookkeeping problem that has bedeviled researchers since the early days of the Standard Model.
In the standard approach to doing calculations, the Higgs boson’s interactions with other particles tend to elevate its mass toward the highest scales present in the equations, dragging the other particle masses up with it. “Quantum mechanics tries to make everybody democratic,” explained theoretical physicist Joe Lykken, deputy director of Fermilab and a collaborator of Bardeen’s. “Particles will even each other out through quantum mechanical effects.”
This democratic tendency wouldn’t matter if the Standard Model particles were the end of the story. But physicists surmise that far beyond the Standard Model, at a scale about a billion billion times heavier known as the “Planck mass,” there exist unknown giants associated with gravity. These heavyweights would be expected to fatten up the Higgs boson — a process that would pull the mass of every other elementary particle up to the Planck scale. This hasn’t happened; instead, an unnatural hierarchy seems to separate the lightweight Standard Model particles and the Planck mass.
With his scale symmetry approach, Bardeen calculated the Standard Model masses in a novel way that did not involve them smearing toward the highest scales. From his perspective, the lightweight Higgs seemed perfectly natural. Still, it wasn’t clear how he could incorporate Planck-scale gravitational effects into his calculations.
Meanwhile, supersymmetry used standard mathematical techniques, and dealt with the hierarchy between the Standard Model and the Planck scale directly. Supersymmetry posits the existence of a missing twin particle for every particle found in nature. If for each particle the Higgs boson encounters (such as an electron) it also meets that particle’s slightly heavier twin (the hypothetical “selectron”), the combined effects would nearly cancel out, preventing the Higgs mass from ballooning toward the highest scales. Like the physical equivalent of x + (–x) ≈ 0, supersymmetry would protect the small but non-zero mass of the Higgs boson. The theory seemed like the perfect missing ingredient to explain the masses of the Standard Model — so perfect that without it, some theorists say the universe simply doesn’t make sense.
Yet decades after their prediction, none of the supersymmetric particles have been found. “That’s what the Large Hadron Collider has been looking for, but it hasn’t seen anything,” said Savas Dimopoulos, a professor of particle physics at Stanford University who helped develop the supersymmetry hypothesis in the early 1980s. “Somehow, the Higgs is not protected.”
The LHC will continue probing for convoluted versions of supersymmetry when it switches back on next year, but many physicists have grown increasingly convinced that the theory has failed. Just last month at the International Conference of High-Energy Physics in Valencia, Spain, researchers analyzing the largest data set yet from the LHC found no evidence of supersymmetric particles. (The data also strongly disfavors an alternative proposal called “technicolor.”)
The multiverse hypothesis has surged in begrudging popularity in recent years. But the argument feels like a cop-out to many, or at least a huge letdown.
The implications are enormous. Without supersymmetry, the Higgs boson mass seems as if it is reduced not by mirror-image effects but by random and improbable cancellations between unrelated numbers — essentially, the initial mass of the Higgs seems to exactly counterbalance the huge contributions to its mass from gluons, quarks, gravitational states and all the rest. And if the universe is improbable, then many physicists argue that it must be one universe of many: just a rare bubble in an endless, foaming “multiverse.” We observe this particular bubble, the reasoning goes, not because its properties make sense, but because its peculiar Higgs boson is conducive to the formation of atoms and, thus, the rise of life. More typical bubbles, with their Planck-size Higgs bosons, are uninhabitable.
“It’s not a very satisfying explanation, but there’s not a lot out there,” Dine said.
As the logical conclusion of prevailing assumptions, the multiverse hypothesis has surged in begrudging popularity in recent years. But the argument feels like a cop-out to many, or at least a huge letdown. A universe shaped by chance cancellations eludes understanding, and the existence of unreachable, alien universes may be impossible to prove. “And it’s pretty unsatisfactory to use the multiverse hypothesis to explain only things we don’t understand,” said Graham Ross, an emeritus professor of theoretical physics at the University of Oxford.
The multiverse ennui can’t last forever.
“People are forced to adjust,” said Manfred Lindner, a professor of physics and director of the Max Planck Institute for Nuclear Physics in Heidelberg who has co-authored several new papers on the scale symmetry approach. The basic equations of particle physics need something extra to rein in the Higgs boson, and supersymmetry may not be it. Theorists like Lindner have started asking, “Is there another symmetry that could do the job, without creating this huge amount of particles we didn’t see?”
Picking up where Bardeen left off, researchers like Salvio, Strumia and Lindner now think scale symmetry may be the best hope for explaining the small mass of the Higgs boson. “For me, doing real computations is more interesting than doing philosophy of multiverse,” said Strumia, “even if it is possible that this multiverse could be right.”
For a scale-symmetric theory to work, it must account for both the small masses of the Standard Model and the gargantuan masses associated with gravity. In the ordinary approach to doing the calculations, both scales are put in by hand at the beginning, and when they connect in the equations, they try to even each other out. But in the new approach, both scales must arise dynamically — and separately — starting from nothing.
“The statement that gravity might not affect the Higgs mass is very revolutionary,” Dimopoulos said.
A theory called “agravity” (for “adimensional gravity”) developed by Salvio and Strumia may be the most concrete realization of the scale symmetry idea thus far. Agravity weaves the laws of physics at all scales into a single, cohesive picture in which the Higgs mass and the Planck mass both arise through separate dynamical effects. As detailed in June in the Journal of High-Energy Physics, agravity also offers an explanation for why the universe inflated into existence in the first place. According to the theory, scale-symmetry breaking would have caused an exponential expansion in the size of space-time during the Big Bang.
However, the theory has what most experts consider a serious flaw: It requires the existence of strange particle-like entities called “ghosts.” Ghosts either have negative energies or negative probabilities of existing — both of which wreak havoc on the equations of the quantum world.
“Negative probabilities rule out the probabilistic interpretation of quantum mechanics, so that’s a dreadful option,” said Kelly Stelle, a theoretical particle physicist at Imperial College, London, who first showed in 1977 that certain gravity theories give rise to ghosts. Such theories can only work, Stelle said, if the ghosts somehow decouple from the other particles and keep to themselves. “Many attempts have been made along these lines; it’s not a dead subject, just rather technical and without much joy,” he said.
Strumia and Salvio think that, given all the advantages of agravity, ghosts deserve a second chance. “When antimatter particles were first considered in equations, they seemed like negative energy,” Strumia said. “They seemed nonsense. Maybe these ghosts seem nonsense but one can find some sensible interpretation.”
Meanwhile, other groups are crafting their own scale-symmetric theories. Lindner and colleagues have proposed a model with a new “hidden sector” of particles, while Bardeen, Lykken, Marcela Carena and Martin Bauer of Fermilab and Wolfgang Altmannshofer of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, argue in an Aug. 14 paper that the scales of the Standard Model and gravity are separated as if by a phase transition. The researchers have identified a mass scale where the Higgs boson stops interacting with other particles, causing their masses to drop to zero. It is at this scale-free point that a phase change-like crossover occurs. And just as water behaves differently than ice, different sets of self-contained laws operate above and below this critical point.
To get around the lack of scales, the new models require a calculation technique that some experts consider mathematically dubious, and in general, few will say what they really think of the whole approach. It is too different, too new. But agravity and the other scale symmetric models each predict the existence of new particles beyond the Standard Model, and so future collisions at the upgraded LHC will help test the ideas.
In the meantime, there’s a sense of rekindling hope.
“Maybe our mathematics is wrong,” Dine said. “If the alternative is the multiverse landscape, that is a pretty drastic step, so, sure — let’s see what else might be.” | <urn:uuid:1b204493-b207-4c87-9aa5-79e238f7d5b7> | {
"date": "2020-11-29T19:58:01",
"dump": "CC-MAIN-2020-50",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141202590.44/warc/CC-MAIN-20201129184455-20201129214455-00336.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.93915194272995,
"score": 3.625,
"token_count": 3007,
"url": "https://institutoflash786.org/2019/12/16/at-multiverse-impasse-a-new-theory-of-scale/"
} |
# N meetings in one room
Problem Statement: There is one meeting room in a firm. You are given two arrays, start and end each of size N.For an index ‘i’, start[i] denotes the starting time of the ith meeting while end[i] will denote the ending time of the ith meeting. Find the maximum number of meetings that can be accommodated if only one meeting can happen in the room at a particular time. Print the order in which these meetings will be performed.
```Example:
Input: N = 6, start[] = {1,3,0,5,8,5}, end[] = {2,4,5,7,9,9}
Output: 1 2 4 5
Explanation: See the figure for a better understanding.
```
# Solution:
Disclaimer: Don’t jump directly to the solution, try it out yourself first.
Initial Thought Process:-
Say if you have two meetings, one which gets over early and another which gets over late. Which one should we choose? If our meeting lasts longer the room stays occupied and we lose our time. On the other hand, if we choose a meeting that finishes early we can accommodate more meetings. Hence we should choose meetings that end early and utilize the remaining time for more meetings.
Approach
To proceed we need a vector of three quantities: the starting time, ending time, meeting number. Sort this data structure in ascending order of end time.
We need a variable to store the answer. Initially, the answer is 1 because the first meeting can always be performed. Make another variable, say limit that keeps track of the ending time of the meeting that was last performed. Initially set limit as the end time of the first meeting.
Start iterating from the second meeting. At every position we have two possibilities:-
• If the start time of a meeting is strictly greater than limit we can perform the meeting. Update the answer.Our new limit is the ending time of the current meeting since it was last performed.Also update limit.
• If the start time is less than or equal to limit ,skip and move ahead.
Let’s have a dry run by taking the following example.
N = 6, start[] = {1,3,0,5,8,5}, end[] = {2,4,5,7,9,9}
Initially set answer =[1],limit = 2.
For Position 2 –
Start time of meeting no. 2 = 3 > limit. Update answer and limit.
Answer = [1, 2], limit = 4.
For Position 3 –
Start time of meeting no. 3 = 0 < limit.Nothing is changed.
For Position 4 –
Start time of meeting no. 4 = 5 > limit. Update answer and limit.
Answer = [1,2,4], limit = 7.
For Position 5 –
Start time of meeting no. 5 = 8 > limit.Update answer and limit.
Answer = [1,2,4,5], limit = 9.
For Position 6 –
Start time of meeting no. 6 = 8 < limit.Nothing is changed.
Final answer = [1,2,4,5]
## C++ Code
``````#include <bits/stdc++.h>
using namespace std;
struct meeting {
int start;
int end;
int pos;
};
class Solution {
public:
bool static comparator(struct meeting m1, meeting m2) {
if (m1.end < m2.end) return true;
else if (m1.end > m2.end) return false;
else if (m1.pos < m2.pos) return true;
return false;
}
void maxMeetings(int s[], int e[], int n) {
struct meeting meet[n];
for (int i = 0; i < n; i++) {
meet[i].start = s[i], meet[i].end = e[i], meet[i].pos = i + 1;
}
sort(meet, meet + n, comparator);
vector < int > answer;
int limit = meet[0].end;
for (int i = 1; i < n; i++) {
if (meet[i].start > limit) {
limit = meet[i].end;
}
}
cout<<"The order in which the meetings will be performed is "<<endl;
for (int i = 0; i < answer.size(); i++) {
cout << answer[i] << " ";
}
}
};
int main() {
Solution obj;
int n = 6;
int start[] = {1,3,0,5,8,5};
int end[] = {2,4,5,7,9,9};
obj.maxMeetings(start, end, n);
return 0;
}
``````
Output:
The order in which the meetings will be performed is
1 2 4 5
Time Complexity: O(n) to iterate through every position and insert them in a data structure. O(n log n) to sort the data structure in ascending order of end time. O(n) to iterate through the positions and check which meeting can be performed.
Overall : O(n) +O(n log n) + O(n) ~O(n log n)
Space Complexity: O(n) since we used an additional data structure for storing the start time, end time, and meeting no.
## Java Code
``````import java.util.*;
class meeting {
int start;
int end;
int pos;
meeting(int start, int end, int pos)
{
this.start = start;
this.end = end;
this.pos = pos;
}
}
class meetingComparator implements Comparator<meeting>
{
@Override
public int compare(meeting o1, meeting o2)
{
if (o1.end < o2.end)
return -1;
else if (o1.end > o2.end)
return 1;
else if(o1.pos < o2.pos)
return -1;
return 1;
}
}
public class Meeting {
static void maxMeetings(int start[], int end[], int n) {
ArrayList<meeting> meet = new ArrayList<>();
for(int i = 0; i < start.length; i++)
meet.add(new meeting(start[i], end[i], i+1));
meetingComparator mc = new meetingComparator();
Collections.sort(meet, mc);
ArrayList<Integer> answer = new ArrayList<>();
int limit = meet.get(0).end;
for(int i = 1;i<start.length;i++) {
if(meet.get(i).start > limit) {
limit = meet.get(i).end;
}
}
System.out.println("The order in which the meetings will be performed is ");
for(int i = 0;i<answer.size(); i++) {
System.out.print(answer.get(i) + " ");
}
}
public static void main(String args[])
{
int n = 6;
int start[] = {1,3,0,5,8,5};
int end[] = {2,4,5,7,9,9};
maxMeetings(start,end,n);
}
}``````
Output:
The order in which the meetings will be performed is
1 2 4 5
Time Complexity: O(n) to iterate through every position and insert them in a data structure. O(n log n) to sort the data structure in ascending order of end time. O(n) to iterate through the positions and check which meeting can be performed.
Overall : O(n) +O(n log n) + O(n) ~O(n log n)
Space Complexity: O(n) since we used an additional data structure for storing the start time, end time, and meeting no.
## Python Code
``````from typing import List
class meeting:
def __init__(self, start, end, pos):
self.start = start
self.end = end
self.pos = pos
class Solution:
def maxMeetings(self, s: List[int], e: List[int], n: int) -> None:
meet = [meeting(s[i], e[i], i + 1) for i in range(n)]
sorted(meet, key=lambda x: (x.end, x.pos))
limit = meet[0].end
for i in range(1, n):
if meet[i].start > limit:
limit = meet[i].end
print("The order in which the meetings will be performed is ")
for i in answer:
print(i, end=" ")
if __name__ == "__main__":
obj = Solution()
n = 6
start = [1, 3, 0, 5, 8, 5]
end = [2, 4, 5, 7, 9, 9]
obj.maxMeetings(start, end, n)``````
Output:
The order in which the meetings will be performed is
1 2 4 5
Time Complexity: O(n) to iterate through every position and insert them in a data structure. O(n log n) to sort the data structure in ascending order of end time. O(n) to iterate through the positions and check which meeting can be performed.
Overall : O(n) +O(n log n) + O(n) ~O(n log n)
Space Complexity: O(n) since we used an additional data structure for storing the start time, end time, and meeting no.
Special thanks to Somparna Chakrabarti and Sudip Ghosh for contributing to this article on takeUforward. If you also wish to share your knowledge with the takeUforward fam, please check out this article | crawl-data/CC-MAIN-2023-40/segments/1695233510903.85/warc/CC-MAIN-20231001141548-20231001171548-00682.warc.gz | null |
Psychological Testing/Psychological Assessment is the administration of standardized tests to gain insight into behavior. Oftentimes, testing is administered as a way to confirm a diagnosis and develop an appropriate treatment plan for the client, whether for therapy, school or for the physician.
We currently are testing for the following areas:
Attention Deficits in Children, Adolescent and Adults
- Difficulty with attention can be attributed to a variety of issues. Most commonly, we see people wanting to confirm a diagnosis of ADHD. Symptoms of ADHD can include inattention, inability to retain information, hyperactivity and distractibility. Sometimes it may not be ADHD at all but due to an underlying condition such as anxiety or depression or difficulty adjusting to changes.
- We have varying tests to determine issues with attention Autism Spectrum.
- Autism is a developmental disorder that affects communication and behaviors. It can range from mild to severe. Symptoms may include poor social skills, difficulty expressing emotions, difficulty understanding other’s feelings, sensory issues, poor eye contact, repeating words or phrases and more.
- Our goal is to test if a client falls on the autism spectrum and look at other behavioral, intellectual or developmental issues.
- We can also administer testing for a sensory profile. This is to help with sensory issues at home and school and make appropriate recommendations.
- In childhood and adolescence, we are often presented with a varying degree of emotions and behaviors. Oftentimes we want to identify specific disorders, personality issues, and behavioral
- We use a variety of assessments to look at behaviors, emotions, personality and psychological adjustment.
Intellectual and Developmental Delays
- Look at developmental and intellectual disabilities due to delays, issues with brain injuries, ADHD, ASD, hearing impairments and more.
- Establishing a firm diagnosis in developmental and intellectual delays is often necessary for special programs.
- Assess for delays academically that might be causing issues. We currently test for basic academic delays. We do not test for dyslexia.
- We can administer an assessment to look at your and skills. These scales reflect an individual’s attraction for specific occupational areas.
- We have several assessments that assess for different emotional issues such as depression, anxiety, personality, disruptive behaviors, anger, emotional distress, personality, mania, and schizophrenia.
- We administer a brief assessment of intelligence in helping with our overall psychological assessment.
- A test battery is a group of tests administered together to get a good overall picture. This is recommended if needing to confirm a diagnosis and look at recommendations for treatment areas in counseling. It is also good for making recommendations for school and home.
- Generally a test battery will include behavioral, personality and intelligence or academic assessments along with a clinical interview of the client and family members.
- A test battery will come with a formal psychological evaluation report.
All testing/assessment issues will vary based on presenting issues conducted during the initial psychological interview. Testing is administered by licensed professionals in the state of Texas. A license and formalized training is required to administer psychological assessments. Please call our office and let them know you are wanting testing and schedule a psychological evaluation.
If using insurance, please verify your insurance will pay for psychological testing. Any copays and deductibles will apply. Testing/Assessment is done over multiple time frames, therefore you may receive a bill when using insurance for multiple testing sessions. With insurance, you are often limited to one set of testing per year. Please verify with your insurance prior. | <urn:uuid:b9998c96-1d43-4939-9542-739238114ed0> | {
"date": "2022-12-02T07:01:39",
"dump": "CC-MAIN-2022-49",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00097.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.928141176700592,
"score": 3.625,
"token_count": 719,
"url": "https://www.coastalsynergyassociates.com/services/psychological-testing"
} |
Quiz Answer Key and Fun Facts
1. By what process do plants create food?
2. What gas is a byproduct of the process that plants use to make food in nature?
3. Plants need nitrogen in order to grow. Nitrogen in the air is not usable by plants. What is the most common process by which nitrogen is made available to plants?
4. What is an organism that breaks down dead organisms called?
5. Ultimately, all of the energy in all life cycles on land originally came from the ...
6. In what phase of the water cycle does rain fall?
7. In the rock cycle, which kind of rocks are made from rocks that undergo heat and pressure?
8. If a pesticide is released into the Arctic that accumulates in body cells, which of the following organisms is apt to have the highest pesticide levels?
9. Under the surface of the Earth, hot molten rock rises, cools, then sinks. This process is called...
10. The state in which organisms maintain internal equilibrium is called...
Source: Author crisw
This quiz was reviewed by FunTrivia editor gtho4
before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system. | <urn:uuid:4ebae6be-57c2-4f3c-b2cf-a1d270e55e9d> | {
"date": "2023-03-21T00:35:47",
"dump": "CC-MAIN-2023-14",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00057.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.950732409954071,
"score": 3.53125,
"token_count": 258,
"url": "https://www.funtrivia.com/trivia-quiz/SciTech/Earthly-Cycles-1866.html"
} |
# The Fermat Point
The Fermat point is named for the point which is the solution to a geometric challenge that Pierre Fermat posed for Evangelista Torricelli, who was briefly an associate of the aged Galileo. Fermat challenged Torricelli to find the point P in an acute triangle ABC which would minimize the sum of the distances to the vertices A, B, and C. The triangle need not actually be acute, but if the largest angle reaches 120 o or more, then the vertex at the largest angle is the solution.
For a general solution, one approach is to construct equilateral triangles on each side of the triangle (actually only two are needed) and draw the segments connecting the opposite vertices of the original triangle and the newly created equilateral vertices. They intersect in a point which is the solution. The point is called the Fermat point.
Because the construction is so similar to the one for Napoleon's Point, students often get the two confused. As a consequence of the construction it can be shown that the segments PA, PB, and PC are all at 120o angles to one another.
The Fermat point is also the common point of intersection of the circumcircles of the three equilateral triangles. The length of each of the three segments A-A', B-B', and C-C' is the same, and even more interesting is that their length is the same as the sum of the distances from the Fermat Point to the three vertices of the triangle.
Here are some comments on the history of the Fermat point by Harold W Kuhn from his post (edited somewhat) to the Historia Matematica list. Note that he refers to the point as the Torricelli point, which is common for mathematicians on the Continent I am told.
"Our story starts with a problem rather casually posed by Fermat early in the 17th century. At the end of his celebrated essay on maxima and minima, in which he presented pre-calculus rules for finding tangents to a variety of curves, he threw out the challenge: "Let he who does not approve of my method attempt the solution of the following problem: Given three points in the plane, find a fourth point such that the sum of its distances to the three given points is a minimum!" The problemmay have travelled to Italy with Mersenne; it is known that before 1640 Torricelli had solved the problem. He asserted that the circles circumscribing the equilateral triangles constructed on the sides of and outside the given triangle intersect in the point that is sought. This point is called the Torricelli point. Also, in Cavalieri's "Exercitationes geometricae" of 1647, it is shown that the sides of the given triangle subtend angles of 120 degrees from the Torricelli point. Furthermore, Simpson asserted and proved in his "Doctrine and Application of Fluxions" (London, 1750) that the three lines joining the outside vertices of the equilateral triangles defined above to the opposite vertices of the given triangle intersect in the Torricelli point. These three lines are called Simpson lines.
I cannot end this historical sketch without mention of the fact that the Fermat problem has been widely popularized by Courant and Robbins (in "What is Mathematics?") under the name of the "Steiner Problem". Although this gifted geometer of the 19th century can be counted among the dozens of mathematicians who have written on the subject, he does not seem to have contributed anything new, either to its formulation or its solution. As for the statement by Courant and Robbins that the generalization of the problem to more than three points is a sterile generalization, their answer is found in the recent literature, which has added new applications and understanding through this "sterile" extension of the problem. | crawl-data/CC-MAIN-2017-17/segments/1492917123270.78/warc/CC-MAIN-20170423031203-00532-ip-10-145-167-34.ec2.internal.warc.gz | null |
|The Open Door Web Site|
Introduction to the Reformation
This period is known as the Reformation, quite simply because it was then that the Church was reformed. That is, people criticised and changed the way the Catholic Church worked.
The desire for reform was not universal - some people wanted change while others did not. There were two main groups of people who were trying to alter the Church: Those within the Church - the clergy and the lay people - ordinary people.
During the Council of Constance (1414-1418) and the Council of Basle (1431-1439), a debate had begun within the Church. At these meetings, high-level clergy met to discuss problems within the Church. The result of these discussions was a call to reform certain things. By discussing its problems the Church highlighted to people what was wrong.
In addition to this, people's attitudes were being radically altered by the Renaissance. For example, men such as Leonardo da Vinci were developing modern science and challenging traditional beliefs about the world. This led to a growth of knowledge that was uncontrolled by the Church and which often challenged what was written in the Bible, as well as what the pope said. Another example was Copernicus who began to argue that the sun, and not the Earth, was the centre of the Universe.
There were challenges to the Bible aided by the invention of the printing press. From around 1450, various people in Europe, including Johannes Gutenberg in Mainz, Germany, developed a way of using printing blocks to produce books rather than copying them by hand. Until then the writing or copying of books had always been under the control of the Church. Monks had laboriously copied pages and pages of text and provided illustrations for them. Gutenberg's press changed all this. The Church could no longer censor books that it considered unsuitable (i.e. those that challenged the Church's ideas). Luther and Calvin were able to develop their own versions of the Bible as a result.
The cost of books came down as their availability increased. This, added to the fact that there was a growing middle class, led to more ideas being easily available to more people. | <urn:uuid:6f014849-56fc-4f89-8468-025170885f81> | {
"date": "2015-01-25T22:19:01",
"dump": "CC-MAIN-2015-06",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115891802.74/warc/CC-MAIN-20150124161131-00081-ip-10-180-212-252.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9874190092086792,
"score": 4.15625,
"token_count": 444,
"url": "http://www.saburchill.com/history/chapters/chap5101.html"
} |
عنوان مقاله [English]
نویسندگان [English]چکیده [English]
The subject of Takfir (excommunicate) is not only discussed in Islamic nations rather any objection with others idea is include in other non- Muslim nations too. Nevertheless, because Takfir, on one hand, for Muslims is an ideal and Kalami affair and on other hand ideals have a remarkable role in human behaviors, we could see influence of Takfir in political and social affairs as well. Historically, Shi’a and Sonni scholars tried to come up with a complete definition about Takfir and its reasons and elements. Despite forbiddance of all Sects from excommunicate (Takfir) each other, we see many examples of Takfir between Islamic Sects’ followers for the reason of differences that is appear in definitions and example of disbelief (Kofr). Jurisconsults are the most suitable people who could send out this judgment (Hokm). For the reason that people doesn’t know the rules and regulations of Takfir many religious radicalism would appear. Furthermore there are different ideas about examples of Takfir in Islamic Sects. Consequently knowledge of people about personal and social effects of Takfir helps them to avoid from immethodical Takfirs. | <urn:uuid:14dde2b7-e8cb-46a9-82f0-76d6e42be1b4> | {
"date": "2022-09-29T10:52:21",
"dump": "CC-MAIN-2022-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335350.36/warc/CC-MAIN-20220929100506-20220929130506-00256.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9188401103019714,
"score": 3.515625,
"token_count": 292,
"url": "http://foroughevahdat.mazaheb.ac.ir/article_6802.html"
} |
# Parametric Differentiation: Summary
by Batool Akmal
My Notes
• Required.
Learning Material 2
• PDF
DLM Parametric Differentiation Calculus Akmal.pdf
• PDF
Report mistake
Transcript
00:01 Once again, just to recap over everything that we've done and we do it more formally now.
00:08 If you have a function of x defined as f of t or any function that includes t and a function of y defined by a different function g of t, you can bring them together firstly by differentiating each part separately. So the x, we have to differentiate with respect to t so we’ll get dx/dt.
00:27 Then the y, we have to differentiate with respect to t as well to get dy of dt. Then to get your dy/dx, you flip dx/dt to give you dt/dx, so that you can cancel the dt’s and you end up with dy/dx.
00:44 So, both methods that I mentioned earlier are now here. You can see that you could either learn dy/dx as dy/dt divided by dx/dt or if you prefer to multiply, you'd have to remember that it's dy/dt left as it is and then you flip the other fraction. So, dx/dt, you flip to make it into dt/dx so you can end up with dy/dx.
01:09 Let’s look at another example now just to consolidate the ideas. We are looking for dy/dx.
01:17 Again, you can see that you have two equations. You can see that this is a parametric equation because you have not only x's and y's but a third variable, t. Don’t ever worry about what this letter is.
01:29 It could be p, or q, or z, or anything. But as long as you spot a third variable, you have a third parameter that’s holding it together. Let’s try and differentiate this using the rules we've just learned.
01:43 We have y = t² - 5 and x = t³ + 5. Remember what we said. Firstly, spot what kind of equation it is.
01:56 I know that you know a lot of different methods and lots of different types of equations.
02:00 You can question all of them. Is it chain rule or product rule or quotient rule, implicit differentiation? Hopefully, when you come to the part of thinking about parametric equations, you'd recognize that this is a parametric equation. So, in order to differentiate it, we're going to have to do this separately. We'll do dy/dt here. So, that just gives me 2t and the constant 5 just disappears. We have dx/dt. When you differentiate that, that gives you 3t².
02:34 Bring the power to the front and decrease the power by 1 and then the 5 just disappears.
02:39 Now, our definition was this. Dy/dx is dy/dt multiplied by dt/dx or if you wanted to do it the other way, you could do dy/dt divided by dx/dt. Both of them are the same thing. If I’m using this form of it, I obviously need to flip this before. So, dx/dt needs to become dt/dx. You can't just do that to one side of the equation. We have to do it to this side as well. So, this is 3t²/1.
03:17 So, you can write it as 1/3t². We just flipped the entire equation. Put it together here in the formula. Dy/dt is 2t. Dt/dx is 1/3t². Nice and straightforward. We can now just simplify this a little bit to say that dy/dx. You can cancel this one t with one of them is 2/3t.
03:48 Moving on then. We now might wonder how to find the second differential of a parametric equation.
03:56 It’s not as straightforward as just differentiating a function again. So, when you're doing the second differential, we have to use the next part of this definition. In order to do d²y/dx², we essentially need to differentiate dy/dx again as we do with any other differentiation. If you have to do a second differential of any function, you just differentiate it again using the same rules.
04:24 However, because this time you have t’s in your equation, you can’t just dy/dx with respect to x.
04:31 So, we use this definition. We use d²y/dx². We differentiate dy/dx which we've already found in the first part with respect to t because that's important. Then to make up for that dt that we've just done there, we divide it by dx/dt or we multiply it with dx/dt flipped, so by dt/dx.
04:56 It looks fairly complicated but it really isn't when you start to use this with numbers or you start to apply it to real questions. So, let’s have a look at an example.
The lecture Parametric Differentiation: Summary by Batool Akmal is from the course Parametric Differentiation.
### Included Quiz Questions
1. dy/dx = (3t² + 5) / (2t - 1)
2. dy/dx = (3t² + 5) / (2t)
3. dy/dx = (3t + 5) / (2t)
4. dy/dx = (t² + 5) / (2t + 1)
5. dy/dx = (t² - 5) / (2t + 1)
1. dy/dx = t - 2
2. dy/dx = 2t - 2
3. dy/dx = 2t - 4
4. dy/dx = t²/2
5. dy/dx = 4t - 8
1. d(dy/dx) /dt . dt/dx
2. (dy/dx)²
3. 2dy/dx
4. d²y/dt² . (dt/dx)²
5. d(dy/dx) / dt . dx/dt
### Customer reviews
(1)
5,0 of 5 stars
5 Stars 5 4 Stars 0 3 Stars 0 2 Stars 0 1 Star 0 | crawl-data/CC-MAIN-2022-49/segments/1669446710936.10/warc/CC-MAIN-20221203175958-20221203205958-00684.warc.gz | null |
Intro: Toy Hacking - What's Inside?
This project unveils the technology and mechanical components inside a toy. You can dissect, diagram and re-design an old toy into a new creation. Plan for this project to take at least 90 minutes, and more depending on your re-design. Through this fun, hands-on project you will gain an understanding of simple circuitry and mechanics. In a classroom, this can be standards aligned with reverse engineering, documentation, circuitry, storytelling. Anybody from 3rd grade and up would enjoy this activity.
It is recommended that you have one facilitator per every 8-10 kids. Before beginning, it is important to go over safe usage of seam rippers, scissors and other tools.
Step 1: Gather Supplies and Select a Toy
Here's what you need to start:
- Various small phillips-head screwdrivers. Its helpful to have a long shaft, because often the screws holding together a toy are molded deep inside the plastic.
- Scissors and a seam ripper
- Safety Glasses
- Jewelry pliers can be helpful when carefully taking a toy apart
- Wire strippers
- Battery packs for your redesign
- Alligator clips
- Hot glue
- Wood or something to mount it on to, if desired
Selecting a toy is easy. If you can feel a plastic shell on the toy, and it moves, lights up and or sings you are in good shape. We find most of our toys at thrift stores, and just give them a good cleaning before we start our adventure.
Step 2: Cut Away the Fur and Open the Toy
Using scissors, you can start cutting the fur carefully away from the battery pack. Be careful not to snip any wires or you will lose functionality. The goal is to cut away all the fabric, and remove stuffing, and unscrew all the plastic covers to have exposed circuitry and mechanics of the toy.
Step 3: Understanding What's Inside
Inside your toy you will likely find several things.
- Wiring to power is general black(-) and red (+)
- Wires to LEDs and / or motors are generally two different colors
- Wring to speakers and sensors are generally two of the same color
The Printed Circuit Board (PCB) is the heart of the mechanical toy. You can follow wires, and printing to understand what does what.
c: capacitor (store an electric charge for a process within the toy)
r: resistor (limits the current passing through a circuit)
q: transistor (working as either an amplifier or a switch)
We like to diagram what is inside the toys we take apart, because it really helps to understand electric connections and the functionality of the toy. Once you dissect and diagram, designing is easy!
Step 4: Building Your Own New Creation
Here are some samples of what others have made in our workshops with their toys. Please remember cutting a wire isn't the end of the world. You can always strip it and tape it, alligator clip it or solder it back together.
We thank the Exploratorium and Wonderful Idea Co. for inspiring us to try toy hacking at ReCreate! | <urn:uuid:c469a7ee-0ca1-4a14-9943-c87f69662323> | {
"date": "2018-09-22T13:43:34",
"dump": "CC-MAIN-2018-39",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158429.55/warc/CC-MAIN-20180922123228-20180922143628-00298.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9229830503463745,
"score": 3.875,
"token_count": 659,
"url": "https://www.instructables.com/id/Toy-Hacking-Whats-Inside/"
} |
Graph each set of curves on the same coordinate system. Use a dashed curve for the first equation and a solid curve for the second.
We need to graph the curves of the equations on the same coordinate system.
To graph the curve , first we find its domain.
Since the square root of a negative number is not a real number, the expression x must be nonnegative.
Thus, the domain of the equation is.
To graph the curve, we take some values of x in the domain as
On substituting these values in, we get the corresponding values of.
Thus, we get the table of values as shown below.
On plotting these points and connecting them, we get the graph of the equation.
The graph of can be obtained by shifting the graph of, h units to the right.
Therefore, the graph the equationis obtained by shifting the graph of by 1 unit to the right.
Thus, the graph of is shown below. | <urn:uuid:f06ac107-7542-4635-8591-40735f6e15e4> | {
"date": "2019-07-23T03:42:52",
"dump": "CC-MAIN-2019-30",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528687.63/warc/CC-MAIN-20190723022935-20190723044935-00458.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.8781384229660034,
"score": 4.125,
"token_count": 199,
"url": "https://www.chegg.com/homework-help/precalculus-mathematics-5th-edition-chapter-4.2-solutions-9780131120952"
} |
# Continued fraction
• Oct 3rd 2009, 12:01 PM
user
Continued fraction
i need help to solve this exercise
To prove the continued fraction of (d^2 +1)^(1/2) is [d;2d,2d,2d,….]
• Oct 4th 2009, 08:19 AM
Soroban
Hello, user!
Quote:
Prove that the continued fraction of . $\sqrt{d^2 +1}$ . is . $\bigg[d,2d,2d,2d, \hdots\bigg]$
$\text{Let: }\;x \;=\;d + \frac{1}{2d + \dfrac{1}{2d + \hdots}}$
$\text{Add }d\text{ to both sides: }\;x + d \;=\;2d + \frac{1}{\left\{2d + \dfrac{1}{2d + \hdots}\right\}} \;\begin{array}{c} \\ \\ \Leftarrow\text{ This is }(x+d) \end{array}$
$\text{Then we have: }\;x + d \;=\;2d + \frac{1}{x+d}$
$\text{Multiply by }(x+d)\!:\;\;(x+d)^2 \;=\;2d(x+d) + 1 \quad\Rightarrow\quad x^2 + 2dx + d^2 \;=\;2dx + 2d^2 + 1$
$\text{Therefore: }\;x^2 \;=\;d^2+1 \quad\Rightarrow\quad x \;=\;\sqrt{d^2+1}$
• Oct 5th 2009, 10:16 AM
user | crawl-data/CC-MAIN-2018-05/segments/1516084886397.2/warc/CC-MAIN-20180116090056-20180116110056-00309.warc.gz | null |
# Solving by Elimination
## Key Questions
• A good start would be to multiply each equation by the least common multiple (LCM) of the denominator. If you multiply all parts of the equation by the LCM, it does not affect the solution. This would eliminate the fractions and you could go forth and solve the system by elimination.
Here is an example:
$- \frac{1}{10} x + \frac{1}{2} y = \frac{4}{5}$
$\frac{1}{7} x + \frac{1}{3} y = - \frac{2}{21}$
Step 1: Multiply Equation 1 by the LCM which 10.
$10 \left(- \frac{1}{10} x + \frac{1}{2} y\right) = \left(\frac{4}{5}\right) 10$
$10 \left(- \frac{1}{10} x\right) + 10 \left(\frac{1}{2} y\right) = \left(\frac{4}{5}\right) 10$
$- x + 5 y = 8$
Step 2: Multiply Equation 2 by the LCM which is 21.
$21 \left(\frac{1}{7} x + \frac{1}{3} y\right) = \left(- \frac{2}{21}\right) 21$
$21 \left(\frac{1}{7} x\right) + 21 \left(\frac{1}{3} y\right) = \left(- \frac{2}{21}\right) 21$
$3 x + 7 y = - 2$
Step 3: Place the new equations together to create a new system:
$- x + 5 y = 8$
$3 x + 7 y = - 2$
Step 4: To solve by elimination, multiply first equation by 3 (this will help to eliminate the $x$ variable).
$3 \left(- x + 5 y\right) = \left(8\right) 3$
$3 x + 7 y = - 2$
becomes
$- 3 x + 15 y = 24$
$3 x + 7 y = - 2$
Step 5: Add the two equations to eliminate the x variable:
$- 3 x + 15 y = 24$
$3 x + 7 y = - 2$
becomes $22 y = 22$
Step 6: Solve for $y$:
$22 y = 22$
$\frac{22 y}{22} = \frac{22}{22}$
and thus
$y = 1$
Step 7: substitute $y$ into one of the equations to solve for $x$.
$- x + 5 y = 8$
$- x + 5 \left(1\right) = 8$
$- x + 5 = 8$
$- x + 5 - 5 = 8 - 5$
$- x = 3$
$\frac{- x}{-} 1 = \frac{3}{-} 1$
$x = - 3$
Step 8: Write the solution to the system as a coordinate.
$x = - 3 , y = 1$
$\left(x , y\right) = \left(- 3 , 1\right)$
• You follow a sequence of steps.
In general, the steps are:
1. Enter the equations.
2. Multiply each equation by a number to get the lowest common multiple for one of the variables.
3. Add or subtract the two equations to eliminate that variable .
4. Substitute that variable into one of the equations and solve for the other variable.
EXAMPLE:
How do you use the elimination method to solve $2 x + 3 y = 7 , 3 x + 4 y = 10$?
Solution:
Step 1. Enter the equations.
[1] $2 x + 3 y = 7$
[2] $3 x + 4 y = 10$
Step 2. Find the lowest common multiple.
Multiply Equation 1 by $3$ and Equation 2 by $2$.
[3] $6 x + 9 y = 21$
[4] $6 x + 8 y = 20$
Step 3. Subtract Equation 4 from Equation 3.
[5] $y = 1$
Step 4. Substitute Equation 5 in Equation 1.
$2 x + 3 y = 7$
$2 x + 3 = 7$
$2 x = 4$
$x = 2$
Check: Substitute the values of $x$ and $y$ in Equation 2.
If you use one equation to get the second variable, use the other equation for the check.
$3 x + 4 y = 10$
3×2+4×1=10
$6 + 4 = 10$
$10 = 10$
It checks!
The solution is correct. | crawl-data/CC-MAIN-2019-09/segments/1550247484648.28/warc/CC-MAIN-20190218033722-20190218055722-00114.warc.gz | null |
Returning to the visual illusion experiment the video above shows the results of applying a change in contrast and colour to the original image. The illusion consists of two parts – the first is produced by the circumference. The alternating colours can produce an afterimage effect particularly when the image is static. The second effect is a ‘leaking’ of colour within the circle as it moves from one side of the screen. The colour gradient within the circle remains invariant during the movement.
In the first transformation demonstrated in the video above, the contrast is increased. This transformation effectively removes the subtle grading effect on the left side of the circle. This lessens the second effect. However the reader may observe that there is a sharp contrast between the grey and white areas within the circle on the left. This boundary may appear to change slightly during the movement and is a third type of subtle effect. As in previous images complex gradients within the image may require more processing than a circle which is the same colour throughout.
The argument for this would be based on an explanation at the level of the retina. In a previous post I looked at an explanation by Professor Meiker of two visual illusions (see below).
Applying the same explanation to the image above, the visual system needs to process the circle as it moves across the screen. Since the circle is filled with a gradient the cells in the retina will be picking up the contrast across the circle. If the circle was stationary there would be no need for the cells to change their activity as there is no new information being presented (the explanation is more complex as under experimental conditions without absolute stability of the fovea in relation to an image, that image will fade. Additionally the eyes undergo microsaccadic movements even during periods of visual fixation). However as the circle is moving across the screen there is a complex change of gradient within the image. This should trigger firing of contrast detection cells in the area of the retina receiving light from the image.
Compared to no change in the image there should be many more contrast cells firing. The signals from these cells would be conveyed to the visual cortex and the visual scene reassembled as the scene is perceived. If we say that the processing of these signals is equivalent to a calculation (the interested reader can find further details of theories about how the organisation of neuronal circuits might facilitate this type of operation here) then a rapidly changing scene with a lot of contrast would require more calculations by the retinal apparatus than a simple unchanging scene. An increase in the number of calculations may lead to an increase in the number of errors from deconstruction of the scene all the way through to reassembly of the scene/perception. This error rate may lead to reduced stability of the boundary in the image in the video above where there is increased contrast. This is one explanation at least. Nevertheless it can be tested by assessing the response to images of increasing complexity.
Index: There are indices for the TAWOP site here and here Twitter: You can follow ‘The Amazing World of Psychiatry’ Twitter by clicking on this link. Podcast: You can listen to this post on Odiogo by clicking on this link (there may be a small delay between publishing of the blog article and the availability of the podcast). It is available for a limited period. TAWOP Channel: You can follow the TAWOP Channel on YouTube by clicking on this link. Responses: If you have any comments, you can leave them below or alternatively e-mail [email protected]. Disclaimer: The comments made here represent the opinions of the author and do not represent the profession or any body/organisation. The comments made here are not meant as a source of medical advice and those seeking medical advice are advised to consult with their own doctor. The author is not responsible for the contents of any external sites that are linked to in this blog. | <urn:uuid:009ce60e-213e-438e-9854-f969c2cd60f1> | {
"date": "2014-09-23T22:23:23",
"dump": "CC-MAIN-2014-41",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657140379.3/warc/CC-MAIN-20140914011220-00174-ip-10-234-18-248.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9360000491142273,
"score": 3.546875,
"token_count": 793,
"url": "http://theamazingworldofpsychiatry.wordpress.com/2013/03/05/the-effects-of-changing-contrast-and-colour-in-an-image-continuing-with-a-visual-illusion-experiment-part-6/"
} |
# Is it possible for a function with range $=R$ have a global max/min without specifying a region?
Let $f(x,y,z) = x^2 + y^2 + z^2$
The gradient of $f$ is $\nabla f=(2x, 2y, 2z)$ and if I solve the 3-equations-system, I will find the critical point $P_0=(0,0,0)$
The Hessian matrix of $f$ is $\nabla^2 f= \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{bmatrix}$
For $P_0$, $\alpha_1 = det \begin{bmatrix} 2\\ \end{bmatrix} = 2 \gt 0$, $\alpha_2 = \det \begin{bmatrix} 2 & 0\\ 0 & 2\\ \end{bmatrix} = 4 \gt 0$, $\alpha_3 = \det \begin{bmatrix} 2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2 \end{bmatrix} = 8 \gt 0$
So $P_0$ is a local minimum and since $f$ is bounded below by $0$, $f(0,0,0) = 0$ is also an global minimum of $f$.
Now, let $g(x,y) = 4 + x^2 + y^3 - 3xy$
The gradient of $g$ is $\nabla g=(2x-3y, 3y^2-3x)$ and if I solve the 2-equations-system, I will find the critical points $P_0(0,0) \text{ and } P_1\left(\frac94, \frac32\right)$
The Hessian matrix of $g$ is $\nabla^2 g= \begin{bmatrix} 2 & -3 \\ -3 & 6y \\ \end{bmatrix}$
For $P_0$, $\alpha_1 = det \begin{bmatrix} 2\\ \end{bmatrix} = 2 \gt 0$, $\alpha_2 = \det \begin{bmatrix} 2 & -3\\ -3 & 0\\ \end{bmatrix} = -9 \lt 0 \mathbf{\text{ saddle point }}$
And for $P_1$, $\alpha_1 = det \begin{bmatrix} 2\\ \end{bmatrix} = 2 \gt 0$, $\alpha_2 = \det \begin{bmatrix} 2 & -3\\ -3 & 9\\ \end{bmatrix} = 9 \lt 0 \mathbf{\text{ local minimum }}$
I also found $g(0,0) = \mathbf{4}$ and $g\left(\frac94, \frac32\right) \approx \mathbf{2,313}$.
My question is, can I affirm that $g$ does not have a global max/min?
And also, will be always the case for a function with range $=R$ when I'm looking for a global max/min without specifying a region?
• Observe that $g(0, y) = y^3 + 4$, hence has no global max/min. Note that FOC and SOC cannot really easily determine if you have global max/min. Take for example $f(x) = x$ on the reals. – Calvin Lin Jun 11 '13 at 0:38
• @CalvinLin: Regarding to your nice comment, I am wonder if the OP is looking for an example of such that function? – mrs Jun 11 '13 at 0:44
• @Calvin Lin: Do you want say that $g$ doesn't have global max/min at all? – user78723 Jun 11 '13 at 1:48
• Consider the functions $z=\sqrt{x^2+y^2}$ and $z=-\sqrt{x^2+y^2}$. – Mhenni Benghorbal Jun 11 '13 at 5:38
• But $g(x,y)$ has no global min at all. Plot it to see that! – mrs Jun 11 '13 at 5:18 | crawl-data/CC-MAIN-2019-43/segments/1570986675598.53/warc/CC-MAIN-20191017172920-20191017200420-00479.warc.gz | null |
The sculpture fragment suggests Romans lived peacefully alongside Germans until a decisive defeat at the Battle of Teutoburg Forest
Some 2,000 years ago, a monumental bronze sculpture of the Roman emperor Augustus and his trusted steed welcomed visitors to the central marketplace of Waldgirmes, an ancient settlement near modern-day Frankfurt, Germany. Made of bronze covered in gold leaf and weighing an estimated 900 pounds, the equestrian statue was an imposing presence in the newly annexed province. It reminded viewers of imperial might with symbols like the Roman war god Mars affixed onto the horse’s bridle.
Today, a gilded horse head and miscellaneous small fragments are all that remain of the sculpture. But as Andrew Curry reports for National Geographic , the 55-pound head retains much of its majestic power. Now on view just north of Frankfurt at the Saalburg Roman Fort, the sculpture introduces a twist in the established story of Roman-Germanic relations.
Prior to the launch of excavations at Waldgirmes in 1993, historians believed the Roman Empire limited its engagement with German affairs to the occasional military raid, Science Magazine notes. Lacking evidence of early Roman settlements across Germany, researchers identified the Battle of Teutoburg Forest as the turning point in Rome’s empire-building trek across Europe. They speculated that the embarrassing defeat delineated the borders of the Roman frontier.
According to Karen Schousboe of Ancient History Encyclopedia , the battle took place late in the year 9 A.D. German warriors ambushed three legions of Roman soldiers led by general Publius Quinctilius Varus. Despite being vastly outnumbered, the Germans annihilated their enemies. The battered Romans retreated, setting up a northern perimeter along the Rhine River.
The artifacts found at Waldgirmes suggest that Teutoburg Forest is only part of the story. They indicate the Romans lived next to and traded with the Germans peacefully for years, National Geographic ’s Curry writes. Researchers have yet to find a barracks or any evidence of a large military presence at Waldgirmes.
Wood buildings dated to around 4 B.C. reveal a surprisingly advanced town. It was filled with Roman-style residences, pottery and woodworking workshops, and classic Roman structures including a forum, or marketplace. Here, archaeologists identified five pedestals that once housed life-size equestrian sculptures—including the one of Augustus now represented solely by the horse’s head.
The head, which was discovered at the bottom of a 33-foot well in 2009, speaks to the previously underestimated presence of Roman settlements in Germany and the disastrous consequences of Teutoburg.
In a separate article for Archaeology , Curry writes that the sculpture fragment was wedged underneath eight millstones, as well as an array of everyday items such as wooden buckets, sticks and fence posts. Littered across the site were more than 160 bronze fragments, mainly consisting of minuscule splinters, indicating the Germans probably recycled bronze sculptures for their own use. As for the horse head, Siegmar von Schnurbein, an archaeologist and director of the German Archaeological Institute’s Romano-Germanic Commission, hypothesizes that it was thrown into the well as part of a ritualized water sacrifice commonly seen in Germanic areas.
Whatever the exact reasoning behind the sculpture’s ignominious end, Teutoburg precipitated the speedy decline of Waldgirmes and other German settlements. Within several years of the battle, the site was evacuated, likely voluntarily due to heightened Roman-Germanic tensions. The buildings of Waldgirmes were torched, perhaps to prevent Germanic tribes from taking over the settlement.
“In the final fire, everything was wiped out, ground down to the earth,” lead researcher Gabriele Rasbach tells Curry. “You can see burning along the entire wall.”
According to a press release, the head has been extensively restored to highlight its gilded exterior and decorative details. Entangled in legal battles for nearly a decade, it is finally being exhibited to the public, enabling viewers to envision its former glory and immerse themselves in the forgotten 2,000-year-old world. | <urn:uuid:4bc95d82-5ed0-40eb-8524-8a70bac466eb> | {
"date": "2019-12-05T17:38:09",
"dump": "CC-MAIN-2019-51",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540481281.1/warc/CC-MAIN-20191205164243-20191205192243-00496.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9530354142189026,
"score": 3.875,
"token_count": 868,
"url": "https://golro.com/a-2000-year-old-golden-horse-head-suggests-romans-actually-got-along-wth-german-barbarians/"
} |
5-Year Olds Get Their Own Standardized Tests
October 16, 2012
Five-year olds are getting their own standardized tests, mandated in over 25 states, in a new Race to the Top requirement. (And a way to get federal dollars.)
What is a standardized test anyway? The basic definition for a standardized test is a test that administered and scored in a standardized way, commercially prepared to measure a student’s performance level as compared to others.
According to Reuters, in some cases, kindergarteners are given an hour-long multiple choice test while other tests are one-on-one with a teacher.
Education experts, parents, and teachers feel concerned about these tests for a number of reasons:
- stressful for kids
- too narrow of a view of a child’s ability
- lack of a post-test to measure growth in some cases (FL & TX)
Those parents and testing proponents (politicians and test makers?) that are in favor of the test are so because:
- they want their children in an academic kindergarten
- it gives a way to evaluate the preschool programs
Unbelievably (or maybe not,) parents can buy a Kindergarten Test Study System! Seven sessions of 30 minutes each for $50.
If you thought the government heard your complaints about over-testing, you would be wrong. Apparently, there can always be more tests.
Are you concerned? Comment here.
Melissa Taylor is a freelance writer, an award-winning educational blogger at ImaginationSoup, an award-winning teacher with a M.A. in Education, and a mom of two children, ages 6 and 9. Follow Taylor on Twitter or find her on Facebook.
Subscribe to Class Notes blog posts in RSS.
You might also like:
Join Mom Congress on Facebook for updates on the 2012 Mom Congress conference, breaking education news, advocacy resources, and exclusive offers. | <urn:uuid:09b21c80-3c8c-4850-a988-d32cfbecb3ef> | {
"date": "2013-05-19T10:24:53",
"dump": "CC-MAIN-2013-20",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697380733/warc/CC-MAIN-20130516094300-00000-ip-10-60-113-184.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9455190896987915,
"score": 3.765625,
"token_count": 396,
"url": "http://www.parenting.com/blogs/mom-congress/melissa-taylor/5-year-olds-get-their-own-standardized-tests?con=blog&loc=bottomnext"
} |
Apple trees produce fruit on spurs. Spurs are stubby stems that form along longer stems. Bourse shoots are vegetative growths that do not produce fruit, but they are an important part of fruit production, and we are still not entirely sure why. [Being cousin to apples, all of this information is relevant to pears, as well.]
Apple tree anatomy
Before we learn about bourse shoots, we need a quick review of apple tree anatomy. Apple trees tend to grow long stems. If those stems grow upright, your apple tree is of the alternate bearing variety. If those stems tend to hang downward, your apple tree is a regular bearing type.
[Many commercial apple growers spray chemicals on apple trees to cause artificial fruit drop on heavy production years to encourage a bigger return bloom the following year. Return bloom refers to the blossoms that appear after the current crop is under way. This evens out annual fruit production, maintaining supply and keeping prices consistent.]
One study, published in the Journal of Horticultural Science, explains how the removal of too many bourse shoots significantly reduces return bloom.
Along those stems, whichever way they happen to grow, are little stubby growths called spurs. The majority of an apple crop is found on the ends of spurs. Each spur can produce fruit for 8 to 10 years, or more. Those spurs grow out of swollen areas, called bourses.
Not to be confused with bourses, bourse shoots are vegetative stems that emerge just below flower buds. In some cases, new spurs can suddenly shift their growth to become a bourse shoot instead of a spur. These bourse shoots feature a whorl of leaves. In the center of those leaves, a bud may form later in the season, but they tend to be less productive than spurs. This transition from vegetative growth to floral growth, called floral inflation, is believed to be caused by an abundance of sunlight and sugar. Other causes of floral inflation include fruit thinning, summer pruning, and bending upright shoots to a more horizontal orientation.
A common term among apple growers is bourse-over-bourse. This refers to bourse shoots emerging from existing bourse shoots, in a waterfall style growth pattern. Too many bourse shoots on one stem can lead to spur extinction. Spur extinction describes the point where a spur is no longer productive. If you see multiple bourse shoots on a stem, you can improve fruit production by pruning back to the innermost bourse shoot.
Pruning apple trees
Standard dormant season apple pruning involves removing all dead, diseased, or rubbing branches, as well as 15 to 20% of the previous year’s growth. Next, you should remove excessive bourse-over-bourse growth, and bourse shoots that are especially long, as they tend to be less productive than shorter or medium-length bourse shoots. Don’t remove too much, however. One study, published in the Journal of Horticultural Science, explains how the removal of too many bourse shoots significantly reduces return bloom [next year’s crop].
Bottom line: next year’s apple (or pear) crop is highly dependent on the number of leaves produced during the current year. If your apple tree has more bourse shoots, it is more likely to have more leaves, ergo, more fruit. But this is only true if those bourse shoots are spread evenly throughout the tree.
You can grow a surprising amount of food in your own yard. Ask me how!
To help The Daily Garden grow, you may see affiliate ads sprouting up in various places. These are not weeds. Pluck one of these offers and, at no extra cost to you, I get a small commission. As an Amazon Associate I earn from these qualifying purchases. You can also get my book, Stop Wasting Your Yard! | <urn:uuid:ea56b6d0-02da-47ec-8235-aa455704e77d> | {
"date": "2022-05-23T23:05:59",
"dump": "CC-MAIN-2022-21",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00658.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9420681595802307,
"score": 3.5,
"token_count": 801,
"url": "https://www.thedailygarden.us/garden-word-of-the-day/bourse-shoots"
} |
Find the principal and general solutions of the equation $$cotx=-\sqrt{3}$$
Asked by Pragya Singh | 1 year ago | 92
##### Solution :-
Here it is given that,
$$cotx=-\sqrt{3}$$
Now we know that
$$cot=\dfrac{\pi}{6}=\sqrt{3}$$
And
$$cot=(\pi-\dfrac{\pi}{6})$$
$$- cot=\dfrac{\pi}{6}$$
$$-\sqrt{3}$$
$$cot=(2\pi-\dfrac{\pi}{6})=-cot\dfrac{\pi}{6}$$
= $$-\sqrt{3}$$
Therefore we have,
$$cot\dfrac{5\pi}{6}= -\sqrt{3}$$ and $$cot\dfrac{11\pi}{6}= -\sqrt{3}$$
Therefore, the principal solutions are
$$x=\dfrac{5\pi}{6}\;and\;\dfrac{11\pi}{6}$$
And we know $$cotx= \dfrac{1}{tanx}$$
Therefore we have,
$$tanx=tan\dfrac{5\pi}{6}$$
Which implies,
$$x=n\pi \pm \dfrac{5\pi}{6}$$ , where $$n\in Z$$
Answered by Abhisek | 1 year ago
### Related Questions
#### prove that sin 8π/3 cos 23π/6 + cos 13π/3 sin 35π/6 = 1/2
prove that $$sin \dfrac{8π}{3} cos \dfrac{23π}{6} + cos \dfrac{13π}{3} sin \dfrac{35π}{6} = \dfrac{1}{2}$$
#### prove that 3 sin π/6 sec π/3 – 4 sin 5π/6 cot π/4 = 1
prove that $$3 sin \dfrac{π}{6} sec \dfrac{π}{3} – 4 sin \dfrac{5π}{6} cot \dfrac{π}{4} = 1$$
#### prove that tan 11π/3 – 2 sin 4π/6 – 3/4 cosec2 π/4 + 4 cos2 17π/6 = (3 – 4\sqrt{3})/2
prove that $$tan \dfrac{11π}{3} – 2 sin \dfrac{4π}{6} – \dfrac{3}{4} cosec^2 \dfrac{π}{4} + 4 cos^2 \dfrac{17π}{6} = \dfrac{(3 – 4\sqrt{3})}{2}$$ | crawl-data/CC-MAIN-2023-14/segments/1679296948951.4/warc/CC-MAIN-20230329054547-20230329084547-00518.warc.gz | null |
- A sense is defined as a way that the body perceives external stimuli, or is an awareness or feeling about something.
- Tasting, touching, seeing and hearing are all examples of a sense.
- If you have a feeling that danger is lurking, this is an example of a sense of danger.
- The definition of sense is to perceive, or be aware of something.
If you believe that someone is angry even if they haven't said so, this is an example of when you can sense their anger.
- the ability of the nerves and the brain to receive and react to stimuli, as light, sound, impact, constriction, etc.; specif., any of five faculties of receiving impressions through specific bodily organs and the nerves associated with them (sight, touch, taste, smell, and hearing)
- the senses considered as a total function of the bodily organism, as distinguished from intellect, movement, etc.
- feeling, impression, or perception through the senses: a sense of warmth, pain, etc.
- a generalized feeling, awareness, or realization: a sense of longing
- an ability to judge, discriminate, or estimate external conditions, sounds, etc.: a sense of direction, pitch, etc.
- an ability to feel, appreciate, or understand some quality: a sense of humor, honor, etc.
- the ability to think or reason soundly; normal intelligence and judgment, often as reflected in behavior
- soundness of judgment or reasoning: some sense in what he says
- something wise, sound, or reasonable: to talk sense
- normal ability to reason soundly: to come to one's senses
- meaning; esp., any of several meanings conveyed by or attributed to the same word or phrase
- essential signification; gist: to grasp the sense of a remark
- the general opinion, sentiment, or attitude of a group
- Math. either of two contrary directions that may be specified, as clockwise or counterclockwise for the circumference of a circle, positive or negative for a line segment, etc.
Origin of senseFrench sens ; from Classical Latin sensus ; from sentire, to feel, perceive: see send
in a sense
- to a limited extent or degree
- in one aspect
- a. Any of the faculties by which stimuli from outside or inside the body are received and felt, as the faculties of hearing, sight, smell, touch, taste, and equilibrium.b. A perception or feeling produced by a stimulus; sensation: a sense of fatigue and hunger.
- senses The faculties of sensation as means of providing physical gratification and pleasure.
- a. An intuitive or acquired perception or ability to estimate: a sense of diplomatic timing.b. A capacity to appreciate or understand: a keen sense of humor.c. A vague feeling or presentiment: a sense of impending doom.d. Recognition or perception either through the senses or through the intellect; consciousness: has no sense of shame.
- a. Natural understanding or intelligence, especially in practical matters: The boy had sense and knew just what to do when he got lost.b. often senses The normal ability to think or reason soundly: Have you taken leave of your senses?c. Something sound or reasonable: There's no sense in waiting three hours.
- a. A meaning that is conveyed, as in speech or writing; signification: The sense of the criticism is that the proposal has certain risks.b. One of the meanings of a word or phrase: The word set has many senses.
- a. Judgment; consensus: sounding out the sense of the electorate on capital punishment.b. Intellectual interpretation, as of the significance of an event or the conclusions reached by a group: I came away from the meeting with the sense that we had resolved all outstanding issues.
transitive verbsensed sensed, sens·ing, sens·es
- To become aware of; perceive: organisms able to sense their surroundings.
- To grasp; understand: sensed that the financial situation would improve.
- To detect automatically: sense radioactivity.
Origin of senseMiddle English, meaning, from Old French sens, from Latin sēnsus, the faculty of perceiving, from past participle of sentīre, to feel; see sent- in Indo-European roots.
- Any of the methods for a living being to gather data about the world; sight, smell, hearing, touch, taste.
- Let fancy still my sense in Lethe steep.
- What surmounts the reach / Of human sense I shall delineate.
- Perception through the intellect; apprehension; awareness.
- a sense of security
- Sound practical or moral judgment.
- It's common sense not to put metal objects in a microwave oven.
- Some are so hardened in wickedness as to have no sense of the most friendly offices.
- The meaning, reason, or value of something.
- You don’t make any sense.
- the true sense of words or phrases
- A natural appreciation or ability.
- A keen musical sense
- (pragmatics) The way that a referent is presented.
- (semantics) A single conventional use of a word; one of the entries for a word in a dictionary.
- (mathematics) One of two opposite directions in which a vector (especially of motion) may point. See also polarity.
- (mathematics) One of two opposite directions of rotation, clockwise versus anti-clockwise.
(third-person singular simple present senses, present participle sensing, simple past and past participle sensed)
From Middle English sense, from Old French sens, sen, san (“sense, reason, direction”); partly from Latin sensus (“sensation, feeling, meaning”), from sentiō (“feel, perceive”); partly of Germanic origin (whence also Occitan sen, Italian senno), from Old Frankish *sinn (“reason, judgement, mental faculty, way, direction”), from Proto-Germanic *sinnaz (“mind, meaning”). Both Latin and Germanic from Proto-Indo-European *sent- (“to feel”). Compare French assener (“to thrust out”), forcené (“maniac”). More at send. | <urn:uuid:6c798e05-b2de-44f6-b13c-6a135279a12b> | {
"date": "2014-04-16T16:05:03",
"dump": "CC-MAIN-2014-15",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609524259.30/warc/CC-MAIN-20140416005204-00355-ip-10-147-4-33.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9174039959907532,
"score": 3.53125,
"token_count": 1339,
"url": "http://www.yourdictionary.com/sense"
} |
# What is the radius vector of a point?
The radius vector of a point A relative to the origin varies as →r=at^i+bt2^j where a and b are positive constants.
## What is radius vector of a curve?
radius vector (plural radii vectores or radius vectors) (mathematics) A straight line (or the length of such line) connecting any point, as of a curve, with a fixed point, or pole, round which the straight line turns, and to which it serves to refer the successive points of a curve, in a system of polar coordinates.
## How can radius be a vector?
CONSTANT ELECTROMAGNETIC FIELDS where R+ − = R+ − R− is the radius vector from the center of negative to the center of positive charge. In particular, if we have altogether two charges, then R+ − is the radius vector between them.
## What is radius vector in a circular motion?
The radius for circular motion is a vector. It is shown at the left drawn in red. This radius vector locates the orbiting object. One should imagine an x, y coordinate system with its origin at the center of the circle. The radius extends from this origin to the position of the object.
## What is the angle between radius vector and centripetal acceleration?
So the angle between centripetal acceleration and radius vector is 180 degrees.
## What is radius vector in circular motion 12th class?
For a particle performing circular motion, its position vector with respect to the centre of the circle is called the radius vector. [Note : The radius vector has a constant magnitude, equal to the radius of the circle. However, its direction changes as the position of the particle changes along the circumference.]
## Is radius a vector or scalar?
Radius is scalar quantity which is fully described by its magnitude.It is defined as the distance between center and any point on circumference of a circle.
## Is area a vector or scalar?
Area is a vector quantity.
## What is angular velocity in circular motion?
In uniform circular motion, angular velocity (𝒘) is a vector quantity and is equal to the angular displacement (Δ𝚹, a vector quantity) divided by the change in time (Δ𝐭). Speed is equal to the arc length traveled (S) divided by the change in time (Δ𝐭), which is also equal to |𝒘|R.
## What is angular displacement in circular motion?
Angular displacement is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path.
## What is uniform circular motion?
uniform circular motion, motion of a particle moving at a constant speed on a circle. In the Figure, the velocity vector v of the particle is constant in magnitude, but it changes in direction by an amount Δv while the particle moves from position B to position C, and the radius R of the circle sweeps out the angle ΔΘ.
## What is the angle between radius vector and angular vector?
This means the angle between the two vectors must be 180∘ or π rad. i.e. they are in opposite directions assuming that radius is measured with its positive axis outwards.
## Is centripetal acceleration a constant vector?
Since v and R are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, centripetal acceleration is not a constant vector.
## What is difference between centripetal and centrifugal force?
Centripetal force is the component of force acting on an object in curvilinear motion which is directed towards the axis of rotation or centre of curvature. Centrifugal force is a pseudo force in a circular motion which acts along the radius and is directed away from the centre of the circle.
## What is vector formula?
the formula to determine the magnitude of a vector (in two dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem. the formula to determine the magnitude of a vector (in three dimensional space) V = (x, y, z) is: |V| = √(x2 + y2 + z2)
## What is magnitude of a vector?
The magnitude of a vector is the length of the vector. The magnitude of the vector a is denoted as ∥a∥. See the introduction to vectors for more about the magnitude of a vector. Formulas for the magnitude of vectors in two and three dimensions in terms of their coordinates are derived in this page.
## Is speed a vector?
Speed is a scalar quantity – it is the rate of change in the distance travelled by an object, while velocity is a vector quantity – it is the speed of an object in a particular direction.
## What is radius of gyration explain its physical significance?
Radius of gyration is defined as the distance from the axis of rotation to a point where total mass of the body is supposed to be concentrated. 1. It the particles of body are distributed lose to axis of rotation,the radius gyration is less.
## What is radius of gyration shaala com?
Radius of gyration of a body is defined as the distance between the axis of rotation and a. point at which the whole mass of the body is supposed to be concentrated, so as to possess the same moment of inertia as that of body.
## What produces angular acceleration?
Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics, torque is what causes an object to acquire angular acceleration. | crawl-data/CC-MAIN-2022-49/segments/1669446711074.68/warc/CC-MAIN-20221206060908-20221206090908-00235.warc.gz | null |
# Math
Solve by eliminnation methods
2x-4y=5
2x-4y=6
solve the system by elimination method
5x+2y= -13
7x-3y=17
Solve
x+6<-7 or x+6>4
Determine whether the given numbers are solutions of the inequality
8,-10,-18,-3
y-8>2y-3
Solve by the substitutioj method
2m+n=9
m-5n=10
1. 👍
2. 👎
3. 👁
1. Please post such problems separately and show your work. If you are unfamiliar with the elimination and substitution methods for solving simultaneous equations, referenc material can be provided.
Your first question has no solution because the two equations are incompatible. They represent two parallel lines.
1. 👍
2. 👎
## Similar Questions
1. ### finite math
Solve the system of linear equations using the Gauss-Jordan elimination method. 3x−2y+ 4z = 22 2x+y− 2z = 3 x+ 4y − 8z = −16
What advantages does the method of substitution have over graphing for solving systems of equations? Choose the correct answer below. A. Graphing cannot be used to solve dependent or inconsistent systems due to the nature of the
3. ### maths
1.solve the set of linear equation by matrix method.a+3b+2c=3,2a-b-3c=-8,5a+2b+c=9 solve for a,b,c 2.solve by Guassian elimination method, (a)a+2b+3c=5,3a-b+2c=8,4a-6b-4c=-2, (b)
4. ### Algebra 1
Which method would be the simplest way to solve the system? 7x +5y = 19 -7x-2y = -16 graphing substitution elimination or distributive
1. ### algebra
use the elimination method to solve the system of equations. Choose the correct ordered pair. 2x+4y=16 2x-4y=0 A.(4,2) B.(2,4) C.(2,-4) D.(4,-2)
2. ### math
Solve the following system using the elimination method: -3x + 4y = 6 9x - 12y = -18
3. ### math
Solve the system of equations by Elimination OR Substitution. Explain why you chose one method over the other. 3x – 2y = 8 2x + 5y = -1
4. ### math
solve the system by the elimination method: 4x=5y+24 5x=4y+21
1. ### MaTh = Algebra = help
Solve this system of linear equaiton by an algebraic method. So If I had to solve this the elimination method way, how would I do it? x-2y = 10 3x-y = 0
2. ### Algebra
Use the elimination method to solve the following system of equations. x + 3y – z = 2 x – 2y + 3z = 7 x + 2y – 5z = –21
3. ### math
What is the first step in solving the linear system {2x − 3y = 11 {−x + 5y = −9 by the substitution method in the most efficient way? A. Solve the first equation for x. B. Solve the first equation for y. C. Solve the second
4. ### math
What is the first step in solving the linear system {2x−3y=11 {−x+5y=−9 by the substitution method in the most efficient way? A. Solve the first equation for x. B. Solve the first equation for y. C. Solve the second equation | crawl-data/CC-MAIN-2021-31/segments/1627046152236.64/warc/CC-MAIN-20210727041254-20210727071254-00178.warc.gz | null |
The TRANSPOSE function transposes an array of rank two.
matrix is an INTENT(IN) rank two array of any type.
The result is of rank two and the same type and kind as matrix. Its shape is (n, m), where (m, n) is the shape of matrix. Element (i, j) of the result has the value matrix(j, i).
Exampleinteger:: a(2,3)=reshape((/1,2,3,4,5,6/),shape(a)) write(*,'(2i3)') a ! writes 1 2 ! 3 4 ! 5 6 write(*,*) shape(a) ! writes 2 3 write(*,'(3i3)') transpose(a) ! writes 1 3 5 ! 2 4 6 write(*,*) shape(transpose(a)) ! writes 3 2 | <urn:uuid:8413bb8f-bc14-4cc0-a142-00ac44775aed> | {
"date": "2015-08-02T14:20:50",
"dump": "CC-MAIN-2015-32",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042989126.22/warc/CC-MAIN-20150728002309-00104-ip-10-236-191-2.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.7663549780845642,
"score": 3.703125,
"token_count": 185,
"url": "http://www.lahey.com/docs/lfprohelp/F95ARTRANSPOSEFn.htm"
} |
Ultimately, it looks ahead to where we might be in the next few decades, moving the story forward into the 2030s, when NASA astronauts are regularly traveling to Mars and living on the surface.
It’s a notion that every science lover dreams about, but what would it take to really get us there?
Well, although the action takes place 20 years in the future, NASA is already developing many of the technologies that appear in the film (and in the book). Indeed, NASA has been gearing up for a manned mission to Mars for some time now. So take a moment to compare the fictional with the factual, and see what “futuristic” technology we already have today, what we’ll need to get to Mars, and just how viable the journey really is.
On the surface of Mars, Watney spends a significant amount of time in the habitation module — the Hab — his home away from home. Future astronauts who land on Mars will need such a home to avoid spending their Martian sols lying on the dust in a spacesuit.
At NASA Johnson Space Center, crews train for long-duration deep space missions in the Human Exploration Research Analog (HERA).
HERA is a self-contained environment that simulates a deep-space habitat. The two-story habitat is complete with living quarters, workspaces, a hygiene module and a simulated airlock. Within the module, test subjects conduct operational tasks, complete payload objectives and live together for 14 days (soon planned to increase to up to 60 days), simulating future missions in the isolated environment.
Astronauts have recently used the facility to simulate ISS missions. These research analogs provide valuable data in human factors, behavioral health and countermeasures to help further NASA’s understanding on how to conduct deep space operations. Additionally, the longest space travel simulation ever conducted on U.S. soil has already started.
On Aug. 28, the fourth Hawaii Space Exploration and Analog and Simulation mission began. The 6 scientists inside will spend a full year inside an isolated, solar-powered dome atop the Mauna Loa volcano. Their goal: Prepare humans for life on Mars. So in this respect at least, we are well on our way.
Today, astronauts on the International Space Station have an abundance of food delivered to them by cargo resupply vehicles, including some from commercial industries. On Mars, humans would not be able to rely on resupply missions from Earth – even with express delivery they would take at least nine months. For humans to survive on Mars, they will need a continuous source of food. They will need to grow crops.
Watney turns the Hab into a self-sustaining farm in “The Martian,” making potatoes the first Martian staple. But how viable is this, really?
Well, today, in low-Earth orbit, lettuce is the most abundant crop in space (not nearly as hearty or sustaining as the potato, I’m afraid). Aboard the International Space Station, Veggie is a deployable fresh-food production system.
Using red, blue, and green lights, Veggie helps plants grow in pillows, small bags with a wicking surface containing media and fertilizer, to be harvested by astronauts. In 2014, astronauts used the system to grow “Outredgeous” red romaine lettuce and just recently sampled this space-grown crop for the first time. This is a huge step in space farming, and NASA is looking to expand the amount and type of crops to help meet the nutritional needs of future astronauts on Mars. However, at this juncture, we haven’t figured out how people can live off of lettuce for a year…because it’s simply not possible. Still, we are at least taking the first tentative steps, and more research is scheduled over the coming years.
There are no lakes, river or oceans on the surface of Mars, and sending water from Earth would take more than nine months. Astronauts on Mars must be able to create their own water supply. The Ares 3 crew does not waste a drop on Mars with their water reclaimer, and Watney needs to use his ingenuity to come up with some peculiar ways to stay hydrated and ensure his survival on the Red Planet.
On the International Space Station, it is the same. No drop of sweat, tears, or even urine goes to waste. The Environmental Control and Life Support System recovers and recycles water from everywhere: urine, hand washing, oral hygiene, and other sources. Through the Water Recovery System (WRS), water is reclaimed and filtered, ready for consumption. One astronaut simply put it, “Yesterday’s coffee turns into tomorrow’s coffee.”
Liquid presents some tricky problems in space. The WRS and related systems have to account for the fact that liquids behave very differently in a microgravity environment. The part of the WRS that processes urine must use a centrifuge for distillation, since gases and liquids do not separate like they do on Earth.
NASA is continuing to develop new technologies for water recovery. Research is being conducted to advance the disposable multifiltration beds (the filters that remove inorganic and non-volatile organic contaminants) to be a more permanent component to the system. Brine water recovery would reclaim every drop of the water from the “bottoms product” leftover from urine distillation. For future human-exploration missions, crews would be less dependent on any resupply of spare parts or extra water from Earth
Interestingly, technology behind this system has been brought down to Earth to provide clean drinking water to remote locations and places devastated with natural disasters.
Food, water, shelter: three essentials for survival on Earth. But there’s a fourth we don’t think about much, because it’s freely available: oxygen. On Mars, Watney can’t just step outside for a breath of fresh air To survive, he has to carry his own supply of oxygen everywhere he goes. But first he has to make it. In his Hab he uses the “oxygenator,” a system that generates oxygen using the carbon dioxide from the MAV (Mars Ascent Vehicle) fuel generator.
On the International Space Station, the astronauts and cosmonauts have the Oxygen Generation System, which reprocesses the atmosphere of the spacecraft to continuously provide breathable air efficiently and sustainably. The system produces oxygen through a process called electrolysis, which splits water molecules into their component oxygen and hydrogen atoms. The oxygen is released into the atmosphere, while the hydrogen is either discarded into space or fed into the Sabatier System, which creates water from the remaining byproducts in the station’s atmosphere.
Oxygen is produced at more substantial rate through a partially closed-loop system that improves the efficiency of how the water and oxygen are used. NASA is working to recover even more oxygen from byproducts in the atmosphere to prepare for the journey to Mars.
The Martian surface is not very welcoming for humans. The atmosphere is cold and there is barely any breathable air. An astronaut exploring the surface must wear a spacesuit to survive outside of a habitat while collecting samples and maintaining systems.
Mark Watney spends large portions of his Martian sols (a sol is a Martian day) working in a spacesuit. He ends up having to perform some long treks on the surface, so his suit has to be flexible, comfortable, and reliable.
NASA is currently developing the technologies to build a spacesuit that would be used on Mars, as the current ones are rather bulky. Engineers consider everything from traversing the Martian landscape to picking up rock samples.
The Z-2 and Prototype eXploration Suit, NASA’s new prototype spacesuits, help solve unique problems to advance new technologies that will one day be used in a suit worn by the first humans to set foot on Mars. Each suit is meant to identify different technology gaps – features a spacesuit may be missing – to complete a mission. Spacesuit engineers explore the tradeoff between hard composite materials and fabrics to find a nice balance between durability and flexibility.
One of the challenges of walking on Mars will be dealing with dust. The red soil on Mars could affect the astronauts and systems inside a spacecraft if tracked in after a spacewalk. To counter this, new spacesuit designs feature a suitport on the back, so astronauts can quickly hop in from inside a spacecraft while the suit stays outside, keeping it clean indoors.
Once humans land on the surface of Mars, they must stay there for more than a year, while the planets move into a position that will minimize the length of their trip home. This allows the astronauts plenty of time to conduct experiments and explore the surrounding area, but they won’t want to be limited to how far they can go on foot. Astronauts will have to use robust, reliable and versatile rovers to travel farther.
In “The Martian,” Watney takes his rover for quite a few spins, and he even has to outfit the vehicle with some unorthodox modifications to help him survive.
On Earth today, NASA is working to prepare for every encounter with the Multi-Mission Space Exploration Vehicle (MMSEV). The MMSEV has been used in NASA’s analog mission projects to help solve problems that the agency is aware of and to reveal some that may be hidden. The technologies are developed to be versatile enough to support missions to an asteroid, Mars, its moons and other missions in the future. NASA’s MMSEV has helped address issues like range, rapid entry/exit and radiation protection. Some versions of the vehicle have six pivoting wheels for maneuverability. In the instance of a flat tire, the vehicle simply lifts up the bad wheel and keeps on rolling.
Slow and steady wins the race, and ion propulsion proves it.
In “The Martian,” the Ares 3 crew lives aboard the Hermes spacecraft for months as they travel to and from the Red Planet, using ion propulsion as an efficient method of traversing through space for over 280 million miles. Ion propulsion works by electrically charging a gas such as argon or xenon and pushing out the ions at high speeds, about 200,000 mph. The spacecraft experiences a force similar to that of a gentle breeze, but by continuously accelerating for several years, celestial vessels can reach phenomenal speeds. Ion propulsion also allows the spacecraft to change its orbit multiple times, then break away and head for another distant world.
This technology allows modern day spacecraft like NASA’s Dawn Spacecraft to minimize fuel consumption and perform some crazy maneuvers. Dawn has completed more than five years of continuous acceleration for a total velocity change around 25,000 mph, more than any spacecraft has accomplished on its own propulsion system. Along the way, it has paid humanity’s first visits to the dwarf planet Ceres and the asteroid Vesta.
Provided by NASA. | <urn:uuid:d83847cc-5105-4ff9-9dcf-410de0aa3237> | {
"date": "2022-05-17T07:29:51",
"dump": "CC-MAIN-2022-21",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00658.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9380596280097961,
"score": 3.6875,
"token_count": 2255,
"url": "https://futurism.com/the-journey-to-mars-7-real-nasa-technologies-in-the-martian"
} |
Astronaut photograph ISS013-E-6947 was acquired April 12, 2006, with a Kodak 760C digital camera using an 800 mm lens, and is provided by the ISS Crew Earth Observations experiment and the Image Science & Analysis Group, Johnson Space Center. The image in this article has been cropped and enhanced to improve contrast. Lens artifacts have been removed. The International Space Station Program supports the laboratory to help astronauts take pictures of Earth that will be of the greatest value to scientists and the public, and to make those images freely available on the Internet. Additional images taken by astronauts and cosmonauts can be viewed at the NASA/JSC Gateway to Astronaut Photography of Earth.
The icefields of Patagonia, located at the southern end of South America, are the largest masses of ice in the temperate Southern Hemisphere (approximately 55,000 square kilometers). The icefields contain numerous valley glaciers that terminate in meltwater-fed lakes. These are known as “calving” glaciers, as they lose mass when large ice chunks collapse from the terminus—or end—of the glacier. These newly separated chunks of ice are then free to float away, much like ice cubes in a punch bowl.
The terminus of the Viedma Glacier, approximately 2 kilometers across where it enters Lake Viedma, is shown in this astronaut photograph. Moraines are accumulations of soil and rock debris that form along the sides and front of a glacier as it flows across the landscape (much like a bulldozer). Independent valley glaciers can merge together as they flow down slope, and the moraines become entrained in the center of the new ice mass. These medial moraines are visible as dark parallel lines within the white central mass of the glacier (image center and left). Crevasses—oriented at right angles to the medial moraines—are also visible in the grey-brown ice along the sides of the glacier. The canyon-like crevasses form as a result of stress between the slower moving ice along the valley sides (where there is greater friction) and the more rapidly moving ice in the center of the glacier. Calving of ice from the southwestern fork of the glacier terminus is visible at image lower left.
As they respond to regional climate change, the Patagonian glaciers are closely monitored using remotely sensed data. Scientists compare series of images collected over time to monitor the change in ice extent and position. Scientists have also estimated changes in volume using topographic data from NASA’s Shuttle Radar Topography Mission. The Global Land Ice Measurements from Space (GLIMS) Website is an excellent resource for glacier-monitoring information.
Note: Often times, due to the size, browsers have a difficult time opening and displaying images. If you experiece an error when clicking on an image link, please try directly downloading the image (using a right click, save as method) to view it locally.
This image originally appeared on the Earth Observatory. Click here to view the full, original record. | <urn:uuid:3a9c276b-2067-4958-a0d1-13f84ffd2e01> | {
"date": "2015-09-05T10:18:54",
"dump": "CC-MAIN-2015-35",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440646242843.97/warc/CC-MAIN-20150827033042-00169-ip-10-171-96-226.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9195660352706909,
"score": 4,
"token_count": 622,
"url": "http://visibleearth.nasa.gov/view.php?id=6534"
} |
## Minggu, 13 November 2011
### Rotation of Rigid Object About a Fixed Axis part 2
10.5 Calculation of moment inertia
Moment of inertia of a rigid object is :
I= ʃ r2dm
Parallel-axis theorem
“Suppose the of inertia about an axis through the center of mass of an object is The parallel-axis theorem states that the moment of inertia about any axis parallel to and a distance D away from this axis is: ICM +MD2
10.6 Torque
where d is the moment arm of the force, which is the perpendicular distance from the
rotation axis to the line of action of the force. Torque is a measure of the tendency of
the force to change the rotation of the object about some axis.
When a force is exerted on a rigid object pivoted about an axis, the object tends to rotate about that axis. The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque τ (Greek tau). Torque is a vector, but we
will consider only its magnitude here and explore its vector nature in Chapter 11.
Consider the wrench pivoted on the axis through O in Figure 10.13. The applied
force F acts at an angle ϕ to the horizontal. We define the magnitude of the torque associate
with the force F by the expression :
10.7 Relationship Between Torque and Angular Acceleration.
In Chapter 4, we learned that a net force on an object causes an acceleration of the object and that the acceleration is proportional to the net force (Newton’s second law). In this section we show the rotational analog of Newton’s second law—the angular acceleration of a rigid object rotating about a fixed axis is proportional to the net torque acting about that axis. Before discussing the more complex case of rigid-object rotation, however, it is instructive first to discuss the case of a particle moving in a circular path about some fixed point under the influence of an external force.
Consider a particle of mass m rotating in a circle of radius r under the influence of a tangential force Ft and a radial force Fr , as shown in Figure 10.16. The tangential force provides a tangential acceleration at, and
The magnitude of the torque about the center of the circle due to Ft is
Because the tangential acceleration is related to the angular acceleration through the relationship at " r( (see Eq. 10.11), the torque can be expressed as Recall, the torque can be expressed as
Because the tangential acceleration is related to the angular acceleration through the relationship at " r( (see Eq. 10.11), the torque can be expressed as Recall, the torque can be expressed as
That is, the torque acting on the particle is proportional to its angular acceleration, and the proportionality constant is the moment of inertia. Note that τ = I α is the rotational analog of Newton’s second law of motion, F = ma.
Now let us extend this discussion to a rigid object of arbitrary shape rotating about a fixed axis, as in Figure 10.17. The object can be regarded as an infinite number of mass elements dm of infinitesimal size. If we impose a Cartesian coordinate system on the object, then each mass element rotates in a circle about the origin, and each has a tangential acceleration at produced by an external tangential force dFt . For any given element, we know from Newton’s second law that
The torque associated with the force dFt acts about the origin and is given by
Because αt = rα the expression for becomes
Although each mass element of the rigid object may have a different linear acceleration at , they all have the same angular acceleration With this in mind, we can integrate the above expression to obtain the net torque ∑τ about O due to the external forces:
where ( can be taken outside the integral because it is common to all mass elements. From Equation 10.17, we know that ʃ r2 dm is the moment of inertia of the object about the rotation axis through O, and so the expression for ∑τ becomes
Note that this is the same relationship we found for a particle moving in a circular path (see Eq. 10.20). So, again we see that the net torque about the rotation axis is proportional to the angular acceleration of the object, with the proportionality factor being I, a quantity that depends upon the axis of rotation and upon the size and shape of the object. In view of the complex nature of the system, the relationship ∑τ = is strikingly simple and in complete agreement with experimental observations.
Finally, note that the result ∑τ = also applies when the forces acting on the mass elements have radial components as well as tangential components. This is because the line of action of all radial components must pass through the axis of rotation, and hence all radial components produce zero torque about that axis.
10.8 work, Power, and Energy in Rotational Motion
Up to this point in our discussion of rotational motion in this chapter, we focused on an approach involving force, leading to a description of torque on a rigid object. We now see how an energy approach can be useful to us in solving rotational problems.
We begin by considering the relationship between the torque acting on a rigid object and its resulting rotational motion in order to generate expressions for power and a rotational analog to the work–kinetic energy theorem. Consider the rigid object pivoted at O in Figure 10.22. Suppose a single external force F is applied at P, where F lies in the plane of the page. The work done by F on the object as it rotates through an infinitesimal
Distance ds = rdθ is
where F sin 3 is the tangential component of F, or, in other words, the component of
the force along the displacement. Note that the radial component of F does no work because
it is perpendicular to the displacement.
Because the magnitude of the torque due to F about O is defined as rF sin θ by Equation 10.19, we can write the work done for the infinitesimal rotation as
The rate at which work is being done by F as the object rotates about the fixed axis through the angle in a time interval dt is
Because dW/dt is the instantaneous power (see Section 7.8) delivered by the forceand d!/dt " &, this expression reduces to
This expression is analogous to P= Fv in the case of linear motion, and the expression dW = τdθ is analogous to dW = Fx dx.
In studying linear motion, we found the energy approach extremely useful in describing the motion of a system. From what we learned of linear motion, we expect that when a symmetric object rotates about a fixed axis, the work done by external forces equals the change in the rotational energy.
To show that this is in fact the case, let us begin with ∑τ = Using the chain rule from calculus, we can express the resultant torque as
Rearranging this expression and noting that ∑τdθ = dW , we obtain
Integrating this expression, we obtain for the total work done by the net external force acting on a rotating system
where the angular speed changes from &i to &f . That is, the work–kinetic energy theorem for rotational motion states that
the net work done by external forces in rotating a symmetric rigid object about a fixed axis equals the change in the object’s rotational energy”
In general, then, combining this with the translational form of the work–kinetic energy theorem from Chapter 7, the net work done by external forces on an object is the change in its total kinetic energy, which is the sum of the translational and rotational kinetic energies. For example, when a pitcher throws a baseball, the work done by the pitcher’s hands appears as kinetic energy associated with the ball moving through space as well as rotational kinetic energy associated with the spinning of the ball.
In addition to the work–kinetic energy theorem, other energy principles can also be applied to rotational situations. For example, if a system involving rotating objects is isolated, the principle of conservation of energy can be used to analyze the system.
Table 10.3 lists the various equations we have discussed pertaining to rotational motion, together with the analogous expressions for linear motion. The last two equations in Table 10.3, involving angular momentum L, are discussed in Chapter 11 and are included here only for the sake of completeness.
10.9 Rolling Motion of a Rigid Object
In this section we treat the motion of a rigid object rolling along a flat surface. Ingeneral, such motion is very complex. Suppose, for example, that a cylinder is rolling on a straight path such that the axis of rotation remains parallel to its initial orientation in space. As Figure 10.26 shows, a point on the rim of the cylinder moves in a complex path called a cycloid. However, we can simplify matters by focusing on the center of mass rather than on a point on the rim of the rolling object. As we see in Figure 10.26, the center of mass moves in a straight line. If an object such as a cylinder rolls without slipping on the surface (we call this pure rolling motion), we can show that a simple relationship exists between its rotational and translational motions.
Consider a uniform cylinder of radius R rolling without slipping on a horizontal surface (Fig. 10.27). As the cylinder rotates through an angle !, its center of mass moves a linear distance s = (See Eq. 10.1a). Therefore, the linear speed of the center of mass for pure rolling motion is given by
Where & is the angular speed of the cylinder. Equation 10.25 holds whenever a cylinder or sphere rolls without slipping and is the condition for pure rolling motion
The magnitude of the linear acceleration of the center of mass for pure rolling motion is
Where α is the angular acceleration of the cylinder.
The linear velocities of the center of mass and of various points on and within the cylinder are illustrated in Figure 10.28. A short time after the moment shown in the drawing, the rim point labeled P might rotate from the six o’clock position to, say, the seven o’clock position, while the point Q would rotate from the ten o’clock position to the eleven o’clock position, and so on. Note that the linear velocity of any point is in a direction perpendicular to the line from that point to the contact point P. At any instant, the part of the rim that is at point P is at rest relative to the surface because slipping does not occur.
All points on the cylinder have the same angular speed. Therefore, because the distance from P1 to P is twice the distance from P to the center of mass, P1 has a speed 2vCM = 2ω. To see why this is so, let us model the rolling motion of the cylinder in Figure 10.29 as a combination of translational (linear) motion and rotational motion. For the pure translational motion shown in Figure 10.29a, imagine that the cylinder does not rotate, so that each point on it moves to the right with speed vCM. For the pure rotational motion shown in Figure 10.29b, imagine that a rotation axis through the center of mass is stationary, so that each point on the cylinder has the same angular speed &. The combination of these two motions represents the rolling motion shown in Figure 10.29c. Note in Figure 10.29c that the top of the cylinder has linear speed vCM + Rω + vCM + vCM = 2vCM, which is greater than the linear speed of any other point on the cylinder. As mentioned earlier, the center of mass moves with linear speed vCM while the contact point between the surface and cylinder has a linear speed of zero.
We can express the total kinetic energy of the rolling cylinder as
Where IP is the moment of inertia about a rotation axis through P. Applying the parallel-axis theorem, we can substitute IP =ICM + MR2 into Equation 10.27 to obtain
or, because vCM =
The term 1/2ICMω2 represents the rotational kinetic energy of the cylinder about its center of mass, and the term ½ Mv CM2 represents the kinetic energy the cylinder would have if it were just translating through space without rotating. Thus, we can say that the total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.
We can use energy methods to treat a class of problems concerning the rolling motion of an object down a rough incline. For example, consider Figure 10.30, which shows a sphere rolling without slipping after being released from rest at the top of the incline. Note that accelerated rolling motion is possible only if a friction force is present between the sphere and the incline to produce a net torque about the center of mass. Despite the presence of friction, no loss of mechanical energy occurs because the contact point is at rest relative to the surface at any instant. (On the other hand, if the sphere were to slip, mechanical energy of the sphere–incline–Earth system would be lost due to the non conservative force of kinetic friction.)
Using the fact that vCM = Rω for pure rolling motion, we can express Equation 10.28
For the system of the sphere and the Earth, we define the zero configuration of gravitational potential energy to be when the sphere is at the bottom of the incline. Thus, conservation of mechanical energy gives us | crawl-data/CC-MAIN-2018-26/segments/1529267863939.76/warc/CC-MAIN-20180620221657-20180621001657-00525.warc.gz | null |
On the 10th of December, the world celebrates the International Human Rights Day. On 10th October 1948, the United Nations Adopted the Universal Declaration of Human Rights. However, the Human Rights push did not begin in 1948, and it was not the first time that human rights ideals were put to paper. Similarly, the Human Rights fight has a long way to go, globally and at home. With a shrinking civil society, blatant and rampant police brutality, a gagged media, and systematic violence against minorities, there is still a lot of work to be done.
Articles articulated in the Universal Declaration of Human Rights are found in the Constitution of Kenya 2010. Kenya prides itself in the fact that it ascribes to this declaration, and as a democracy, it works to ensure the safety and freedom of all the people within its borders. Unfortunately, whereas this is the desire of the Kenyan people, this is not the case. Human Rights Violations still exist, perpetrated in part by government agencies and other positions of power and authority. A healthy democracy has a vibrant Civil Society that perpetually holds the Government to account. And while civic spaces are rapidly shrinking the bastions of human rights remain and keep the fight.
Eleanor Roosevelt said that Human Rights begin in the small spaces, that cannot be seen on maps. The Gay and Lesbian Coalition of Kenya joins Civil Society Organizations in creating a safe and enabling environment for all sexual and gender diverse Kenyans. We work tirelessly to ensure that the human rights of all Kenyans regardless of their sexual orientation, gender identity or expression prevail.
As we observe and celebrate Human Rights gains made so far, we recognise that the road to universal access to human rights will be tough. Much is yet to be achieved and can only be achieved by a coordinated, collaborative, resilient, open-minded and determined civil society. | <urn:uuid:cdf865d0-9d6a-450e-b1ed-7519d3f15a39> | {
"date": "2020-07-06T17:39:07",
"dump": "CC-MAIN-2020-29",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655881763.20/warc/CC-MAIN-20200706160424-20200706190424-00257.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9428307414054871,
"score": 3.53125,
"token_count": 374,
"url": "https://www.galck.org/international-human-rights-day-2017/"
} |
A blockchain is a decentralized, distributed database that maintains a continuously growing list of records called blocks. These blocks are linked and secured using cryptography, and each block contains a cryptographic hash of the previous block, a timestamp, and transaction data.
What is blockchain and how does it work?
In simple terms, it’s like a digital ledger that records transactions in a secure and transparent way. It allows multiple parties to record and verify transactions without the need for a central authority, making it a decentralized system.
One of the key features of blockchain technology is its ability to achieve distributed consensus among all participants in the network. This means that all participants must agree on the state of the blockchain and the validity of transactions before they can be recorded.
To achieve this, blockchains use consensus algorithms, which are mechanisms that enable participants to reach agreement on the state of the network. There are several types of consensus algorithms, such as Proof of Work (PoW) and Proof of Stake (PoS).
For example, in the Proof of Work consensus algorithm, miners compete to solve a complex mathematical problem and the first one to solve it gets to add the next block to the chain. In the Proof of Stake algorithm, the right to add the next block is given to the participant who holds the most tokens, or stake, in the network.
Understanding blockchain data structure
A blockchain maintains a continuously growing list of records called blocks. These blocks are linked and secured using cryptography, and each block contains a cryptographic hash of the previous block, a timestamp, and transaction data.
The data structure of a blockchain is designed to ensure the security, transparency, and immutability of the data it stores. It consists of a chain of blocks, where each block contains a list of transactions and a link to the previous block. This creates a tamper-evident record of all transactions on the blockchain.
The structure of a block in a blockchain includes these elements
1) Block header
This contains metadata about the block, such as the block height (the position of the block in the chain), the timestamp, and the cryptographic hash of the previous block.
2) Transaction data
This is the actual data that is being recorded on the blockchain, such as financial transactions or data records.
This is a random number that is used in the Proof of Work consensus algorithm to ensure that the block is difficult to create, but easy to verify.
Blockchain data structure is designed to be efficient, secure, and scalable. It allows for the efficient storage and validation of transactions, and its decentralized nature ensures that it is resistant to tampering and censorship.
Key points on data storage in blocks
- In a blockchain network, each block contains a list of transactions.
- These transactions can be anything from financial transactions to data records.
- When a new transaction is made, it is broadcast to all participants in the network.
- Each participant then verifies the transaction to ensure its validity and adds it to their own copy of the blockchain.
- Once a predetermined number of transactions have been verified, they are grouped together into a block and added to the chain.
- This process ensures that all transactions are recorded in a secure and transparent manner, as all participants in the network have a copy of the entire blockchain.
In summary, a blockchain data structure uses cryptography and consensus algorithms to maintain a secure and transparent record of transactions.
It consists of a chain of blocks, where each block contains a list of transactions and a link to the previous block, creating a tamper-evident record of all transactions on the blockchain. | <urn:uuid:74f24a45-5044-4d5b-9978-9abc2821d064> | {
"date": "2023-04-02T04:58:29",
"dump": "CC-MAIN-2023-14",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00458.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9143728613853455,
"score": 3.8125,
"token_count": 735,
"url": "https://metaschool.so/articles/blockchain-data-structure/"
} |
+0
# Geometry Help
0
230
1
+78
Hi forum!
Man I haven't been active in a while.
Okay, here's the problem.
The median of a triangle connects a vertex of the triangle to the midpoint of the side opposite the vertex. In triangle ABC, we have AB=3 and AC=4. Side BC and the median from A to BC have the same length. What is the length of BC?
I used the Law of Cosines to try to find the answer.
I got close: basically, BC squared is the same as the cosine of angle A.
But that's where I get stuck; I can't find angle A from the given information(or maybe I'm just not looking hard enough!).
Thanks guys! - BasicMaths
Oct 11, 2019
edited by BasicMaths Oct 11, 2019
#1
+111438
+2
We can use the Law of Cosines twice to find BC
Let the intersection of the median drawn from A to BC = D
The angles formed by the intersection of the median with BC will be supplementary...so, their cosines will have opposite signs.....so cos BDA = - cos CDA .....so -cos BDA = cos CDA
So we have that
3^2 = [ (1/2) BC]^2 + (BC)^2 - 2[ (1/2)BC] [BC] cos BDA (1)
4^2 = [ (1/2)BC]^2 + (BC)^2 - 2[(1/2)BC] [BC] cos CDA
4^2 = [ (1/2)BC]^2 + (BC)^2 - 2[ (1/2)BC][BC] (-cos BDA)
4^2 = [ (1/2)BC]^2 + (BC)^2 + 2[ (1/2)BC][BC] (cos BDA) (2)
Add (1) and (2) and we get that
25 = 2[ (1/2)BC]^2 + 2[BC]^2 simplify
25 = 2 (1/4)BC^2 + 2BC^2
25 = (1/2)BC^2 + 2BC^2
25 = (2.5)BC^2 divide both sides by 2.5
10 = BC^2
BC = √10
Here's a pic :
Oct 11, 2019
edited by CPhill Oct 11, 2019
edited by CPhill Oct 11, 2019 | crawl-data/CC-MAIN-2020-34/segments/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00237.warc.gz | null |
A female skeleton made from parts of at least three separate people. (Michael Parker-Pearson )
An international team of archaeologists have discovered that two mummies found on an island off the coast of Scotland are, like Dr. Frankenstein's monster, composed of body parts from several different humans. The mummified remains, as much as 3,500 years old, suggest that the first residents of the island of South Uist in the Hebrides had some previously unsuspected burial practices.
The West Coast of South Uist was densely populated from around 2000 BC until the end of the Viking period around AD 1300. Researchers led by archaeologist Michael Parker-Pearson of the University of Sheffield have been working at a site near the modern graveyard of Cladh Hallan, which gives the site its name. The team has so far excavated three roundhouses from a village that was apparently occupied from around 2200 BC to 800 BC. A little more than a decade ago, they found the two skeletons under one of the houses, as well as the remains of a teenage girl and a 3-year-old child.
The two primary skeletons were buried in a fetal position and showed evidence of having been preserved. Chemical evidence suggests they were mummified by being placed in nearby peat bogs for a year or longer. The high acidity and low oxygen content of the bog prevents bacteria from breaking down body tissues. After preservation, the skeletons were apparently removed from the bog and buried.
But the skeletons did not "look right" to the researchers. The female's jaw didn't fit into the rest of her skull, for example. Closer examination of the male, they reported in the Journal of Archaeological Science, showed that arthritis was present on the vertebrae of the neck, but not on the rest of the spine. The lower jaw had all of its teeth, while the upper jaw had none; but the condition of the lower jaw's teeth showed that they had been paired with upper teeth. The team concluded that the skeleton has been assembled from parts of at least three bodies, some of which were separated by several hundred years of time.
DNA analysis of the female bones by archaeologist Terry Brown of the University of Manchester revealed that the lower jaw, arm bone and thigh bone all came from different people, none of them related maternally. The bones were apparently assembled between 1310 BC and 1130 BC. Although there is overlap between the estimated times of assembly of the two skeletons, Parker-Pearson believes that they were put together at different times.
Why is a question that is not so easily answered. One simple possibility might be that pieces of a skeleton were inadvertently lost and spare parts were used to assemble a complete skeleton for burial. But Parker-Pearson thinks it more likely that the skeletons had ceremonial purpose. Rights to land, for example, depended on ancestral claims, so it is possible that having ancestors around might have strengthened claims. Alternatively, the fusion of the bones to make one skeleton might had symbolized the fusion of several families in one village or roundhouse.
"Altogether, these results have completely changed our ideas about treatment of the dead in prehistoric Britain," Parker-Pearson told LiveScience. "Other archaeologists are now identifying similar examples now that the breakthrough has been made -- beforehand, it was just unthinkable." | <urn:uuid:544cdba1-ad23-4ebe-abc4-c65a84e5cfca> | {
"date": "2014-03-09T07:40:18",
"dump": "CC-MAIN-2014-10",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999675557/warc/CC-MAIN-20140305060755-00008-ip-10-183-142-35.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9808121919631958,
"score": 3.515625,
"token_count": 679,
"url": "http://articles.latimes.com/2012/jul/10/science/la-sci-sn-frankenstein-mummies-20120710"
} |
download materi computer assisted instruction edisi revisi terbaru disini..
Minggu, 07 November 2010
Rabu, 27 Oktober 2010
Minggu, 24 Oktober 2010
What Is Computer-Assisted Instruction?“Computer-assisted instruction” (CAI) refers to instruction or remediation presented on a computer. Many educational computer programs are available online and from computer stores and textbook companies. They enhance teacher instruction in several ways.
Computer programs are interactive and can illustrate a concept through attractive animation, sound, and demonstration. They allow students to progress at their own pace and work individually or problem solve in a group. Computers provide immediate feedback, letting students know whether their answer is correct. If the answer is not correct, the program shows students how to correctly answer the question. Computers offer a different type of activity and a change of pace from teacher-led or group instruction.
Computer-assisted instruction improves instruction for students with disabilities because students receive immediate feedback and do not continue to practice the wrong skills. Computers capture the students’ attention because the programs are interactive and engage the students’ spirit of competitiveness to increase their scores. Also, computer-assisted instruction moves at the students’ pace and usually does not move ahead until they have mastered the skill. Programs provide differentiated lessons to challenge students who are at risk, average, or gifted. *
What Does CAI Look Like for Writing?
Computer-Assisted Writing Instruction
Computer programs for writing help students with developing ideas, organizing, outlining, and brainstorming. Templates provide a framework and reduce the physical effort spent on writing so that students can pay attention to organization and content.
The example at the right, similar to the program Inspiration, demonstrates how a student has organized her writing. Her topic is the Chesapeake Bay. She thinks about three main ideas for her topic: food, fun, and jobs. Next, she adds supporting details for each of her three main ideas. Now she can compose her paragraph. Programs like Inspiration or Kidspiration are fun because students can use pictures, change the shape or colors of the circles, and change the chart into an outline.
Computer Programs for WritingWord processors are excellent tools for students who find handwriting tedious. Often, students with disabilities have difficulty with all the requirements for the writing process. They have trouble organizing their thoughts and then retaining those thoughts long enough to put them on paper. Their handwriting must be neat enough and their spelling and grammar correct enough to convey their message, tasks that they may find difficult.
- Student-specific programs that identify words that student uses repeatedly; when the student types the first few letters, the program lists frequently used words that start with those letters
- speeds up the typing process
- student speaks into a microphone and the program types the words
- program must be “trained” to the student’s word pronunciation and speech style
- student must be taught how to use the program
- increased speed from thought to text
- student can hear what she has typed to check if it says what she wants it to say
- good for editing
- helps student identify misspelled words
- automatically corrects words if the teacher set the program that way
- offers student other words that mean the same as the word he or she is using
- adds variety to student’s writing and increases student vocabulary
But before word-processing can save time during the actual writing process, students must know how to type and how to use the computer. Typing speeds may be slower without proper instruction in typing; slower typing may lead to less quality and shorter length in writing assignments (MacArthur, 2000; MacArthur, Ferretti, Okolo, & Cavalier, 2001). If students cannot type fluently or must search for letters and numbers, the process may be slower than handwriting.
Examples of computer programs that assist students in the writing process are listed in the box at left. If students are taught to type early in elementary school and taught to use these programs, the writing process can become less frustrating. This is not to say that students should not be taught how to spell and to use proper grammar. Students can learn to use these programs to increase the speed from thought to paper to make the process less stressful for them. It can increase their vocabulary and their attitude toward writing. Students with disabilities may actually find they enjoy the writing process.
How Is CAI Implemented?Teachers should review the computer program or the online activity or game to understand the context of the lessons and determine which ones fit the needs of their students and how they may enhance instruction.
- Can this program supplement the lesson, give basic skills practice, or be used as an educational reward for students?
- Is the material presented so that students will remain interested yet not lose valuable instruction time trying to figure out how to operate the program? Does the program waste time with too much animation?
- Is the program at the correct level for the class or the individual student?
- Does this program do what the teacher wants it to do (help students organize the writing, speed up the writing process, or allow students to hear what they wrote for editing purposes)?
Writing programs are beneficial to writing instruction because they allow students to learn in a variety of ways and can speed up the writing process. With proper training, students can learn to focus on the message instead of the mechanics.
References and ResourcesCastellani, J., & Jeffs, T. (2001). Emerging reading and writing strategies using technology. Teaching Exceptional Children, 33, 60–67.
Graham, S., Harris, K. R., Fink-Chorzempa, B., & MacArthur, C. (2003). Primary grade teachers’ instructional adaptations for struggling writers: A national survey. Journal of Educational Psychology, 95, 279–292.
MacArthur , C. A. (2000). New tools for writing: Assistive technology for students with writing difficulties. Top Language Disorders, 20, 85–100.
MacArthur , C. A., Ferretti, R. P., Okolo, C. M., & Cavalier, A. R. (2001). Technology applications for students with literacy problems: A critical review. The Elementary School Journal, 101, 273–378.
MacArthur , C. A., & Graham, S. (1987). Learning disabled students’ composing with three methods: Handwriting, dictation, and word processing. Journal of Special Education, 21, 22–42.
Vaughn, S., Schumm, J. S., & Gordon, J. (1993). Which motoric condition is most effective for teaching spelling to students with and without learning disabilities? Journal of Learning Disabilities, 26, 191–198.
Wong, B. Y. L. (2001). Commentary: Pointers for literacy instruction from educational technology and research on writing instruction. The Elementary School Journal, 101, 359–378.
Web sites *http://www.suite101.com/links.cfm/teaching_computers#top ― This site has information and programs for teaching typing and other topics. Although it is directed toward parents, teachers will also find it useful.
http://www.inspiration.com/home.cfm ― This is the Web site for Inspiration and Kidspiration, which are organizational writing programs.
http://www.brighteye.com/texthelp.htm ― This site reads text out loud and gives students a word predictor, a homophone locator, a thesaurus, a spell checker, and a dictionary. A Word Wizard guides students to the word they are looking for.
* The programs cited in this discussion are based on research; however, it is not the purpose of this report to evaluate the rigor of the research supporting the programs themselves.
* Few Web sites are dedicated to computerized writing assistance. | <urn:uuid:53ef1561-6d72-4316-aeed-e1682f4ddaac> | {
"date": "2016-06-28T13:07:15",
"dump": "CC-MAIN-2016-26",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396887.54/warc/CC-MAIN-20160624154956-00158-ip-10-164-35-72.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9224923849105835,
"score": 3.890625,
"token_count": 1636,
"url": "http://caipbpd.blogspot.com/"
} |
The part of the blood that does not return from body tissue to the capillaries but drains into lymph vessels and is filtered through a series of lymph nodes to remove any foreign material or bacteria. So lymph is basically excess tissue fluid
only carries fluid away from the tissues provides a continuous special cleaning of the fluid portion of blood. This process is essential to the body's resistance to disease. The lymph nodes and organs, such as the spleen, tonsils, and thymus, all contain lymphoid tissue, primarily leukocytes that perform important immune functions.
describe the lymphatic vessels
Lymphatic vessels are extensive; every region of the body is supplied richly with lymphatic capillaries, • Lymphatic vessels are very much like vascular vessels; they even have valves
• The movement of lymph within these vessels is dependent upon skeletal muscle contraction—when the muscles contract, lymph is squeezed past a valve that closes, preventing lymph from flowing backward
• This system is a one-way system
o Begins with lymphatic capillaries that lie near blood capillaries
o These lymphatic capillaries take up fluid that exited from, and was not reabsorbed by the blood capillaries
o When the tissue fluid enters the lymphatic vessels, it is called lymph
o The lymphatic capillaries then join to form the lymphatic vessels that merge in the thoracic cavity before entering one of 2 ducts: the thoracic duct or the right lymphatic duct
• The thoracic duct is much larger than the right lymphatic duct
• Serves the lower extremities, abdomen, left arm, and left side of the head and neck
• In the thorax, the left thoracic duct enters the left subclavian vein
Right lymphatic duct
• Smaller than the thoracic duct
• Serves only the right arm and the right side of the head and neck
• Enters the right subclavian vein
Lymphatic organs contain lymphatic tissue, which consists of many lymphocytes, macrophages, and other cells. The lymphocytes originate from red bone marrow and are carried by the blood to lymph organs. When the body is exposed to microorganisms or foreign substances, the lymphocytes divide and increase in number.
there are three groups of tonsils- palatine, pharyngeal (also called adenoid when it is enlarged) and lingual; the tonsils provide protection against pathogens and other potentially harmful material entering the nose and mouth. Sometimes the tonsils or adenoids become chronically infected and must be removed. In adults the tonsils decrease in size.
these are small, round structures distributed along the various lymph vessels. They are all over the body, but there are three groups which are superficial which are the inguinal nodes in the groin, the axillary nodes in the armpit region, and the cervical nodes of the neck; functions are activation of the immune system and removal (phagocytosis) of microorganisms and foreign substances from the lymph by macrophages
The lymph nodes are filled with?
lymphocytes and macrophages and as lymph passes through the sinuses, it is purified of infectious organisms and any other debris.
size of a clenched fist, located in the left upper quadrant of the abdomen just below the diaphragm and behind the stomach; it is the largest lymphatic organ in the body; it is divided into lobules, one red and one white. The red pulp contains RBCs, lymphocytes and macrophages. The white pulp contains only lymphocytes and macrophages
how does the pulps help filter blood
helps to purify the blood that passes through the spleen. The spleen filters blood, destroying microorganisms, foreign substances, and worn out red blood cells; activates the immune system;
how does the spleen function as a reservoir?
holding a small volume of blood; in emergencies, ; can rupture in traumatic injuries causing severe bleeding, shock, and death; if removed (splenectomy), other lymphatic tissue and the liver compensate for its function.
bilobed gland, triangular in shape, in superior mediastinum, just beneath the sternum; also an endocrine gland; size depends on age of the individual; grows until puberty, then starts decreasing in size until it may even become difficult to find.
what is produced in the thymus?
large numbers of lymphocytes are produced here, but most degenerate; functions as a site for the processing and maturation of lymphocytes.
Red Bone Marrow
This is the site of origination for all blood cells. In the adult, red bone marrow is found in the bones of the skull, sternum, ribs, clavicle, pelvis, and spinal column, and in the ends of the femur and humerus.
Functions of the lymphatic system:
• Helps maintain fluid balance in the tissues; take up excess tissue fluid and return it to the bloodstream
• Absorbs fats and other substances from the digestive tract
• Is part of the body's defense system; remove microorganisms and other foreign substances
• Oil glands: secretions have chemicals which weaken or kill bacteria
• Respiratory tract: cilia
• Stomach: acidic pH inhibits growth of many types of bacteria
• Other organs: have bacteria which prevent pathogens from colonizing vulnerable tissues
• Right after injury, capillaries and several tissue cells release histamine (makes vessels dilate and become more permeable)
• Neutrophils and monocytes squeeze through capillary walls to enter tissue fluid where they carry out phagocytosis
• After phagocytosis occurs, an intracellular vacuole is formed
• Inside this vacuole, the bacterium is destroyed
• As the infection is being overcome, some neutrophils die
• The neutrophils, along with the dead tissue, cells, bacteria, and living white blood cells, form pus, a thick, yellowish fluid: the presence of pus indicates that the body is trying to overcome the infection
• Complement system:
o Consists of a number of plasma proteins designated by the letter C and number or letter
o Once a complement protein is activated, it , in turn, activates another protein in a set series of reactions
o Each protein in the series is capable of activating many proteins next in line
Complement proteins form holes in bacterial cell walls and membranes; these
holes allow fluids and salt to enter the bacterial cell until it bursts
o Complement also activates chemicals that attract phagocytes to the site and induce inflammation
Interferon binds to receptors on the surface of noninfected cells
causing them to prepare for possible attack by producing substances that interfere with viral replication
• Immunity usually lasts for a long time
• Immunity is primarily the result of the action of B lymphocytes and T lymphocytes:
o B stands for bone marrow
o T stands for thymus
o B lymphocytes become plasma cells that produce antibodies
• Antibodies are proteins capable of combining with and inactivating antigens
• These are secreted into the blood, lymph, and mucus
T lymphocytes do not produce antibodies
These directly attack cells bearing antigens they recognize; other T cells regulate the immune response
The cells have receptors which secrete antibodies when there is an invasion from an antigen
• The B cells
• The B cells divide and produce plasma cells which also secrete antibodies against the antigen
• Once there is enough amount of antibodies present in the body, the antigen disappears
Some of the antibodies remain in the blood to become memory B cells
• Some of the antibodies remain in the blood to become memory B cells which are capable of producing the antibody specific to a particular antigen for some time, maybe even a lifetime; so if the same antigen were to attack again, the body would recognize it and begin its invasion
• Defense by B cells is the "antibody-mediated immunity or humoral immunity"
• There are many classes of antibodies with specific functions
o Most belong to the class IgG
o Learn the antibodies
• T cells are responsible for cell-mediated immunity
• They contain a major histocompatibility protein as a receptor, These contribute to specific tissue and are the ones responsible of making it difficult to transplant tissue from one person to another
helper T cells
stimulate B cells and also release lymphokines (messenger proteins that stimulate the immune system)
As long as T cells are capable of ?
recognizing newly developed changed cells (cancer cells), it releases chemicals that perforate the cell membrane and killing the cell
• Provides long-lasting protection against a disease-causing organism
• Develops after an individual is infected with a virus or bacterium or after being artificially immunized
• Use of vaccines
o Vaccines are antigens to which the immune system responds
o After it is given, you measure the antibody titer in the blood
o When this titer is high enough, it prevents the disease even if exposed | <urn:uuid:f4b96f06-89ef-4648-97d2-5e7c3f251f33> | {
"date": "2014-10-25T07:11:58",
"dump": "CC-MAIN-2014-42",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647865.10/warc/CC-MAIN-20141024030047-00105-ip-10-16-133-185.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9238169193267822,
"score": 3.796875,
"token_count": 1897,
"url": "http://quizlet.com/15451074/lymphatic-system-anatomy-and-physiology-flash-cards/"
} |
American Art: 1900s
GENERAL UNIT GOALS
The student will be able to identify how the work “American Gothic” by artist Grant Wood reflects the strong American spirit during the Great Depression. The student will demonstrate a strong knowledge of the elements and principles of art in their own interpretation of the painting. Also, the student will demonstrate skills with acrylic paints.
American Gothic Parody
3-50 minute class periods
GENERAL LESSON OBJECTIVE
Students will be able to:
1) Understand the basics of the Great Depression
2) Identify “American Gothic by Grant Wood and it’s representation of American during that period
3) Show knowledge of the element and principles in the work and their own work and write in their sketchbooks how they achieved good composition using them in their work.
4) Create two characters (real or imagined) in place of the man and woman
5) Add a background that represents those characters and the time/place they come from
6) Use acrylic paints effectively
VIRGINIA ART STANDARDS OF LEARNING
Cultural Context and Art History
6.12 The student will identify the components of an artist’s style, including materials, design, technique, and subject matter.
6.13 The student will identify major art movements in American culture from 1877 to the present
6.14 The student will identify how artists contribute to society.
VIRGINIA CORE STANDARS OF LEARNING
History and Social Science
USII.5 The student will demonstrate knowledge of the social, economic, and technological changes of the early twentieth century by
a) identifying the causes of the Great Depression and its impact on Americans
Laminated print of “American Gothic” by Grant Wood. Laminated poster with “Art Elements and Principles”. Laminated examples of finished projects. Magnets to hang examples on chalk board. Paper towels and soap.
Heavy white paper (18” x 24”)
Various paint brushes
Containers holding water
Work of Grant Wood, Finished project examples, and Elements and Principles poster will be posted on the chalk board with magnets. The counter where the sink is located will be stocked with all of the acrylic paints, a bucket of various sized paint brushes, white palettes, and jars for water. It is important to make sure ahead of time that soap and paper towels are fully stocked.
Great Depression – The Great Depression was a worldwide economic downturn starting in most places in 1929 and ending at different times in the 1930s. he Great Depression originated in the United States; historians most often use as a starting date the stock market crash on October 29, 1929, known as Black Tuesday. The end of the depression in the U.S. is associated with the onset of the war economy of World War II, beginning around 1939.
Gothic Architecture – Gothic architecture is a style of architecture which flourished during the high and late medieval period. It evolved from Romanesque architecture and was succeeded by Renaissance architecture. Gothic architecture is most familiar as the architecture of many of the great cathedrals, abbeys and parish churches of Europe. It is also the architecture of many castles, palaces, town halls, guild halls, universities, and to a less prominent extent, private dwellings.
ANTICIPATORY SET- 5 min.
“Who recognizes this painting (Grant Wood’s ‘American Gothic’)” “What do you know about the Great Depression?”
TEACHING MOTIVATION- 20 Min INPUT/DEMO/DIRECTIONS/CHECKING
INPUT-Look at “American Gothic” by Grant Wood. Discuss Great Depression. Discuss the paintings portrayal of the Great Depression. Also, discuss the elements and principles used in the painting that make it effective. MODELING-Display and talk about prepared examples of some finished projects. DEMO/DIRECTIONS- Go over instructions and be sure to remind students of the elements and principles by putting up and going over the element and principle poster. CHECKING- Have the students verbally go over some ideas of characters they were thinking about painting.
GUIDED PRACTICE- (1st session last 30 minutes) – Students will sketch out their characters in their sketchbooks and get them approved.
DISTRIBUTION/SUPPLIES- (1st session) Students will receive from teacher the pencils. The students must bring their sketchbooks to class. (2nd and 3rd session) Teacher will hand out heavy white paper, water jars, and white palates to each student. Students will come up the sink as necessary to get the paint and paintbrushes they need.
INDEPENDENT PRACTICE- (2nd and 3rd sessions) Students will lightly sketch their characters and backgrounds onto their white paper. Next, they will begin to paint with the acrylics.
CLOSURE Critique/Clean Up/Summary-10 Min.
CRITIQUE- There will be no class critique on this project. The student will write in their sketchbooks how they believe they used elements and principles and their work. Sketchbooks are graded separately from this assignment at the end of the semester.
CLEAN-UP- Students will clean off all brushes and white palettes and put them back in their proper place on the sink. Wet paintings will be put on the art room drying rack. The teacher will put back palettes, brushes, and paint after all class sessions are over.
SUMMARY/TRANSITION- The work of artists can portray a certain time period and social issues and strengthen the moral of citizens.
Students will be evaluated on these criteria:
RUBRIC Superior A Satisfactory C Minimal E
Used Elements yes somewhat not at all
Used Principles yes somewhat not at all
Two Characters yes somewhat not at all
Appropriate background yes somewhat not at all
Can Identify Importance of Painting yes somewhat not at all
MODIFICATIONS/ SELF EVALUATION OF LESSON/REFLECTIONS
REFERENCES, BIBLIOGRAPHY, RESOURCES | <urn:uuid:83052669-b7e2-4926-ac72-16b0b799bbb6> | {
"date": "2014-10-01T14:14:31",
"dump": "CC-MAIN-2014-41",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663460.43/warc/CC-MAIN-20140930004103-00271-ip-10-234-18-248.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9113099575042725,
"score": 3.671875,
"token_count": 1281,
"url": "http://sarahspracticumexperience.wordpress.com/lesson-plans/american-gothic-parody/"
} |
Check out these tiny Ocotopus hatchlings at Mote Marine Laboratory & Aquarium in Florida!
Octopi reproduction is really quite interesting. Males have a specially adapted arm, called a hectocotylus, which they use to transfer sperm packets called spermatorphores into to a female's mantle cavity. Octopi lead short, solitary lives of one to two years; the pair do not remain together, and males die within a few months of mating.
A female can store the sperm in her mantle until she is ready to fertilize and lay her eggs. A female may lay hundreds of thousands of eggs, which she anchors to a hard surface in a protected den.
After eggs are laid, she devotes the rest of her life to caring for them. She will guard the eggs and keep water circulating around them so that the developing offspring receive enough oxygen. The mother stops eating after her eggs are laid, and she will die soon after they hatch.
Newly-hatched octopi are called larvae, and will develop into hatchlings or fry. The newborn octopi, though tiny, are independant and require no more maternal care. Survival in the ocean is often a matter of luck, and very few of these offpspring will survive to adulthood— which is why so many eggs are laid to begin with. | <urn:uuid:2040139a-6b67-4124-8c80-e8f0acc355b9> | {
"date": "2014-10-23T10:10:26",
"dump": "CC-MAIN-2014-42",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413510834349.43/warc/CC-MAIN-20141017015354-00359-ip-10-16-133-185.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9731234312057495,
"score": 3.625,
"token_count": 275,
"url": "http://www.zooborns.com/zooborns/octopus/"
} |
# What Boolean Logic Is & How It’s Used In Programming
03/21/2022
Boolean logic is a key concept in any programming language, whether you’re creating a video game with C++, developing the next best app in Swift, searching through relational databases in SQL, or working with big data in Python. In this article, we’ll cover what Boolean logic is, how it works, and how to build your own Boolean expressions.
## What is Boolean logic?
Boolean logic is a type of algebra in which results are calculated as either TRUE or FALSE (known as truth values or truth variables). Instead of using arithmetic operators like addition, subtraction, and multiplication, Boolean logic utilizes three basic logical operators: AND, OR, and NOT.
### TRUE and FALSE: There can only be two
Behind Boolean logic are two very simple words: TRUE and FALSE.
Note that a Boolean TRUE or FALSE is very different from typing the strings “True” and “False” into your code. In fact, programming languages put these two Boolean values into their own object type separate from integers, strings, and floating-point numbers. But while there can be practically infinite possibilities for a numerical or string value in programming, there are only two possible Boolean values: TRUE and FALSE.
How does this work? Boolean logic looks at a reported relationship between things and determines whether the relationship holds. For example, let’s take the equation:
2 + 2 = 4
Here, we have two parts, 2 + 2 and 4, and we’re reporting that those two parts are equal to each other. Is that right? Yes it is, so the Boolean result of this would be TRUE. In this example, the combination of the two parts 2 + 2 and 4, together with the relationship (= equals), is called a Boolean expression.
Let’s look at another Boolean expression:
10 – 4 = 5
Here, we’re reporting that 4 subtracted from 10 is the same as 5. Is that right? Of course not, and that’s why this Boolean expression would return a value of FALSE.
Boolean Expression Result 2 + 2 = 5 FALSE 5 – 1 = 4 TRUE 4 * 5 > 10 TRUE 40 / 10 < 1 FALSE
## Building Boolean expressions
Keep in mind that Boolean logic only works when an expression can be TRUE or FALSE. For example, the expression 3 + 8 isn’t a Boolean expression because it’s not being compared or related to something else. But the expression 3 + 8 = 10 is a Boolean expression because we can now evaluate each side and see if the reported relationship between them is TRUE or FALSE (in this case, it’s FALSE).
We can build Boolean expressions with all kinds of data, including variables. For example, let’s suppose that we’ve assigned these values to variables x and y somewhere in our code:
x is 7
y is 3
Now, we can build Boolean expressions using our variables:
Boolean Expression Result x + y < 11 FALSE x * y = 21 TRUE x / y > 10 FALSE x + (2 * y) = 13 TRUE
Boolean expressions can also determine whether two strings are identical. Just remember that most programming languages are case-sensitive.
Boolean Expression Result “I love Codecademy” = “I love Codecademy” TRUE “I love Codecademy” = “Codecademy” FALSE “I love Codecademy” = “I LOVE Codecademy” FALSE
There are many other ways to build Boolean expressions, depending on the programming language. For example, you could use a Boolean expression to determine whether a number is contained within a list in Python or whether a text string is within a SQL database table.
## Boolean operators
Now that you understand the basics of Boolean expressions, let’s look at another key aspect of Boolean logic: Boolean operators. There are three basic Boolean operators, AND, OR, and NOT.
To better understand how Boolean operators work, let’s suppose for a moment that we’re in an ice cream shop. Say we’re going to put together a two-scoop sundae with different flavors. But I’m a bit of a picky eater, so I may not accept every sundae combination that I get. We can use Boolean expressions and Boolean operators to figure out whether I’ll eat a sundae or not.
### AND
The Boolean AND operator is used to confirm that two or more Boolean expressions are all true.
For example, in my sundae, I want the first flavor to be chocolate and the second flavor to be vanilla. We could turn this into a Boolean expression with an AND operator that looks something like this:
Flavor_1 = Chocolate AND Flavor_2 = Vanilla
This means that both the first flavor must be chocolate and the second flavor must be vanilla. Otherwise, I won’t eat the sundae.
We could organize this situation into a table of possibilities like this:
Flavor_1 Flavor_2 Eat Sundae? Chocolate Vanilla Yes Chocolate Strawberry No Mango Vanilla No Mango Strawberry No
Tables like this are used in Boolean logic all the time. They’re called truth tables, and we can put one together for our sundae example. If something meets my picky sundae flavor conditions, then it’s TRUE. If not, then it’s FALSE.
Here’s how the table above would look like in truth table form:
Flavor_1 Flavor_2 Result TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
### OR
The Boolean OR operator checks that either one condition or another is true.
For example, if I wanted either the first flavor to be strawberry or the second flavor to be mango, then the Boolean expression would be:
Flavor_1 = Strawberry OR Flavor_2 = Mango
We could organize the possibilities as:
Flavor_1 Flavor_2 Eat Sundae? Strawberry Mango Yes Strawberry Cherry Yes Cherry Mango Yes Vanilla Raspberry No
And the truth table would look like this:
Flavor_1 Flavor_2 Result TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE
Note that the OR operator returns TRUE if one of the two Boolean expressions is true, but also when both expressions are true. For this reason, this OR operator is also known as an inclusive OR operator. Alternatively, there’s also the XOR (exclusive or) operator, which only returns TRUE when one of the two expressions is true.
### NOT
The Boolean NOT operator is different from AND and OR as it only takes one argument. It tests if a value is FALSE or not. Put another way, it changes TRUE values to FALSE and FALSE values to TRUE. For example, I hate Rum Raisin and absolutely will not eat anything with Rum Raisin in it. How might that look in table form?
Flavor Eat Ice Cream? Chocolate Yes Rum Raisin No
The truth table looks like this:
Flavor Result FALSE TRUE TRUE FALSE
You can combine Boolean expressions to express my sundae preference when Rum Raisin is involved like so:
NOT (Flavor_1 = Rum Raisin OR Flavor_2 = Rum Raisin)
Flavor_1 Flavor_2 Eat Sundae? Chocolate Raspberry Yes Peach Rum Raisin No Rum Raisin Mint No Rum Raisin Rum Raisin No
The OR clause within the parentheses will return TRUE for anything with Rum Raisin in it. Applying the NOT to it will change the OR expression’s value from TRUE to FALSE and vice versa. Much like operators in arithmetic, Boolean operators have an order of precedence: elements within a parentheses are addressed first, then the NOT operator, AND, and lastly OR. Our new truth table looks like this:
Flavor_1 Flavor_2 Result FALSE FALSE TRUE FALSE TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE
## Applying your Boolean logic
So, what’s next after learning the basics of Boolean logic?
Boolean logic is critical to creating code that helps your program quickly make decisions about data and inputs, so try putting your Boolean knowledge to use with an online programming course. And if you’re not sure which course to try next, take a look at our developer career paths. We’ll help you focus on the best skills you need to succeed in your desired role.
7 articles
# Behind the Build: Designing Post-Quiz Review
09/06/2024
9 minutes
Feedback is back in town with post-quiz review.
# How to Estimate the Amount of Time You Need for a Project
09/03/2024
7 minutes
How long is a piece of string? Estimating software engineering work is part science, part finger in the air — here’s some practical advice to get started.
# How to Use AI to Get Ahead in School
09/03/2024
4 minutes
Get AI-ready for the school year by learning these concepts.
# 8 Ways Students Use Codecademy to Excel in Class (& Life)
09/03/2024
6 minutes
Learn the skills you’ll actually use in the real world with Codecademy Student Pro.
# 7 Small Wins To Celebrate On Your Journey To Becoming A Professional Developer
08/06/2024
7 minutes
Having an end goal is important, but so is celebrating your progress. Here are some milestones to look forward to as you learn how to code.
# 7 Most Popular Programming Languages for Game Development
07/26/2024
6 minutes
Learn the best languages for game development and why developers choose to use them. Discover how our classes can get you started with game design.
# 8 Organizations Helping Girls & Women Build Careers in Tech
03/05/2024
7 minutes
There’s a gender gap in tech — but it’s getting smaller thanks to organizations like these. | crawl-data/CC-MAIN-2024-38/segments/1725700651098.19/warc/CC-MAIN-20240909103148-20240909133148-00781.warc.gz | null |
You can program using a variety of numeric data types, each with different qualities and ranges. The differences among the numeric data types are the number of bits they use to store data and the data values they represent.
The following table describes the differences among the numeric data types.
|Type||Description||Representation on the Diagram|
|Integers||Represent whole numbers. Signed integers can be positive or negative. Use unsigned integers when you know the integer is always zero or positive.|
|Floating-Point Numbers||Represent fractional numbers. Double-precision floating-point numbers store more digits than single-precision floating-point numbers.|
|Complex Numbers||Represent a point in the complex numeric plane. Each value is comprised of two floating-point numbers, one representing the real part and the other representing the imaginary part.|
On the panel, you can use many types of controls and indicators to represent numeric values. | <urn:uuid:647743af-ff12-414a-becb-a52fdcc5d897> | {
"date": "2019-03-25T12:11:23",
"dump": "CC-MAIN-2019-13",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203947.59/warc/CC-MAIN-20190325112917-20190325134917-00257.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.8125224709510803,
"score": 3.65625,
"token_count": 194,
"url": "http://www.ni.com/documentation/en/labview-comms/2.1/data-types/numeric-data/"
} |
Britannica Web Sites
Articles from Britannica encyclopedias for elementary and high school students.
- catacomb - Children's Encyclopedia (Ages 8-11)
In ancient times people in the region surrounding the Mediterranean Sea buried their dead in underground tunnels and rooms. They cut these tunnels and rooms, called catacombs, out of a layer of soft stone below the ground.
- catacomb - Student Encyclopedia (Ages 11 and up)
The great plain on which the city of Rome is located has three volcanic layers, one of which-granular tufa-is relatively easy to cut. Out of this rock were cut the underground passageways and chambers known as the catacombs. These were primarily subterranean burial sites, used by Jews and by Christians during the period of the Roman Empire from about the 1st century AD until about the 5th century AD. | <urn:uuid:18547a1b-1aea-4361-803b-17747f297a86> | {
"date": "2014-03-09T16:15:13",
"dump": "CC-MAIN-2014-10",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394009829804/warc/CC-MAIN-20140305085709-00006-ip-10-183-142-35.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.953306257724762,
"score": 3.671875,
"token_count": 186,
"url": "http://www.britannica.com/topic/99008/websites"
} |
# statistics log gamma distribution
The Goodness of Fit test is used to check the sample data whether it fits from a distribution of a population. Population may have normal distribution or Weibull distribution. In simple words, it signifies that sample data represents the data correctly that we are expecting to find from actual population. Following tests are generally used by statisticians:
• Chi-square
• Kolmogorov-Smirnov
• Anderson-Darling
• Shipiro-Wilk
## Chi-square Test
The chi-square test is the most commonly used to test the goodness of fit tests and is used for discrete distributions like the binomial distribution and the Poisson distribution, whereas The Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests are used for continuous distributions.
## Formula
${ X^2 = \sum {[ \frac{(O_i – E_i)^2}{E_i}]} }$
Where −
• ${O_i}$ = observed value of i th level of variable.
• ${E_i}$ = expected value of i th level of variable.
• ${X^2}$ = chi-squared random variable.
## Example
A toy company builts football player toys. It claims that 30% of the cards are mid-fielders, 60% defenders, and 10% are forwards. Considering a random sample of 100 toys has 50 mid-fielders, 45 defenders, and 5 forwards. Given 0.05 level of significance, can you justify company’s claim?
Solution:
### Determine Hypotheses
• Null hypothesis $H_0$ – The proportion of mid-fielders, defenders, and forwards is 30%, 60% and 10%, respectively.
• Alternative hypothesis $H_1$ – At least one of the proportions in the null hypothesis is false.
### Determine Degree of Freedom
The degrees of freedom, DF is equal to the number of levels (k) of the categorical variable minus 1: DF = k – 1. Here levels are 3. Thus
${ DF = k – 1 \\[7pt] \, = 3 -1 = 2 }$
### Determine chi-square test statistic
${ X^2 = \sum {[ \frac{(O_i – E_i)^2}{E_i}]} \\[7pt] \, = [\frac{(50-30)^2}{30}] + [\frac{(45-60)^2}{60}] + [\frac{(5-10)^2}{10}] \\[7pt] \, = \frac{400}{30} + \frac{225}{60} + \frac{25}{10} \\[7pt] \, = 13.33 + 3.75 + 2.50 \\[7pt] \, = 19.58 }$
### Determine p-value
P-value is the probability that a chi-square statistic,$X^2$ having 2 degrees of freedom is more extreme than 19.58. Use the Chi-Square Distribution Calculator to find ${ P(X^2 \gt 19.58) = 0.0001 }$.
### Interpret results
As the P-value (0.0001) is quite less than the significance level (0.05), the null hypothesis can not be accepted. Thus company claim is invalid.
2.statistics analysis of variance
3.statistics arithmetic mean
4.statistics arithmetic median
5.statistics arithmetic mode
6.statistics arithmetic range
7.statistics bar graph
8.statistics best point estimation
9.statistics beta distribution
10.statistics binomial distribution
11.statistics blackscholes model
12.statistics boxplots
13.statistics central limit theorem
14.statistics chebyshevs theorem
15.statistics chisquared distribution
16.statistics chi squared table
17.statistics circular permutation
18.statistics cluster sampling
19.statistics cohens kappa coefficient
20.statistics combination
21.statistics combination with replacement
22.statistics comparing plots
23.statistics continuous uniform distribution
24.statistics cumulative frequency
25.statistics coefficient of variation
26.statistics correlation coefficient
27.statistics cumulative plots
28.statistics cumulative poisson distribution
29.statistics data collection
30.statistics data collection questionaire designing
31.statistics data collection observation
32.statistics data collection case study method
33.statistics data patterns
34.statistics deciles statistics
35.statistics dot plot
36.statistics exponential distribution
37.statistics f distribution
38.statistics f test table
39.statistics factorial
40.statistics frequency distribution
41.statistics gamma distribution
42.statistics geometric mean
43.statistics geometric probability distribution
44.statistics goodness of fit
45.statistics grand mean
46.statistics gumbel distribution
47.statistics harmonic mean
48.statistics harmonic number
49.statistics harmonic resonance frequency
50.statistics histograms
51.statistics hypergeometric distribution
52.statistics hypothesis testing
53.statistics interval estimation
54.statistics inverse gamma distribution
55.statistics kolmogorov smirnov test
56.statistics kurtosis
57.statistics laplace distribution
58.statistics linear regression
59.statistics log gamma distribution
60.statistics logistic regression
61.statistics mcnemar test
62.statistics mean deviation
63.statistics means difference
64.statistics multinomial distribution
65.statistics negative binomial distribution
66.statistics normal distribution
67.statistics odd and even permutation
68.statistics one proportion z test
69.statistics outlier function
70.statistics permutation
71.statistics permutation with replacement
72.statistics pie chart
73.statistics poisson distribution
74.statistics pooled variance r
75.statistics power calculator
76.statistics probability
78.statistics probability multiplicative theorem
79.statistics probability bayes theorem
80.statistics probability density function
81.statistics process capability cp amp process performance pp
82.statistics process sigma
84.statistics qualitative data vs quantitative data
85.statistics quartile deviation
86.statistics range rule of thumb
87.statistics rayleigh distribution
88.statistics regression intercept confidence interval
89.statistics relative standard deviation
90.statistics reliability coefficient
91.statistics required sample size
92.statistics residual analysis
93.statistics residual sum of squares
94.statistics root mean square
95.statistics sample planning
96.statistics sampling methods
97.statistics scatterplots
98.statistics shannon wiener diversity index
99.statistics signal to noise ratio
100.statistics simple random sampling
101.statistics skewness
102.statistics standard deviation
103.statistics standard error se
104.statistics standard normal table
105.statistics statistical significance
106.statistics formulas
107.statistics notations
108.statistics stem and leaf plot
109.statistics stratified sampling
110.statistics student t test
111.statistics sum of square
112.statistics tdistribution table
113.statistics ti 83 exponential regression
114.statistics transformations
115.statistics trimmed mean
116.statistics type i amp ii errors
117.statistics variance
118.statistics venn diagram
119.statistics weak law of large numbers
120.statistics z table
121.discuss statistics | crawl-data/CC-MAIN-2020-45/segments/1603107894890.32/warc/CC-MAIN-20201027225224-20201028015224-00055.warc.gz | null |
# Crossing out a digit
Find the largest integer $N$ whose decimal representation has the following properties:
• The rightmost digit in the decimal representation is not $0$.
• There exists a digit $d$ in the decimal representation which is not the leftmost digit, so that crossing out this digit $d$ yields the decimal representation of an integer divisor of $N$.
Example:
The integer $121$ is not divisible by $10$, and crossing out the digit $2$ yields the divisor $11$ of $121$.
• Do you know if $N$ is a finite number? (I'm not asking if it is or not.) – ghosts_in_the_code Oct 24 '15 at 14:52
• Yes, $N$ is finite. (To ensure finiteness, one needs these conditions on the leftmost and rightmost digit.) – Gamow Oct 24 '15 at 14:53
Answer: $180625 = 17*10625$.
Proof:
we have:
$N = a*10^{n+1}+d*10^n+c = k*(a*10^n+c)$, $a,d,c,k$ is positive integers. $d < 10; c < 10^n; k > 1$.
move some terms:
$(10-k)*a*10^n + d*10^n = (k-1)*c$
Now. First of all we need to maximise $n$. In that case $(k-1)*c$ must be divisible by maximum power of 10. The only limit is that $c$ is not divisible by 10 and $k <= 19$ (otherwise left part of equation become negative). Then $k = 2^4+1 = 17, c = 5^4*c'$ and:
$(-7)*a*10^n + d*10^n = c'*10^4$
max $n$ is 4, then:
$-7*a + d = c'$
$7*a = d - c'$
Now $a$ must be maximised. $d <= 9$, then $a_{max} = 1$, also $c'_{max} = 1$, since $c'_{max}*5^4 = c$ is not divisible by 10.
That means $a = 1, d = 8, c = 1; N = 180000+1*5^4 = 180625$
• What if $c$ is divisible by 2 and $k-1$ is divisible by 5 but not 10? – Zandar Oct 24 '15 at 20:01
• @Zandar, thanks! I changed my answer a little bit:) – klm123 Oct 24 '15 at 20:34 | crawl-data/CC-MAIN-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00628.warc.gz | null |
## 31.3 Determining the Integrand
A flux integral is one of the general form
Suppose now we have a parametric representation for S, which means we have equations x = x(u, v), y = y(u, v) and z = z(u, v), which define our surface.
We can reduce this integral to a sequence of ordinary integrals over u and v by expressing (Wn)dS as an explicit function of u and v multiplied by dudv and determining an order and limits on the resulting integrals.
The first step in this procedure is straightforward:
Form the vectors
and similarly
Then the integrand, integrating over u and v, can be written as the absolute value of the determinant of the matrix with columns given by the components of W, multiplied by an appropriate sign.
For the reason why, see section 24.1. (The vector n here in the integral is generally meant to represent the outward directed normal with respect to some region and the sign of the integral is the one such that if W has positive dot product with this outward direction, the result is positive.)
The appropriate sign must be determined separately, but only once per surface, from the context of the original integral.
Thus to within a sign, the integral becomes
While this reduction straightforward, the steps necessary to perform it in practice involve a sufficient amount of algebraic manipulation that I for one almost always make at least one error in doing it, and so rarely get the same answer twice.
Fortunately there is a computationally simpler answer in the most common case, in which u and v are actually two of your original variables, say x and y.
In that case the vectors become and their cross product becomes
The integrand and area element can then be written as
which result is much easier to apply. We have assumed here that the sign should be positive in the direction that is upward in the z direction, and the sign must be reversed if that assumption is incorrect.
If your surface is described by an equation f(x, y, z) = 0, the corresponding formula with the same sign assumption becomes
(When you must integrate over two other variables, say y and z instead of x and y.)
The answers given here give both the integrand and the area element.
The only time you really have to worry about the area element is when you want to change variables and have to determine what the area element dxdy means in terms of other variables u and v.
Here is an example: we want to compute the flux of the vector (x, y, z) outward through the surface defined by the equation
(This surface is called an ellipsoid.)
We will integrate over the portion of the surface for which z > 0 only and double the result since the lower part of the surface gives the same flux.
Writing this as f = 0 we compute and the integrand becomes, with the last formula, which in this case is which is
Our integral therefore becomes
over appropriate limits of integration. Those limits are the bounds (which we will discuss below) determined by the area in the xy plane that we are integrating over, and that is, the region in which the denominator in that integral is positive. | crawl-data/CC-MAIN-2013-48/segments/1386163053883/warc/CC-MAIN-20131204131733-00047-ip-10-33-133-15.ec2.internal.warc.gz | null |
In your language arts and English classes, you will encounter many specific terms that relate to writing. Knowing the meanings of these terms will make you a more effective reader and writer. Here are twenty important writing terms whose meanings you should know.
Anecdote – A short account of a particular incident or event, typically of an interesting or amusing nature.
Autobiography – A writer's account of his or her own life. This is in contrast to a biography, which is a story of someone's life written by another person.
Characterization – A process by which a writer reveals a fictional character's personality to the reader.
Cliché – A phrase or expression that has been so overused that it has lost its significance. Good writing avoids the use of clichés.
Connotation - The emotion or feeling that a word creates.
Denouement – The final clarification or resolution of a plot in a written work.
Dialog – A conversation between two or more characters in a literary work. Dialog is set off by quotation marks.
Didactic – A form of writing that teaches something.
Epigram – A brief or witty saying or poem.
Hyperbole – An excessive exaggeration.
Irony – An outcome of events that is contrary to what was expected to happen.
Juxtaposition – Placing two words or ideas close together for contrast or interest.
Myth – A story passed down over the generations that was once believed to be true.
Oxymoron – Two words of contradictory meaning that are placed next to each other to make a point.
Parable – A short story that teaches a moral or religious lesson.
Protagonist – The main character or hero in a story.
Pseudonym – A false name used by a writer, often referred to as a pen name.
Style – The manner in which a writer chooses to write to his or her audience.
Theme – The idea that a writer wishes to convey about a subject.
Tone – The attitude of a writer toward his or her subject.
Knowing the meanings of these twenty terms will be helpful to you in your language arts and English classes. | <urn:uuid:41e9162a-4705-4c87-9e9d-81870da87452> | {
"date": "2018-05-21T20:20:41",
"dump": "CC-MAIN-2018-22",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864544.25/warc/CC-MAIN-20180521200606-20180521220606-00538.warc.gz",
"int_score": 5,
"language": "en",
"language_score": 0.9549718499183655,
"score": 4.59375,
"token_count": 443,
"url": "https://www.how-to-study.com/study-skills-articles/writing-terms.asp"
} |
In a world where kids can buy virtual goods with real money and where credit card companies target college students, teaching kids about money has never been more important. And yet, financial literacy rates in the U.S. are shockingly low. A study by the Financial Industry Regulatory Authority found that only 24% of Americans could correctly answer four out of five basic financial literacy questions.
There are a number of ways to improve financial literacy for kids. One is through education: making sure that personal finance is taught in schools at all levels. Another is through parents and guardians taking the time to talk to kids about money and model good financial behavior themselves. Finally, there are a number of great resources available online and in libraries that can help both kids and adults learn more about personal finance.
No matter what approach you take, increasing financial literacy for kids is crucial for their future success.
7 Reasons Why Teaching Financial Literacy for Kids is Important
1. A child’s future is bright when they have a strong foundation of financial literacy.
A child’s future is bright when they have a strong foundation of financial literacy. When children understand the basics of money management, they are more likely to make sound financial decisions later in life.
Teaching children about money is one of the most important things parents can do to set their kids up for success. By instilling good financial habits early on, parents can help their children avoid common money mistakes later in life.
There are a few key things parents can do to help their children develop financial literacy: teach them the importance of budgeting and saving, explain how credit works, and help them understand the power of compound interest. By taking the time to educate their children about money, parents can give them a valuable gift that will last a lifetime.
2. Financial literacy for kids is important because it teaches them how to manage money wisely.
Financial literacy is important for kids because it teaches them how to manage money wisely. It’s never too early to start learning about money and how to save, spend, and invest it. Financial literacy can help children avoid debt and build a strong foundation for their future.
There are a few key things that kids can learn through financial literacy programs. They can learn about budgeting, saving, and investing money. They can also learn about credit, loans, and interest rates. By understanding these concepts, children can make wiser decisions with their own money when they grow up.
There are plenty of resources available to help kids learn about financial literacy. Many schools offer programs or classes on the subject. There are also many books, websites, and games that teach financial literacy in a fun and engaging way.
3. Kids who are financially literate are more likely to make sound financial decisions as adults.
A new study has found that children who are taught financial literacy are more likely to make sound financial decisions as adults. The study, which was conducted by researchers at the University of Cambridge, looked at a group of children aged 7-9 and found that those who received financial education were more likely to understand concepts such as interest and inflation.
The researchers believe that this is because children who are taught about money are given the opportunity to practice making decisions with real money. This allows them to develop a better understanding of how money works and how to make wise choices with their finances.
The findings of the study suggest that financial education should be a priority in schools, in order to help children develop into responsible adults.
4. Financial literacy also helps children understand the role of money in society and the economy.
In a world where money dominates society, it’s important for children to understand the role of money in society and the economy. Financial literacy also helps children understand the role of money in society and the economy. Money is a powerful tool that can be used for good or bad, and it’s important for children to understand how to use it wisely.
Financial literacy can help children understand how to save money, how to budget, and how to invest. It can also help them understand how to avoid debt and how to make responsible decisions with their money. Financial literacy is an important life skill that can help children thrive in our society.
5. Teaching financial literacy to kids can help prevent them from making common money mistakes later in life.
It’s never too early to start teaching your kids about money. Financial literacy can help prevent them from making common money mistakes later in life.
You can start by teaching them the basics of earning, saving and spending money. Help them understand the value of a dollar and how to budget their money. As they get older, you can teach them more about credit, investing and other financial topics.
Financial literacy is an important life skill that can help your kids make smart financial decisions now and in the future.
6. Financial literacy is an essential life skill that every child should learn.
In today’s society, it is more important than ever for children to learn financial literacy. With the cost of living continuing to rise and the economy in a constant state of flux, it is essential that children understand how to manage money.
There are a number of ways parents can teach their children financial literacy. One way is to have them help with household budgeting and expenses. This will give them a practical understanding of where money goes and how it needs to be managed. Another way is to encourage them to save their allowance or earnings from part-time jobs. This will instill the importance of saving for future goals.
Last but not least, parents should set a good example when it comes to their own finances. Children learn by example, so if they see their parents being responsible with money, they are more likely to follow suit.
7. By teaching kids about money, we can help them build a bright future full of financial security and success.
In a world where money is everything, it’s important that our children are taught about money from a young age. By teaching kids about money, we can help them build a bright future full of financial security and success.
It’s important for kids to understand the basics of money and how to manage it. Financial literacy is a key life skill that will help them in their future. Teaching kids about money can help them make better decisions with their own finances, and avoid making costly mistakes.
With proper financial education, kids can learn how to save money, budget properly, and make smart investments. This will set them up for a bright future full of financial security and success. | <urn:uuid:fd2a27a7-4ef6-446d-ab95-c75ce441025e> | {
"date": "2022-10-01T18:44:39",
"dump": "CC-MAIN-2022-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336880.89/warc/CC-MAIN-20221001163826-20221001193826-00656.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9649542570114136,
"score": 3.859375,
"token_count": 1336,
"url": "https://www.goodfaithinvesting.com/7-reasons-why-teaching-financial-literacy-for-kids-is-important/"
} |
1,197 Pages
In geometry, a polygon is a plane figure bounded by a finite sequence of line segments, a two-dimensional polytope.
The line segments that make up the polygon are called sides; their intersections are called vertices.
In geometry a polygon (Template:Pron-en or Template:IPAlink-en) is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.
The word "polygon" derives from the Greek πολύς ("many") and γωνία (gōnia), meaning "knee" or "angle". Today a polygon is more usually understood in terms of sides.
Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge.
The basic geometrical notion has been adapted in various ways to suit particular purposes. For example in the computer graphics (image generation) field, the term polygon has taken on a slightly altered meaning, more related to the way the shape is stored and manipulated within the computer.
## Classification
### Number of sides
Polygons are primarily classified by the number of sides, see naming polygons below.
### Convexity
Polygons may be characterised by their degree of convexity:
• Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
• Non-convex: a line may be found which meets its boundary more than twice.
• Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
• Concave: Non-convex and simple.
• Star-shaped: the whole interior is visible from a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
• Self-intersecting: the boundary of the polygon crosses itself. Branko Grünbaum calls these coptic, though this term does not seem to be widely used. The term complex is sometimes used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
• Star polygon: a polygon which self-intersects in a regular way.
### Miscellaneous
• Rectilinear: a polygon whose sides meet at right angles, i.e., all its interior angles are 90 or 270 degrees.
• Monotone with respect to a given line L, if every line orthogonal to L intersects the polygon not more than twice.
## Properties
We will assume Euclidean geometry throughout.
### Angles
Any polygon, regular or irregular, self-intersecting or simple, has as many corners as it has sides. Each corner has several angles. The two most important ones are:
• Interior angle - The sum of the interior angles of a simple -gon is radians or degrees. This is because any simple -gon can be considered to be made up of triangles, each of which has an angle sum of radians or 180 degrees. The measure of any interior angle of a convex regular -gon is radians or degrees. The interior angles of regular star polygons were first studied by Poinsot, in the same paper in which he describes the four regular star polyhedra.
• Exterior angle - Imagine walking around a simple -gon marked on the floor. The amount you "turn" at a corner is the exterior or external angle. Walking all the way round the polygon, you make one full turn, so the sum of the exterior angles must be 360°. Moving around an n-gon in general, the sum of the exterior angles (the total amount one "turns" at the vertices) can be any integer multiple of 360°, e.g. 720° for a pentagram and 0° for an angular "eight", where is the density or starriness of the polygon. See also orbit (dynamics).
The exterior angle is the supplementary angle to the interior angle. From this the sum of the interior angles can be easily confirmed, even if some interior angles are more than 180°: going clockwise around, it means that one sometime turns left instead of right, which is counted as turning a negative amount. (Thus we consider something like the winding number of the orientation of the sides, where at every vertex the contribution is between −½ and ½ winding.)
### Area and centroid
The area of a polygon is the measurement of the 2-dimensional region enclosed by the polygon. For a non-self-intersecting (simple) polygon with vertices, the area and centroid are given by:[1]
To close the polygon, the first and last vertices are the same, i.e., . The vertices must be ordered clockwise or counterclockwise; if they are ordered clockwise, the area will be negative but correct in absolute value. This is commonly called the Surveyor's Formula.Template:Fix/category[citation needed]
The formula was described by MeisterTemplate:Fix/category[citation needed] in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, but it can also be seen as a special case of Green's theorem.
The area A of a simple polygon can also be computed if the lengths of the sides, a1,a2, ..., an and the exterior angles, are known. The formula is
The formula was described by Lopshits in 1963.[2]
If the polygon can be drawn on an equally-spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon. This is the Bolyai-Gerwien theorem.
For a regular polygon with n sides of length s, the area is given by:
### Through the area of a triangle
The area of a polygon can sometimes be found by multiplying the area of a triangle by therefore the following formulas are:
### Self-intersecting polygons
The area of a self-intersecting polygon can be defined in two different ways, each of which gives a different answer:
• Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region. For example the central convex pentagon in the centre of a pentagram has density 2. The two triangular regions of a cross-quadrilateral (like a figure 8) have opposite-signed densities, and adding their areas together can give a total area of zero for the whole figure.
• Considering the enclosed regions as point sets, we can find the area of the enclosed point set. This corresponds to the area of the plane covered by the polygon, or to the area of a simple polygon having the same outline as the self-intersecting one (or, in the case of the cross-quadrilateral, the two simple triangles).
### Degrees of freedom
An n-gon has degrees of freedom, including 2 for position, 1 for rotational orientation, and 1 for over-all size, so for shape. In the case of a line of symmetry the latter reduces to .
Let k ≥ 2. For an nk-gon with k-fold rotational symmetry (Ck), there are degrees of freedom for the shape. With additional mirror-image symmetry (Dk) there are degrees of freedom.
### Other formulas
The sector area of a polygon is:
The spiral length of a polygon is:
The arc length of a polygon is:
## Generalizations of polygons
In a broad sense, a polygon is an unbounded (without ends) sequence or circuit of alternating segments (sides) and angles (corners). An ordinary polygon is unbounded because the sequence closes back in itself in a loop or circuit, while an apeirogon (infinite polygon) is unbounded because it goes on for ever so you can never reach any bounding end point. The modern mathematical understanding is to describe such a structural sequence in terms of an 'abstract' polygon which is a partially ordered set (poset) of elements. The interior (body) of the polygon is another element, and (for technical reasons) so is the null polytope or nullitope.
A geometric polygon is understood to be a 'realization' of the associated abstract polygon; this involves some 'mapping' of elements from the abstract to the geometric. Such a polygon does not have to lie in a plane, or have straight sides, or enclose an area, and individual elements can overlap or even coincide. For example a spherical polygon is drawn on the surface of a sphere, and its sides are arcs of great circles. So when we talk about "polygons" we must be careful to explain what kind we are talking about.
A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc of a different great circle and you have a digon. Tile the sphere with digons and you have a polyhedron called a hosohedron. Take just one great circle instead, run it all the way round, and add just one "corner" point, and you have a monogon or henagon - although many authorities do not regard this as a proper polygon.
Other realizations of these polygons are possible on other surfaces - but in the Euclidean (flat) plane, their bodies cannot be sensibly realized and we think of them as degenerate.
The idea of a polygon has been generalized in various ways. Here is a short list of some degenerate cases (or special cases, depending on your point of view):
• Digon. Interior angle of 0° in the Euclidean plane. See remarks above re. on the sphere.
• Interior angle of 180°: In the plane this gives an apeirogon (see below), on the sphere a dihedron
• A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions. The Petrie polygons of the regular polyhedra are classic examples.
• A spherical polygon is a circuit of sides and corners on the surface of a sphere.
• An apeirogon is an infinite sequence of sides and angles, which is not closed but it has no ends because it extends infinitely.
• A complex polygon is a figure analogous to an ordinary polygon, which exists in the complex Hilbert plane.
## Naming polygons
The word 'polygon' comes from Late Latin polygōnum (a noun), from Greek polygōnon/polugōnon πολύγωνον, noun use of neuter of polygōnos/polugōnos πολύγωνος (the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A variable can even be used, usually n-gon. This is useful if the number of sides is used in a formula.
Some special polygons also have their own names; for example the regular star pentagon is also known as the pentagram.
Polygon names
Name Edges Remarks
henagon (or monogon) 1 In the Euclidean plane, degenerates to a closed curve with a single vertex point on it.
digon 2 In the Euclidean plane, degenerates to a closed curve with two vertex points on it.
triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane.
quadrilateral (or quadrangle or tetragon) 4 The simplest polygon which can cross itself.
pentagon 5 The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle.
hexagon 6
heptagon 7 avoid "septagon" = Latin [sept-] + Greek
octagon 8
enneagon (or nonagon) 9
decagon 10
hendecagon 11 avoid "undecagon" = Latin [un-] + Greek
dodecagon 12 avoid "duodecagon" = Latin [duo-] + Greek
tridecagon (or triskaidecagon) 13
pentadecagon (or quindecagon or pentakaidecagon) 15
icosagon 20
No established English name 100 "hectogon" is the Greek name (see hectometre), "centagon" is a Latin-Greek hybrid; neither is widely attested.
chiliagon 1000 Pronounced Template:IPAlink-en), this polygon has 1000 sides. The measure of each angle in a regular chiliagon is 179.64°.
René Descartes used the chiliagon and myriagon (see below) as examples in his Sixth meditation to demonstrate a distinction which he made between pure intellection and imagination. He cannot imagine all thousand sides [of the chiliagon], as he can for a triangle. However, he clearly understands what a chiliagon is, just as he understands what a triangle is, and he is able to distinguish it from a myriagon. Thus, he claims, the intellect is not dependent on imagination.[3]
myriagon 10,000 See remarks on the chiliagon.
megagon [4] 1,000,000 The internal angle of a regular megagon is 179.99964 degrees.
To construct the name of a polygon with more than 20 and less than 100 edges, combine the prefixes as follows
Tens and Ones final suffix
-kai- 1 -hena- -gon
20 icosi- 2 -di-
30 triaconta- 3 -tri-
40 tetraconta- 4 -tetra-
50 pentaconta- 5 -penta-
60 hexaconta- 6 -hexa-
70 heptaconta- 7 -hepta-
80 octaconta- 8 -octa-
90 enneaconta- 9 -ennea-
The 'kai' is not always used. Opinions differ on exactly when it should, or need not, be used (see also examples above).
That is, a 42-sided figure would be named as follows:
Tens and Ones final suffix full polygon name
tetraconta- -kai- -di- -gon tetracontakaidigon
and a 50-sided figure
Tens and Ones final suffix full polygon name
pentaconta- -gon pentacontagon
But beyond enneagons and decagons, professional mathematicians generally prefer the aforementioned numeral notation (for example, MathWorld has articles on 17-gons and 257-gons). Exceptions exist for side numbers that are difficult to express in numerical form.
## History
Polygons have been known since ancient times. The regular polygons were known to the ancient Greeks, and the pentagram, a non-convex regular polygon (star polygon), appears on the vase of Aristophonus, Caere, dated to the 7th century B.C..Template:Fix/category[citation needed] Non-convex polygons in general were not systematically studied until the 14th century by Thomas Bredwardine.Template:Fix/category[citation needed]
In 1952, ShephardTemplate:Fix/category[citation needed] generalised the idea of polygons to the complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons.
## Polygons in nature
Numerous regular polygons may be seen in nature. In the world of geology, crystals have flat faces, or facets, which are polygons. Quasicrystals can even have regular pentagons as faces. Another fascinating example of regular polygons occurs when the cooling of lava forms areas of tightly packed hexagonal columns of basalt, which may be seen at the Giant's Causeway in Ireland, or at the Devil's Postpile in California.
The most famous hexagons in nature are found in the animal kingdom. The wax honeycomb made by bees is an array of hexagons used to store honey and pollen, and as a secure place for the larvae to grow. There also exist animals who themselves take the approximate form of regular polygons, or at least have the same symmetry. For example, sea stars display the symmetry of a pentagon or, less frequently, the heptagon or other polygons. Other echinoderms, such as sea urchins, sometimes display similar symmetries. Though echinoderms do not exhibit exact radial symmetry, jellyfish and comb jellies do, usually fourfold or eightfold.
Radial symmetry (and other symmetry) is also widely observed in the plant kingdom, particularly amongst flowers, and (to a lesser extent) seeds and fruit, the most common form of such symmetry being pentagonal. A particularly striking example is the Starfruit, a slightly tangy fruit popular in Southeast Asia, whose cross-section is shaped like a pentagonal star.
Moving off the earth into space, early mathematicians doing calculations using Newton's law of gravitation discovered that if two bodies (such as the sun and the earth) are orbiting one another, there exist certain points in space, called Lagrangian points, where a smaller body (such as an asteroid or a space station) will remain in a stable orbit. The sun-earth system has five Lagrangian points. The two most stable are exactly 60 degrees ahead and behind the earth in its orbit; that is, joining the centre of the sun and the earth and one of these stable Lagrangian points forms an equilateral triangle. Astronomers have already found asteroids at these points. It is still debated whether it is practical to keep a space station at the Lagrangian point — although it would never need course corrections, it would have to frequently dodge the asteroids that are already present there. There are already satellites and space observatories at the less stable Lagrangian points.
## Uses for polygons
• Cut up a piece of paper into polygons, and put them back together as a tangram.
• Join many edge-to-edge as a tiling or tessellation.
• Join several edge-to-edge and fold them all up so there are no gaps, to make a three-dimensional polyhedron.
• Join many edge-to-edge, folding them into a crinkly thing called an infinite polyhedron.
• Use computer-generated polygons to build up a three-dimensional world full of monsters, theme parks, aeroplanes or anything - see Polygons in computer graphics below.
### Polygons in computer graphics
A polygon in a computer graphics (image generation) system is a two-dimensional shape that is modelled and stored within its database. A polygon can be coloured, shaded and textured, and its position in the database is defined by the co-ordinates of its vertices (corners).
Naming conventions differ from those of mathematicians:
• A simple polygon does not cross itself.
• a concave polygon is a simple polygon having at least one interior angle greater than 180 deg.
• A complex polygon does cross itself.
Use of Polygons in Real-time imagery. The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system (screen, TV monitors etc) so that the scene can be viewed. During this process, the imaging system renders polygons in correct perspective ready for transmission of the processed data to the display system. Although polygons are two dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation so that as the viewing point moves through the scene, it is perceived in 3D.
Morphing. To avoid artificial effects at polygon boundaries where the planes of contiguous polygons are at different angle, so called 'Morphing Algorithms' are used. These blend, soften or smooth the polygon edges so that the scene looks less artificial and more like the real world.
Polygon Count. Since a polygon can have many sides and need many points to define it, in order to compare one imaging system with another, "polygon count" is generally taken as a triangle. A triangle is processed as three points in the x,y, and z axes, needing nine geometrical descriptors. In addition, coding is applied to each polygon for colour, brightness, shading, texture, NVG (intensifier or night vision), Infra-Red characteristics and so on. When analysing the characteristics of a particular imaging system, the exact definition of polygon count should be obtained as it applies to that system.
Meshed Polygons. The number of meshed polygons (`meshed' is like a fish net) can be up to twice that of free-standing unmeshed polygons, particularly if the polygons are contiguous. If a square mesh has points (vertices) per side, there are n squared squares in the mesh, or squared triangles since there are two triangles in a square. There are vertices per triangle. Where n is large, this approaches 1/2. Or, each vertex inside the square mesh connects four edges (lines).
Vertex Count. Because of effects such as the above, a count of Vertices may be more reliable than Polygon count as an indicator of the capability of an imaging system.
Point in polygon test. In computer graphics and computational geometry, it is often necessary to determine whether a given point P = (x0,y0) lies inside a simple polygon given by a sequence of line segments. It is known as the Point in polygon test.
Community content is available under CC-BY-SA unless otherwise noted. | crawl-data/CC-MAIN-2021-31/segments/1627046154878.27/warc/CC-MAIN-20210804142918-20210804172918-00697.warc.gz | null |
Aatish Bhatia noticed a plant in his backyard whose leaves naturally repelled water. He took a sample to a friend who had access to a high-speed camera and an electron microscope to investigate what made the leaves so hydrophobic.
But how does a leaf become superhydrophobic? The trick to this, Janine explained, is that the water isn’t really sitting on the surface. A superhydrophobic surface is a little like a bed of nails. The nails touch the water, but there are gaps in between them. So there’s fewer points of contact, which means the surface can’t tug on the water as much, and so the drop stays round.
The leaf is so water repellant that drops of water bounce right off of it: | <urn:uuid:3dfa0e7d-c4b1-4d16-92be-d3a10b51c28e> | {
"date": "2016-10-22T16:07:45",
"dump": "CC-MAIN-2016-44",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719027.25/warc/CC-MAIN-20161020183839-00283-ip-10-171-6-4.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9802573919296265,
"score": 3.8125,
"token_count": 165,
"url": "http://kottke.org/14/06/the-leaf-that-hates-water"
} |
# Free Printable Multiplication Flash Cards 3rd Grade
Understanding multiplication right after counting, addition, and subtraction is good. Youngsters understand arithmetic using a all-natural progression. This advancement of understanding arithmetic is usually the subsequent: counting, addition, subtraction, multiplication, and lastly department. This assertion leads to the query why understand arithmetic with this series? Most importantly, why discover multiplication following counting, addition, and subtraction just before division?
## The next information answer these queries:
1. Kids discover counting first by associating aesthetic things because of their fingertips. A real case in point: Just how many apples are there any within the basket? Far more abstract illustration is just how aged are you currently?
2. From counting numbers, the following rational move is addition combined with subtraction. Addition and subtraction tables can be very useful teaching tools for the kids since they are visual equipment creating the move from counting much easier.
3. Which should be discovered up coming, multiplication or division? Multiplication is shorthand for addition. At this moment, youngsters use a company understand of addition. As a result, multiplication is the following logical type of arithmetic to understand.
## Review basic principles of multiplication. Also, review the basics using a multiplication table.
Allow us to review a multiplication illustration. Employing a Multiplication Table, multiply four times three and acquire an answer a dozen: 4 x 3 = 12. The intersection of row 3 and line several of your Multiplication Table is a dozen; a dozen may be the response. For kids starting to learn multiplication, this is effortless. They can use addition to resolve the trouble as a result affirming that multiplication is shorthand for addition. Example: 4 x 3 = 4 4 4 = 12. It is an outstanding introduction to the Multiplication Table. The additional benefit, the Multiplication Table is aesthetic and demonstrates returning to discovering addition.
## In which should we commence understanding multiplication making use of the Multiplication Table?
1. Initial, get informed about the table.
2. Get started with multiplying by one. Start off at row number 1. Go on to column primary. The intersection of row 1 and column one is the answer: a single.
3. Repeat these steps for multiplying by 1. Multiply row 1 by posts one particular via 12. The solutions are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 respectively.
4. Perform repeatedly these actions for multiplying by two. Flourish row two by columns 1 by way of 5 various. The replies are 2, 4, 6, 8, and 10 respectively.
5. Allow us to bounce in advance. Perform repeatedly these actions for multiplying by five. Multiply row five by columns 1 via 12. The responses are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 correspondingly.
6. Now we will improve the quantity of difficulty. Repeat these techniques for multiplying by three. Multiply row 3 by columns one particular via a dozen. The answers are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, and 36 correspondingly.
7. When you are more comfortable with multiplication so far, try a examination. Remedy these multiplication problems in your head and then evaluate your responses towards the Multiplication Table: multiply 6 and two, flourish 9 and 3, multiply one particular and eleven, flourish a number of and 4, and flourish six as well as 2. The trouble replies are 12, 27, 11, 16, and 14 respectively.
In the event you obtained several away from 5 difficulties right, build your own multiplication exams. Estimate the responses in your head, and appearance them utilizing the Multiplication Table. | crawl-data/CC-MAIN-2021-17/segments/1618038088264.43/warc/CC-MAIN-20210415222106-20210416012106-00221.warc.gz | null |
Holman Bible Dictionary
Number Systems and Number Symbolism
To understand properly the number systems of the biblical world, one must look to the neighbors of Israel. The Egyptians were already using relatively advanced mathematics by 3000 B.C. The construction of such structures as the pyramids required an understanding of complex mathematics. The Egyptian system was decimal. The Sumerians by that same time had developed their own number system. In fact, the Sumerians knew two systems, one based on ten (a decimal system) and one based on six or twelve (usually designated as a duodecimal system). We still make use of remnants of the Sumerian system today in our reckoning of time—12 hours for day and 12 hours for night, 60 minutes and 60 seconds as divisions of time. We also divide a circle into 360 degrees. Our calendar was originally based on the same division with the year having 12 months of 30 days for a total of 360. Even our units of the dozen (12) and gross (144) and inches to the foot may have their origin in the Sumerian mathematical system.
The Hebrews did not develop the symbols to represent numbers until the postexilic period (after 539 B.C.). In all preexilic inscriptions, small numbers are represented by individual strokes (for example, //// for four). Larger numbers were either represented with Egyptian symbols, or the name of the number was written out (“four” for the number 4). The Arad inscriptions regularly used Egyptian symbols for numbers, individual strokes for the units and hieratic numbers for 5,10, and larger numbers. The Samaria ostraca more frequently wrote out the number. Letters of the Hebrew alphabet are first used to represent numbers on coins minted in the Maccabean period (after 167 B.C.).
With the coming of the Hellenistic and Roman periods to Palestine, Greek symbols for numbers and Roman numerals appeared. The Greeks used letters of their alphabet to represent numerals, while the Romans used the familiar symbols I,V,X,L,C,M, and so on
Biblical passages show that the Hebrews were well acquainted with the four basic mathematical operations of addition (Numbers 1:20-46 ), subtraction (Genesis 18:28-33 ), multiplication (Numbers 7:84-86 ), and division (Numbers 31:27 ). The Hebrews also used fractions such as a half (Genesis 24:22 ), a third (Numbers 15:6 ), and a fourth (Exodus 29:40 ).
In addition to their usage to designate specific numbers or quantities, many numbers in the Bible came to have a symbolic meaning. Thus seven came to symbolize completeness and perfection. God's work of creation was both complete and perfect—and it was completed in seven days. All of mankind's existence was related to God's creative activity. The seven-day week reflected God's first creative activity. The sabbath was that day of rest following the work week, reflective of God's rest (Genesis 1:1-2:4 ). Israelites were to remember the land also and give it a sabbath, permitting it to lie fallow in the seventh year (Leviticus 25:2-7 ). Seven was also important in cultic matters beyond the sabbath: major festivals such as Passover and Tabernacles lasted seven days as did wedding festivals (Judges 14:12 ,Judges 14:12,14:17 ). In Pharaoh's dream, the seven good years followed by seven years of famine (Genesis 41:1-36 ) represented a complete cycle of plenty and famine. Jacob worked a complete cycle of years for Rachel; then, when he was given Leah instead, he worked an additional cycle of seven (Genesis 29:15-30 ).
A major Hebrew word for making an oath or swearing, shava' , was closely related to the word seven , sheva' . The original meaning of “swear an oath” may have been “to declare seven times” or “to bind oneself by seven things.”
A similar use of the number seven can be seen in the New Testament. The seven churches (Revelation 2-3 ) perhaps symbolized by their number all the churches. Jesus taught that forgiveness is not to be limited, even to a full number or complete number of instances. We are to forgive, not merely seven times (already a gracious number of forgivenesses), but seventy times seven (limitless forgiveness, beyond keeping count) (Matthew 18:21-22 ).
As the last example shows, multiples of seven frequently had symbolic meaning. The year of Jubilee came after the completion of every forty-nine years. In the year of Jubilee all Jewish bondslaves were released and land which had been sold reverted to its former owner (Leviticus 25:8-55 ). Another multiple of seven used in the Bible is seventy. Seventy elders are mentioned (Exodus 24:1 ,Exodus 24:1,24:9 ). Jesus sent out the seventy (Luke 10:1-17 ). Seventy years is specified as the length of the Exile (Jeremiah 25:12 , Jeremiah 29:10; Daniel 9:1 : 2 ). The messianic kingdom was to be inaugurated after a period of seventy weeks of years had passed (Daniel 9:24 ).
After seven, the most significant number for the Bible is undoubtedly twelve. The Sumerians used twelve as one base for their number system. Both the calendar and and the signs of the Zodiac reflect this twelve base number system. The tribes of Israel and Jesus' disciples numbered twelve. The importance of the number twelve is evident in the effort to maintain that number. When Levi ceased to be counted among the tribes, the Joseph tribes, Ephraim and Manasseh, were counted separately to keep the number twelve intact. Similarly, in the New Testament, when Judas Iscariot committed suicide, the eleven moved quickly to add another to keep their number at twelve. Twelve seems to have been especially significant in the Book of Revelation. New Jerusalem had twelve gates; its walls had twelve foundations (Revelation 21:12-14 ). The tree of life yielded twelve kinds of fruit (Revelation 22:2 ).
Multiples of twelve are also important. There were twenty-four divisions of priests (1 Chronicles 24:4 ), and twenty-four elders around the heavenly throne (Revelation 4:4 ). Seventy-two elders, when one includes Eldad and Medad, were given a portion of God's spirit that rested on Moses, and they prophesied (Numbers 11:24-26 ). An apocryphal tradition holds that seventy-two Jewish scholars, six from each of the twelve tribes, translated the Old Testament into Greek, to give us the version we call today the Septuagint. The 144,000 servants of God (Revelation 7:4 ), were made up of 12,000 from each of the twelve tribes of Israel.
Three as a symbolic number often indicated completeness. The created cosmos had three elements: heaven, earth, and underworld. Three Persons make up the Godhead: Father, Son, and Holy Spirit. Prayer was to be lifted at least three times daily (Daniel 6:10; compare Psalm 55:1 : 17 ). The sanctuary had three main parts: vestibule, nave, inner sanctuary (1 Kings 6:1 ). Three-year-old animals were mature and were, therefore, prized for special sacrifices (1 Samuel 1:24; Genesis 15:9 ). Jesus said He would be in the grave for three days and three nights (Matthew 12:40 ), the same time Jonah was in the great fish (Jonah 1:17 ). Paul often used triads in his writings, the most famous being “faith, hope and charity” (1 Corinthians 13:13 ). One must also remember Paul's benediction: “The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost be with you all” (2 Corinthians 13:14 ).
Four was often used as a sacred number. Significant biblical references to four include the four corners of the earth (Isaiah 11:12 ), the four winds (Jeremiah 49:36 ), four rivers which flowed out of Eden to water the world (Genesis 2:10-14 ), and four living creatures surrounding God (Ezekiel 1:1; Revelation 4:6-7 ). God sent forth the four horsemen of the Apocalypse (Revelation 6:1-8 ) to bring devastation to the earth.
The most significant multiple of four is forty, which often represented a large number or a long period of time. Rain flooded the earth for forty days (Genesis 7:12 ). For forty days Jesus withstood Satan's temptations (Mark 1:13 ). Forty years represented approximately a generation. Thus all the adults who had rebelled against God at Sinai died during the forty years of the Wilderness Wandering period. By age forty, a person had reached maturity (Exodus 2:11; Acts 7:23 ).
A special system of numerology known as gematria developed in later Judaism. Gematria is based on the idea that one may discover hidden meaning in the biblical text from a study of the numerical equivalence of the Hebrew letters. The first letter of the Hebrew alphabet, aleph represented one; beth , the second letter represented two, and so on. With gematria one takes the sum of the letters of a Hebrew word and seeks to find some meaning. For example, the Hebrew letters of the name Eliezer, Abraham's servant, have a numerical value of 318. When Gensis Acts 14:14 states that Abraham took 318 trained men to pursue the kings from the east, some Jewish commentaries interpret this to mean that Abraham had but one helper, Eliezer, since Eliezer has the numerical value of 318. Likewise, the number 666 in Revelation is often taken as a reverse gematria for the emperor Nero. The name Nero Caesar, put in Hebrew characters and added up following gematria, total 666. Any interpretation based on gematria must be treated with care; such interpretation always remains speculative.
Joel F. Drinkard, Jr.
Visit Our Sponsors | <urn:uuid:8f39fa50-cc43-4b85-9be1-1108f87d6620> | {
"date": "2015-05-29T10:19:58",
"dump": "CC-MAIN-2015-22",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929978.35/warc/CC-MAIN-20150521113209-00112-ip-10-180-206-219.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9452282786369324,
"score": 3.921875,
"token_count": 2147,
"url": "http://www.studylight.org/dictionaries/hbd/view.cgi?number=T4649"
} |
Tangent Circles
assignment #7
Lets begin by looking at circles tangent to a line. We can use the following construction, to do this:
1. draw a line segment AB,
2. pick a point in the plane, not on segment AB, call it C because it will be the center of our tangent circle.
3. Drop a perpindicular from point C to the AB segment.
4. The segment from point P perpindicular to AB, will be the radius.
5. Now, construct the circle.
script tool for this construction
Next, lets try to draw a circle tangent to another circle.
We can do this by drawing one circle and picking a point on the original circle, and picking a point in the plane to be the center of the tangent circle. We connect the center of the original circle and the point we in the plane with a segment. The point in which the segment intersects the original circle will be point of tangency. We can construct our tangent circle using the center and the point of tangency.
sript tool for two tangent circles
Given two circles, lets explore finding a third circle tangent to the other two.
The construction is as follows:
Label the intersection of AB with the two circles, C and D and construct segment CD. Find the midpoint of CD and label it E.
Construct a third circle with E as the center and ED as the radius. This circle is tangent to the other two.
script tool for three tangent circles
For the next exploration, lets figure out how to take two circles, one inside the other and find a circle tangent to both circles.
Through the chosen point of tangency on the bigger circle, construct a line connecting the chosen tangent point and the center of the bigger circle.
Next construct a copy of the smaller circle with center the chosen point of tangency on the larger circle.
Construct the outermost intersection of the original line through C2 with the constructed circle. Connect the intersection with C1, the center of the smaller circle. Find the perpindicular bisector of the segment. The point where the perpindicular bisector and the original line intersect will be the center of our tangent circle.
Now construct the isoceles triangle. This triangle will always be isoceles.
Using C3 as the center and the segment C3C2 as the radius, construct the tangent circle.
Script tool to make tangent circle | crawl-data/CC-MAIN-2018-47/segments/1542039741340.11/warc/CC-MAIN-20181113173927-20181113195927-00353.warc.gz | null |
Welcome to Parsimony’s blog, where we help K-12 educators identify evidence based ways to maximize student outcomes.
This blog post is part of our What Works Clearinghouse review series. The What Works Clearinghouse (WWC) is an initiative by the Institute of Education Sciences (IES) which is the independent statistics, research, and evaluation arm of the United States Department of Education. WWC estimates the effectiveness of programs by evaluating the quality and quantity of evidence for that program.
This week’s blog post is about the evidence behind Ready, Set, Leap!® ’s impact on students. Here’s the short version:
Ready, Set, Leap!® is a comprehensive preschool curriculum that focuses on early reading skills, such as phonemic awareness, letter knowledge, and letter-sound correspondence using multi-sensory technology that incorporates touch, sight, and sound. Teachers may adopt either a theme-based or a literature-based teaching approach.
The evidence for Ready, Set, Leap!® covers students in pre-kindergarten.
The outcomes examined include: early reading/writing, general mathematics achievement, oral language, phonological processing, and print knowledge. Here’s what the evidence suggests about Ready, Set, Leap!® ’s impact on each outcome:
- Early reading/writing: No detectable impact
- General mathematics achievement: Negative impact
- Oral language: No detectable impact
- Phonological processing: Positive impact (an average student would be expected to improve by 2 percentile points)
- Print knowledge: No detectable impact
The studies looking into Ready, Set, Leap!® had student samples that were in urban areas in New Jersey, had students who were White, Black, and Hispanic, and were male and female.
You can find the full report from the What Works Clearinghouse here:
Find this blog post helpful? Then sign up for our newsletter (if you haven’t already) so you can get notified of new posts. Just click on the subscribe button below and enter your email address. | <urn:uuid:b1c4fe2d-decb-49b6-9f04-fa22f066c30b> | {
"date": "2021-05-18T23:50:19",
"dump": "CC-MAIN-2021-21",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989874.84/warc/CC-MAIN-20210518222121-20210519012121-00418.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9298150539398193,
"score": 3.546875,
"token_count": 431,
"url": "https://blog.parsimonyinc.com/what-does-the-what-works-clearinghouse-say-about-ready-set-leap-r/"
} |
Dust devils raging across the arctic plains of Mars were caught on film by NASA's Phoenix Mars Lander.
Phoenix captured images of at least six different dust devils that danced across the planet's surface last week, and sensed a dip in air pressure as one passed near the lander.
These whirlwinds, which are somewhat like gentle tornadoes and are common in the American Southwest, too, had been expected in Phoenix's landing site near the north pole (they've been seen from above by orbiting spacecraft) but not confirmed by the spacecraft until now.
Dust devils are whirlwinds that often occur when the sun heats the surface of Mars (this also happens in some areas on Earth). The warmed surface heats the layer of atmosphere closest to it, and the warm air rises in a whirling motion, stirring dust up from the surface and whisking it high into the air. They have been photographed by the Mars rovers operating near the equator, too.
Phoenix's Surface Stereo Imager camera took 29 images of the western and southwestern horizon on Monday, during midday hours of the lander's 104th Martian day. When the Phoenix science team analyzed the images the next day, they noticed a dust devil immediately.
"It was a surprise to have a dust devil so visible that it stood with just the normal processing we do," said Mark Lemmon of Texas A&M University, lead scientist for the stereo camera. "Once we saw a couple that way, we did some additional processing and found there are dust devils in 12 of the images."
The dust devils seen range in diameter from about 7 feet to about 16 feet (2 to 5 meters).
"It will be very interesting to watch over the next days and weeks to see if there are lots of dust devils or if this was an isolated event," Lemmon said.
The day the camera saw dust devils, Phoenix's pressure meter recorded a sharp dip in the thin atmosphere. The drop was less than the overall daily change in air pressure from daytime to nighttime, but this dip occurred over a much shorter time.
"Throughout the mission, we have been detecting vortex structures that lower the pressure for 20 to 30 seconds during the middle part of the day," said Peter Taylor of York University in Toronto, a member of the Phoenix science team. "In the last few weeks, we've seen the intensity increasing, and now these vortices appear to have become strong enough to pick up dust."
Still, the dust devils observed by Phoenix are much smaller than those seen closer to the planet's midsection by NASA's Mars Exploration Rover Spirit.
"We expected dust devils, but we are not sure how frequently," said Phoenix project scientist Leslie Tamppari of NASA's Jet Propulsion Laboratory, in Pasadena, Calif. "It could be they are rare and Phoenix got lucky. We'll keep looking for dust devils at the Phoenix site to see if they are common or not."
© 2013 Space.com. All rights reserved. More from Space.com. | <urn:uuid:4deb3aee-f781-435d-b3ff-aeb751e8b04f> | {
"date": "2015-04-26T22:36:17",
"dump": "CC-MAIN-2015-18",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246656747.97/warc/CC-MAIN-20150417045736-00082-ip-10-235-10-82.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9660881757736206,
"score": 3.703125,
"token_count": 614,
"url": "http://www.nbcnews.com/id/26675656/ns/technology_and_science-space/"
} |
# Use comparison test to determine convergence of the following series?
## sum_(n=0)^oo 5/(2+3^n
May 6, 2018
The series is convergent by Comparison to an infinite and convergent geometric series.
#### Explanation:
The comparison test basically tells us that if there are two series ${S}_{1}$ and ${S}_{2}$ and we have that ${S}_{1} \le {S}_{2}$, then if
1. ${S}_{2}$ converges, so does ${S}_{1}$
2. ${S}_{1}$ diverges, so does ${S}_{2}$
The trick to making the problem simpler is to choose ${S}_{2}$ and ${S}_{1}$ in such a way that it makes the algebraic computation fairly easy for you. Whenever you have to use the comparison test, try to look for geometric series which are similar to what is given in the question.
For this case, we know that:
$\frac{5}{2 + {3}^{n}} < \frac{1}{2} ^ n$ because we are just multiplying the LHS by '5' and as n approaches infinity, the +2 in the denominator hardly makes a difference. However, on the RHS, we are taking ${2}^{n}$, which is much smaller than ${3}^{n}$ as n gets infinitely large. Hence, the above inequality holds. (If you are not convinced, I encourage you to sketch a graph using a graphic calculator)
Now this problem is much simpler for us. We already know that ${u}_{n} = \left(\frac{1}{2} ^ n\right)$ is a geometric series that converges to a finite sum $S$ given by
$S = {u}_{1} / \left(1 - r\right)$ where r is the common ratio
Hence, for the above case, ${u}_{1} = 1$ (because we replace 0 in u_n) and $r = \frac{1}{2}$
Hence: $S = \frac{1}{1 - \frac{1}{2}} = 2$
And since $\frac{5}{2 + {3}^{n}} < \frac{1}{2} ^ n$, and $S$ converges, by the Comparison test, the sum given in the question also converges (to a finite sum that is less than 2).
Hope this helps! | crawl-data/CC-MAIN-2022-27/segments/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00689.warc.gz | null |
Pigeons are monogamous and typically mate for life. Pigeons build a flimsy platform nest of straw and sticks, put on ledge, under cover, often located on the window ledges of buildings. In captivity, pigeons commonly live up to 15 years and sometimes longer. In urban populations, however, pigeons seldom live more than 3 or 4 years. Natural mortality factors, such as predation by mammals and other birds, diseases, and stress due to lack of food and water, reduce pigeon populations by approximately 30% annually. Pigeons are found to some extent in nearly all urban areas around the world. It is estimated that there are 400 million pigeons worldwide and that the population is growing rapidly together with increased urbanization. Sexes look nearly identical, although males are larger and have more iridescence on their neck. Juveniles are very similar in appearance to adults, but duller and with less iridescence. Pigeons are highly dependent on humans to provide them with food and sites for roosting, loafing, and nesting. They are commonly found around farm yards, grain elevators, feed mills, parks, city buildings, bridges, and other structures, although they can live anywhere where they have adequate access to food, water and shelter. | <urn:uuid:e61ea5a0-1813-4265-828d-ab9cc5fff4e4> | {
"date": "2018-06-18T19:14:21",
"dump": "CC-MAIN-2018-26",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860776.63/warc/CC-MAIN-20180618183714-20180618203714-00018.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9782677292823792,
"score": 3.6875,
"token_count": 260,
"url": "https://pestgone.co.uk/pests/"
} |
In Moscow, Soviet officials arrest four dissidents and prevent at least 20 others from attending a peaceful protest against communist political oppression on United Nations Human Rights Day. According to some of the protesters, Soviet officials threatened them with violence should the protest be held. The incident was more evidence of an increasingly hard line being taken by the Soviet government against any political protest.
Approximately 25 protesters met at the statue of the Russian poet Pushkin in Moscow to assert their right to freedom of assembly, which had been guaranteed by the new Soviet constitution approved in October. Twenty other dissidents had been dissuaded from attending when they saw Soviet plainclothes police stationed outside their apartments. In addition, Soviet officials detained four other known dissidents to keep them from the protest. Andrei Sakharov, perhaps the most famous Soviet political dissident, refrained from attending because he feared that violence would break out. The protest, however, was peaceful and uneventful. Nevertheless, the Soviet actions were a chilling reminder that political freedom in Russia was still far from being a reality. Human rights abuses in the Soviet Union continued to be a sore point in U.S.-Soviet relations into the Gorbachev years of the 1980s. | <urn:uuid:f05a3158-f04a-455f-94b5-63a523d3fe0e> | {
"date": "2014-09-30T10:20:58",
"dump": "CC-MAIN-2014-41",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037662882.4/warc/CC-MAIN-20140930004102-00283-ip-10-234-18-248.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9824474453926086,
"score": 3.578125,
"token_count": 241,
"url": "http://www.history.com/this-day-in-history/soviets-arrest-dissidents-on-united-nations-human-rights-day?catId=3"
} |
# Permutation – Examples, PDF
In a given set of data, all of its values can be arranged in various possible combinations that are very hard to manually count. A permutation is a formula arithmeticians use to get a value that can indicate the total possible and viable number of unique combinations.
## What Is Permutation
A permutation is a type of arrangement that is often used in mathematics. This arrangement allows the person to obtain all the possible combinations of a given arrangement without the need to exclude any of the elements in a given dataset. Not only that but this will also eliminate any repetition in the dataset. If you want to learn more about permutations and the generation of permutations, you may refer to the articles named Irreducible and Connected Permutations, Variations Twins in Permutations, Permutation Covers Template, and Restricted Permutations Template.
## How To Write a Permutation Arrangement
A permutation is a really easy and intuitive way to know a specific value in a given situation, without needing to overcomplicate the formula. The formula of permutation comes in the form of P(n,r) = n!/(n-r)!m, where n is the positive integer that represents the object selected, r is the whole number that would represent the objects that are not in repetition, and P(n,r) is the number that represents all the possible permutation arrangements.
### Step 1: Write the Formula
Begin by writing down the formula of permutation on an accessible notepad or digital note-taking software. This will help you easily outline the whole process and allow you to easily substitute the given numbers in a later step.
### Step 2: List Out the Given Numbers
After writing down the formula on the notepad or digital note-taking software, you must separate and list out the given numbers in the question. Doing this will allow you to immediately have a reference when substituting the given irrational numbers, rational numbers, and real numbers into the formula.
### Step 3: Substitute The Correct Values
You must substitute the corresponding given numbers to their variables in the formula. The product of this step creates a working equation that will allow you to obtain the missing variable.
### Step 4: Solve the Equation
You will then solve the equation using the given variables. Do note that the (!) symbol represents all the preceding values of the number beside the (!) in descending order.
## What is a permutation example?
A permutation is a mathematical concept that is used as an arrangement of mathematical objects in a specified order. An example of a permutation is a dataset of 3 pairs where set A = {3,2}, set B = {3,2} {4,1}, and set C = {3,2}, {4,1}, {5,0}. A real-life application of a permutation is the arrangement of a group of people based on the first letter of their surnames, their birthdays, and other types of filters.
## What is the difference between permutation and combination?
A permutation is an arrangement of all objects inside a specified group. This means that no member of the chosen group will be exempted or excluded from the arrangement and sortation. This is juxtaposed with another type of arrangement called a combination. This type of arrangement focuses on the specific selection of members within the chosen group, which is sorted by a specified filter. This represents the biggest difference between the two types of arrangement as a permutation does not exclude members in the group, unlike a combination.
## How do you know if it’s a permutation or combination?
The most common factor that differentiates a permutation from a combination is the inclusion of all the parts or members within the given group. A permutation does not exclude and discriminate against any of the members within the group when a person uses said arrangement. A combination, on the other hand, excludes and discriminates the members in a group that do not fit the specified filter. For example, when a person asks a group of people to arrange themselves based on their birthdays in ascending order, this is a real-life application of a permutation. Using the same setting as the example above, when a person asks a group of people whose birthdays range from May to June in descending order. This example is a real-life application of a combination.
A permutation is a type of arrangement that groups and arranges all the members in a specified group without excluding or ignoring any of the members in the group. When done properly you can easily arrange all the members in a dataset using broad and non-exclusive filters and context. | crawl-data/CC-MAIN-2023-40/segments/1695233510924.74/warc/CC-MAIN-20231001173415-20231001203415-00310.warc.gz | null |
### Learning Objectives
• (9.5.1) – Solving Radical Equations
• Identify a radical equation with no solutions, or extraneous solutions
• (9.5.2) – Applications with radical equations
• Kinetic Energy
• Volume
• Free-fall
# (9.5.1) – Solving Radical Equations
Now that you understand how to combine radical terms and expressions using algebraic operations, you can solve equations that contain radicals. Soon, we will be able to help Joan (and Anne) figure out how tall the ladder needs to be! In this lesson you will use the addition and multiplication properties of equality as well as the rules for exponents.
An equation that contains a radical expression is called a radical equation. Solving radical equations requires applying the rules of exponents and following some basic algebraic principles. In some cases, it also requires looking out for errors generated by raising unknown quantities to an even power.
A basic strategy for solving radical equations is to isolate the radical term first, and then raise both sides of the equation to a power to remove the radical. (The reason for using powers will become clear in a moment.) This is the same type of strategy you used to solve other, non-radical equations—rearrange the expression to isolate the variable you want to know, and then solve the resulting equation.
There are two key ideas that you will be using to solve radical equations. The first is that if $a=b$, then ${{a}^{2}}={{b}^{2}}$. (This property allows you to square both sides of an equation and remain certain that the two sides are still equal.) The second is that if the square root of any nonnegative number $x$ is squared, then you get $x$: ${{\left( \sqrt{x} \right)}^{2}}=x$. (This property allows you to “remove” the radicals from your equations.)
Let’s start with a radical equation that you can solve in a few steps:$\sqrt{x}-3=5$.
### Example
Solve. $\sqrt{x}-3=5$
To check your solution, you can substitute 64 in for $x$ in the original equation. Does $\sqrt{64}-3=5$? Yes—the square root of 64 is 8, and $8−3=5$.
Notice how you combined like terms and then squared both sides of the equation in this problem. This is a standard method for removing a radical from an equation. It is important to isolate a radical on one side of the equation and simplify as much as possible before squaring. The fewer terms there are before squaring, the fewer additional terms will be generated by the process of squaring.
In the example above, only the variable $x$ was underneath the radical. Sometimes you will need to solve an equation that contains multiple terms underneath a radical. Follow the same steps to solve these, but pay attention to a critical point—square both sides of an equation, not individual terms. Watch how the next two problems are solved.
### Example
Solve. $\sqrt{x+8}=3$
In the following video example you will see two more examples that are similar to the ones above.
### Example
Solve. $1+\sqrt{2x+3}=6$
In the next example, we present a radical equation with a radical of index 3:
### ExAMPLE
Solve. $\sqrt[3]{5x+1}+8+4$
1. Isolate the radical expression (index $n$) to one side.
2. Raise both sides of the equation to the $n^{th}$ power : If $x=y$ then $x^{n}=y^{n}$.
3. Once the radical is removed, solve for the unknown. (If necessary, repeat first two steps, until all radicals are removed.)
### Identify a radical equation with no solutions or extraneous solutions
Following rules is important, but so is paying attention to the math in front of you—especially when solving radical equations. Take a look at this next problem that demonstrates a potential pitfall of squaring both sides to remove the radical.
### Example
Solve. $\sqrt{a-5}=-2$
Look at that—the answer $a=9$ does not produce a true statement when substituted back into the original equation. What happened?
Check the original problem: $\sqrt{a-5}=-2$. Notice that the radical is set equal to $−2$, and recall that the principal square root of a number can only be positive. This means that no value for a will result in a radical expression whose positive square root is $−2$! You might have noticed that right away and concluded that there were no solutions for a. But why did the process of squaring create an answer, $a=9$, that proved to be incorrect?
The answer lies in the process of squaring itself. When you raise a number to an even power—whether it is the second, fourth, or 50th power—you can introduce a false solution because the result of an even power is always a positive number. Think about it: $3^{2}$ and $\left(−3\right)^{2}$ are both 9, and $2^{4}$ and $\left(−2\right)^{4}$ are both 16. So when you squared $-2$ and got $4$ in this problem, you artificially turned the quantity positive. This is why you were still able to find a value for $a$—you solved the problem as if you were solving$\sqrt{a-5}=2$! (The correct solution to $\sqrt{a-5}=-2$ is actually “no solution.”)
Incorrect values of the variable, such as those that are introduced as a result of the squaring process are called extraneous solutions. Extraneous solutions may look like the real solution, but you can identify them because they will not create a true statement when substituted back into the original equation. This is one of the reasons why checking your work is so important—if you do not check your answers by substituting them back into the original equation, you may be introducing extraneous solutions into the problem.
Have a look at the following problem. Notice how the original problem is $x+4=\sqrt{x+10}$, but after both sides are squared, it becomes ${{x}^{2}}+8x+16=x+10$. Squaring both sides may have introduced an extraneous solution.
In the following video we present more examples of solving radical equations by isolating a radical term on one side.
### Example
Solve. $x+4=\sqrt{x+10}$
It may be difficult to understand why extraneous solutions exist at all. Thinking about extraneous solutions by graphing the equation may help you make sense of what is going on.
You can graph $x+4=\sqrt{x+10}$ on a coordinate plane by breaking it into a system of two equations: $y=x+4$ and $y=\sqrt{x+10}$. The graph is shown below. Notice how the two graphs intersect at one point, when the value of x is $−1$. This is the value of x that satisfies both equations, so it is the solution to the system.
Now, following the work we did in the example problem, let’s square both of the expressions to remove the variable from the radical. Instead of solving the equation $x+4=\sqrt{x+10}$ we are now solving the equation $\left(x+4\right)^{2}=\left(\sqrt{x+10}\right)^{2}$ , or $x^{2}+8x+16=x+10$. The graphs of $y=x^{2}+8x+16$ and $y=x+10$ are plotted below. Notice how the two graphs intersect at two points, when the values of x are $−1$ and $−6$.
Although $x=−1$ is shown as a solution in both graphs, squaring both sides of the equation had the effect of adding an extraneous solution, $x=−6$. Again, this is why it is so important to check your answers when solving radical equations!
### Example
Solve. $4+\sqrt{x+2}=x$
In the next video we show another example of radical equations that have extraneous solutions. Always remember to check your answers for radical equations.
In our last example we will use a difference of squares to solve a radical equation with two radicals. You will see that we have to isolate and eliminate one radical first, then tackle isolating and eliminating the other. We will also use factoring techniques for trinomials and the zero product principle to solve this equation.
### Example
Solve $\sqrt{2x+3}+\sqrt{x - 2}=4$.
In our last video we show the solution for another radical equation that has square roots on both sides of the equation. Pay special attention to how you square the side that has the sum of a radical term and a constant.
# (9.5.2) – Applications with Radical Equations
Kinetic Energy
One way to measure the amount of energy that a moving object (such as a car or roller coaster) possesses is by finding its Kinetic Energy. The Kinetic Energy ($E_{k}$, measured in Joules) of an object depends on the object’s mass ($m$), measured in kg) and velocity ($v$), measured in meters per second), and can be written as $v=\sqrt{\frac{2{{E}_{k}}}{m}}$.
### Example
What is the Kinetic Energy of an object with a mass of 1,000 kilograms that is traveling at 30 meters per second?
Here is another example of finding the kinetic energy of an object in motion.
### Volume
Harvester ants found in the southwest of the U.S. create a vast interlocking network of tunnels for their nests. As a result of all this excavation, a very common above-ground hallmark of a harvester ant nest is a conical mound of small gravel or sand [1]
The radius of a cone whose height is is equal to twice it’s radius is given as: $r=\sqrt[3]{\frac{3V}{2\pi }}$.
### Example
A mound of gravel is in the shape of a cone with the height equal to twice the radius. Calculate the volume of such a mound of gravel whose radius is 3.63 ft. Use $\pi =3.14$.
Here is another example of finding Volume given the radius of a cone.
## Free-Fall
When you drop an object from a height, the only force acting on it is gravity (and some air friction) and it is said to be in free-fall. We can use math to describe the height of an object in free fall after a given time because we know how to quantify the force of the earth pulling on us – the force of gravity.
An object dropped from a height of 600 feet has a height, $h$, in feet after $t$ seconds have elapsed, such that $h=600 - 16{t}^{2}$. In our next example we will find the time at which the object is at a given height by first solving for $t$.
### Example
Find the time is takes to reach a height of 400 feet by first finding an expression for $t$.
Radical equations play a significant role in science, engineering, and even music. Sometimes you may need to use what you know about radical equations to solve for different variables in these types of problems.
1. Taber, Stephen Welton. The World of the Harvester Ants. College Station: Texas A & M University Press, 1998. | crawl-data/CC-MAIN-2021-49/segments/1637964358673.74/warc/CC-MAIN-20211128224316-20211129014316-00329.warc.gz | null |
Most landscape professionals are familiar with the discomfort and pain that venomous arthropods-ants, wasps, spiders, fleas, ticks, scorpions, etc.-can cause. However, their venom can cause more than mere pain. More human deaths in the United States are attributed to venomous arthropods than any other group of venomous animals, including snakes. Deaths caused by arthropod bites or stings represent only a tiny fraction of the millions of victims. However, a higher number-about 25,000 per year in the United States-have severe reactions.
Arthropods often live in close proximity to people and can be abundant, resulting in a high contact rate with people. The venomous pests I'll discuss in this article include those whose bites or stings can be severe and have frequent contact with people. The greatest risk is in the Southern part of the United States where venomous pests are most numerous in population and variety, and where longer seasons allow multiple generations and longer periods of activity. However, every part of the United States is home to at least some of these pests. Grounds-maintenance employees need to understand the biology and behavior of venomous pests. This is essential in developing a good avoidance and management program.
Many chemical treatments for these pests are within the normal scope of operations for landscape professionals. However, if you are unsure about what treatment to use, contact a county extension agent, licensed consultant or qualified pest-control operator for recommendations. But use good judgment: Some operations, such as controlling hornet nests, can be dangerous for inexperienced people.
Arthropods cause three types of envenomization (exposure to venom): piercing/biting, vesicating/urticating and stinging. Piercing/biting arthropods inject a toxin through their mouth parts. Vesicating/urticating arthropods release toxins on contact through venomous hairs (urticating) or small body openings (vesicating). Stinging arthropods inject a toxin through a stinger located on the posterior end of the abdomen.
Piercing/biting pests *Chiggers. These are the larvae of mites sometimes referred to as "red bugs" or "harvest mites." Their bite results in itching around the infected area. The larvae crawl up grass blades, weeds or other vegetation and attach themselves to a passing host (human or animal). One to six generations occur each year depending on the geographical region. Each generation takes 30 to 60 days to complete depending on temperatures.
Contact with chiggers usually occurs where tall grass grows at the edge of lawns, or in densely vegetated areas bordering lawns, playgrounds, parks or golf roughs. Mowing weeds and grasses and removing overgrown vegetation on a regular basis reduces chigger populations. In addition, residual miticides applied to freshly cut tall grass will penetrate to target areas to reduce or eliminate chigger populations.
For personal protection, you can use insect repellents. You can apply certain permethrin-based products to clothing for chigger control. You also can apply diethyl toluamide (DEET-formulatedin many retail insect repellents) to clothing or skin around the waist, ankles or other favorite chigger-feeding sites. Pants tucked into socks or boots provides some protection. People exposed to chiggers can take a hot soapy bath to help remove them. For temporary relief from itching, apply antiseptic or anesthetic ointments to infected areas.
*Fleas. The cat flea is the most common flea, and it attacks cats, dogs and humans. The adult female must seek out a host to obtain a meal of blood before she can produce eggs. The bite results in skin irritation. You generally can eliminate flea problems by treating the host animals (pets) and the home interior or yard where pets spend most of their time. Frequent cleaning of pet bedding helps reduce populations.
Focus outdoor treatments on areas frequented by pets, such as resting areas close to building foundations, under decks and porches, doghouses and kennels. Keeping turf mowed and thatch at a minimal level allows insecticides to penetrate target flea populations. If possible, control wild hosts (stray cats and dogs, raccoons, opossums, moles, etc.) that maintain a reservoir of fleas. Many of these animals feed on grubs and other soil insects. You can discourage them by controlling their food source with an approved soil insecticide.
*Ticks. Ticks may be a problem in tall grass, weeds and wooded or shrubby areas. They occur mainly in overgrown vegetation around yards, picnic areas and golf roughs. Seldom do they pose a problem in well-maintained areas. Ticks come in contact with their victims by climbing up vegetation to await a passing host. They tend to crawl upward and attach to their hosts in areas constricted by skin folds or clothing and often attach to the base of the scalp, waist, knee or armpit.
Tick bites are quite irritating, but most ticks you'll encounter do not carry disease. However, the genera Ixodes and Rickettsis may transmit the bacterial infections we know familarly as Lyme disease and Rocky Mountain spotted fever. If you find a tick on yourself, remove it promptly to reduce the chance of disease transmission. With tweezers, grasp the tick's head as close to the skin as possible and slowly and gently pull it away from skin until it detaches. Then wash the bite area with soap and water and apply an antiseptic. If disease symptoms occur within 3 weeks, see a doctor.
Reduce tick populations by cutting grass, weeds and overgrown vegetation. Eliminate hiding places for wild host animals. Several insecticides control ticks in outdoor vegetation. Treat thoroughly where tall grass and weeds occur around lawns, pathways, golf roughs, doghouses and ornamental plantings. Treat when you first start to notice ticks-generally in early spring.
Ticks normally do not infest well-kept, closely mown lawns. For personal protection, avoid walking through overgrown vegetation and use precautions and treatments as you would for chiggers.
*Spiders. The female black-widow spider, with its familiar red-hourglass marking (see photo, page 33) on the underside of its abdomen, is the most feared spider inhabiting outdoor areas. You typically find this pest in its web under stones, woodpiles, loose bark, storage buildings, barns, outhouses and water faucets. Most people contact spiders accidentally by trapping them against their body-spiders do not actively seek out people.
Manage spiders by frequently cleaning to remove them and their webs from buildings and outdoor living areas. Routine hose washing of potential spider habitats helps discourage spider buildup. Wear gloves and long-sleeved shirts when working in spider-infested areas. You can apply approved insecticides to buildings and infested areas. Spray cracks, corners, around windows, stairs, closets, etc., according to label instructions.
*Centipedes. During the day, these long multi-segmented arthropods generally hide under rocks, boards or bark and in crevices, basements, porches, patios and moist, protected areas. They become active at night to feed on prey such as small insects.
Centipedes have two powerful claws located on the lower part of their body immediately behind their heads, which they use to inject venom. Most species are not a threat to people. However, the bites of some of the larger species, when accidentally picked up, stepped on or trapped against the body, can be a hazard. To avoid them, wear shoes and protective gloves when moving rocks or debris from the ground. Some insecticides are registered for use on centipedes, and you may want to use them in heavily infested areas.
*Wheel bug. This pest gets its name from a distinctive cogwheel-like crest located on the top side of the thorax. People accidentally contact this insect when handling vegetation, boards, rocks or other objects. When attacking humans, this insect penetrates the skin with its proboscis ("beak") and injects a toxic fluid. Some bites can be quite painful.
To avoid contact, learn to identify the wheel bug. If you encounter one, do not handle it. Wear protective gloves while working in bushes and vegetation. Despite occasionally biting humans, this insect feeds on other insects and is beneficial. Thus, control is not recommended.
Urticating/vesicating arthropods *Blister beetles. The predacious larvae of blister beetles feed on other insects, especially grasshopper eggs. We generally encounter the striped and marginal blister beetles, though other species occur. The adult beetles may leave a clear, amber-colored fluid on human skin. Ruptured thin membranes on the insect's body secrete this fluid, a vesicating (blister-causing) agent called cantharidin. It doesn't take much pressure against the beetles' body to trigger fluid release.
Avoid contact with these beetles. If one lands on your skin, blow it off-don't crush it. Where high populations occur, use yellow light bulbs for outdoor lighting to reduce their attraction to lights. Chemical control is normally not practical because of the mobility and wide distribution of blister beetles.
*Caterpillars. The three species of caterpillars listed in the following sections have stinging hairs or spines. In each case, victims typically contact them by accidentally brushing against them when working among shrubs on which the caterpillars feed. If you encounter them, do not handle them. When working on infested shrubs, wear protective gloves, long-sleeved shirts and long pants. If an area is heavily infested, you can use one of the insecticides registered for leaf-feeding caterpillars.
*Io moth caterpillar. This rather large (2 to 3 inches) caterpillar is pale green with stripes of red or maroon over white running the length of the body. Green and black venomous spines are near the center of each body segment. These caterpillars feed on shrubbery in the spring and summer. When the victim's skin touches the spines, they break off in or on the skin, allowing the toxin to flow.
*Puss caterpillar. These caterpillars, sometimes incorrectly referred to as "asps," grow to 0.8 to 1.2 inches long. They are completely covered with hairs, resembling elongated tufts of cotton, varying in color from nearly white to dark brown or gray. The body hairs can penetrate human skin and toxin is transferred under the skin. Normally, natural enemies keep populations under control. *Saddleback caterpillar. This caterpillar is rather easy to identify. It has a green to brown slug-like body (0.8 to 1.2 inches long) and has a distinctive brown or purplish saddle-shaped marking on a green and white saddle blanket. It has stout spines along its sides and on its four tubercles (appendages arising from its body). These spines connect at their bases to poison glands. The caterpillars usually feed on shrubs during the summer and fall.
Stinging arthropods *Paper wasps, hornets and yellowjackets. These are common pests on golf courses and in landscapes. They are social insects that live in nests or colonies. Mated queens emerge in the spring and begin constructing nests in which they lay their first clutch of eggs. As the summer progresses, the nests enlarge and populations grow rapidly.
*Paper wasps. These wasps build umbrella-shaped nests attached to buildings, trees and shrubs by a single stalk (see photo, page 36). They are less aggressive than hornets or yellowjackets but will sting people if they disturb their nests. When they attack, they release an alarm pheromone, a chemical that alerts other wasps to swarm and defend their colony.
People maintaining ornamental shrubs or hedges should be cautious of paper-wasp nests. Examine shrubs before trimming and treat any nests present. You can use insecticides formulated as "wasp-and-hornet spray" for control. Although you can spray nests during the day, it is safer to treat them at night. When treating a nest, don't stand directly under it. Wasps drop immediately when sprayed and if you are standing directly under the nest, your chances of getting stung are high. After a few hours or a day, you can knock down the nest.
*Hornets. Hornets are more difficult to deal with than paper wasps. The more common species, the bald-faced hornet, is long (up to 0.75 inch) and black with white markings on its face, thorax and the posterior end of its abdomen. They build their nests in shrubs, trees, on overhangs of buildings and other structures. The nests are large, multi-combed, made of gray paper-like material and resemble a large football. Hornets are easy to disturb, and nests may contain hundreds of wasps.
Occasionally, it may be necessary to contact a professional pest-control operator to remove their nest because many times they are out of reach. Treat the nests only at night. Be sure to cover all parts of your body with clothes including face, hands, wrists and ankles, during treatment. Apply an aerosol-type wasp-and-hornet spray or dust to the single opening of the nest, usually at the bottom where wasps enter and exit. Be sure not to break the paper envelope of the nest, as this will cause wasps to scatter everywhere. Several days after treatment, you can remove the nest provided all the wasps are dead. If not, retreat.
*Yellowjackets. Yellowjackets can be even more aggressive than hornets when their nests are disturbed. They get their name from their distinctive black and yellow coloration. They usually build their nests underground in burrows or under rocks or landscape timbers. However, some build their nests in attics, sheds or other structures.
Yellowjackets scavenge for food outdoors around picnic areas, parks and similar sites. They are more of a problem in late summer and fall when the colonies increase in number. Maintenance people can reduce contact with this pest by practicing good sanitation, thus reducing their food sources. Empty and clean trash cans frequently and equip them with tight-fitting lids. When practical, locate trash cans and dumpsters away from where people congregate.
Yellowjackets are less active in their nests at night. Therefore, treat their nests with an insecticide after dark. Wear protective clothing and use indirect light if you need it. Don't shine light directly into the nest-this may startle or disturb them, and angry wasps tend to fly toward light. It may be necessary to call a professional pest-control operator if the nest is difficult to treat or reach.
*Cicada killers. These large wasps burrow into turf and produce a frightening, loud buzz that annoys people. They seldom sting unless hemmed up in close quarters and will not defend their solitary nest. However, if they do sting, it is painful. They prey on cicadas, for which they search in shrubs and trees in the spring and summer.
Although these insects are beneficial, their behavior may interfere with human activity. They prefer areas with sparse vegetation for nesting. Therefore, good cultural practices that promote thick turf discourage their burrowing. Placing mulch or bark chips under play structures instead of sand also discourages wasp nesting. Where large populations occur, a broadcast application of an approved insecticide may be necessary.
*Fire ants. This probably is the most problematic pest of landscape areas in the South. Fire ants produce unsightly mounds on lawns, playgrounds, golf courses and other landscape areas and can inflict painful stings on humans an d animals. The ants can sting repeatedly and aggressively defend their nests. Scratching stung areas may result in secondary infection and scarring. If you've been stung, place ice packs or antibiotic ointments on the infected area. If an allergic reaction occurs, seek medical attention immediately.
The key to control is to kill the queens, because they are the only ants capable of laying eggs. Some nests may have up to 150 queens per nest. Chemical control includes two tactics: treating individual mounds and broadcast treatments. The best approach for control is to use both tactics together.
When only a few mounds are present, mound treatments are more practical. You need only a small amount of insecticide compared to broadcast treatments. You can treat individual mounds with baits, contact insecticides or injectable materials. When applying a bait, sprinkle it around each undisturbed mound but not on top of the mound. When using contact mound drenches, pour the diluted insecticide on top of the undisturbed mound and about 2 feet around it, thoroughly soaking the mound. The amount of water you use depends on the size of the mounds. If you use granules or dust, cover mounds thoroughly, and, if the label instructs you to, water the granules into the undisturbed mound. Injectable products, often formulated as vapors or aerosols, may be more expensive and time-consuming to use but tend to give good results as mound treatments.
The best method of controlling fire ants over a large area with many mounds is by applying spring and fall broadcast applications of ant baits. With broadcast applications, it is not necessary to locate individual nests because foraging ants pick up the bait and carry it back to their nest. This method is effective and also controls mounds too small to see above the turf. You can make supplemental treatments with a contact insecticide applied to individual mounds that become established between bait applications.
Fire-ant control programs are most effective when every turf or grounds manager in the area treats for the ants. Thus, managers should take a team approach when implementing their fire-ant management program.
*Scorpions. These pests are flattened crab-like creatures with ten legs and a fleshy tail bearing a stinger (see photo, below). They normally live outdoors under boards, rocks, stones or other structures and vary in size from 1 to 4 inches long. Normally, scorpions live for 3 to 5 years. They feed on insects, other species of scorpions and sometimes even their own young.
Scorpions are primarily active at night, and they sting when provoked or disturbed. If you are stung, wash and disinfect the stung area. If the sting becomes persistently sore and swollen, see a medical doctor.
You can control scorpions mechanically (swatting or crushing). However, do not handle them. Wear gloves, shoes and clothing when working in a suspected infested area. Natural predators often provide good suppression of scorpions, but you can apply insecticides if necessary.
General precautions You can minimize the danger of being bitten or stung by venomous arthropods in several ways. Some are common-sense steps, such as not walking around in the yard in bare feet. Keep sweet items like ripe fruits and watermelons covered outdoors, because they attract bees and wasps. When bees and wasps are collecting nectar from flowers outside, avoid mowing and working in flowerbeds, if possible. If a venomous insect is near you, stand still. Brush it off if it attacks, but don't slap it to prevent a bite or sting. Implement chemical-control measures if these pests become numerous near heavily used areas. Finally, if you are attacked by a swarm of wasps, yellowjackets, hornets or bees, leave immediately using your arms and hands to protect your face.
Prompt action is necessary when anyone is bitten or stung. First of all, identify the pest. If possible, capture it and have it identified. If you suspect the victim is having an allergic reaction or has a history of hay fever, allergy or asthma, contact a medical doctor immediately.
Dr. J. Pat Harris is an extension entomologist at Mississippi State University (Decatur, Miss.).
Want to use this article? Click here for options!
© 2014 Penton Media Inc. | <urn:uuid:3177aac3-ceea-4501-8cf9-6d35991b6696> | {
"date": "2014-11-01T09:35:18",
"dump": "CC-MAIN-2014-42",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637905189.48/warc/CC-MAIN-20141030025825-00086-ip-10-16-133-185.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9421015977859497,
"score": 3.5625,
"token_count": 4209,
"url": "http://grounds-mag.com/mag/grounds_maintenance_venomous_anthropods/"
} |
The cell membrane is a semi-permeable membrane composed of all four types of macromolecules, with lipids and proteins being the most prevalent in dry weight. The membrane is present in all cells and functions to regulate incoming and outgoing materials, maintain intracellular homeostasis, and participate in signal transduction.
Various models have been created to help visualize the complex structure of the cellular membrane, the most famous being the fluid mosaic model, which describes the membrane as a two-dimensional "sea" of molecular units, and the liquid crystal model, which describes the membrane as a sea of crystals with liquid properties.
The fluid mosaic model was developed in 1972 by S.J. Singer and Garth Nicolson. In their report, they proposed that biological membranes can be considered as a two-dimensional fluid composed of a mosaic of molecules, the majority of which had hydrophobic and hydrophilic properties (phospholipids). Thus, the molecular interactions create a membrane that is not solid, but which behaves like a fluid as molecules change positions and has the ability to stretch and contract vertically.
Liquid Crystal Model
The liquid crystal model was developed in 1970 by Freye and Edinin. It proposes that the phospholipid bilayer behaves like a series of crystals moving in an fluid, yet ordered manner.
Elements of the Membrane
The phospholipid bilayer is composed of the following in dry weight:
- 50% proteins
- 30% lipids
- 5% glycolipids
- 15% other
Each element of the membrane performs a specific function in sensory transduction, transport, etc.
Glycoproteins are transmembrane proteins with oligosaccharides covalently bonded to their amino acid chains. Glycoproteins generally play an important role in sensory transduction, particularly with regard to immune system responses.
Transmembrane proteins are proteins that extend through the membrane, having both an exterior and an interior domain. They are integral proteins, meaning they are permanently bonded to the PLB. Many function as hormone/signal acceptors, ion channels, and transport proteins. As a rule, they act as channels between the intra- and extracellular spaces.
There are two structural categories of transmembrane protein:
- Alpha-helical, those composed of repeating hydrogen bonds that make up alpha helices on the secondary level of structure
- Beta barrel, those which have repeating hydrogen bonds that form pleated sheets
Alpha-helical make up the largest group, with beta barrel proteins found primarily in mitochondrial and other prokaryotic gram-positive membranes.
Peripheral proteins are proteins that are bonded by weaker interactions to either the interior or the exterior of the membrane. Their loose bonds allow them to detach and function as secondary messengers or extracellular messengers upon receipt of a signal from the cell. Some prominent functions are in metabolism and in sensory transduction.
Phospholipids are the "glue" that gives the membrane its distinct structure. Their amphipathic nature and tendency to create micelles in water were likely the origin of the first cells.
Glycolipids are lipids with attached carbohydrates. Their most prominent function is providing extracellular support to form tissues in multicellular organisms.
Cholesterol molecules are lipids distinguished by their four-ring structure. In the membrane, they act to resist as a type of "anti-freeze" to prevent freezing and overheating.
Osmosis and Diffusion
phospholipid bilayer (plasma membrane)
- proteins (peripheral, integral, transmembrane, adhesion, recepto, channel, recognition and adhesion)
simple diffusion osmosis channel proteins facilitated transport active transport pumps (h+ and na/k) endo-, pino-, phago- cytosis receptor-mediated endocytosis bulk flow exocytosis | <urn:uuid:b1b1144c-9886-4d18-9fbd-4bc302e61603> | {
"date": "2017-08-23T04:36:22",
"dump": "CC-MAIN-2017-34",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886117519.92/warc/CC-MAIN-20170823035753-20170823055753-00297.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9121381640434265,
"score": 3.53125,
"token_count": 820,
"url": "https://en.wikibooks.org/wiki/AP_Biology/Membranes"
} |
RachelleMota596
12
# Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.
$k:12x-5y=2\to-5y=-12x+2\ \ \ /:(-5)\to y=\frac{12}{5}y-\frac{2}{5}\\\\l:y=mx+b\\\\k\ ||\ l\iff m=\frac{12}{5}\\\\ l:y=\frac{12}{5}x+b;\ (2;\ 3)\\\\\frac{12}{5}\cdot2+b=3\\\\\frac{24}{5}+b=3\\\\b=\frac{15}{5}-\frac{24}{5}\\\\b=-\frac{9}{5}\\\\Answer:y=\frac{12}{5}x-\frac{9}{5}\to\frac{12}{5}x-y=\frac{9}{5}\ \ \ \ /\cdot5\to12x-5y=9$ | crawl-data/CC-MAIN-2022-33/segments/1659882571869.23/warc/CC-MAIN-20220813021048-20220813051048-00596.warc.gz | null |
Factorial program in Java
A classic program in Java is the Factorial Calculator.
What is the factorial of a number?
According to the Britannica:
Factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. Thus, factorial seven is written 7! meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1.
In everyday life, we use factorial as the total number of arrangements. It means we can arrange n objects in n! different ways.
How is calculated the factorial of a number?
The factorial of a number n is the product of all numbers from 1 to n.
Based on this rule, let’s write the algorithm of the factorial calculator.
Step 1: Declare the variable i, and initialize it to 1.
Step 2: Declare the variable result, which will store the factorial, and initialize it to 1;
Step 3: Read the variable n.
Step 4: The result is multiplied with i, and the product is stored in the variable result.
Step 5: Repeat step 4, for each i, from 1 to n.
The next step is to implement this algorithm in Java.
The factorial program in Java
Each program in Java is within a class. We will implement the calculation part inside a method called calculateFactorial.
`static void calculateFactorial(int n)`
Let’s build the loop for, which will calculate the product of each number, from 1 to n.
```for(i = 1; i <= n; i++){
fact = fact * i;
}```
The complete code of this example in Java is:
```public class FactorialProgram {
static void calculateFactorial(int n) {
int i;
int fact = 1;
for(i = 1; i <= n; i++){
fact = fact * i;
}
System.out.println("Factorial of "+n+" is: "+fact);
}
public static void main(String[] args) {
calculateFactorial(5);
}
}
```
In Console:
`Factorial of 5 is: 120`
a recursive Version
The nature of the algorithm is recursive: the calculations for the factorial of n are based on the factorial of (n-1). Let’s try to implement the recursive version of the factorial program.
The base condition is:
`if (n == 0)`
This means the recursion will stop when n is equal to zero. Otherwise, the method calls itself, but with another parameter, which will be (n-1).
`factorial(n-1)`
The code of the recursive version of the factorial program in Java is this one:
```class FactorialRecursiveProgram{
static int factorial(int n){
if (n == 0)
return 1;
else
return(n * factorial(n-1));
}
public static void main(String args[]){
int fact=1;
int number=4;
fact = factorial(number);
System.out.println("Factorial of "+number+" is: "+fact);
}
}```
In Console:
`Factorial of 4 is: 24`
Hopefully, this will help you understand this classic problem, solved in both iterative and recursive ways. | crawl-data/CC-MAIN-2022-33/segments/1659882573630.12/warc/CC-MAIN-20220819070211-20220819100211-00100.warc.gz | null |
Pentas lanceolata is the scientific name of pentas flowers. These warm-climate plants are upright perennial flowers that grow 3 to 4 feet tall and blossom year-round in tropical areas. The oval leaves and stems are covered with fine hairs. The tubular, star-shaped flowers reach 3 inches wide and bloom in white, pink, red and light purple colours. Pentas flowers attract hummingbirds and butterflies to the landscape.
Loosen well-draining soil in an area of full sun exposure to a depth of 12 inches with a shovel. Wait until late spring to plant the pentas flowers, so the new plants are exposed to the heat of the coming summer to increase their growth rates. Plant pentas flower bedding plants 15 inches apart in the ground. Space pentas closer together in a container.
Water pentas well by soaking the soil around the base of the plants. Allow the water to soak into the soil down to the root zone. Water only when there isn't any rainfall for five to seven days once the flowers are established and new growth appears.
Pinch new growth stem tips back to create a bushier, fuller plant. Take just the top 1-inch section of the tips off during the first month of growth. Pinching causes new branches to form along the stem. Pentas flower plants grow fine without pinching, but they look thin and scraggly with fewer branches.
Feed the pentas flowers every six weeks with slow-release 10-10-10 fertiliser. Sprinkle 1 tbsp around the root zone of the plant and scratch it into the top inch of soil with a hand cultivator. Water the fertilised soil immediately after applying to activate the fertiliser. Feed the plants only while they are actively growing during the spring and summer.
Take cuttings in the spring and summer from a strong, healthy pentas plant. Use a sterilised, sharp knife. Dip the 3- to 4-inch cutting into rooting hormone and plant in a small container filled with damp sand. Once roots form, transplant the new pentas bedding plants to their new locations.
Pentas flowers are low-maintenance flowers; their blossoms are located on terminal flower clusters and self-deadhead, which means they fall off naturally when they start to die.
Treat this perennial plant as an annual in areas with freezing temperatures. Pentas die in cold weather and have to be replanted the following spring. For winter survival, protect these flowers in a heated greenhouse. | <urn:uuid:8fea639b-59c9-451c-95ef-fda31c7ebd09> | {
"date": "2018-09-24T17:11:32",
"dump": "CC-MAIN-2018-39",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160620.68/warc/CC-MAIN-20180924165426-20180924185826-00177.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9216355681419373,
"score": 3.5,
"token_count": 516,
"url": "http://www.ehow.co.uk/how_8062624_care-pentas-flowers.html"
} |
Caring for plants as they grow and observing the changes encourages my curiosity in the environment and the world around me.
It promotes social skills when playing games, increases attention span, provides a natural source of vitamin D and allows children to get creative and messy without having to worry about the clean-up
Building with blocks your child develops problem solving and basic math/science concepts. Children learn concepts such as cause and effect, quantity, classification and order. The Block Book (Hirsch 1996) supports these claims, adding that 'children expand architectural learning through block play.
Children also learn and develop a number of skills while cooking and following a recipe: language skills, counting, fractions, sequencing, measuring, problem-solving, sharing, fine motor skills and even learning about other cultures and how they eat. | <urn:uuid:74be24c0-6fd0-420a-9f16-a59d7afbdba1> | {
"date": "2020-09-24T04:43:13",
"dump": "CC-MAIN-2020-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400213454.52/warc/CC-MAIN-20200924034208-20200924064208-00257.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9395155310630798,
"score": 3.609375,
"token_count": 163,
"url": "https://www.childsworldllc.com/for-parents.html"
} |
Honey bee workers collect pollen and nectar from a variety of flowering plants to use as a food source. Honey bees typically forage from up to 1-2 miles away from the hive, though sometimes they travel even further, including up to 10 miles away. However, much of the modern landscape consists of agricultural fields, which limits the foraging options for honey bees in these areas.
Honey bees that guard hive entrances are twice as likely to allow in trespassers from other hives if the intruders are infected with the Israeli acute paralysis virus, a deadly pathogen of bees, researchers report.
Their new study, reported in the Proceedings of the National Academy of Sciences, strongly suggests that IAPV infection alters honey bees’ behavior and physiology in ways that boost the virus’s ability to spread, the researchers say. | <urn:uuid:691422d3-af4c-43cf-a6c7-b9753066bed5> | {
"date": "2023-09-24T10:44:30",
"dump": "CC-MAIN-2023-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506632.31/warc/CC-MAIN-20230924091344-20230924121344-00258.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9479326605796814,
"score": 3.65625,
"token_count": 170,
"url": "https://www.igb.illinois.edu/wheeler/taxonomy/term/1316"
} |
3) What does the taproot system do?
Often stores organic nutrients that the plant consumes during flowering and fruit production.
4) Why are root crops such as carrots, turnips, and sugar beets harvested before they flower?
Because the taproot system stores organic nutrients in the root part.
7) What is an organ system consisting of nodes (the points at which leaves are attached), and internodes (the stem segments between nodes).
9) What is an axillary bud?
A structure that has the potential to form a lateral shoot, commonly called a branch.
10) What happens if the terminal bud is removed?
Stimulates the growth of axillary buds resulting in more lateral shoots. That is why pruning trees and shrubs and pinching back houseplants will make them bushier.
18) What is a vertical, underground shoot consisting mostly of the enlarged bases of leaves that store food?
20) What is the main photosynthetic organ of most plants, although green stems also perform photosynthesis?
22) What leaves (like grass) have parallel major veins that run the length of the leaf blade.
23) What leaves (like trees and most other plants) generally have a multi-branched network of major veins?
27) The red parts of a poinsettia plant are often mistaken for petals but are actually modified leaves called what?
29) Those leaves which produce tiny plantlets, which fall off the leaf and take root in the soil are modified for what?
30) The dermal tissue in non woody plants, which usually consists of a single layer of tightly packed cells is called?
31) Name the protective tissues in woody plants that replace the epidermis in older regions of the stems and roots.
33) In plants, vascular tissue made of dead cells that transport water and minerals from the roots is called what?
34) Name the transport tissue of a plant that delivers nutrients such as sugars from where they are made (usually leaves) to where they are needed (usually roots).
35) In plants, vascular tissue that consists of living cells that distribute sugars throughout the plant is called
38) How long does it take Annuals to complete their lifecycle (from germination to flowering to seed production to death)?
A single year or less
42) What tissues of the plant are located at the tips of the roots and in the buds of the shoots, and enable the plant to grow in length (primary growth)?
43) What tissues of the plant allow for growth in thickness? Also known as secondary growth.
44) In woody plants, the lateral meristems are called_____, meaning an added layer of xylem (wood).
46) Vascular tissue made of dead cells that transport water and minerals from the roots is called?
47) The term used to describe "pushing the xylem sap upward especially at night" is called what?
48) Root pressure can only force water upward a few meters, and it cannot keep pace with transpiration after sunrise. Xylem sap is pulled upward. This is attributed to what biological term?
49) What is the vascular tissue that consists of living cells that distribute sugars throughout the plant?
53) What is a deficiency of magnesium, a component of chlorophyll, that causes yellowing of the leaves?
57) What are the most fertile soils, that are made up of equal amounts of sand, silt(medium-size particles) and clay?
59) Each year, soil fertility diminishes unless what is used to replace these lost minerals?
60) What are commercially produced fertilizers are enriched with?
Nitrogen (N), Phosphorus (P), and Potassium (K)
61) What are the commercially produced fertilizers, Nitrogen (N), Phosphorus (P), and Potassium (K), labelled with?
A three-number code called the N-P-K ratio, indicating the content of these minerals
62) What are thousands of acres of topsoil lost to each year in the United States alone?
Water and wind erosion
63) What certain precautions are used to prevent loss of topsoil?
Planting rows of trees as windbreaks, terracing hillside crops, and cultivating in a contour patterns.
65) What mineral has the greatest effect on plant growth and crop yields?
Nitrogen (N), Phosphorus (P), and Potassium (K)
66) What is nitrogen-fixing bacteria?
The decomposition of dead vegetation by certain kinds of bacteria
68) In this practice, a non-legume such as corn is planted one year, and the following year alfalfa or some other legume is planted to restore the concentration of nitrogen in the soil. What is this practice called?
70) How do angiosperms disperse their seeds?
They disperse their seeds by producing fleshy, edible fruits that are consumed by animals which defecate the seeds, seeds that sometimes attach to animals or seeds may catch the wind.
71) What do most angiosperms depend on for pollination and see dispersal?
Insects, birds, or mammals
75) What refers to innovations in the use of plants or substances obtained from plants to make products that are useful to humans?
76) What is a form of biotechnology that refers to the use of genetically modified organisms that produce beneficial results?
77) What contain genes from particular bacteria that produce a protein that repels insect pests?
78) One concern that certain molecules within a plant cause allergies in humans is caused by what process?
Plant genetic engineering
79) What is the concern about allergy molecules being transferred to a plant?
People are concerned that the plant will be used for food.
80) Who removes the genes that encode for the allergenic proteins from soybeans and crops?
81) The fear is that the undesirable weeds will become resistant to insects, creating a ______ that would be difficult to control in the fields.
82) Because of "superweeds" efforts are underway to breed what into transgenic crops?
83) These plants will still produce seeds and fruit if pollinated, but they will produce no _____.
84) According to the endosymbiotic theory of the origin of chloroplasts, photosynthetic prokaryotic cells were...?
Were incorporated by larger cells
85) Plants have always had _______, even before they went from living in the oceans to living on land.
86) What are the five key adaptations that plants had to make in order to live on land?
Flowers, dependent embryos, gametangia, vascular tissues, and seeds
87) The key step in adaptation of seed plants to dry land was the evolution of what?
wind dispersed pollen
95) What is usually the most striking part of the flower, and functions to attract hummingbirds and insects?
96) Plants dependent on nocturnal pollinators typically have flowers that are ......?
97) What does an insect do when it comes to collect the nectar, and picks up some pollen grains?
The insect carries the pollen grains to the stigma of another flower.
99) What consists of a stalk with the stigma at the top (which catches the pollen) and an ovary at the base? | <urn:uuid:019cc329-db64-4da4-bcb4-37cd22165d76> | {
"date": "2015-10-09T05:29:04",
"dump": "CC-MAIN-2015-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737913815.59/warc/CC-MAIN-20151001221833-00102-ip-10-137-6-227.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9280832409858704,
"score": 3.78125,
"token_count": 1533,
"url": "https://quizlet.com/29910633/plants-flash-cards/"
} |
The flight deck of an aircraft carrier is the surface from which its aircraft take off and land, essentially a miniature airfield at sea. On smaller naval ships which do not have aviation as a primary mission, the landing area for helicopters and other VTOL aircraft is also referred to as the flight deck. The official U.S. Navy term for these vessels is "aviation capable ships".
On 2 August 1917, while performing trials, Squadron Commander Edwin Dunning landed a Sopwith Pup successfully on board the flying-off platform of HMS Furious, becoming the first person to land an aircraft on a moving ship. However, on his second attempt, a tyre burst as he attempted to land, causing the aircraft to go over the side, killing him; thus Dunning also has the dubious distinction of being the first person to die in an aircraft carrier landing accident. The landing arrangements on Furious were highly unsatisfactory, however. In order to land, aircraft had to manoeuvre around the superstructure. Furious was therefore returned to dockyard hands have a 300 foot (91 m) deck added aft for landing, on top of a new hangar. However, the central superstructure remained, and turbulence caused by this badly affected the landing deck.
The first aircraft carrier that began to show the configuration of the modern vessel was the converted liner HMS Argus, which had a large flat wooden deck added over the entire length of the hull, giving a combined landing and take-off deck unobstructed by superstructure turbulence. Because of her unobstructed flight deck, Argus had no fixed conning superstructure and no funnel. Rather, exhaust gasses were trunked down the side of the ship and ejected under the fantail of the flight deck (which, despite arrangements to disperse the gasses, gave an unwelcome "lift" to aircraft immediately prior to landing). The lack of a command position and funnel was unsatisfactory, and Argus was used to experiment with various ideas to remedy the solution. A photograph in 1917 shows her with a canvas mock-up of a starboard "island" superstructure and funnel. This was to starboard as the rotary engines of early aircraft caused a force to the left, meaning an aircraft naturally yawed to port on take-off, therefore it was desirable that they turned away from the fixed superstructure. This became the typical aircraft carrier arrangement and was used in the next British carriers, HMS Hermes and Eagle.
After World War I, battlecruisers that otherwise would have had to have been discarded under the Washington Naval Treaty - such as the British HMS Furious and Glorious class and the American USS Lexington and Saratoga - were converted to carriers along the above lines. Being large and fast they were perfectly suited to this role; the heavy armouring and scantlings and low speed of the converted battleship Eagle served to be something of a handicap in practice. Because the military effectiveness of aircraft carriers was then unknown, early ships were typically equipped with cruiser-calibre guns to aid in their defence if surprised by enemy warships. These guns were generally removed during World War II and replaced with anti-aircraft guns, as carrier doctrine developed the "task force" (later called "battle group") model, where the carrier's defence against surface ships would be a combination of escorting warships and its own aircraft.
In ships of this configuration, the hangar deck was the strength deck, and an integral part of the hull, and the hangar and wooden flight deck were considered to be part of the superstructure. Such ships were still being built into the late 40s, classic examples being the US Navy's Essex and Ticonderoga class carriers. However, in 1936, the Royal Navy began construction of the Illustrious class. In these ships, the flight deck was now the strength deck, an integral part of the hull, and was heavily armoured to protect the ship and her air complement. Although the armoured carrier concept in this form remained something of a dead end, the flight deck as the strength deck was adopted for later construction. This was necessitated by the ever-increasing size of the ships, from the 13,000 ton USS Langley (CV-1) in 1922 to over a hundred thousand tons in the latest Nimitz-class carriers.
When aircraft carriers supplanted battleships as the primary fleet capital ship, there were two schools of thought on the question of armour protection being included into the flight deck. The addition of armour to the flight deck offered aircraft below some protection against aerial bombs. However the extra space required did not allow the carriers to hang aircraft above, thus reducing the maximum number of airplanes carried.
Landing arrangements were originally primitive, with aircraft simply being "caught" by a team of deck-hands who would run out from the wings of the flight deck and grab a part of the aircraft to slow it down. This dangerous procedure was only possible with early aircraft of low weight and landing speed. Arrangements of nets served to catch the aircraft should the latter fail, although this was likely to cause structural damage. Landing larger and faster aircraft on a flight deck was made possible through the use of arresting cables installed on the flight deck and a tailhook installed on the aircraft. Early carriers had a very large number of arrestor cables or "wires". Current U.S. Navy carriers have three or four steel cables stretched across the deck at 20-foot (6 m) intervals which bring a plane, traveling at 150 miles per hour (240 kilometres per hour), to a complete stop in about 320 feet (98 m). The cables are set to stop each aircraft at the same place on the deck, regardless of the size or weight of the plane. During World War II, large net barriers would be erected across the flight deck in order that aircraft could be parked on the forward part of the deck and recovered on the after part. This allowed increased complements, but resulted in lengthened turn-around times as aircraft were shuffled around the carrier to allow take-off or landing operations.
With an angled flight deck (also referred to as a "skewed deck" or the "angle"), the aft part of the deck is widened and a separate runway is positioned at an angle from the centreline. The angled flight deck was designed with the higher landing speeds of jet aircraft in mind, which would have required the entire length of a centreline flight deck to stop. The design also allowed for concurrent launch and recovery operations, and allowed aircraft failing to connect with the arrestor cables to abort the landing, accelerate, and relaunch (or "bolt") without risk to other parked or launching aircraft. The redesign allowed for several other design and operational modifications, including the mounting of a larger island (improving both ship-handling and flight control), drastically simplified aircraft recovery and deck movement (aircraft now launched from the bow and re-embarked on the angle, leaving a large open area amidships for arming and fuelling), and damage control. Because of its utility in flight operations, the angled deck is now a defining feature of STOBAR and CATOBAR equipped aircraft carriers.
The angled flight deck was first tested on HMS Triumph, by painting angled deck markings onto the centeline flight deck. Following successful trials, USS Antietam and HMS Centaur were modified with overhanging angled flight decks in 1953 and 1954 respectively. The U.S. Navy installed the decks as part of the SCB-125 upgrade for the Essex class and SCB-110/110A for the Midway class. In February 1955, HMS Ark Royal became the first carrier to be constructed and launched with the deck, followed in the same year by the lead ships of the British Majestic class (HMAS Melbourne) and the American Forrestal class (USS Forrestal).
Another British innovation is the ski-jump ramp, which came about as means of improving take off for the VSTOL BAE Sea Harrier "jump-jet" on the small Invincible class aircraft carriers. The ski jump is a ramp which is curved upwards at its forward end. This converts the short run up available into vertical motion and reduces the fuel used at take-off compared to a vertical take off, and allows the aircraft to carry a higher payload. Because aircraft that use the ski-jump ramp are usually jump-jets, such carriers do not use angled flight decks. Similarly, the catapult and arrester wire are also not necessary. The ski-jump ramp is now used on several aircraft carriers world wide.
An idea tested but never taken to completion was the "flexible deck". In the early jet age it was seen that by eliminating the landing gear for carrier borne aircraft the inflight performance would be improved. This led to the concept of a deck that would absorb the energy of landing, the risk of damaging propellers no longer being an issue though take off would require some sort of launching cradle. Test were carried out with a Sea Vampire, and Supermarine designed their Type 508 for rubber deck landing, but the flexible deck idea was found to be impracticable due to the loads imposed on both pilot and airframe when landing. The Supermarine Type 508 was subsequently developed into a 'normal' carrier aircraft, the Scimitar. | <urn:uuid:d57e302a-9cfd-48bb-986e-0010f7c9a4c9> | {
"date": "2014-11-21T20:41:53",
"dump": "CC-MAIN-2014-49",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400373899.42/warc/CC-MAIN-20141119123253-00240-ip-10-235-23-156.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.974396824836731,
"score": 4.03125,
"token_count": 1887,
"url": "http://www.reference.com/browse/flight+deck"
} |
Β
VIEW IN FULL SCREEN
AQA A-level Maths Introduction to sequences
1. Series
A series is the sum of the terms of a sequence up to its nth term. It is denoted by Sn and is expressed as:
1
What is the term of the sequence Un = 5n β 2 given by the expression ββ·β Un β ββΆβ Un?
2
Given the sequence Un = 2n, is the series Sβ
= 2 + 4 + 6 + 8 β 10 + 12 a series for the sequence Un?
3
What is the sum of the first 5 terms of the sequence Un = 7n β 3?
4
Adam eats 5 apples in a week, 3 apples the next and 1 apple the week after. How many apples has Adam eaten in the past 3 weeks?
5
What basic operation does β perform?
End of page
Β | crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00067.warc.gz | null |
# Precalculus : Linear Modeling
## Example Questions
### Example Question #1 : Linear Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday for work. Each Monday he drives 350 miles to LaGrange. Once he arrives to his home away from home he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job.
Explanation:
The rate of change of his mileage is 700 per week (350 x 2=700 there and back). The rate of change is the same thing as slope. Since we are looking for equation an equation that models his odometer reading as a function of the number of weeks he has been driving we can extract the point (23 , 18600) since after 23 weeks his odometer read 18,600 miles. Now we will use the point slope formula:
distribute the right side
isolate y
### Example Question #2 : Linear Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday. Each Monday he drives 350 miles to LaGrange. Once he arrives to his apartment he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job. Using the equation you just made, what is the y intercept or his original mileage before starting?
y intercept=16,100 miles
y intercept=186,000 miles
y intercept=169,900 miles
y intercept=153,800 miles | crawl-data/CC-MAIN-2017-04/segments/1484560284429.99/warc/CC-MAIN-20170116095124-00106-ip-10-171-10-70.ec2.internal.warc.gz | null |
display | more...
Vector addition is the process of summing vectors. It is analagous to adding together more than one matrix, each having one and only one row. To accomplish this, one must add corresponding individual corresponding components, placing the results in a new vector. For example, to add <a, b, c, d> to <a, f, g, h>, you add a to e, b to f, etc. and obtain <a+e, b+f, c+g, d+h>
If you are unfamiliar with this mathematical notation of vectors, consult the "vector" node.
If you wish to assimilate the knowledge in this node fully, you will benefit from graph paper and an understanding of the knowledge ensconced here.
Draw two lines, one from (1,1) to (1,3) and one from (1,3) to (2,5). The vector which represents the first line is (0,2), and the one for the second is (1,2).
Now draw a line from (1,1) to (2,5). What's the vector representing that line? It's (1,4), which happens to be (1,2) + (0,2). This is very logical when you think about it - the vector from (1,1) to (2,5), which we call the resultant vector of the other two, represents the entire "journey" made by the other two vectors - they are merely components of it.
This relationship can come in very useful (admittedly, mainly in math classes). You can learn a lot about the vector triangles you've been drawing by using geometry and trigonometry. It's possible to calculate the resultant or either of the other two vectors by knowing the other two. If you know the resultant and one of the others, then simply subtracting the other from the resultant will give you the remaining vector.
Vectors are often used in velocity calculations. A system where velocity is at a constant, and then is effected and changed by some other factor is a consistent player in maths questions. The "riverboat question" comes up again and again.
In this scenario, a boat is said to be sailing through the water at a velocity of, say, (0,-3) - directly downwards. The velocity of the water is said to be, say, (-5,0) - directly right. What is the resultant velocity of the boat?
Easy. Resultant velocity = (0,-3) + (-5,0) = (-5,-3). We can use the techniques we learnt earlier to work out the magnitude of this resultant velocity vector, which is the speed -
``` h2 = a2 + b2
h2 = -52 + -32
h = √34
h = 5.8 km h-1
```
Often, we see problems in Physics that ask you to compute the sum of two vectors, given the position, direction, and scalar. This is known as vector addition. Consider the following question as an example:
Vector A = 40cm, 60°
Vector B = 20cm, 90°
What is the sum of Vector A and Vector B?
To do this addition, realize that when two vectors are added like this, they simply form a new vector. We will call this Vector C.
Doing it the Visual Way
This is a method to add vectors visually, using measuring tools such as rulers and protractors.
Imagine Vector A from tail to head and plot it on a Cartesian Coordinate System like so:
```
(y)
^
|
| & -- Vector A 40cm, 60°
| /
| /
|/
-+-----------------> (x)
|
|
|
v
```
Now plot Vector B, except have the tail of Vector B start at the head of Vector A. Keep in mind the appropriate angles, it's the same as if you were at the origin of the Cartesian plane.
```(y)
^
|
|
| & -- Vector B. 20cm, 90°
| |
| |
| & -- Vector A 40cm, 60°
| /
| /
|/
-+-----------------> (x)
|
|
|
v
```
Now you have both vectors in the correct position. To find Vector C, simply draw a line from the tail of Vector A to the head of Vector B. Use whatever tools of measurement you have to find the angle and length of the new vector. Remember to keep in mind the scale of the vector.
To subtract Vectors, we will use the same question as before in the example.
```Vector A = 40cm, 60°Vector B = 20cm, 90°
What is Vector A - Vector B?
(y)
^
|
| & -- Vector A 40cm, 60°
| /
| /
|/
-+-----------------> (x)
|
|
|
v
```
This time, for Vector B, we draw the Vector B in the opposite direction from the tail of Vector A, so it would look like this:
```(y)
^
| & -- Vector A 40cm, 60°
| /|
| / |
|/ & -- Vector B. 20cm, 270°
-+-----------------> (x)
|
|
|
v
```
To find Vector C, draw a line from the tail of Vector A to the head of Vector B...just like addition, and measure.
To add more than two vectors, use the same method. Such as Vector A + Vector B + Vector C. Simply put the tail of B onto the head of A, and then put the tail of C onto the head of B.
Note: the addition and subtraction of number is commutative. So is the addition and subtractions of Vectors. You can add them any way you like, but the final vector will always be the same.
Doing it the Mathematical Way
There is an equation to find the sum of Vectors being added or subtracted. All it requires is some skill in Algebra and depending on the angles and lengths given, possibly a calculator with Cosine, Tangent, and Square Root functions.
Vector A = 40cm, 60°
Vector B = 20cm, 90°
What is the sum of Vector A and Vector B?
We did this problem visually before, but there is always error due to incorrect measurements or misjudgement by the human eye. Now we will plug these values into an equation and recieve an exact answer.
Vector A = Vector A + Vector B
Α = Length of Vector A
α = Angle of Vector A
Β = Length of Vector B
β = Angle of Vector B
Y coordinate of Vector C = Αsin(α) + Βsin(β)
X coordinate of Vector C = Αcos(α) + Βcos(β)
So we plug in:
Α = 40 cm
α = 60°
Β = 20 cm
β = 90°
Y coordinate of Vector C = 40sin(60°) + 20sin(90°)
= 40(0.866) + 20(1)
= 34.640 + 20.000
= 54.640 cm
X coordinate of Vector C = 40cos(60°) + 20cos(90°)
= 40(0.500) + 20(0)
= 20.000 + 0
= 20.000 cm
Now that we know the X and Y of Vector C, we can easily find out the Hypotenuse, which will be the scalar of C by using the Pythagorean Theorem.
length of vector C = (x^2 + y^2)^(1/2)
= (2985.530+400)^(1/2)
= (3385.530)^(1/2)
= 58.185 cm
We know that tan(C) will is x/y, so we plug in the x and y values for the inverse tangent:
Angle of Vector C = tan-1(y/x)
= tan-1(54.640/20)
= tan-1(2.732)
= 69.896°
Now that we have the length (58.185) and the angle (69.896°) of Vector C, we have solved the addition of Vector A and Vector B accurately to three decimal places.
To subtract Vectors, just change the + signs in the original equations to - signs. This too can be done commutatively and with more than two vectors.
Note 2: Remember to set your calculator to "degrees" not "radians" otherwise you will get strange answers."
Note 3: If you notice any errors in my arithmetic, please inform me. Thanks.
Log in or register to write something here or to contact authors. | crawl-data/CC-MAIN-2021-21/segments/1620243990449.41/warc/CC-MAIN-20210514091252-20210514121252-00287.warc.gz | null |
It was recently suggested in a health magazine, that hunger genes commonly referred to as DNA mutations were solely responsible for almost if not every instance of low metabolism rates, daily cravings, and overeating disorders resulting in a person's severe overweight.
What are hunger genes and do you have them?
In a scientific research conducted at the University of Cambridge in the United Kingdom it was observed that possible mutation levels in a specific gene known as the KSR2, also called the hunger genes caused an increase in hunger cravings and sensations along with inducing a slower metabolism rate of which the body burns calories in obese people.
Possible Obesity Increase Explanation
These primary conclusions when observed by scientists from the Centers for Disease Control and Prevention have provided researchers with some levels of explanation for the increase in cases observed of obesity experienced in children. A situation which has more than doubled in the United States over the last 35 years. Researchers stunned by this development have increased their drive to identify the specific causes of this epidemic with the hope to present a much needed solution to alleviate this increasing problem.
Earlier conducted studies in mice revealed that by deleting the KSR2 gene in their DNA caused them to become even more obese than those who maintained the KSR2 gene. This allowed scientists to realize that the KSR2 gene though responsible for increasing hunger sensation and slowing metabolic rate was additionally responsible for controlling hunger cravings and effectively regulating a correct balance of energy and metabolism rate.
However scientists even today are still unable to determine the specific effects this particular gene has on humans.
How does it affect children?
Researchers conducted an additional study in which the genetic sequences within over 2000 children suffering from early-onset obesity were analyzed and compared to children of a normal weight. During this analysis it was observed that those children who displayed instances showing the mutation of the KSR2 gene were seen to have an increased level in appetite, lower cardiovascular function, slower metabolism rate and a higher resistance to insulin than the children who did not display the mutation of the KSR2 gene. It was also discovered that mutation of the KSR2 gene effectively disabled oxidization of glucose and fatty acids a function which is the key to the human body's metabolism process.
The role of nutrition
The study of the KSR2 gene and it's mutation was observed by Sadaf Faroqi, a researcher based at the University of Cambridge who went on to explain that although some people had made changes within their daily diet to lower calorie consumption and even introduced an exercise workout routine to stimulate weight loss and weight control, the rates of which the calories were burned were significantly different in each person. This discovery led to the conclusion that some people had the potential to gain weight at a faster rate than others.
Treatment Options for KSR2 Genes
Researchers through scientific studies found that by using specific drugs to regulate the protein content encoded by the KSR2 gene a successful treatment option could be developed for patients suffering from obesity and type 2 diabetes.
Experiments using the existing drug metformin which has been successfully used in the treatment of diabetics, revealed that it had the ability to lower oxidation levels of cells contained within KSR2 mutated genes which proved as a viable option for the treatment of type 2 diabetics and people suffering from obesity. | <urn:uuid:e30b7e2e-5c12-4a1d-b646-6d1933081b74> | {
"date": "2020-07-02T22:52:38",
"dump": "CC-MAIN-2020-29",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880243.25/warc/CC-MAIN-20200702205206-20200702235206-00058.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9728938937187195,
"score": 3.640625,
"token_count": 666,
"url": "https://www.mensfitclub.com/mens-health/hunger-genes-causing-fat/"
} |
- This letter was sent to the British Foreign Office in June 1916, two
months after the Easter Rising in April 1916. It is likely that the
writer was an Irishman from a Unionist background. This is why he was
concerned about the views being expressed towards Britain.
- In April 1916, during Easter Week, Republicans took over the centre
of Dublin. They took the British forces completely by surprise. It took
a week of fighting to get them to surrender. The centre of the city
was wrecked and many civilians were killed or injured in the fighting.
- After the rising, the British executed 15 of the leaders. The only
senior commander who survived was Eamon de Valera. The executions caused
outrage. The British regarded these men as traitors, but many Irish
people saw them as prisoners of war. They resented Irish men being executed
for treason to the British Crown.
- The British took other rebels prisoner and rounded up people all over
Ireland whom they suspected of being rebels. In total, this was 1,841
people. The British also put Ireland under military law with strict
restrictions on people's freedom to move around the country.
- Historians disagree about how much support the extremists had before
the Rising. However, they generally agree that the actions of the British
after the Rising made people in Ireland bitter and greatly increased
support for Sinn Fein and the extreme Nationalists.
- As this letter shows, the British actions made them deeply unpopular
in America, where there was a large Irish community. This meant that
United States politicians became concerned, because many of them represented
the Irish Americans in the big cities.
- The UIL was the United Irish League. This organisation helped Irish
people to find work, helped them if they were ill or out work etc.
- Clann na Gael was the American branch of the Fenians - extreme Republicans. | <urn:uuid:7d12eaea-f33e-4764-8e39-e88b84094e75> | {
"date": "2017-04-24T21:03:51",
"dump": "CC-MAIN-2017-17",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119838.12/warc/CC-MAIN-20170423031159-00116-ip-10-145-167-34.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.984786331653595,
"score": 3.625,
"token_count": 400,
"url": "http://www.nationalarchives.gov.uk/education/empire/usefulnotes/g3cs4s6u.htm"
} |
# Integrate the function$x\;logx$
$\begin{array}{1 1} \large \frac{\log x}{x^2}-\frac{x^2}{4}+c \\ \frac{\log x}{x^2}+\frac{x^2}{4}+c \\ \frac{\log x}{x}-\frac{x^2}{4}+c \\ \frac{\log x}{x}-\frac{x}{4}+c\end{array}$
Toolbox:
• (i)When there are two functions u and v and if they are of the form $\int u dv,$then we can solve it by the method of integration by parts$\int udv=uv-\int vdu$
• (ii)$\int\frac{1}{x}dx=log x+c.$
Given $I=\int xlog xdx.$
Clearly the given integral function is of the form $\int u dv$,so let us follow the method of integration by parts where $\int udv=uv-\int vdu$
Let u=log x.
On differentiating we get
$du=\frac{1}{x}dx.$
let dv=x dx.
On integrating we get
$v=\frac{x^2}{2}$.
On substituting for u,v,du and dv we get,
$\int xlog x=(log x.\frac{1}{x^2})-\int\frac{x^2}{2}.\frac{1}{x}dx.$
$\;\;\;\;=\frac{log x}{x^2}-\frac{1}{2}\int xdx.$
On integrating we get,
$\;\;\;\;=\frac{log x}{x^2}-\frac{1}{2}{x^2}{2}+c.$
$\;\;\;=\frac{log x}{x^2}-\frac{x^2}{4}+c.$
edited Feb 8, 2013 | crawl-data/CC-MAIN-2017-51/segments/1512948529738.38/warc/CC-MAIN-20171213162804-20171213182804-00086.warc.gz | null |
SW downward flux is part of Earth’s energy budget. This concept is used to understand how much energy the Earth gets from the Sun, and how much energy the Earth system radiates back to outer space. All energy budget parameters describe the ‘flux,’ or flow, of a specific type of electromagnetic energy.
This parameter is reported on a 72-Day cycle and is an average value for that 72-day period.
This parameter is a TOA measurement, meaning that it’s measured at the top of the atmosphere. For the purposes of Earth’s radiation budget, TOA is considered to be about 20 km above the surface of the Earth. Above that there is little interaction between the energy flux and the atmosphere.
Because this is an All-sky parameter, it includes all types of conditions, including clear or cloudy skies when they occur.
It specifically measures ‘SW’ or ‘shortwave’ energy. SW is visible light, emitted by the Sun and then reflected or absorbed by the Earth and Earth’s atmosphere. This visible light has wavelengths shorter than 5 micrometers.
This parameter is a measurement of Downward flux, or the energy that’s coming toward the Earth.
Flux is the rate of energy flow coming in or out. In other words, flux measures how much energy is coming or going.
Overall, this parameter measures the amount of visible light energy entering the Earth system at the top of the atmosphere. | <urn:uuid:e68260ac-f7be-458e-a99c-bff3bacb9e3a> | {
"date": "2017-12-11T05:45:03",
"dump": "CC-MAIN-2017-51",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948512208.1/warc/CC-MAIN-20171211052406-20171211072406-00656.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.8869681358337402,
"score": 3.78125,
"token_count": 308,
"url": "https://mynasadata.larc.nasa.gov/glossary/72-day-toa-all-sky-sw-downward-flux-erbenonscan-2/"
} |
What Did it Look Like When Europe Met America?
This What Did it Look Like When Europe Met America? lesson plan also includes:
- Join to access all included materials
Students view the film 'Black Robe,' which further develop students' abilities to see an event or era of history from multiple perspectives. After the movie, they utilize worksheets imbedded in this plan to write about what they've seen.
18 Views 21 Downloads
When You Were My Age, What Was This Place Like?
Here is a lesson that includes many great ideas for investigating and discovering how our communities have physically changed over the years, and how land use changes over time may affect a community's water supply. The lesson's...
7th - 12th English Language Arts CCSS: Adaptable
Money Matters: Why It Pays to Be Financially Responsible
What does it mean to be financially responsible? Pupils begin to develop the building blocks of strong financial decision making by reviewing how their past purchases are examples of cost comparing, cost-benefit analysis, and budgeting.
9th - 12th Math CCSS: Adaptable
New Review War and Nation Building in Latin America: Crash Course World History 225
Does war hinder the growth of nation-states, or does it facilitate development? A video from Crash Course World History examines this question in the context of Latin America, particularly how the lack of international war in Central and...
12 mins 9th - 12th Social Studies & History CCSS: Adaptable
What Did Democracy Really Mean in Athens?
Did you know elections only played a small role in Athenian democracy? Take a look at the fascinating origins of Athenian direct democracy in ancient Greece, and compare their political structures to our understanding of representative...
5 mins 6th - 12th Social Studies & History CCSS: Adaptable
Growing Up in a Segregated Society, 1880s–1930s
What did segregation look like in the beginning of the 20th century? Middle and high schoolers view images of segregated areas, read passages by Booker T. Washington and W.E.B. DuBois, and come to conclusions about how the influence of...
9th - 12th Social Studies & History CCSS: Adaptable
Unit 2: Development of Feudalism in Western Europe
How did feudalism help to establish order in Europe during the Middle Ages after the fall of the Roman Empire? Here you'll find a collection of videos and a student packet of worksheets to supplement your unit on the subject.
7th - 9th Social Studies & History CCSS: Adaptable
The Meaning of America: Enterprise and Commerce
Using Mark Twain's The Man That Corrupted Hadleyburg, invite your learners to consider the concept of virtue in a democratic society devoted to gain and self-interest. This stellar resource guides your class members through a close...
9th - 12th English Language Arts CCSS: Designed
What is Love?
Love is "potentially the most intensely thought about thing in all of human history." We rank, define, and fall into love...but what is it really? Explore the various ways humanity has come to define love, from a set of behaviors or an...
5 mins 9th - 12th Social Studies & History CCSS: Adaptable
What Happens When You Remove the Hippocampus?
Imagine not being able to remember what day it is or what food you had for breakfast this morning. This nightmare was a reality for Henry Molaison, whose life story is the focus of this video explaining how different parts of the...
5 mins 9th - 12th Science CCSS: Adaptable | <urn:uuid:f9de4d69-2831-4be0-8d04-1cc01e6925a9> | {
"date": "2018-02-20T02:34:36",
"dump": "CC-MAIN-2018-09",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812871.2/warc/CC-MAIN-20180220010854-20180220030854-00057.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9133321046829224,
"score": 3.765625,
"token_count": 756,
"url": "https://www.lessonplanet.com/teachers/what-did-it-look-like-when-europe-met-america"
} |
Find the equations of the bisectors of the angles between the coordinate axes.
Asked by Aaryan | 1 year ago | 43
##### Solution :-
There are two bisectors of the coordinate axes.
Their inclinations with the positive x-axis are 45° and 135°
The slope of the bisector is m = tan 45° or m = tan 135°
i.e., m = 1 or m = -1, c = 0
By using the formula, y = mx + c
Now, substitute the values of m and c, we get
y = x + 0
x – y = 0 or y = -x + 0
x + y = 0
The equation of the bisector is x ± y = 0
Answered by Aaryan | 1 year ago
### Related Questions
#### Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
#### Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices
Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.
#### Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.
Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0. | crawl-data/CC-MAIN-2023-23/segments/1685224650409.64/warc/CC-MAIN-20230604225057-20230605015057-00159.warc.gz | null |
Some of the different kinds of radioactive atoms used to date objects are shown in the following table: Potassium-Argon Dating Potassium atoms are used to date rocks that have formed from molten rock. Argon is an inert gasit does not chemically bond to other atoms.
Argon in molten rock can just bubble out and escape.
By measuring the amounts of Potassium and Argon present we can date volcanic rocks that are millions of years old.
Carbon Dating Another important dating technique is Carbon-14 dating.
Once the rock cools and solidifies, Argon that is formed by radioactive decay is trapped inside.
As no Argon was present in the rock when it first solidified, all Argon in the rock is due to the radioactive decay of Potassium.
This process is called radiometric or radioactive dating.This is used to date the remains of things that were once living.Radiometric dating is possible because the radioactive decay of large numbers of radioactive atoms follows a predictable pattern.This predictability allows scientists to measure the age of an object if they can work out how many radioactive atoms were originally present.The original radioactive atom is known as a parent isotope, while the atom produced by the decay process is known as a daughter isotope. For example Uranium-235 and Uranium-238 are both Uranium atoms with the same number of protons, but they have a different number of neutrons.
The number used to identify the isotope refers to the total number of particles in the nucleus of each atom. | <urn:uuid:d8a59463-adf7-4879-9aae-59bf3f24d34f> | {
"date": "2018-10-21T16:44:57",
"dump": "CC-MAIN-2018-43",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514162.67/warc/CC-MAIN-20181021161035-20181021182535-00298.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9356600046157837,
"score": 4,
"token_count": 311,
"url": "http://aktiv-t.ru/radioactive-or-radiometric-dating-17992.html"
} |
# High School Math : Sequences and Series
## Example Questions
← Previous 1 3
### Example Question #1 : Sequences And Series
Evaluate:
None of the other answers are correct.
Explanation:
This sum can be determined using the formula for the sum of an infinite geometric series, with initial term and common ratio :
### Example Question #1 : Sequences And Series
The fourth term in an arithmetic sequence is -20, and the eighth term is -10. What is the hundredth term in the sequence?
110
105
210
220
55
220
Explanation:
An arithmetic sequence is one in which there is a common difference between consecutive terms. For example, the sequence {2, 5, 8, 11} is an arithmetic sequence, because each term can be found by adding three to the term before it.
Let denote the nth term of the sequence. Then the following formula can be used for arithmetic sequences in general:
, where d is the common difference between two consecutive terms.
We are given the 4th and 8th terms in the sequence, so we can write the following equations:
.
We now have a system of two equations with two unknowns:
Let us solve this system by subtracting the equation from the equation . The result of this subtraction is
.
This means that d = 2.5.
Using the equation , we can find the first term of the sequence.
Ultimately, we are asked to find the hundredth term of the sequence.
### Example Question #1 : Sequences And Series
Find the sum, if possible:
Explanation:
The formula for the summation of an infinite geometric series is
,
where is the first term in the series and is the rate of change between succesive terms. The key here is finding the rate, or pattern, between the terms. Because this is a geometric sequence, the rate is the constant by which each new term is multiplied.
Plugging in our values, we get:
### Example Question #1 : Sequences And Series
Find the sum, if possible:
Explanation:
The formula for the summation of an infinite geometric series is
,
where is the first term in the series and is the rate of change between succesive terms in a series
Because the terms switch sign, we know that the rate must be negative.
Plugging in our values, we get:
### Example Question #1 : Sequences And Series
Find the sum, if possible:
No solution
No solution
Explanation:
The formula for the summation of an infinite geometric series is
,
where is the first term in the series and is the rate of change between succesive terms in a series.
In order for an infinite geometric series to have a sum, needs to be greater than and less than , i.e. .
Since , there is no solution.
### Example Question #1 : Using Sigma Notation
Determine the summation notation for the following series:
Explanation:
The series is a geometric series. The summation notation of a geometric series is
,
where is the number of terms in the series, is the first term of the series, and is the common ratio between terms.
In this series, is is , and is . Therefore, the summation notation of this geometric series is:
This simplifies to:
### Example Question #5 : Sequences And Series
Determine the summation notation for the following series:
Explanation:
The series is a geometric series. The summation notation of a geometric series is
,
where is the number of terms in the series, is the first term of the series, and is the common ratio between terms.
In this series, is is , and is . Therefore, the summation notation of this geometric series is:
This simplifies to:
### Example Question #6 : Sequences And Series
Indicate the sum of the following series:
Explanation:
The formula for the sum of an arithmetic series is
,
where is the first value in the series, is the number of terms in the series, and is the difference between sequential terms in the series.
In this problem we have:
Plugging in our values, we get:
### Example Question #1 : Sequences And Series
Indicate the sum of the following series:
Explanation:
The formula for the sum of an arithmetic series is
,
where is the first value in the series, is the number of terms in the series, and is the difference between sequential terms in the series.
Here we have:
Plugging in our values, we get:
### Example Question #31 : Pre Calculus
Indicate the sum of the following series:
Explanation:
The formula for the sum of a geometric series is
,
where is the first term in the series, is the rate of change between sequential terms, and is the number of terms in the series
For this problem, these values are:
Plugging in our values, we get:
← Previous 1 3 | crawl-data/CC-MAIN-2023-06/segments/1674764495001.99/warc/CC-MAIN-20230127164242-20230127194242-00856.warc.gz | null |
It's a living legal community making laws accessible and interactive. Click Here to get Started »
Franklin Delano Roosevelt
Franklin Delano Roosevelt served as the thirty-second president of the United States from 1933 to 1945. During his unprecedented four terms in office, Roosevelt established himself as a towering national leader, leading the United States out of the Great Depression through the active involvement of the federal government in the national economy. The federal government grew dramatically in size and power as Congress enacted Roosevelt's New Deal program. As president, Roosevelt was responsible for the creation of Social Security, federal labor laws, rural electrification programs, and myriad projects that assisted farmers, business, and labor. During World War II Roosevelt's leadership was vital to rallying the spirits of the citizenry and mobilizing a wartime economy. Nevertheless, Roosevelt was a controversial figure. Many economic conservatives believed his programs owed more to state socialism than to free enterprise.
Roosevelt was born on January 30, 1882, in Hyde Park, New York, the only son of James and Sara Delano Roosevelt. The young Roosevelt was taught to be a gentleman and to exercise Christian stewardship through public service. He graduated from Harvard University in 1904 and in 1905 wed Eleanor Roosevelt, the niece of his fifth cousin, President Theodore Roosevelt.
Roosevelt attended Columbia University Law School but left without receiving a degree when he passed the New York bar exam in 1907. In 1910 Roosevelt was elected to the New York Senate as a member of the Democratic Party. Reelected in 1912, he resigned in 1913 to accept an appointment from President Woodrow Wilson as assistant secretary of the Navy. For the next seven years, Roosevelt proved an effective administrator and an advocate of reform in the U.S. Navy.
Roosevelt was nominated for vice president on the 1920 Democratic party ticket. He waged a vigorous campaign in support of the presidential nominee, James M. Cox, but the Republican ticket headed by Warren G. Harding soundly defeated Cox and Roosevelt. After the election Roosevelt joined a Maryland bonding company and began investing in various business schemes.
Roosevelt's life changed in August 1921, when he was stricken with poliomyelitis while vacationing at Campobello Island, New Brunswick. Initially, Roosevelt was completely paralyzed, but over several years of intense therapy, he made gradual improvement. His legs, however, suffered permanent paralysis. For the rest of his life, he used a wheelchair and could walk only a few steps with the help of leg braces.
Eleanor Roosevelt believed her husband's recovery depended on his reentry into New York politics. She attended meetings, made speeches, and reported back to him on the political events of the day. By 1924 Roosevelt was at the Democratic National Convention nominating Governor Alfred E. Smith of New York for president. Smith, who lost the presidential elections in 1924 and 1928, showed Roosevelt the ways of New York state politics and pushed him to run for governor in 1928. A reluctant Roosevelt won by a narrow margin, but soon was governing as if he had won by a landslide. With the stock market crash of October 25, 1929, the United States was thrown into a national economic depression of unprecedented severity. As governor, Roosevelt set up the first state public relief agency and tried to find ways to spark an economic recovery. His landslide reelection in 1930 made him the logical candidate to face the Republican president Herbert Hoover in the next presidential election.
Roosevelt was nominated for president on the third ballot of the 1932 Democratic National Convention. During the campaign Roosevelt called for the federal government to take action to revive the economy and end the suffering of the thirteen million unemployed people. Hoover advocated a more limited role for the federal government in the national economy. Roosevelt easily defeated Hoover and brought with him large Democratic majorities in both houses of Congress.
Roosevelt took office on March 4, 1933, at a time when the economy appeared hopeless. In his inaugural address he reassured the nation that "the only thing we have to fear is fear itself." He proposed a New Deal for the people of the United States and promised to use the power of the executive branch to address the economic crisis.
During his first hundred days in office, Roosevelt sent Congress many pieces of legislation that sought to boost economic activity and restore the circulation of money through federally funded work programs. The Civilian Conservation Corps (CCC) provided unemployment relief and an opportunity for national service to young workers, while promoting conservation through reforestation and flood control work. Federal funds were given to state relief agencies for direct relief, and the Reconstruction Finance Company was given the authority to make loans to small and large businesses.
The centerpieces of Roosevelt's New Deal legislation were the Agricultural Adjustment Act (AAA) of 1933 (7 U.S.C.A. § 601 et seq.) and the National Industrial Recovery Act (NIRA) of 1933 (48 Stat. 195). The AAA sought to raise farm prices by giving farmers federal subsidies if they reduced their agricultural production.
The NIRA was a comprehensive attempt to manage all phases of U.S. business. It established the National Recovery Administration (NRA) to administer codes of fair practice within each industry. Under these codes labor and management negotiated minimum wages, maximum hours, and fair-trade practices for each industry. The Roosevelt administration sought to use these codes to stabilize production, raise prices, and protect labor and consumers. By early 1934 there were 557 basic codes and 208 supplementary ones. In 1935, however, the Supreme Court struck down the NIRA in A.L.A. Schechter Poultry Corp. v. United States, 295 U.S. 495, 55 S. Ct. 837, 79 L. Ed. 1570.
In 1935 Roosevelt and the Congress passed the Social Security Act (42 U.S.C.A. § 301 et seq.), a fundamental piece of social welfare legislation that provided unemployment compensation and pensions for those over the age of sixty-five. More groundbreaking legislation came with the passage of the Wagner Act, also known as the National Labor Relations Act (NLRA) of 1935 (29 U.S.C.A. § 151 et seq.), which recognized for the first time the right of workers to organize unions and engage in collective bargaining with employers.
Roosevelt handily defeated Republican Alfred M. Landon, the governor of Kansas, in the 1936 presidential election. In his second term, however, Roosevelt met more resistance to his legislative initiatives. Between 1935 and 1937, the Supreme Court struck down as unconstitutional eight New Deal programs that attempted to regulate the national economy. Most of the conservative justices who voted against the New Deal statutes were over the age of seventy. Roosevelt responded by proposing that justices be allowed to retire at age seventy at full pay. Any justice who declined this offer would be forced to have an assistant with full Voting Rights. The assistant, of course, as a Roosevelt appointee, would be more likely to be sympathetic to the president's political ideals. This plan to "pack" the Court was met with hostility by Democrats and Republicans and rejected as an act of political interference. Despite the rejection of his plan, Roosevelt ultimately prevailed. In 1937 the Supreme Court upheld the Wagner Act in NLRB v. Jones and Laughlin Steel Corp. 301 U.S. 1, 57 S. Ct. 615, 81 L. Ed. 893, signaling an end to the invalidation of New Deal laws that sought to reshape the national economy. From Jones onward the Court permitted the federal government to take a dominant role in matters of commerce.
By 1937 the national economy appeared to be recovering. In the fall of 1937, however, the economy went into a recession, accompanied by a dramatic increase in unemployment. Roosevelt responded by instituting massive government spending, and by June 1938 the economy had stabilized.
During the late 1930s, Roosevelt had also become preoccupied with foreign policy. The rise of Adolf Hitler and Nazism in Germany, coupled with a militaristic Japanese government that had invaded Manchuria in 1933, created international tensions that Roosevelt realized might come to involve the United States. U.S. foreign policy had traditionally counseled against entanglements with other nations, and the 1930s had seen a resurgence of isolationist thought. Roosevelt, while publicly agreeing with isolationist legislators, quietly moved to enhance U.S. military strength.
With the outbreak of World War II in Europe in August 1939, Roosevelt sought to aid Great Britain and France against Germany and Italy. The Neutrality Act of 1939 (22 U.S.C.A. § 441), however, prohibited the export of arms to any belligerent. With some difficulty Roosevelt secured the repeal of this provision so that military equipment could be sold to Great Britain and France.
In 1940 Roosevelt took the unprecedented step of seeking a third term. Although there was no constitutional prohibition against a third term, President George Washington had established the tradition of serving only two terms. Nevertheless, Roosevelt was concerned about the approach of war and decided a third term was necessary to continue his plans. He defeated the Republican nominee, Wendell L. Willkie, pledging that he would keep the United States out of war. Roosevelt's margin of victory in the popular vote was closer than in 1936, but he still won the Electoral College vote easily.
Following his reelection, Roosevelt became more public in his support of the Allies. At his urging, Congress moved further away from neutrality by passing the Lend-Lease Act of 1941 (55 Stat. 31). Lend-Lease provided munitions, food, machinery, and services to Great Britain and other Allies without immediate cost.
The United States entered World War II following the Japanese attack on the U.S. naval base at Pearl Harbor, Hawaii, on December 7, 1941. Roosevelt rallied a stunned citizenry and began the mobilization of a wartime economy. In his public speeches and "fireside chats" on the radio, Roosevelt imparted the strong determination that the United States would prevail in the conflict. He met with Winston Churchill, the prime minister of Great Britain, and Joseph Stalin, the leader of the Soviet Union, several times during the war to discuss military strategy and to plan power-sharing in the postwar world. Roosevelt, who needed the Soviet Union's cooperation in defeating Germany, sought to minimize conflicts with Stalin over postwar boundaries in Europe.
In 1944 Roosevelt decided to run for a fourth term. Though his health had seriously declined, he wished to remain commander in chief for the remainder of the war. The Republican Party nominated Governor Thomas E. Dewey of New York for president, but again Roosevelt turned back the challenge, winning 432 electoral votes to Dewey's 99.
In February 1945 Roosevelt traveled to Yalta in the Crimea to meet with Churchill and Stalin. Germany was on the edge of defeat, but Japan's defeat did not appear imminent. Stalin accepted Roosevelt and Churchill's offer of territorial concessions in Asia in return for his promise that the Soviet Union would enter the war against Japan once Germany was defeated. At Yalta the leaders reaffirmed earlier agreements and made plans for the establishment of democratic governments in eastern Europe. The Yalta agreements were not clearly written, however, and therefore were open to differing interpretations by the Allies. Within a month after Yalta, Roosevelt sent a sharp message to Stalin concerning Soviet accusations that Great Britain and the United States were trying to rob the Soviets of their legitimate territorial interests.
Early in the war, Roosevelt decided that an effective international organization should be established after the war to replace the League of Nations. At Yalta, Roosevelt pressed for the creation of the United Nations as a mechanism to preserve world peace. A conference attended by fifty nations was scheduled to begin on April 25, 1945, in San Francisco, California, to draft a United Nations charter. Roosevelt had planned to attend, but his health had steadily declined since the 1944 election.
Instead, Roosevelt went to his retreat in Warm Springs, Georgia, where he had begun his rehabilitation from polio in the 1920s. He died there on April 12, 1945. Vice President Harry S. Truman succeeded Roosevelt. On May 7 the war in Europe ended with Germany's surrender; four months later, on September 2, Japan also surrendered, ending the war in the Pacific.
Jenkins, Roy. 2003. Franklin Delano Roosevelt. New York: Times Books.
Kline, Stephan O. 1999. "Revisting FDR's Court Packing Plan: Are the Current Attacks on Judicial Independence So Bad?" McGeorge Law Review 30 (spring).
McElvaine, Robert S. 2002. Franklin Delano Roosevelt. Washington, D.C.: CQ Press. | <urn:uuid:a92b7645-a63b-4109-9389-ed9a8230032f> | {
"date": "2014-03-08T13:44:18",
"dump": "CC-MAIN-2014-10",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999654667/warc/CC-MAIN-20140305060734-00007-ip-10-183-142-35.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9666459560394287,
"score": 3.734375,
"token_count": 2575,
"url": "http://lawbrain.com/wiki/Franklin_Delano_Roosevelt"
} |
Common People and Economic Games in the Early Modern Era
Since the beginnings of the Christian era the most alarming feature
concerning Judas has been the inadequacy of his economic behaviour, not his
betrayal. What kind of man would exchange the infinite value for Christ for
the paltry sum of thirty pieces of silver? Judas thus became the negative prototype
of people who ignore the authentic value of things: Over time, in the Middles
Ages and the Modern Era, Judas came to exemplify misapprehension of how the
market and the economy work. On the other hand, Mary Magdalene, who "wastes"
a valuable balm in order to anoint Jesus's head, became a symbol of proper,
far-sighted economic behaviour, aware of the difference between petty, private
interest and the social uses of wealth. The implications of this opposition
can be seen in the social exclusion codes which characterize European economic
modernization and feed the shame of ordinary people, whom Judas fundamentally
Giacomo Todeschini teaches Medieval History
at the University of Trieste.
Anteprima del testo delle prime cinque pagine a stampa del primo capitolo.
Il tuo browser non supporta la tecnologia necessaria per visualizzare l'anteprima.
Per visualizzzare l'anteprima utilizza uno dei seguenti browser. | <urn:uuid:bb54deeb-05c3-492b-b27d-3534bc2aa095> | {
"date": "2021-01-20T01:29:56",
"dump": "CC-MAIN-2021-04",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00018.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.7813301086425781,
"score": 3.59375,
"token_count": 307,
"url": "https://www.mulino.it/isbn/9788815150479"
} |
...how some made their way to Beaufort.
This etching shows how French Huguenots fled from Brittany and Normandyin small boats across the English Channel to England. Image from www.betheafamily.org
Besides those who settled in Florida in 1564 and South Carolina in 1679, about 1705 small colonies settled on the Pamlico River and on the Trent where Baron DeGraffenried’s colony found them in 1710 when he founded New Bern.
In 1708, the region, known today as Carteret County, began to attract settlers. A few families moved into the area about North River, known then as the “the Core Sound” settlement.
It is believed that Pivers and Shackelfords were among those first settlers. In later years these frontiersmen were followed by families with names of Paquinet, Noe, Manney, Delamar, Midyette and Geoffroy—all descendants of French Huguenots:
Shackelford: Roger Shackelford the immigrant (1629-1704) fled England about 1658, on a boat with Edward Palmer and his siblings, who had received a land grant in Virginia. The Palmers were French Huguenots. Roger married Mary Palmer about 1660.
Roger's sons John (1688–1734) and Francis patented a "plantation" on the west side of North River in 1708. John Shackelford served in the local militia from 1712 to 1743. In 1713 he and Enoch Ward purchased 7000 acres referred to as the “Sea Banks.” Shackelford’s western part later became known as Shackelford Banks. It is believed the Shackelford ancestors lived in a small town near London, England, known until 1620 as “Shackelford Village.”
Piver: Though not documented, Peter Piver circa 1690-1758 may have been the first Piver to come to the Core Sound area. Over the generations, he, son Peter and grandson Peter acquired various plots of land including acreage west of what is now Moore Street. Peter Piver, Jr. (1717-1795) served under the command of Colonel Thomas Lovick during the 1747 Spanish attacks. Peter III was born about 1740. In 1795, Carteret County court minutes note that Peter Piver and wife Lydia sold half of Piver’s Island (seven acres) to Elijah Bell. Peter Piver and his descendants built many houses in Beaufort.
Paquinet: The 1790 US Census shows Ann, James, Isaiah and John Paquinet in Carteret County. The 1772 Will of Michael Paquinet left his sons James, John and Isaiah his plantation, 100 acres on Cane Creek and 200 acres on Broad Creek. Third generation names were Belcher Fuller and Mary Severn—both Huguenot descendants through Michael Paquinet, born in Paris in 1690. The Paquinet House circa 1769 is on Front Street. Rebecca Paquinet married John Mades, 16 Jun 1803. Betsey Paquinet married Francis Dennis, 18 Jan 1804. Elizabeth Paquinet married Jesse Piver, 19 June 1817.
Noe: In early 1800s there were two Noe families - James Noes and Peter Noes. James Noe, Jr. married Mary Polly Paquinet in 1829. In 1862 Thomas Noe married Frances Ann Mades, daughter of Rebecca and John Mades. The James Noe House circa 1828 is on Moore Street.
Manney: Jean Magny left France after the revocation of the Edict of Nantes in 1685. He first settled in Rhode Island in 1686. About 1691 most of the Huguenots were forced to leave. Jean Magny settled briefly in Oxford, Mass, but soon moved to New York City.
Magny, Manee, and Maney evolved to Manney. James Manney came to Beaufort from Poughkeepsie, NY. The Dr. James Manney House circa 1812 is at the corner of Craven and Ann Streets. In 1848, Dr. Manney's son, Dr. James Lente Manney, married William Fulford's daughter, Julia Ann.
Delamar: 1668 Francis De Lamar, or De la Mar, born in Boucre, Calais, France, died in 1713 in Pacquotank County, NC. Some of his descendants came to Beaufort from New Bern before 1850. The Gibble-Delamar House circa 1866 is on the corner of Turner and Broad Streets.
Midyett: Midyett families, originally from Normandy, France, were early inhabitants of Bodie Island and the Outer Banks in the late 1600s. "Many Midyett girls married sailors off Black Beard's three ships. The name was spelled different ways: Midyett, Midyette, Midgett, Midgette, but no matter how you spell it, they all came from Matthew Midyett who landed at Bodie Island, NC around 1600. He was a ship captain and was shipwrecked off the coast of the outer banks."--Donald Midyett. Midyetts helped start the US Coast Guard by establishing life-saving stations on the Outer Banks. Some of the family found their way to Beaufort by 1850.
Geffroy: Malachi R. Geffroy, husband of Nannie Pasteur Davis, had roots back to France then Canada. The M.R. Geffroy House circa 1885 is in the third block of Ann Street.
Beaufort resident David DuBuisson is an indirect descendant of brothers Henry Martyn Baird and Charles Washington Baird - both Huguenot historians. In 1885 Charles W. Baird, D.D. (1828-1887), Presbyterian minister and historian, wrote the History of the Huguenot Emigration to America. The Baird brothers contributed perhaps two-thirds of the Huguenot scholarship in English that exist today. Their mother was Fermine Amaryllis Opheia DuBuisson Baird. Fermine was David DuBuisson's great-great aunt, the older sister of his great-great grandfather, George Washington DuBuisson.
David DuBuisson wrote: The Huguenots in the U.S. quickly dispersed and assimilated. Many of them had already assimilated in English or Dutch or German societies before crossing the Atlantic. As a religious denomination, the Huguenot church essentially disappeared under the relentless persecution of Rome. So, with a few exceptions, by the time they reached America Huguenots were generally affiliated with the Dutch Reformed (NY), Presbyterian or Anglican (VA, SC) churches. As they spread out through the colonies, they did not do so as a coherent group, but rather as individual families colonizing mainly with the English. This would explain why there would be no recognizable “Huguenot colonies” in, say, North Carolina, though there would be individual families.
Beaufort resident Jimmy Piver and his children are descendants of Peter Piver through his son Peter Piver, Jr. | <urn:uuid:86eabd0d-49e9-4883-a745-b4e77701289c> | {
"date": "2014-03-09T16:12:09",
"dump": "CC-MAIN-2014-10",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394009829804/warc/CC-MAIN-20140305085709-00006-ip-10-183-142-35.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9582770466804504,
"score": 3.546875,
"token_count": 1506,
"url": "http://beaufortartist.blogspot.com/2009/01/tricentennial-series-french-huguenot.html"
} |
Question Video: Rounding Fractions to The Nearest Half Mathematics
Round 4/37 to the nearest half.
02:47
Video Transcript
Round four thirty-sevenths to the nearest half.
We’re given the fraction four thirty-sevenths. And we’re asked to round it to the nearest half. But what are the different multiples of half that we could round it to? Well, one times a half equals one-half and two lots of a half make one whole. But on our number line, we can also include one other multiple of a half. Zero lots of one-half equals zero. And it’s important that we do include this as a multiple of one-half.
So we need to think where four thirty-sevenths might be on our number line and which half it’s nearest to. What makes our fraction tricky to deal with? Well, the denominator in the fraction is an odd number. Because it’s an odd number, we can’t convert it to a fraction that’s exactly the same as one-half. If we could, we’d be able to compare four thirty-sevenths with our fraction that was the same as one-half. And we’d be able to see whether it was close to this.
Instead, we’re going to have to use estimation to help. And the first thing we can do is to change our denominator into an even number, an even number that’s close to 37. Let’s change it into 36. Let’s change it to 36. Four thirty-sevenths is approximately the same as four thirty-sixths. Now, if we divide 36 by two, we get the answer 18. Eighteen thirty-sixths is the same as one-half.
Four thirty-sixths seems a lot less than this. It may even be less than a quarter. 36 split into four equals nine. Nine thirty-sixths equals the same as a quarter. And so four thirty-sixths is even less than this. So we can estimate that four thirty-sevenths has a value less than a quarter. And so the multiple of one-half that it’s nearest to is actually zero.
We know one whole is the same as thirty-seven thirty-sevenths. Zero is obviously the same as zero thirty-sevenths. And we can’t give the exact amount for one-half, but it’s between eighteen thirty-sevenths and nineteen thirty-sevenths. So we can see that the multiple of one-half that four thirty-sevenths is nearest to is zero. | crawl-data/CC-MAIN-2021-31/segments/1627046154310.16/warc/CC-MAIN-20210802075003-20210802105003-00236.warc.gz | null |
# INTEGRATION | INTEGRATION TUTORIAL IN PDF
## INTEGRATION |INTEGRATION TUTORIAL IN PDF [ BASIC INTEGRATION, SUBSTITUTION METHODS, BY PARTS METHODS]
### INTEGRATION :-
Hello students, I am Bijoy Sir and welcome to our educational forum or portal.
Today we will discuss about the Integration, but you of all know that very well, Integration is a huge part in mathematics. Then all of the topics of Integration can’t be covered in one class, so we will discuss the all topics but lightly, means we will see all types of Integration in with the some example. We will take more illustration on the topic of Integration in upcoming classes or tutorials.
Let’s start the discussion –
##### Now take a heading – Integration
– Students this is the class of Integration so we will start from very beginning. Before starting Integration I want to tell you something that, Integration mainly developed by Newton Sir.
#### History of Integration –
When Newton sir was trying to calculate the value gravitational potential, but the same time had no sufficient formula for proper calculation. Then Newton sir was thinking we need a new type of formula, that can give us a new way to sum. Then Newton sir had given a way to adding some element, which known as summation or Integration. We can add the very small element by the Integration. Which we will discuss very well in the tutorials of Definite Integration or Summation Series
#### Definition of Integration –
In the earlier section we already learnt the derivatives or differentiation, foe properly understanding the Integration we have to just remind the derivatives or differentiation.
Definition- In generally Integration is the inverse process of derivatives or in simple language integration is anti derivative s or primitive of derivatives.
In mathematically,
Let the derivative of a function [ f(x)] is g(x). Then,
$$\frac {df(x)}{dx}= g(x)$$
Then we can say Integration of g(x) is equal to f(x). [ where derivative of f(x) is g(x).]
So, we can write ,
$$\frac{df(x)}{dx}=g(x)$$
Or, d f(x) = g(x) ·dx
or, f(x) = $$\frac{1}{d}$$g(x)· dx
Hence, f(x) = ∫ g(x)· dx + c [ where ‘c’ is integral constant ]
Note: If we take limit on integration the constant term ‘c’ will be automatically vanished.
# We can write that equation in another way
like, $$\frac {df(x)}{dx}=g(x)$$
Or, d f(x) = g(x) . dx
Now taking the integration on the both side we get,
or, ∫ d f(x) = ∫ g(x)· dx + c
or, $$\frac{1}{d}$$ · df(x) = ∫ g(x)· dx + c
∴ f(x) = ∫ g(x)· dx + c
[ where, ∫ = 1/d we already learnt that ]
Now it’s time to see the illustration or time to learning the integration, that how can we deal with the integration.
#### Now we discuss the types of integration
Integration is two types – (a) Indefinite Integration and (b) Definite Integration. We study both of them but in separate classes.
Indefinite Integration :
Indefinite Integration mainly use learning the integration that we can apply in Definite integration or in higher studies.
Indefinite integration divides in three types according to the solving method – i) Basic integration ii) By substitution, iii) By parts method, and another part is integration on some special function.
Downlad Here Integration Formula In Pdf File
i) Basic Integration :
Basic integration is simplest type of integration comparison to other types of integration. We just do it by separation the function, means in this case first of all we convert the given function in a simple form and then do it.
Let try to understanding by some illustration.
Illustration :1
Evaluate the given integral $$\int \frac{1}{x^(\frac{-2}{3})} dx$$
This is the most of basic integration like,
∫ xn dx =$$\frac {x^(n+1)}{n+1}$$+ c
Here n = +2/3, hence the required integration
or, $$\int \frac{1}{x^(\frac{-2}{3})} dx$$=$$\frac{x^(\frac{2}{3}+1)}{(\frac{2}{3}+1)}$$+c
or, $$\int \frac{1}{x^(\frac{-2}{3})} dx$$ = $$\frac{3}{5}x^\frac{5}{3}$$ + c
Illustration :2
##### Evaluate the integration of ∫ cos2x · dx or integration of cos^2x
Ans: Let, I = ∫ cos2 x · dx
or, I = 1/2 [∫ 2·cos2x dx]
or, I = [ ∫ (1 + cos2x) dx]
or, 2I = ∫ dx + ∫ cos2x dx +c
or, 2I = x + sin2x/2 + c
or, I = $$\frac{1}{2}[ x + \frac{sin2x}{2}]$$ + c
II) Substitution Method :
Definition of substitution method – Integration is made easier with the help of substitution on various variables. We will see a function will be simple by substitution for the given variable. This is one of the most important and useful methods for evaluating the integral.
Now we will take few examples that help us to understanding the concepts.
Example :1
Evaluate the integration of $$\int \frac{1}{x (lnx)^n} dx$$, n ≠ 1
Ans: Let, I = $$\int \frac{1}{x (lnx)^n} dx$$
[Now we are trying to understand that how to use substitution methods in integral]
Now, we substitute the (lnx) by replacing ‘z’
Hence, lnx = z
Now differentiate on both sides with respect to ‘x’ we get,
or, $$\frac{d(lnx)}{dx} = \frac{dz}{dx}$$
or, (1/x)· dx = dz
And now putting the value of 1/x and( lnx) we get,
Hence the required integration is equal to $$\frac{(lnx)^(-n+1)}{-n+1}$$ + c
Example :2
Evaluate the integration of
Now we will replace the xn – 1 by z2, hence xn – 1 = z2
And now differentiate both sides with respect to ‘x’ we get,
or, $$\frac {d(x^n-1)}{dx} = \frac{dz^2}{dx}$$
or, n · xn – 1 dx = 2 z dz
or, n · $$\frac {x^n}{x}$$· dx = 2 z dz
Now putting the value of xn , from xn – 1 = z2, xn = z2 + 1
We get, or, n·$$\frac {z^2 + 1}{x}dx = 2zdz$$
or, $$\frac{dx}{x} = \frac{2z} {n(z^2+1)}dz$$
And now putting the value of dx/x and xn-1 in the given integral we get,
III) By parts methods of Integration :
When the integration has given in the form of a product of two functions, in this case the integral can’t be able to solve by transformation or substitution methods, then we use this method to solve the given integral.
# Fundamental rules of By parts Methods –
In this case we use, a product of two functions f(x) and g(x) . So now our Integral looks like in the form = ∫ f(x) · g(x) dx .
* The fundamental formula of By Parts Methods –
I = ∫ f(x) · g(x) dx = f(x) ∫ g(x) dx – $$\int[\frac{df(x)}{dx}\int g(x)dx] dx$$
This is the main fundamental rule to solving by parts methods.
But, there has some problems or confusion that which function we take first f(x) or g(x), to clear this problem, we have a solution that also fundamental rule is the form of ILATE or LIATE, we take the function first according to this name, as which come first.
So, let’s see some example to better understanding.
Example :1
Evaluate the integral ∫ x2 ex dx
Ans: Let, I = ∫ x2 ex dx and x2 = f(x) & ex = g(x)
Then, according to the rule we have to take f(x) first due to algebraic function.
Given I = ∫ x2 ex now write the fundamental formula we get,
In the second part, we have to use by parts once again due to product of two functions.
Note: Students, a full class on by parts methods will be coming soon, so there we will discuss briefly about the by parts methods. Then please subscribe our website [jeewithbijoy.com | crawl-data/CC-MAIN-2020-34/segments/1596439740838.3/warc/CC-MAIN-20200815094903-20200815124903-00502.warc.gz | null |
The standard normal distribution can also be useful for computing percentiles. For example, the median is the 50th percentile, the first quartile is the 25th percentile, and the third quartile is the 75th percentile. In some instances it may be of interest to compute other percentiles, for example the 5th or 95th. The formula below is used to compute percentiles of a normal distribution.
where μ is the mean and σ is the standard deviation of the variable X, and Z is the value from the standard normal distribution for the desired percentile.
- The mean BMI for men aged 60 is 29 with a standard deviation of 6.
- The mean BMI for women aged 60 the mean is 28 with a standard deviation of 7.
What is the 90th percentile of BMI for men?
The 90th percentile is the BMI that holds 90% of the BMIs below it and 10% above it, as illustrated in the figure below.
To compute the 90th percentile, we use the formula X=μ + Zσ, and we will use the standard normal distribution table, except that we will work in the opposite direction. Previously we started with a particular "X" and used the table to find the probability. However, in this case we want to start with a 90% probability and find the value of "X" that represents it.
So we begin by going into the interior of the standard normal distribution table to find the area under the curve closest to 0.90, and from this we can determine the corresponding Z score. Once we have this we can use the equation X=μ + Zσ, because we already know that the mean and standard deviation are 29 and 6, respectively.
When we go to the table, we find that the value 0.90 is not there exactly, however, the values 0.8997 and 0.9015 are there and correspond to Z values of 1.28 and 1.29, respectively (i.e., 89.97% of the area under the standard normal curve is below 1.28). The exact Z value holding 90% of the values below it is 1.282 which was determined from a table of standard normal probabilities with more precision.
Using Z=1.282 the 90th percentile of BMI for men is: X = 29 + 1.282(6) = 36.69.
Interpretation: Ninety percent of the BMIs in men aged 60 are below 36.69. Ten percent of the BMIs in men aged 60 are above 36.69.
What is the 90th percentile of BMI among women aged 60? Recall that the mean BMI for women aged 60 the mean is 28 with a standard deviation of 7.
The table below shows Z values for commonly used percentiles.
Z Values for Commonly Used Percentiles
Percentiles of height and weight are used by pediatricians in order to evaluate development relative to children of the same sex and age. For example, if a child's weight for age is extremely low it might be an indication of malnutrition. Growth charts are available at http://www.cdc.gov/growthcharts/.
For infant girls, the mean body length at 10 months is 72 centimeters with a standard deviation of 3 centimeters. Suppose a girl of 10 months has a measured length of 67 centimeters. How does her length compare to other girls of 10 months?
A complete blood count (CBC) is a commonly performed test. One component of the CBC is the white blood cell (WBC) count, which may be indicative of infection if the count is high. WBC counts are approximately normally distributed in healthy people with a mean of 7550 WBC per mm3 (i.e., per microliter) and a standard deviation of 1085. What proportion of subjects have WBC counts exceeding 9000?
Using the mean and standard deviation in the previous question, what proportion of patients have WBC counts between 5000 and 7000?
If the top 10% of WBC counts are considered abnormal, what is the upper limit of normal? | <urn:uuid:7d1ae61c-27c6-4e1b-af15-f239803af09f> | {
"date": "2015-03-28T00:29:59",
"dump": "CC-MAIN-2015-14",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131297146.11/warc/CC-MAIN-20150323172137-00084-ip-10-168-14-71.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.914265513420105,
"score": 3.703125,
"token_count": 834,
"url": "http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability10.html"
} |
A Monarch Butterfly on pink coneflowers in my backyard garden in northeast Iowa.
(source from: EnchantedLearning.com)
The Monarch is a common poisonous butterfly that eats poisonous milkweed in its larval stage and lays its eggs on the milkweed plant. Monarchs have a wingspan of 3 3/8 – 4 7/8 inches (8.6 – 12.4 cm).
Butterflies are beautiful, flying insects with large scaly wings. Like all insects, they have six jointed legs, 3 body parts, a pair of antennae, compound eyes, and an exoskeleton. The three body parts are the head, thorax (the chest), and abdomen (the tail end). The four wings and the six legs of the butterfly are attached to the thorax. The thorax contains the muscles that make the legs and wings move.
. Egg: Spherical, ridged and white.
Caterpillar: The larva is banded with white/cream, black, and yellow stripes. It has three pairs of thoracic legs and five pairs of prolegs (which will disappear during the pupal stage). It has 2 pairs of sensory tentacles, one pair on the head and another pair near the end of the abdomen.
Pupa: The monarch remains in its pupa for about 10 to 14 days. The green cylindrical pupa becomes transparent a day before the adult emerges.
Adult: Bright orange with black wing veins and outer margins. The wings have white spots on outer margins, and three orange patches are found near the top of the forewings. The hindwings are very rounded, and they are lighter in color than the forewings. The body is black with white spots.
HOW TO TELL A MALE FROM A FEMALE
Male monarchs have a dark spot (scent scales) on the hindwing and have small claspers at the end of the abdomen. Females have thicker wing veins.
LIFE CYCLE OF A MONARCH BUTTERFLY
Butterflies and moths undergo complete metamorphosis in which they go through four different life stages. It takes about a month for the egg to mature into an adult.
Egg – The Monarch starts its life as a ridged, spherical egg only l/8th of an inch long. The eggs are always laid singly, on the underside of milkweed leaves. The female attaches the egg to the leaf with a quick-drying glue which she secretes along with the egg. The egg hatches in about 3 to 5 days. A tiny wormlike larva emerges.
Larva – The larva (caterpillar) hatches from its egg and eats it. Then it eats milkweed leaves almost constantly. The caterpillar molts (loses its old skin) four times as it grows; after each molt it eats its old skin. When the larva is about 2 inches (5 cm) long, it will stop eating and find a place (like a protected branch) on which to pupate.
Pupa – The caterpillar turns into a pupa (chrysalis). The caterpillar spins silk from its spinneret and attaches its hind end to a branch with the silk and small hooks in the anal prolegs. it hangs head down and molts for the last time. When the newly-exposed skin dries and hardens, it takes the form of a jade green chrysalis. During this stage the caterpillar turns into a butterfly as its entire body is reorganized. In about 10-12 days the chrysalis becomes transparent and a damp butterfly soon emerges.
Adult – A beautiful but damp adult emerges from the chrysalis. It pumps liquid into the wing veins to inflate them. They soon dry, but during this process, the butterfly is extremely vulnerable to predators. There is no growth during the adult stage. It can only eat liquids, which it does through its proboscis. This adult will continue the cycle by reproducing.
Female Monarchs lay their ridged, spherical eggs singly on the underside of milkweed leaves. When the egg hatches into a caterpillar, its meals (the leaves of the milkweed plant) are easily available.
The caterpillar’s first meal is its own eggshell. After that, Monarch caterpillars eat the poisonous milkweed leaves to incorporate the milkweed toxins into their bodies in order to poison their predators. Milkweed (genus Asclepius) is a common plant that contains toxins. There are more than 100 species of this perennial herb, containing varying concentrations of toxic chemicals (glycosides). The Monarch is considered a beneficial insect because its caterpillar eats the noxious milkweed plant which invades some farms
Monarch butterflies, like all butterflies, can only sip liquid food using a tube-like proboscis, which is a long, flexible “tongue.” This proboscis uncoils to sip food, and coils up again into a spiral when not in use. Monarchs drink nectar from many flowers, including milkweed, dogbane, red clover, thistle, lantana, lilac, goldenrod, etc.
PROTECTION FROM PREDATORS
The Monarch is a poisonous butterfly. Animals that eat a Monarch get very sick and vomit (but generally do not die). These animals remember that this brightly-colored butterfly made them very sick and will avoid all Monarchs in the future.
The monarch gets its poison (cardenolide glycosides) when it is a caterpillar, from eating the poisonous milkweed plant (genus Asclepias) while in its larval (caterpillar) stage.
The poisonous Monarch is mimicked by the non-poisonous North American Viceroy butterfly (Limenitis archippus), which has a similar shape, coloration and patterns. Predators who have learned to avoid the Monarch will also avoid the similar-looking Viceroy.
Monarchs are found all around the world in sub-tropical to tropical areas. They are found in open habitats including meadows, fields, marshes, and cleared roadsides.
Monarchs live through most of the USA, in southern Canada, Central America, most of South America, some Mediterranean countries, the Canary Islands, Australia, Hawaii, Indonesia, and many other Pacific Islands.
Some groups of Monarchs migrate for over 2,000 miles during August-October, flying from Canada and the USA to overwinter in coastal southern California to the transvolcanic mountains of central Mexico; this was determined by the Canadian scientist Dr. Fred A. Urquhart in 1975. Females lay their eggs along the migratory route. This migration takes up to three generations of Monarchs to complete.
Other Monarchs stay in one area their entire lives.
It takes about a month for the adult to develop (from egg to pupa to adult).
The life span of the adult Monarch varies, depending on the season in which it emerged from the pupa and whether or not it belongs to a migratory group of Monarchs. Adults that emerged in early summer have the shortest life spans and live for about two to five weeks. Those that emerged in late summer survive over the winter months. The migratory Monarchs, which emerge from the pupa in late summer and then migrate south, live a much longer life, about 8-9 months.
Order: Lepidoptera (butterflies and moths)
Family: Nymphalidae (over 5,000 species of butterflies with dwarfed front legs)
Subfamily: Danaidae (milkweed butterflies)
Genus and species: Danaus plexippus | <urn:uuid:f44c1668-22d3-403f-a093-58b37dfb240e> | {
"date": "2015-10-10T03:43:41",
"dump": "CC-MAIN-2015-40",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737940789.96/warc/CC-MAIN-20151001221900-00052-ip-10-137-6-227.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9371659159660339,
"score": 3.71875,
"token_count": 1606,
"url": "http://www.redbubble.com/people/lorilee/works/5501585-beauty-and-the-blossoms"
} |
# How to Write a Point-slope Form Equation from a Graph?
The point-slope form of a linear equation is $$y - y_1 = m(x - x_1)$$, where m is the slope of the line and $$(x_1, y_1)$$ is a point on the line. To write a point-slope form equation from a graph, you will need to find the slope of the line and a point on the line.
## A Step-by-step Guide to Write a Point-slope Form Equation from a Graph
Here are the steps to follow:
### Step 1: Identify a point on the line
Look for any point on the line. This can be any point that lies on the line. The coordinates of the point should be written in the form $$(x_1, y_1)$$.
### Step 2: Find the slope of the line
The slope of a line is the change in $$y$$ divided by the change in $$x$$, also known as rise over run. To find the slope of the line, select two points on the line, and then use the following formula:
$$m = \frac{(y_2 – y_1)}{(x_2 – x_1)}$$
where $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are two points on the line.
### Step 3: Write the equation using the point-slope form
Now that you have a point on the line and the slope of the line, you can write the equation of the line using the point-slope form:
$$y – y_1 = m(x – x_1)$$
Substitute the values you found in steps $$1$$ and $$2$$ into the equation:
$$y – y_1 = m(x – x_1)$$
$$y – y_1 = m(x – x_1)$$
This is the point-slope form equation of the line. You can simplify it further by expanding the brackets:
$$y – y_1 = m(x – x_1)$$
$$y – y_1 = mx – mx_1$$
$$y = mx – mx_1 + y_1$$
This is the equation of the line in slope-intercept form $$(y = mx + b)$$, where $$b = -mx_1 + y_1$$ is the $$y$$-intercept.
In summary, to write a point-slope form equation from a graph, you need to identify a point on the line and find the slope of the line. Then, use these values to write the equation in point-slope form and simplify it to slope-intercept form.
### Writing a Point-slope Form Equation from a Graph – Examples 1
According to the following graph, what is the equation of the line in point-slope form?
#### Solution:
Step 1: Identify two points on the line
The graph shows that the line passes through point $$(0, 2)$$. Therefore, $$(x_1, y_1) = (0, 2)$$. Consider another random point on the line such as $$-2,-1)$$
Step 2: Find the slope of the line
Using the two points $$(0, 2)$$ and $$(-2, -1)$$, you can find the slope of the line as follows:
$$m = \frac{(y_2 – y_1)}{(x_2 – x_1)}$$
$$m = \frac{(2+1)}{(0+2)}$$
$$m = \frac{3}{2}$$
Therefore, the slope of the line is $$\frac{3}{2}$$.
Step 3: Write the equation using the point-slope form
Now that you have the slope and a point on the line, you can write the equation of the line in the point-slope form:
$$y – y_1 = m(x – x_1)$$
$$y +1 = \frac{3}{2}(x +2)$$
This is the equation of the line in point-slope form.
## Exercises forWriting a Point-slope Form Equation from a Graph
### Write the equation of the line in point-slope form.
1.
2.
1. $$\color{blue}{y\:+\:2\:=−2\left(x\:−\:1\right)}$$
2. $$\color{blue}{y\:-\:3\:=\left(-\frac{1}{2}\right)\left(x+1\right)}$$
### What people say about "How to Write a Point-slope Form Equation from a Graph? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.
X
45% OFF
Limited time only!
Save Over 45%
SAVE $40 It was$89.99 now it is \$49.99 | crawl-data/CC-MAIN-2024-38/segments/1725700652031.71/warc/CC-MAIN-20240919125821-20240919155821-00842.warc.gz | null |
Why it matters where your food comes from and how it was grown, raised or produced
Nutrition is about understanding how food works in your body. The way food was produced can affect how it works in your body and have impacts on your health. Whether an apple was grown organically in nutrient-rich soil, a steak came from a cow that was fed grass or corn, or if a piece of bread is free of additives and preservatives all have impacts for your health and wellness. Understanding where food comes from and how it was grown, raised or produced can help you make educated choices about nourishing yourself with the best food possible. Food choices matter and we should be mindful of how our food gets to our plates.
Our Health Matters
A growing body of research indicates that industrial agriculture has had an increasingly negative effect on human health. Foods produced in more traditional ways (farming without synthetic pesticides and fertilizers, pasture-raised animals, no additives and preservatives) are often better for human health. Organic foods have been shown to be higher in nutrients, minerals and antioxidants, while having lower levels of toxic metals and pesticide residue. Food coming from factory farms often contains harmful bacteria, pesticide residue, antibiotics and artificial hormones, all of which can be harmful to consumers. Factory farms and industrial agriculture also impact human heath through air, water and soil pollution.
Pasture-raised animals produce meat, dairy and eggs that are better for consumers' health than conventionally-raised, grain-fed animals. In addition to being lower in calories and total fat, meat from pasture-raised animals have higher levels of vitamins, and a healthier balance of omega-3 and omega-6 fats than conventional meat and dairy products. Studies have shown that milk from pasture-fed cows has as much as five times the CLA (a “good” type of fatty acid) than milk from grain-fed cows. And meat from pasture-fed cows has from 200 to 500 percent more CLA as a proportion of total fatty acids than meat from cows that eat a primarily grain-based diet. Free-range chickens have 21% less total fat, 30% less saturated fat and 28% fewer calories than their factory-farmed counterparts. Eggs from poultry raised on pasture have 10% less fat, 40% more vitamin A and 400% more omega-3's.
The Animals Matter
Each year, hundreds of thousands of animals are subjected to terrible living conditions in industrialized factory farms. Animals are viewed as units of productions, instead of living creatures, and their well being is exchanged for profit. Closely-confined animals in factory farms are exposed to high levels of toxins from decomposing manure, pesticides, unhealthy additives and fed foods they would not normally eat. This situation is counteracted with low levels of daily antibiotics, which is contributing to the development of antibiotic-resistant bacteria. Animals are also frequently fed hormones to increase production.
To learn more about the humane animal products purchased by Dining Services, please follow this link.
The Environment Matters
In a healthy farm system, agriculture works with the natural environment. Farmers keep healthy soil in balance, rotate crops and use animal waste to fertilize the land. While farmers take from the land, they also give back. Industrial farms ignore the need for natural balance. They take without giving back. To compensate, chemical fertilizers are used to replenish dead soil. As a result, land, air and waterways become polluted. The soil is unusable without chemical fertilizers. Researchers from the Department of Economics at the University of Essex put the annual cost of environmental damage caused by industrial farming in the United States at $34.7 billion.
To learn more about Dining Services' sustainable practices, please click here.
The People Matter
Many industrialized farms put profits above farm workers, who are often subject to hazardous working conditions and unfair labor management practices. Working conditions at confined animal feeding operations (CAFOs) are particularly unhealthy, dangerous and extreme. Harmful gases contaminate the air breathed by workers, which leads to respiratory ailments. As many as 25% of all workers at CAFOs experience chronic bronchitis, while up to 70% will have acute bronchitis at some point during the year. According to the Centers for Disease Control and Prevention, “agriculture ranks among the most hazardous industries. Farmers are at high risk for fatal and nonfatal injuries, work-related lung diseases, noise-induced hearing loss, skin diseases, and certain cancers associated with chemical use and prolonged sun exposure. Farming is one of the few industries in which the families (who often share the work and live on the premises) are also at risk for injuries, illness, and death.”
Local Economies and Communities Matter
Industrial farms not only produce foods that are potentially harmful to human, they also negatively affect local economies and communities. Agribusiness often claims that its presence will have a positive impact on a local economy by creating new jobs and investing in the community. Recent experience, however, has shown that when large-scale farms enter communities and replace small farmers, they can actually create a downturn in the local economy.
Factory farms affect communities by introducing hazardous substances into the air and water. Air pollutants such as hydrogen sulfide, ammonia, and particulate matter are released in significant quantities by these large confined animal feeding operations, and all have the potential to negatively affect their surrounding communities. Large farms also often pollute local water sources, mainly through the release of nitrates and nitrites from chemical fertilizers. While many physical problems have been linked to factory farm runoff and air pollution, there is evidence that psychological and social problems can also result from living close to such facilities.
Source: Sustainable Table | <urn:uuid:d8e6eb45-71d4-45c6-9038-7d249d961b7d> | {
"date": "2017-06-22T20:31:11",
"dump": "CC-MAIN-2017-26",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128319902.52/warc/CC-MAIN-20170622201826-20170622221826-00336.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9558241367340088,
"score": 3.625,
"token_count": 1165,
"url": "https://www.pomona.edu/administration/dining/health-wellness/food-for-thought"
} |
Food is design. It is design when you compose plates, but it is amazing, even better and most delightful design when it's about the units. [Small thing.] [Big idea.] "Pasta" comes from Latin, and it means "paste." It's about putting together water and some powder, so that you can actually shape it. There are cultures in the world that use rice powder, others use soy powder. In Italy, we tend to use durum wheat. Pasta existed for centuries, but it really blossomed during the Renaissance. And it's only later on in the 17th century that it became more mass produced. Whenever you design an object of any kind, you think of how you want it to perform. So think about the same for pasta. Do you want it to be ribbed or you want it to be smooth? The ribbed ones absorb the sauce better. Do you want them to be round or do you want them to be square? They have a different feel on the palate. Everything is for a reason. In the amazing taxonomy of the pasta species, there are many different ways to divide it, but one of the basic divisions is between fresh pasta and dry pasta. Dry pasta is always durum wheat flour and water. Fresh pasta could be either that or it could be flour and eggs. Just think of having a dough that you can shape in any way you want. I mean, really, wouldn't you go crazy? So fresh and dry, but then, there's also long and short. And then within those families, there's even more diversity. Let's talk about some really classical types of short pasta. Penne — we all know them, right? They are cut at a slanted angle, perfect to pick up some of the sauce. "Farfalle" means "butterflies," or how do you call it here, bow ties, because they are, like, pinched in the middle. "Orecchiette" means "little ears," and they're typical from Puglia, and they are delicious. And "conquilla," shells, and of course, they look like shells. They are ribbed, so they scoop up the sauce on the outside and they are smooth on the inside. Pasta is definitely gorgeous, but the form also is about how it touches the palate, how it touches the tongue, so it's never just about giving it a shape. When you hone one object across centuries, standards become really, really high. Many so-called great designers failed miserably, because they tried to impose a shape onto pasta. The great Philippe Starck tried mandala. Some parts of it, the walls, were very thick, and the others were thinner, so when you would boil the pasta, some of it would be completely mushy while part of it was too crunchy and uncooked. So really wrong, but they were not women from Bologna, they were not chefs from Naples, they were not centuries of families of grandmothers that were trying to improve on the thinness of the walls of the pasta. There's no way to trace pasta back to one designer, one inventor, and that's the beauty of it. It belongs to the people. And if you think about it, this simple mixture of a carbohydrate and water becomes the scaffold for a whole culture to be built. | Why pasta comes in all shapes and sizes | null |
Autism is a condition that affects how an individual communicates with, and relates to, other people. It also affects how they make sense of the world around them.
Children and young people with autism vary enormously but they all share the two 'core' features of autism:
- persistent difficulties with social communication and social interaction. For example, they may find it hard to begin or carry on a conversation, they may not understand social rules such as how far to stand from somebody else, or they may find it difficult to make friends.
- Restricted, repetitive patterns of behaviour, interests, or activities. For example, they may develop an overwhelming interest in something, they may follow inflexible routines or rituals, they may make repetitive body movements, or they may be hypersensitive to certain sounds.
Children and young people with autism also have significant strengths. These often include reliability, a good eye for detail, producing highly accurate work, an excellent memory for facts and figures, and the ability to thrive in a structured, well-organised work environment.
More about Autism
Getting a diagnosis of autism can be a positive thing. It means you have an explanation for some of the difficulties your child may be experiencing, and it may also give you access to services and support.
The process of getting a diagnosis varies from country to country and sometimes even within the same country. In the UK you start the process by contacting your GP or health visitor who will then refer you on to more specialist services.
More about Diagnosis
Children and young people on the autism spectrum- and their parents and carers- face many issues and challenges on a day to day basis. Some issues - such as difficulties with communication or excessive anxiety - affect many people with autism, whatever their age. Other issues - such as finding the right school - are more likely to affect children with autism.
However it is important to remember that each child with autism is a unique individual, with unique needs and abilities. Because of this, he or she will experience those issues in a unique way or may not experience them at all.
There are a number of interventions - treatments and therapies - that are designed to improve the quality of life for children and young people on the autism spectrum. There are also some interventions that are designed to improve the quality of life of parents and carers.
However there is no one-size fits all solution. Each child or young person with autism is a unique individual, with unique needs and abilities. The most effective interventions are personalised to meet the unique characteristics of each individual.
As the parent or carer of a person on the autism spectrum living in the UK you have some legal rights, especially if your child has a formal diagnosis of autism. This is because the government considers autism to be a disability.
Many countries provide services to help children and young people on the autism spectrum, although the range and qualify of those services varies enormously between countries and may even vary within the same country.
Some services - such as some specialist schools - are specifically designed to help children with autism. Other services are designed to help a range of people, irrespective of their age or disability
More Autism forums
NICE (the National Institute for Health and Care Excellence) is a UK agency which provides national guidance and advice to improve health and social care.
NICE has produced a range of clinical guidance on the topic of children and young people on the autism spectrum
Please see Useful Resources on Autism for a list of additional resources inc.apps, blogs, events, journals, podcasts and videos. | <urn:uuid:a61d1bdb-b1c8-45f7-b4c4-27f1d6d03150> | {
"date": "2018-03-20T07:59:29",
"dump": "CC-MAIN-2018-13",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647322.47/warc/CC-MAIN-20180320072255-20180320092255-00657.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9612924456596375,
"score": 4.125,
"token_count": 725,
"url": "http://www.researchautism.net/autism/children-and-young-people-on-the-autism-spectrum?a_col=whiteblue"
} |
What is jaundice?
Jaundice is yellowing of your newborn's eyes and skin. It is caused by too much bilirubin in the blood. Bilirubin is a yellow substance found in red blood cells. It is released when the body breaks down old red blood cells. Bilirubin usually leaves the body through bowel movements. Jaundice happens because your newborn's body breaks down cells correctly, but it cannot remove the bilirubin. Jaundice is common in newborns. It usually happens during the first week of life.
What increases the risk for jaundice in newborns?
• Sepsis (blood infection) or a blood disorder, such as the mother and newborn having different blood types
• Passing through a narrow birth canal and developing a large bruise on the head
• Not enough breast milk
• Premature birth that prevents the liver from developing correctly
• Liver disease, biliary atresia (bile duct disorder), or an infection
How is jaundice diagnosed?
Your newborn's healthcare provider will check your newborn's skin and eyes. Tell the provider how long your newborn has had signs of jaundice. Tell him or her if you or your newborn have a blood disease, different blood types, or if any siblings also had jaundice. Tell the provider if your newborn was bruised during birth or has trouble breastfeeding. Your newborn may also need blood tests to check for bilirubin and to measure red blood cell levels. These tests will show if he or she has jaundice or is at risk for developing it.
How is jaundice treated in newborns?
Jaundice often goes away on its own. If it continues or becomes severe, your newborn may need treatment. This may happen at home or in the hospital. You will be able to stay with him or her in the hospital so you can continue to breastfeed. Treatment for jaundice includes the following:
• Phototherapy is a procedure that uses light to turn bilirubin into a form that your newborn's body can remove. One or more lights will be placed above your newborn. He or she will be placed on his or her back to absorb the most light. Your newborn may also lie on a flexible light pad, or his or her healthcare provider may wrap him or her in the light pad. Eye covers may be used to protect his or her eyes from the light. Do notput your newborn in direct sunlight. He or she may get a sunburn or become dehydrated. The only light therapy your newborn should have is phototherapy guided by a healthcare provider
• Exchange transfusion is a procedure used to replace part of your newborn's blood with blood from a donor. This will be done in the hospital and may be used if your newborn has severe jaundice
How can I help decrease my newborn's risk for jaundice?
Breastfeed your newborn as early and as often as possible. Talk to your newborn's healthcare provider about using formula along with breast milk if you do not produce enough breast milk alone. Look for signs of thirstin your newborn, such as lip smacking and restlessness. Try to breastfeed 8 to 12 times daily for the first few days to boost your milk supply. Ask your healthcare provider for help if you have trouble breastfeeding.
When should I seek immediate care?
• Your newborn has a fever
• Your newborn is limp (too weak to move)
• Your newborn moves his or her legs in a cycling motion
• Your newborn changes his or her sleep patterns
• Your newborn has trouble feeding, or he or she will not feed at all
• Your newborn is cranky, hard to calm, arches his or her back, or has a high-pitched cry
• Your newborn has a seizure, or you cannot wake him or her
When should I contact my newborn's pediatrician?
• Your newborn has new or worsened yellow skin or eyes
• You think your newborn is not drinking enough breast milk, or he or she is losing weight
• Your newborn has pale, chalky bowel movements
• Your newborn has dark urine that stains his or her diaper
You have the right to help plan your baby's care. Learn about your baby's health condition and how it may be treated. Discuss treatment options with your baby's caregivers to decide what care you want for your baby.
© 2017 Truven Health Analytics LLC All illustrations and images included in CareNotes® are the copyrighted property of A.D.A.M., Inc. or Truven Health Analytics. | <urn:uuid:dc520d43-87e6-48dd-9c47-d51bbb7862bd> | {
"date": "2022-07-01T08:46:19",
"dump": "CC-MAIN-2022-27",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103922377.50/warc/CC-MAIN-20220701064920-20220701094920-00058.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9532042741775513,
"score": 3.703125,
"token_count": 944,
"url": "https://www.jiahui.com/en/healthLibrary/21"
} |
# permutations
• Dec 7th 2007, 10:42 PM
anncar
permutations
Suppose we have a deck of 10 cards - say the ace to ten of spades
(denoted 1,. . . , 10 for definitiveness). Permutations of the deck may be
regarded as elements of S(10).
Define s to be the ‘shuffle’ which hides the top card:
s = 1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 1 3 5 7 9 .
Let t be the ‘shuffe’ that leaves the first card unchanged:
t = 1 2 3 4 5 6 7 8 9 10
1 3 5 7 9 2 4 6 8 10.
Finally, let c be the ‘cut’:
c = 1 2 3 4 5 6 7 8 9 10
6 7 8 9 10 1 2 3 4 5 .
(a) Write s, t, c, cs and scs using cycle notation, as a product of disjoint
cycles, and find the sign of each.
(b) For each of these basic and combined shuffes s, t, c, cs and scs, how many times must it be repeated before the cards are returned to their original positions?
• Dec 8th 2007, 04:01 AM
kalagota
Quote:
Originally Posted by anncar
Suppose we have a deck of 10 cards - say the ace to ten of spades
(denoted 1,. . . , 10 for definitiveness). Permutations of the deck may be
regarded as elements of S(10).
Define s to be the ‘shuffle’ which hides the top card:
s = 1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 1 3 5 7 9 .
Let t be the ‘shuffe’ that leaves the first card unchanged:
t = 1 2 3 4 5 6 7 8 9 10
1 3 5 7 9 2 4 6 8 10.
Finally, let c be the ‘cut’:
c = 1 2 3 4 5 6 7 8 9 10
6 7 8 9 10 1 2 3 4 5 .
(a) Write s, t, c, cs and scs using cycle notation, as a product of disjoint
cycles, and find the sign of each.
(b) For each of these basic and combined shuffes s, t, c, cs and scs, how many times must it be repeated before the cards are returned to their original positions?
a)
$\displaystyle s = (1,2,4,8,5,10,9,7,3,6)$
$\displaystyle t = (2,3,5,9,8,6)(4,7)$
$\displaystyle c = (1,6)(2,7)(3,8)(4,9)(5,10)$
$\displaystyle cs = (1,6)(2,7)(3,8)(4,9)(5,10)(1,2,4,8,5,10,9,7,3,6)$
$\displaystyle cs = \left( {\begin{array}{cccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ 7 & 9 & 1 & 3 & 5 & 6 & 8 & 10 & 2 & 4 \end{array} } \right) = (1,7,8,10,4,3)(2,9)$
$\displaystyle scs = (1,2,4,8,5,10,9,7,3,6)(1,6)(2,7)(3,8)(4,9)(5,10)(1 ,2,4,8,5,10,9,7,3,6)$
$\displaystyle scs = \left( {\begin{array}{cccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ 3 & 7 & 2 & 6 & 10 & 1 & 5 & 9 & 4 & 8 \end{array} } \right) = (1,3,2,7,5,10,8,9,4,6)$
b) n times where n is the length of the longest cycle..
• Dec 12th 2007, 09:27 AM
Wilmer
Nice! | crawl-data/CC-MAIN-2018-22/segments/1526794865595.47/warc/CC-MAIN-20180523102355-20180523122355-00471.warc.gz | null |
Things You Will Need
- a stopwatch that measures hundredths of seconds (like found on a smartphone)
- a meter stick or ruler (or really, just a length of string roughly \(20cm\) long)
- a light object that exhibits the effects of air resistance as it falls (though not too much – no feathers!):
- should require no less than about \(0.6s\) and no more than about \(1.0s\) to fall a distance of about \(1m\) from rest
- should be easy to release quickly/cleanly, and should not drift too much side-to-side
- examples: coffee filter (flat side down), cotton ball, under-inflated balloon (or inflated zip-lock bag), crumpled tissue paper (this should be a last resort, as its air-resistance properties can change during the course of the experiment if the "degree of crumple" changes (such as if it unravels between runs).
It is well-known that an object dropped from rest near the Earth's surface with negligible air resistance will fall a distance as a function of time given by the equation:
A physics paper written by a classmate seeks to determine the equation of motion that applies when air resistance isn't negligible. The author of this paper argues that the opposing force of air resistance reduces the downward net force on the falling object. Then, according to Newton's 2nd law, a smaller net force results in a smaller acceleration. Since the constant \(g\) in the equation above assumes acceleration due to a net force that is only due to gravity, we can simply replace this constant with a smaller value (which we will call \(k\)) to account for the smaller net force. You classmate therefore proposes that the equation of motion for an object in free fall from rest under the influence of both gravity and air resistance looks like:
where \(k\) depends upon details specific to the falling object, such as its density and its cross-sectional area.
Your task is to perform an experiment that either confirms or refutes this thesis, and if it is confirmed, compute the \(k\)-value of the item used in your experiment.
The procedure here is straightforward: Drop an object from several known heights, measure the time elapsed for each journey, and use the best-fit-line method with error bars to draw conclusions. Here are some suggestions that should help you achieve reasonable results:
- Perform at least 5 drops from each height, so that the uncertainty (standard deviation) of the time elapsed for each height can be computed.
- If you "spaz" during a time measurement and know you have made a mistake, there's no reason that you need to keep that data point. But don't keep trying over and over to get close to what you think is about the right value! There is supposed to be some uncertainty, after all. [It generally works better if you don't look at the timer at all, and focus on the falling object – then you know if you made a good measurement without tainting your opinion by seeing the actual number.]
- Perform drops from 6 different heights, with the lowest being about 1 meter (there is no need for precision on this, since we are looking for a functional dependence as the heights change). The other heights should be equally-spaced by about \(20cm\), so that the highest drop height is about 2 meters. The easiest way to mark these heights is on a wall with tape or a light, erasable pencil mark.
- There is uncertainty in both the drop height and the time of drop, but the latter much more significant (you can measure the height accurately to within about \(1cm\), which is \(\le 1\%\) of the total height, and time uncertainties will be a much larger percentage). For this reason, you do not need to include error bars for the height variable on the graph – treat height measurements as "exact."
- This lab is designed to be performed in the very basic manner described above (and works very well that way), but if you have the resources and are so inclined, you are free to greatly reduce the uncertainties by having someone assist you by taking video of the dropping process (with a stopwatch running in the video).
Data Analysis and Additional Discussion
- Create a table of your data.
- Use the data in your table to compute the standard deviations for each data point.
- Plot the points and error bars on a graph.
- If you find it is possible to sketch an acceptable best-fit line, do so. If you cannot, sketch a line that shows an acceptable best-fit line is not possible. Draw a conclusion about the author's theory.
- Assume for a moment that the theory is correct. In this case, what physical properties of the system do the slope and intercept of the line represent?
- Discuss any issues that you feel need to be addressed regarding the physics behind this experiment. If you find that the theory is confirmed, this is your opportunity to explain why it had to be so, and if you find that it is refuted, you can explain the theory's fatal flaw.
Download, print, and complete this document, then upload your lab report to Canvas. [If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.] | <urn:uuid:5308a3ef-0364-4e11-b3f9-34b91f4a2e51> | {
"date": "2022-01-26T14:41:11",
"dump": "CC-MAIN-2022-05",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304954.18/warc/CC-MAIN-20220126131707-20220126161707-00458.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9398746490478516,
"score": 4.09375,
"token_count": 1123,
"url": "https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HA_Lab/03%3A_Testing_a_Theory_of_Air_Resistance/3.02%3A_Activities"
} |
I'll just take you to Bangladesh for a minute. Before I tell that story, we should ask ourselves the question: Why does poverty exist? I mean, there is plenty of knowledge and scientific breakthroughs. We all live in the same planet, but there's still a great deal of poverty in the world. And I think — so I want to throw a perspective that I have, so that we can assess this project, or any other project, for that matter, to see whether it's contributing or — contributing to poverty or trying to alleviate it. Rich countries have been sending aid to poor countries for the last 60 years. And by and large, this has failed. And you can see this book, written by someone who worked in the World Bank for 20 years, and he finds economic growth in this country to be elusive. By and large, it did not work. So the question is, why is that? In my mind, there is something to learn from the history of Europe. I mean, even here, yesterday I was walking across the street, and they showed three bishops were executed 500 years ago, right across the street from here. So my point is, there's a lot of struggle has gone in Europe, where citizens were empowered by technologies. And they demanded authorities from — to come down from their high horses. And in the end, there's better bargaining between the authorities and citizens, and democracies, capitalism — everything else flourished. And so you can see, the real process of — and this is backed up by this 500-page book — that the authorities came down and citizens got up. But if you look, if you have that perspective, then you can see what happened in the last 60 years. Aid actually did the opposite. It empowered authorities, and, as a result, marginalized citizens. The authorities did not have the reason to make economic growth happen so that they could tax people and make more money for to run their business. Because they were getting it from abroad. And in fact, if you see oil-rich countries, where citizens are not yet empowered, the same thing goes — Nigeria, Saudi Arabia, all sorts of countries. Because the aid and oil or mineral money acts the same way. It empowers authorities, without activating the citizens — their hands, legs, brains, what have you. And if you agree with that, then I think the best way to improve these countries is to recognize that economic development is of the people, by the people, for the people. And that is the real network effect. If citizens can network and make themselves more organized and productive, so that their voices are heard, so then things would improve. And to contrast that, you can see the most important institution in the world, the World Bank, is an organization of the government, by the government, for the governments. Just see the contrast. And that is the perspective I have, and then I can start my story. Of course, how would you empower citizens? There could be all sorts of technologies. And one is cell phones. Recently "The Economist" recognized this, but I stumbled upon the idea 12 years ago, and that's what I've been working on. So 12 years ago, I was trying to be an investment banker in New York. We had — quite a few our colleagues were connected by a computer network. And we got more productive because we didn't have to exchange floppy disks; we could update each other more often. But one time it broke down. And it reminded me of a day in 1971. There was a war going on in my country. And my family moved out of an urban place, where we used to live, to a remote rural area where it was safer. And one time my mother asked me to get some medicine for a younger sibling. And I walked 10 miles or so, all morning, to get there, to the medicine man. And he wasn't there, so I walked all afternoon back. So I had another unproductive day. So while I was sitting in a tall building in New York, I put those two experiences together side by side, and basically concluded that connectivity is productivity — whether it's in a modern office or an underdeveloped village. So naturally, I — the implication of that is that the telephone is a weapon against poverty. And if that's the case, then the question is how many telephones did we have at that time? And it turns out, that there was one telephone in Bangladesh for every 500 people. And all those phones were in the few urban places. The vast rural areas, where 100 million people lived, there were no telephones. So just imagine how many man-months or man-years are wasted, just like I wasted a day. If you just multiply by 100 million people, let's say losing one day a month, whatever, and you see a vast amount of resource wasted. And after all, poor countries, like rich countries, one thing we've got equal, is their days are the same length: 24 hours. So if you lose that precious resource, where you are somewhat equal to the richer countries, that's a huge waste. So I started looking for any evidence that — does connectivity really increase productivity? And I couldn't find much, really, but I found this graph produced by the ITU, which is the International Telecommunication Union, based in Geneva. They show an interesting thing. That you see, the horizontal axis is where you place your country. So the United States or the UK would be here, outside. And so the impact of one new telephone, which is on the vertical axis, is very little. But if you come back to a poorer country, where the GNP per capita is, let's say, 500 dollars, or 300 dollars, then the impact is huge: 6,000 dollars. Or 5,000 dollars. The question was, how much did it cost to install a new telephone in Bangladesh? It turns out: 2,000 dollars. So if you spend 2,000 dollars, and let's say the telephone lasts 10 years, and if 5,000 dollars every year — so that's 50,000 dollars. So obviously this was a gadget to have. And of course, if the cost of installing a telephone is going down, because there's a digital revolution going on, then it would be even more dramatic. And I knew a little economics by then — it says Adam Smith taught us that specialization leads to productivity. But how would you specialize? Let's say I'm a fisherman and a farmer. And Chris is a fisherman farmer. Both are generalists. So the point is that we could only — the only way we could depend on each other, is if we can connect with each other. And if we are neighbors, I could just walk over to his house. But then we are limiting our economic sphere to something very small area. But in order to expand that, you need a river, or you need a highway, or you need telephone lines. But in any event, it's connectivity that leads to dependability. And that leads to specialization. That leads to productivity. So the question was, I started looking at this issue, and going back and forth between Bangladesh and New York. There were a lot of reasons people told me why we don't have enough telephones. And one of them is the lacking buying power. Poor people apparently don't have the power to buy. But the point is, if it's a production tool, why do we have to worry about that? I mean, in America, people buy cars, and they put very little money down. They get a car, and they go to work. The work pays them a salary; the salary allows them to pay for the car over time. The car pays for itself. So if the telephone is a production tool, then we don't quite have to worry about the purchasing power. And of course, even if that's true, then what about initial buying power? So then the question is, why can't we have some kind of shared access? In the United States, we have — everybody needs a banking service, but very few of us are trying to buy a bank. So it's — a bank tends to serve a whole community. So we could do that for telephones. And also people told me that we have a lot of important primary needs to meet: food, clothing, shelter, whatever. But again, it's very paternalistic. You should be raising income and let people decide what they want to do with their money. But the real problem is the lack of other infrastructures. See, you need some kind of infrastructure to bring a new thing. For instance, the Internet was booming in the U.S. because there were — there were people who had computers. They had modems. They had telephone lines, so it's very easy to bring in a new idea, like the Internet. But that's what's lacking in a poor country. So for example, we didn't have ways to have credit checks, few banks to collect bills, etc. But that's why I noticed Grameen Bank, which is a bank for poor people, and had 1,100 branches, 12,000 employees, 2.3 million borrowers. And they had these branches. I thought I could put cell towers and create a network. And anyway, to cut the time short — so I started — I first went to them and said, "You know, perhaps I could connect all your branches and make you more efficient." But you know, they have, after all, evolved in a country without telephones, so they are decentralized. I mean, of course there might be other good reasons, but this was one of the reasons — they had to be. And so they were not that interested to connect all their branches, and then to be — and rock the boat. So I started focusing. What is it that they really do? So what happens is that somebody borrows money from the bank. She typically buys a cow. The cow gives milk. And she sells the milk to the villagers, and pays off the loan. And this is a business for her, but it's milk for everybody else. And suddenly I realized that a cell phone could be a cow. Because some way she could borrow 200 dollars from the bank, get a phone and have the phone for everybody. And it's a business for her. So I wrote to the bank, and they thought for a while, and they said, "It's a little crazy, but logical. If you think it can be done, come and make it happen." So I quit my job; I went back to Bangladesh. I created a company in America called Gonofone, which in Bengali means "people's phone." And angel investors in America put in money into that. I flew around the world. After about a million — I mean, I got rejected from lots of places, because I was not only trying to go to a poor country, I was trying to go to the poor of the poor country. After about a million miles, and a meaningful — a substantial loss of hair, I eventually put together a consortium, and — which involved the Norwegian telephone company, which provided the know-how, and the Grameen Bank provided the infrastructure to spread the service. To make the story short, here is the coverage of the country. You can see it's pretty much covered. Even in Bangladesh, there are some empty places. But we are also investing around another 300 million dollars this year to extend that coverage. Now, about that cow model I talked about. There are about 115,000 people who are retailing telephone services in their neighborhoods. And it's serving 52,000 villages, which represent about 80 million people. And these phones are generating about 100 million dollars for the company. And two dollars profit per entrepreneur per day, which is like 700 dollars per year. And of course, it's very beneficial in a lot of ways. It increases income, improves welfare, etc. And the result is, right now, this company is the largest telephone company, with 3.5 million subscribers, 115,000 of these phones I talked about — that produces about a third of the traffic in the network. And 2004, the net profit, after taxes — very serious taxes — was 120 million dollars. And the company contributed about 190 million dollars to the government coffers. And again, here are some of the lessons. "The government needs to provide economically viable services." Actually, this is an instance where private companies can provide that. "Governments need to subsidize private companies." This is what some people think. And actually, private companies help governments with taxes. "Poor people are recipients." Poor people are a resource. "Services cost too much for the poor." Their involvement reduces the cost. "The poor are uneducated and cannot do much." They are very eager learners and very capable survivors. I've been very surprised. Most of them learn how to operate a telephone within a day. "Poor countries need aid." Businesses — this one company has raised the — if the ideal figures are even five percent true, this one company is raising the GNP of the country much more than the aid the country receives. And as I was trying to show you, as far as I'm concerned, aid does damages because it removes the government from its citizens. And this is a new project I have with Dean Kamen, the famous inventor in America. He has produced some power generators, which we are now doing an experiment in Bangladesh, in two villages where cow manure is producing biogas, which is running these generators. And each of these generators is selling electricity to 20 houses each. It's just an experiment. We don't know how far it will go, but it's going on. Thank you. | How mobile phones can fight poverty | null |
# What Does The Equal Sign Mean In Math?
## Can an equation have 2 equal signs?
Two equals signs means that the first quantity is equal to the second quantity, and the second quantity is equal to the third quantity, or that all three quantities are equal.
No surprises.
x+2=6, and 6=y+3, so x=4,y=2..
## Does an equation need an equal sign?
An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given. An equation is a mathematical statement or sentence comprised of two equalities or expressions joined with an equal sign.
## What is this symbol called in music?
A clef (from French: clef “key”) is a musical symbol used to indicate the pitch of written notes. Placed on one of the lines at the beginning of the stave, it indicates the name and pitch of the notes on that line.
## What does == mean in math?
It usually means: “we are defining what’s on the left of := to be wha’t on the right”. This distinction originates from computer languages, where the mere equality symbol “=” denotes an assignment of one variable’s value to another’s. For example, in Mathematica they use “==” for being equal, and “=” for assignment.
## What is the use of equal sign?
An equation is a mathematical statement where the equal sign is used to show equivalence between a number or expression on one side of the equal sign to the number or expression on the other side of the equal sign. Every equation has two sides (i.e., left and right).
## Why is equality so important?
Equality is about ensuring that every individual has an equal opportunity to make the most of their lives and talents. It is also the belief that no one should have poorer life chances because of the way they were born, where they come from, what they believe, or whether they have a disability.
## What is a () called?
The most familiar of these symbols is probably the ( ), called parentheses. Fun fact: one of them is called a parenthesis, and as a pair, the plural are parentheses. Parenthesis literally means “to put beside,” from the Greek roots par-, -en, and thesis.
## What does the 3 equal sign mean?
A triple equals sign means equivalent. Equivalent is not the same ask ‘equals’.
## Who invented sign?
Robert Recorde1512 – 1558) was a Welsh physician and mathematician. He invented the equals sign (=) and also introduced the pre-existing plus sign (+) to English speakers in 1557….Robert RecordeKnown forInventing the equals sign (=)Scientific careerFieldsPhysician and mathematicianInstitutionsUniversity of Oxford Royal Mint6 more rows
## How do I type an equal sign?
Creating the = symbol on a U.S. keyboard To create an equal sign using a U.S. keyboard press the equals key (same key as the plus ( + )), which is left of the backspace or delete key.
## What does the two finger peace sign mean?
V-sign /ˈviː saɪn/ noun 1 a sign made by holding up the first two fingers of your hand with the front of your hand facing forwards. … During World War II it was used to mean victory, and it was used again by hippies in the 1960s and 1970s to mean peace.
## What does equal sign mean?
The symbol = Shows that what is on the left of the sign is exactly the same amount or value as what is on the right of the sign. Examples: 3 + 4 = 7 means that 3 + 4 is equal to 7.
## What is the meaning of this == symbol?
In programming languages == sign or double equal sign means we are comparing right side with left side. And this comparison returns true or false. We usually use this comparison inside if condition to do something specific. Double equal operator is a very common used operator after single equal.
## What is called in keyboard?
A computer keyboard is an input device that allows a person to enter letters, numbers, and other symbols (these are called characters in a keyboard) into a computer. … Using a keyboard to enter lots of data is called typing. A keyboard contains many mechanical switches or push-buttons called “keys”.
## What does 2 equal signs mean?
Single Equal Sign. A double equal sign means “is equal to.” …
## What means == in Python?
comparison operator== is a comparison operator: returns True is the two items are equal, returns False if not, throws error if used to assign variable before definition and if the two items are not compatible. = is an assignment operator: will assign values like strings or numbers to variables.
## What is the name of this symbol?
This table contains special characters.SymbolNameSee also (similar glyphs or related concepts)≈Almost equal toEquals sign, Approximation&Ampersand⟨ ⟩Angle bracketsBracket, Parenthesis, Greater-than sign, Less-than sign’ ‘ApostropheQuotation mark, Guillemet, Prime, foot (unit), minute77 more rows
## What is this sign called in English?
British vs. American EnglishBritish EnglishAmerican EnglishThe ” ! ” symbol is calledan exclamation markan exclamation pointThe ” ( ) ” symbols are calledbracketsparenthesesThe ” [ ] ” symbols are calledsquare bracketsbracketsThe position of quotation marksJoy means “happiness”.Joy means “happiness.”2 more rows
## What is ‘#’ called?
Pound sign or Pound. Pound sign or pound are the most common names used in the United States, where the ‘#’ key on a phone is commonly referred to as the pound key or simply pound. Dialing instructions to an extension such as #77, for example, can be read as “pound seven seven”.
## What is the caret symbol called?
circumflex symbolThe free-standing circumflex symbol ^ has many uses in programming languages, where it is typically called a caret. It can signify exponentiation, the bitwise XOR operator, string concatenation, and control characters in caret notation, among other uses. | crawl-data/CC-MAIN-2021-17/segments/1618038075074.29/warc/CC-MAIN-20210413213655-20210414003655-00492.warc.gz | null |
# Most efficient worker time [max/min problem]
A student wrote us with the following (lightly edited):
Hello Matheno!
It’s me again. I am so grateful find you to help me about my question. I have another 2 questions that i want to ask you. I am a little bit curious and i hope that you can teach me with details on this question. Thanks Matheno!
We’ll post her other question as a separate topic.
Hi! Welcome back and thanks for the new questions.
First, let’s translate the question “At what time during the morning is the worker performing most efficiently?” into what I like to call Calculus language.
• How are we measuring efficiency?
There are many ways to measure efficiency, but based on the function you are given, an efficient worker will likely be one who produces more units per hour, and therefore you need to find the time for which the rate of production r(t) of the worker is at its maximum.
The rate of production r(t) is just the derivative of Q(t)
r(t) = Q'(t)
and is a measure of the speed of an average worker in \, \tfrac{\text{units}}{\text{hour }} . So the question you’re trying to answer in more Calculus type language is:
**
What is the maximum of r(t) = Q'(t) for t\gt 0?
**
I’m assuming that since this is a question about finding a maximum point, you have covered maxima and minima in your course. I won’t give you the solution outright, but I will outline the steps you need to take, which you can find here on Matheno: Maxima & Minima - Matheno.com | Matheno.com
1. Find the derivative of the function you are trying to maximize. You are trying to maximize r(t), so in this case you want to calculate the derivative r'(t).
2. Then find all the times t>0 for which r'(t) = 0. You may know this as finding the critical points. Normally you need to look for all the places where r'(t) is undefined as well, but since Q(t) is a polynomial, all of its derivatives are well-defined everywhere.
3. Finally, you need to show that the time(s) you found in part 2 result in either a maximum or a minimum. One way to do this is by checking the sign of r'(t) for times less than the critical point and times greater than the critical point.
Since you’re being asked for a supporting graph or diagram to help explain your solution, it might not be a bad idea to head over to Desmos.com, and reason about this question using a graph. Here’s my graph to get you started: Worker efficiency. We’re interested in finding the point on Q(t) where the slope of the tangent line is at its steepest (positive) slope.
As always, let me know if you have further questions about this problem, or if you want to check your solution with us! | crawl-data/CC-MAIN-2023-23/segments/1685224650620.66/warc/CC-MAIN-20230605021141-20230605051141-00165.warc.gz | null |
A publication of the Archaeological Institute of America
November is the Month of the Dead. The deceased were removed from their graves, redressed with rich garments and feathers. They gave the dead food and drink. The people danced and sang with the dead, parading them around the streets.
Missionaries working in Peru following the Spanish conquest were disgusted by the Inka's worshiping the mummified remains of their ancestors. During religious festivals the preserved bodies of Inka lords would be lavishly dressed, publicly displayed, and even given cups of chicha, or corn beer, to toast each other and the living. While such practices were abhorred by the Spanish, they played an integral role in the lives of Andean people for whom death marked not the end of a life but a period of transition during which the souls of the deceased were to be cared for and entertained, easing their passage into the afterlife. In exchange for such hospitality, it was believed that they would intercede with the gods on behalf of the living to ensure fertility and good crops.
The Inka were the last in a long line of Andean peoples to preserve and display the remains of their forebears that began with the Chinchorro, a little known fisherfolk who inhabited a 400-mile stretch of South American coast--from Ilo in southern Peru to Antofagasta in northern Chile--more than 7,000 years ago.
The earliest known mummy, that of a child from a site in the Camarones Valley, 60 miles south of Arica, dates to ca. 5050 B.C. During the next 3,500 years Chinchorro mummification evolved through three distinct styles--black, red, and mud-coated--before the practice died out sometime in the first century B.C.
The black style (ca. 5050-2500 B.C.), was by far the most complex. The body was completely dismembered and reassembled with all but the bones and skin replaced by clay, reeds, and various stuffing materials. A mask of clay incised with small slits for the eyes and mouth was placed over the face to give the body the impression of a peaceful slumber. In a technical sense, a black mummy, with its bone and wood inner frame, intermediate and ash paste layers, and external covering of human and sea lion skin was more like a statue than a mummy, a work of art. Today these mummies are extremely fragile due to the disintegration of the unbaked clay.
About 2500 B.C., black went out of fashion, perhaps reflecting a change in ideology. It is also possible that manganese became scarce. For the next five centuries the bodies were finished with red ochre, which is found in abundance near Arica. The mummification process also changed. The corpses were not totally disarticulated as they were with the black mummies. Instead, the head was removed to extract the brain while neat incisions were made on the arms, legs, and abdomen to remove muscles and internal organs, which were replaced with reeds, clay, sticks, and llama fur. After the body was filled out, incisions were sutured with human hair using a cactus spine needle. The body cavities in many red mummies show signs of burning, suggesting that they had been dried with glowing coals. With the red style also came a change in the sculpting of the clay face masks. Open mouths and eyes convey a sense of alertness rather than sleep. The open mouth may foreshadow the Inka practice of feeding and talking to the ancestors. It may have also served to ease the return of the soul should it wish to reinhabit the body.
By the end of the third millennium, complex mummification had ceased among the Chinchorro and bodies were simply desiccated, covered with a thick layer of mud, and buried.
Wear and tear, especially on the black and red mummies, as well as extensive repairs and repainting, suggest that they may have been displayed in family or communal shrines or used in processions for many years before being interred in groups of four, five, or six individuals, likely related. Few burial goods were placed in the graves, but most objects present were associated with fishing--harpoons, shell and cactus fishhooks, weights, and basketry.
Why did these ancient people go to such extraordinary lengths to preserve their dead? Though we have no written records of the ancient Chinchorro, we believe that their relationship with the dead was much like that of their Inka descendants, the mummies providing that vital link between this world and the next. But these well-preserved remains may have served another purpose as well. We believe that they represent the earliest form of religious art found in the Americas.
It is not surprising that the Chinchorro mummies have not been viewed as works of art, but as an unusual mortuary expression of an early Andean people. In many cultures icons exist as part of propitiation rites rather than as items to be collected. Religious art is then the expression of the believers attempting to reach the gods. The symbolism in religious art is context-specific, often associated with mythical heroes, deities, or ancestors. However, the icon is often not as important as what it represents.
How then do the Chinchorro mummies fit this paradigm of religious art? We see the black and red Chinchorro mummies as art because of the plasticity of their shapes, colors, and the mixed media used in their creation. These statues, the encased skeletons of departed ones, became sacred objects to be tended and revered by Chinchorro mourners.
Perhaps the most interesting aspect of Chinchorro mortuary practice was the democracy with which it was carried out. In contrast to the Egyptians, who mummified kings and nobility, the Chinchorro show no discrimination in age, sex, or social status in the mummification of their dead. The mummification of children is particularly fascinating, since in cultures throughout the world they receive little if any mortuary attention, especially those who never lived--the stillborn. The Chinchorro seemed to honor all human beings whether they contributed to society or not, paying particular attention to those who never achieved their potential. In the minds of the Chinchorro, life as a mummy may have been viewed as a second chance.
The Chinchorro mummies deserve much more attention than they have received from scholars, not only because they are now the oldest examples of intentionally mummified human remains, but because they are powerful artistic accomplishments of an ancient society.
Bernardo T. Arriaza is an associate professor of anthropology at the University of Nevada, Las Vegas and an adjunct researcher at the Universidad de Tarapacá, Arica, Chile. He is the author of Beyond Death: The Chinchorro Mummies of Ancient Chile (Smithsonian Institution Press, 1995). Russell A. Hapke, a graduate of the University of Nevada, Las Vegas, is director of Branson Illustrations, Co. Vivien G. Standen is a professor and researcher at the Museo Arqueologico San Miguel de Azapa, Universidad de Tarapaca, Arica, Chile. She has extensively studied the Chinchorro mummies of the El Morro-1 site. This research was in part supported by Fondecyt grant No. 1970525 and by National Geographic Society grant No. 5712-96.
Arriaza, B. Beyond Death: The Chinchorro Mummies of Ancient Chile. Smithsonian Institution Press, 1995. In the first book written in English about the Chinchorro culture, the author reconstructs daily life, and challenges our assumption that preceramic cultures had a simple socioreligious life.
Allison, M. "Chile's Ancient Mummies." Natural History 94:10 (1995), pp. 74-81. Describes the events that led to the discovery of the Chinchorro mummies in 1983 and discusses mummification techniques and health.
Standen, V. "Temprana complejidad funeraria de la cultura Chinchorro (norte de Chile)." Latin American Antiquity 8:2 (1997), pp.134-156. Presents a detailed bioarchaeological study of the El Morro-1 site in Arica.
During the nineteenth century, mummies from the Andes were exhibited in Paris, where they inspired European artists to new heights. The crouched position of Inka mummies inspired Paul Gauguin's figures in the famous paintings Life and Death and Eve. The "expression of agony" in them, which is a normal phenomenon, did not escape the eyes of Norwegian artist Edvard Munch, who immortalized the expression in a series of paintings entitled The Scream. | <urn:uuid:fa0ba9d9-d012-4da2-b0ae-b414013a54f0> | {
"date": "2014-07-22T23:37:28",
"dump": "CC-MAIN-2014-23",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997869778.45/warc/CC-MAIN-20140722025749-00193-ip-10-33-131-23.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9647125005722046,
"score": 3.671875,
"token_count": 1847,
"url": "http://archive.archaeology.org/online/features/chinchorro/index.html"
} |
In my last post I pointed out that teaching math has basically two components: math concepts and fact recall (or in other words: speed and accuracy when recalling math facts). Last week I discussed how I teach math concepts and listed some curriculum options that may work for you. This week I want to discuss the various resources I have used to improve my children’s speed of recall and accuracy when it comes to math facts.
I began home-schooling our oldest child and only daughter in 1990. She was in first grade. At the end of the year she took a standardized test. She scored off the charts in every area but one: math facts. It seems that a common problem for home-schoolers is that they are very good at teaching the concepts of math, but they sometimes need more work on helping their children get math facts down cold. The next year I spent time making sure my daughter knew her math facts and it showed when she took her standardized tests the next year.
I have been home-schooling now for over 20 years and have used a variety of drills to help my children get their math facts down so that they don’t have to stop and think – in other words, they need to have automatic recall. One thing I DON’T use is flash cards. Frankly, I find them to be boring. And if I think they’re boring I can imagine what my kids think of them.
So here are the resources I do recommend that you look into, to make sure your children not only understand math, but can also instantly recall math facts:
- Calculadder – I place Calculadder on the top of the list because I believe it is the #1 best resource for teaching fast recall of math facts. Besides being effective, Calculadder drills take only a few minutes a day to use. I have been using Calculadder for as long as I can remember and will continue to use them with my youngest for probably at least a couple more years.
- Math-It – I used Math-It with a couple of my boys. It is sort of a game: it uses a large card that is divided into squares with numbers on them. The child holds cards with equations on them and places those cards on the correct answer. Over time, your child will be able to quickly place the equations on the correct answer. Math-It teaches addition equations, “dubblit” equations (2+2, 3+3, etc.) and multiplication. You might consider using this before using Calculadder, especially with a child who is very tactile.
- Quarter Mile Math – – Quarter-Mile Math is a computer game that covers pretty much anything your child will need to know in regards to math facts, in a fun “race-themed” game. Your child gets to choose whether to use race cars or race horses as they solve equations. One advantage of this program is that your child can save their scores (so ultimately they are racing against themselves) and you can keep track of their progress. Great resource!
- Kumon Math Workbooks – My friend CaptiousNut introduced me to Kumon. Though I have been home-schooling over two decades, I had never heard of them until he mentioned them on his blog. I started my 8-year old on the 3rd grade “Addition and Subtraction” workbook just a couple of weeks ago and I find it is helping him already. Also, because they use the concept of “levels” he thinks it is a game (along the lines of computer and video games) so he actually gets excited about it (hey, whatever works, right?!)
These are the products I have used over the years to help my children get to the point where their recall of math facts is quick and automatic. If you have had success with other math drills, I would appreciate if you would let me (and my readers) know by leaving a note in the comments.Print This Post | <urn:uuid:fa077901-6386-4c99-8cb4-829926a0309e> | {
"date": "2015-04-25T04:12:46",
"dump": "CC-MAIN-2015-18",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246646036.55/warc/CC-MAIN-20150417045726-00280-ip-10-235-10-82.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9780338406562805,
"score": 3.796875,
"token_count": 822,
"url": "http://homeschooling911.com/how-to-teach-math-drills/"
} |
Prime numbers have exactly two factors. Now find some numbers that have exactly three factors. What do these numbers have in common? That is, how would you categorize these numbers?
Look for numbers with three factors, not three prime factors. The number itself and 1 are always factors, so there must be exactly one other factor. When we factor a number, we typically get two distinct factors. How could we get only one new factor? Close Tip
There is a way to find the number of factors of a positive integer without writing out all the factors, and it requires finding the prime factorization first. This problem will help you discover that rule.
Go through the table, and list all the factors for each number. Then in the table enter the total number of factors (including the number itself and 1). Look for patterns, and try to write a general rule for the number of factors for any integer.
A number is called a perfect number if the sum of all of its factors is equal to twice the value of the number. What are the two smallest perfect numbers?
An abundant number is one in which the sum of its factors is greater than twice the number. A deficient number is one in which the sum of its factors is less than twice the number. Which numbers less than 25 are abundant and which are deficient?
You have seen that every prime number greater than 3 is one less or one more than a multiple of 6. It is also true that every prime number greater than 2 is one more or one less than a multiple of 4. How would you prove this fact? | <urn:uuid:cab95f61-5c7e-48a7-abd8-6800c7be5c44> | {
"date": "2014-07-29T04:37:18",
"dump": "CC-MAIN-2014-23",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510265454.51/warc/CC-MAIN-20140728011745-00312-ip-10-146-231-18.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9575464129447937,
"score": 3.59375,
"token_count": 323,
"url": "http://learner.org/courses/learningmath/number/session6/part_h/homework.html"
} |
# Question #df17c
Nov 26, 2014
By raising $6$ to both sides of the equations,
$\left\{\begin{matrix}3 {x}^{2} + {y}^{2} = 28 \\ x + y = 6 \implies y = 6 - x\end{matrix}\right.$
by substituting the second equation into the first equation,
$3 {x}^{2} + {\left(6 - x\right)}^{2} = 28 \implies 4 {x}^{2} - 12 x + 8 = 0$
by dividing by $4$,
$\implies {x}^{2} - 3 x + 2 = 0$
by factoring out,
$\implies \left(x - 1\right) \left(x - 2\right) = 0 \implies x = 1 , 2 \implies y = 5 , 4$
Hence, the solutions are
$\left(x , y\right) = \left(1 , 5\right)$ and $\left(2 , 4\right)$
I hope that this was helpful. | crawl-data/CC-MAIN-2020-10/segments/1581875145966.48/warc/CC-MAIN-20200224163216-20200224193216-00132.warc.gz | null |
This animation shows predicted changes in temperature across the globe, relative to pre-industrial levels, under two different emissions scenarios in the COP 17 climate model. The first is with emissions continuing to increase through the century. The second is with emissions declining through the century.
This is an interactive map that illustrates the scale of potential flooding in Alabama, Mississippi, and Florida due to projected sea level rise. It is a collaborative project of NOAA Sea Grant Consortium and U.S.G.S. It is a pilot project, so there is some possibility that the resource may not be maintained over time.
In this activity, students explore the increase in atmospheric carbon dioxide over the past 40 years with an interactive online model. They use the model and observations to estimate present emission rates and emission growth rates. The model is then used to estimate future levels of carbon dioxide using different future emission scenarios. These different scenarios are then linked by students to climate model predictions also used by the Intergovernmental Panel on Climate Change.
This video is narrated by climate scientist Richard Alley. It examines studies US Air Force conducted over 50 years ago on the warming effects of CO2 in the atmosphere and how that could impact missile warfare. The video then focuses on the Franz Josef glacier in New Zealand; the glacier is used to demonstrate glaciers formation, depth of snow fall in the past, and understand atmospheric gases and composition during the last Ice Age. Supplemental resources are available through the website.
This homework problem introduces students to Marcellus shale natural gas and how an unconventional reservoir rock can become an attractive hydrocarbon target. It is designed to expand students' understanding of hydrocarbon resources by introducing an unconventional natural gas play. Students explore the technological factors that make conventional source rocks attractive reservoir rocks and how this advance impacts both U.S. energy supply and the environment.
These five short videos are an introduction to the pros and cons of energy issues, including cost, choices, efficiency, environmental impact, and scale. The videos are segments of a feature documentary entitled, Switch: Discover the Future of Energy.
This interactive visualization depicts sea surface temperatures (SST) and SST anomalies from 1885 to 2007. Learn all about SST and why SST data are highly valuable to ocean and atmospheric scientists. Understand the difference between what actual SST readings can reveal about local weather conditions and how variations from normalâcalled anomaliesâcan help scientists identify warming and cooling trends and make predictions about the effects of global climate change. Discover the relationships between SST and marine life, sea ice formation, local and global weather events, and sea level.
This activity focuses on wind energy concepts, which are introduced through a Reading Passage and by answering assessment questions. Students construct and test a windmill to observe how design and position affect the electrical energy produced. | <urn:uuid:84ec2d0b-b291-41f8-8a11-a5ee2ad11821> | {
"date": "2016-02-12T18:27:26",
"dump": "CC-MAIN-2016-07",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701165070.40/warc/CC-MAIN-20160205193925-00230-ip-10-236-182-209.ec2.internal.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.9064987897872925,
"score": 3.78125,
"token_count": 564,
"url": "https://www.climate.gov/teaching/resources/education/college-lower-13-14?keywords=&page=33"
} |
A team of Israeli and American marine archaeologists discovered on Israel’s northern coast, just outside the ancient city of Tel Dor, the traces of what could have been a gigantic tsunami, which occurred about 10 millennia ago. The natural disaster could have devastated several settlements in the area.
During the study, researchers drilled several holes on the coast and examined the seabed to determine the causes and extent of the tsunami. In addition, they created a digital model of the terrain and concluded that the natural disaster would have occurred between 9,910 and 9,290 years ago, in the early Holocene epoch.
Scientists also found a layer of sand and seashells in dry Neolithic terrain, which also serves as proof that it was a large-scale tsunami. It could have formed waves between 16 and 40 meters high and destroyed everything in its path at an impressive distance of up to 3.5 kilometers from the coastline, a route considerably greater than 300 meters from the other tsunamis documented in the area.
- Coronavirus: The cheap drug that reduces the risk of death by up to three times
- Musk pledges a $ 100 million reward for developing best carbon capture technology
- Surgeons find a new solution to restore vision in a blind patient in 24 hours
- Scientists reveal a new method to accurately diagnose depression and bipolar disorder
- Netherlands imposes curfew for the first time since World War II
Another indication pointing to the likely historical moment when the tsunami took place is the almost absolute absence of archaeological sites in the places that were densely populated before the pre-ceramic Neolithic (between 11,700 and 9,800 years ago). At the same time, the presence of archaeological sites dated between 9,250 and 7,800 years ago indicates that the area has been repopulated after the natural disaster.
The researchers also reported that the megatsunami was generated by a very powerful earthquake that, in turn, caused an underwater movement. The probable origin of the gigantic wave was located about 10 miles west of the coastline.
The full study has been published in the scientific journal PLOS ONE. If you’re interested in geology, here you can see what’s behind the mysterious killer waves. And artifact, found in Israel, could belong to the time of Jesus Christ. | <urn:uuid:0eef7a5b-068a-4f44-869e-d1e52c498f4e> | {
"date": "2021-01-22T06:59:01",
"dump": "CC-MAIN-2021-04",
"file_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00416.warc.gz",
"int_score": 4,
"language": "en",
"language_score": 0.967276394367218,
"score": 3.546875,
"token_count": 469,
"url": "https://www.revyuh.com/news/science-and-research/scientific-research/scientists-find-evidence-of-a-megatsunami-that-hit-present-day-israel-10000-years-ago/"
} |
# Kirubha gives a pen to karan on first day. The next day, it will be doubled and so on. Totally how many pens are given in 10 days?
#### Solution RequiredKIRUBHAKARAN DURAIRAJ on 8-Sep-2016 10:37
Kirubha gives a pen to karan on first day. The next day, it will be doubled and so on. Totally how many pens are given in 10 days?
on 8-Sep-2016 11:31
n=int(input()) count=1 for i in range(1,n): new_num=count*2 count=count+new_num print(count) ans: 19683
on 8-Sep-2016 16:40
719
on 9-Sep-2016 11:17
2048
on 9-Sep-2016 11:23
1023
on 9-Sep-2016 11:28
Formula = (2^n)-1. Logic: 1st day = 1 =1 =(2^1) -1 2nd day = 1+2 =3 = (2^2) -1 3rd day = 1+2+4=7 = (2^3)-1 .......... 10th day=(2^10)-1 =1023.
on 12-Sep-2016 08:53
1023 is the answer
on 12-Sep-2016 08:54
1023
on 12-Sep-2016 08:54
1+4=5 is n^1
on 12-Sep-2016 11:03
1023
on 12-Sep-2016 11:26
1023 is the answer
on 12-Sep-2016 21:45
1023
on 12-Sep-2016 22:46
1st day 1 2nd day 2 3rd day 2^2 4th day 2^3 . . . 10th day 2^9 total no. of pens=1+2^1+2^2+......+2^9=2047 pens
on 15-Sep-2016 10:41
1023 pens
on 17-Sep-2016 10:26
2047 pens
on 17-Sep-2016 12:33
1 2 4 8 16 32 64 128 256 512 ------- tot:1023 ans:1023
on 17-Sep-2016 14:10
1023
on 19-Sep-2016 15:05
1023
on 22-Sep-2016 09:01
what is the answer
on 22-Sep-2016 09:07
ok
Solution:
Formula = (2^n)-1. Logic: 1st day = 1 =1 =(2^1) -1 2nd day = 1+2 =3 = (2^2) -1 3rd day = 1+2+4=7 = (2^3)-1 .......... 10th day=(2^10)-1 =1023. | crawl-data/CC-MAIN-2017-26/segments/1498128320438.53/warc/CC-MAIN-20170625050430-20170625070430-00571.warc.gz | null |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.